Porcupine temperament modal harmony: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
[[Porcupine]] is a temperament splitting 4/3 into three equal parts representing 10/9 and 27/25, so that two steps represent 6/5. This results in a slightly flat 4/3 and a slightly sharp 6/5, meaning that 5/4 is accurately tuned.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
__TOC__
: This revision was by author [[User:k9assassin|k9assassin]] and made on <tt>2015-04-05 00:35:36 UTC</tt>.<br>
== Porcupine scales ==
: The original revision id was <tt>546321670</tt>.<br>
{{Todo|rework|inline=1|text=Explain in a non-MOS-centric way}}
: The revision comment was: <tt></tt><br>
Porcupine is one of the few reasonably good 5-limit temperaments, alongside [[meantone]], which possesses a 7-note MOS scale ("porcupine[7]" or "onyx") that is well-supplied with 5-limit major and minor triads (specifically, it has two of each of them). What is perhaps more significant about it is how naturally it extends those triads to involve the 11th harmonic; for instance, the first five consecutive notes of the Lssssss mode approximate the consecutive harmonics 8:9:10:11:12. This makes it a prime candidate for using extended JI-style harmonies in a compact and intuitive scale structure.
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[toc]]
=Intro To [[Porcupine]]=  
Porcupine is significant as a 5-limit temperament because it is the only 5-limit temperament other than meantone which possesses a 7-note MOS scale that is well-supplied with 5-limit major and minor triads (specifically, it has two of each of them). What is perhaps more significant about it is how naturally it extends those triads to involve the 11th harmonic; for instance, the first five consecutive notes of the Lssssss mode approximate the consecutive harmonics 8:9:10:11:12. This makes it a prime candidate for using extended JI-style harmonies in a compact and intuitive scale structure.


It is also significant because it is supported by both [[@15edo]] and [[@22edo]], the smallest ETs which improve on the 11-limit damage of [[@12edo]] (other than [[@19edo]]). In those ETs, Porcupine is an excellent candidate for providing a 7-nominal notational basis and 7-interval-class categorical framework for those ETs (which is important because it allows 5-limit major and minor triads to share a triad class, in keeping with common-practice conventions). Or, in other words, if you want to use 15edo or 22edo in such a way that allows you to think of 5/4 and 6/5 as types of "third", and 4/3 and 3/2 as types of "fifth", thinking of those ETs in terms of porcupine temperament is the ideal conceptual approach. //(To be continued...)//
It is also significant because it is supported by both [[15edo]] and [[22edo]], the smallest ETs which improve on the 11-limit damage of [[12edo]] (other than [[19edo]]). In those edos, porcupine is an excellent candidate for providing a 7-nominal notational basis and 7-interval-class categorical framework. This is important, because if you want to use 15edo (or to a lesser extent, 22edo) in a somewhat "heptatonic" fashion, where 5/4 and 6/5 are types of "thirds", 3/2 is a type of "fifth," and 5-limit major and minor triads share the same "{{nowrap|{{dash|1, 3, 5}}}}" triad shape, thinking of those ETs in terms of porcupine temperament is, in a certain sense, the natural approach. This most transparently leads to notation systems based upon porcupine[7], but 15edo and 22edo also contain a [[zarlino]] scale which can be naturally interpreted as a porcupine scale (what this means for zarlino is that the three sizes of step are equidistant). In fact, *any* heptatonic scale in [[15edo]] or [[22edo]] can be viewed as a [[MODMOS]] of porcupine[7].


=Brief Intro to Modal Harmony and MODMOS's=
In summary:
Porcupine is a temperament completely capable of diverse harmony. Using it's MOS in conjunction with it's modmos will allow for some very diverse chordal movement that will still be tonally solid. Porcupine mode and modmos names are based on animal names because none of the scales remotely are similar to any existing mode name from anywhere. The initial four modes: Porcupine, Chinchilla, Zebra, and Dog all contain 3/2 from the root while the latter three: Gazette, Lemur, and Panda lack 3/2 and instead have a triad similar to a diminished triad on the root. In order to remedy this problem, it may be fruitful to use other methods than triadic tertian harmony to build tonal frameworks in porcupine.
# Porcupine is the simplest 5-limit temperament that has less [[Tenney–Euclidean temperament measures#TE_error|tuning error]] than 12edo which 12edo does not support.
# In a [http://x31eq.com/pyscript/pregular.html?limit=5&error=5.0 temperament search] of 5-limit temperaments, using the standard search parameter of 5{{cent}} of error, porcupine is the first temperament in the results that is not supported by 12.


Because the generator of porcupine is 9/8, secondual harmony tends to work quite well. William lynch considers varying subsets of 8:9:10:11:12 to work really well for building harmonic movement in porcupine. In addition, the second inversion which produces chords of stacked sevenths of varying sizes, also works well as an additional sonority to create better voice leading and variety. If the mode position of porcupine contains no 3/2 from the root, then a chord without 3/2 is played on the root.  
Porcupine remains the "best" such temperament in the 5-limit even if the maximum error is relaxed somewhat. While [[mavila]] eventually supersedes it due to being simpler, mavila's accuracy is much lower as its fifths are extremely flat ({{nowrap|{{dash|670, 680{{c}}}}}}).


The Modmos of porcupine can be used in conjunction with the regular mos in order to build powerful tonal movement. While each useful modmos has it's own distinct name, they most likely will be useful to use as a particular function in each porcupine mode. They can also be used stand alone but little is known about the very complex system of tonality.
== Brief intro to modal harmony and MODMOSes ==
=Reasons Why Porcupine Will Make for The Best Modal Harmony Ever=  
Porcupine is a temperament completely capable of diverse harmony. Its MOS and its MODMOS scales (including zarlino) allow for some very diverse chordal movement that will still be tonally solid.
The 7-note MOS of porcupine is great, but it lumps all the consonant chords together at one end of the scale (see below). It also fails to contain a complete 11-limit otonal hexad (4:5:6:7:9:11), even though porcupine is not excessively complex in the 11-limit. Thankfully, unlike in meantone[7] where the MODMOSs all reduce the number of consonant triads available, there are several MODMOSs of porcupine that contain an equal or greater number of consonant triads to the MOS (these are highlighted in blue text below). These MODMOSs also conveniently alter the distribution of triads within the scale, providing much-needed variety of possible chord progessions. Even better, some single-alteration MODMOSs make at least one full 11-limit hexad available, meaning 6 of the 7 notes of the scale can be sounded simultaneously and produce a consonant otonal harmony. The fact that porcupine temperament provides not just one 7-note scale but several that are equally-rich in harmonic resources makes it extremely fertile for modal harmony.
//(To be continued...)//


=Porcupine[7] and its MODMOSs=
Because the generator of porcupine is simultaneously 10/9, 11/10, and 12/11, a chord made up of consecutive generators approximates 9:10:11:12; since -6 generators approximates 9/8, the chord 8:9:10:11:12 can be approximated by a series of consecutive 2nds in porcupine[7]. Varying subsets of 8:9:10:11:12 provide fruitful ground for building harmonic movement in porcupine.
Additionally, chords of stacked sevenths of varying sizes may be used to improve voice leading and add variety. Chords without a 'fifth' are recommended for use on the root for modes without a 3/2 from the root. Further, quartal triads, tetrads, and pentads are available in more variety than in Meantone, and make good use of Porcupine's 11-limit consonances.


The below mode names are given in [[Modal UDP Notation|UDP notation]]. For porcupine[7], the chroma-aligned generator is the 9/5, or the 11/6 if you prefer. All generators below refer to this generator, NOT the 10/9 one. For an explanation of the spellings, see [[Porcupine Notation]]. William Lynch proposed the fun idea of naming modes of porcupine by various animal names.
Stacked 3-step triads may be employed in Porcupine[8] and it's MODMOS, comprising in their root position three 3:4:5 triads (second inversion major triad) as major 3-step, minor 3-step: major[8] triad; three 15:20:24 triads (first inversion minor triad) as minor 3-step, major 3-step: minor[8] triad; and two 9:12:16 triads (second inversion suspended triad) as major 3-step, major 3-step: augmented[8] triad.
At least one MODMOS of Porcupine[8] contains the same number of major and minor triads as the MOS, but more spread out across the scale, similar to Porcupine[7] MODMOS.


==**The Porcupine[7] MOS**==
The MODMOS scales of porcupine can be used in conjunction with the regular MOS in order to build powerful tonal movement. While each useful MODMOS has its own distinct name, they most likely will be useful to use as a particular function in each porcupine mode. They can also be used stand alone but little is known about the very complex system of tonality.
|| Mode Name ||= 22edo Step Pattern ||= 15edo Step Pattern ||= UDP Name || Spelling || Triad Qualities ||= Other Notes ||  ||
|| Chinchillian ||= 4333333 ||= 3222222 ||= 6|0 || G A B C D E F || I iiº iiiº ivº v vi VII ||= Bright, otonal major (VII chord is major) || [[media type="file" key="porcupineotonalmajor22edo.mp3" width="240" height="20"]] ||
|| Badgerian ||= 3433333 ||= 2322222 ||= 5|1 || G Av B C D E F || I II iiiº ivº vº vi vii ||= Darker major (vii is minor) ||  ||
|| Zebrian ||= 3343333 ||= 2232222 ||= 4|2 || G Av Bv C D E F || i II III ivº vº viº vii ||= Bright minor (II is major) ||  ||
|| Dingoian ||= 3334333 ||= 2223222 ||= 3|3 || G Av Bv Cv D E F || i ii III IV vº viº viiº ||= Symmetric minor (ii is minor) || [[media type="file" key="porcupinesymmetricminor22edo.mp3" width="240" height="20"]] ||
|| Gazettian ||= 3333433 ||= 2222322 ||= 2|4 || G Av Bv Cv Dv E F || iº ii iii IV V viº viiº ||= Diminished ||  ||
|| Lemurian ||= 3333343 ||= 2222232 ||= 1|5 || G Av Bv Cv Dv Ev F || iº iiº iii iv V VI viiº ||= Diminished ||  ||
|| Pandian ||= 3333334 ||= 2222223 ||= 0|6 || G Av Bv Cv Dv Ev Fv || iº iiº iiiº iv v VI VII ||= [[magical seventh chord|Magical seventh]] mode ||  ||


==Single-alteration MODMOS's==
Porcupine[7] is great, but it lumps all the consonant chords together at one end of the scale (see below). It also fails to contain a complete 11-limit otonal hexad (4:5:6:7:9:11), even though porcupine is not excessively complex in the 11-limit. Thankfully, unlike in meantone[7] where the MODMOSs all reduce the number of consonant triads available, there are several MODMOSs of porcupine that contain an equal or greater number of consonant triads to the MOS (these are highlighted in blue text below). These MODMOSs also conveniently alter the distribution of triads within the scale, providing much-needed variety of possible chord progressions. Even better, some single-alteration MODMOSs make at least one full 11-limit hexad available, meaning 6 of the 7 notes of the scale can be sounded simultaneously and produce a consonant otonal harmony. The fact that porcupine temperament provides not just one 7-note scale but several that are equally-rich in harmonic resources makes it extremely fertile for modal harmony.
**MODMOS with 1st note in generator chain flattened: #.......######**
**Note: Contains a broken 4/3 chain so it has only 3 4/3s**
||= 22edo Steps ||= 15edo Steps ||= UDP Name || Spelling ||= Other Notes ||
||= 5333332 ||= 4222221 ||= 6|0 ^2^3^4^5^6^7 || G A^ B^ C^ D^ E^ F^ ||=  ||
||= 2533333 ||= 1422222 ||= 5|1 v2 || G Avv B C D E F ||=  ||
||= 3253333 ||= 2142222 ||= 4|2 v3 || G Av Bvv C D E F ||=  ||
||= 3325333 ||= 2214222 ||= 3|3 v4 || G Av Bv Cvv D E F ||=  ||
||= 3332533 ||= 2221422 ||= 2|4 v5 || G Av Bv Cv Dvv E F ||=  ||
||= 3333253 ||= 2222142 ||= 1|5 v6 || G Av Bv Cv Dv Evv F ||=  ||
||= 3333325 ||= 2222214 ||= 0|6 v7 || G Av Bv Cv Dv Ev Fvv ||=  ||


**MODMOS with 2nd note in generator chain flattened: #.....#.#####**
== Porcupine[7] and its MODMOSes ==
**Note: Contains a broken 4/3 chain so it has only 3 4/3s**
The below mode names are given in [[Modal UDP Notation|UDP notation]]. For porcupine[7], the bright generator is the 9/5, or the 11/6 if you prefer. All generators below refer to this generator, NOT the 10/9 one. For an explanation of the spellings, see [[Porcupine Notation]].
||= 22edo Steps ||= 15edo Steps ||= UDP Name || Spelling ||= Other Notes ||
||= 4333324 ||= 3222213 ||= 6|0 v7 || G A B C D E Fv ||= 8:9:10:11:12:14 hexad on the tonic,
in both 15edo and 22edo as G-A-B-C-D-Fv ||
||= 4433332 ||= 3322221 ||= 6|0 ^3^4^5^6^7 || G A B^ C^ D^ E^ F^ ||=  ||
||= 2443333 ||= 1332222 ||= 4|2 v2 || G Avv Bv C D E F ||=  ||
||= 3244333 ||= 2133222 ||= 3|3 v3 || G Av Bvv Cv D E F ||=  ||
||= 3324433 ||= 2213322 ||= 2|4 v4 || G Av Bv Cvv Dv E F ||=  ||
||= 3332443 ||= 2221332 ||= 1|5 v5 || G Av Bv Cv Dvv Ev F ||=  ||
||= 3333244 ||= 2222133 ||= 0|6 v6 || G Av Bv Cv Dv Evv Fv ||=  ||


**MODMOS with 3rd note in generator chain flattened: #....##.####**
The functional names are pretty straightforward: there are two major modes, one bright and one dark (differing in the second scale degree), two similarly-named minor modes (differing in the fourth scale degree), and then three modes with a diminished triad on the tonic (differing in the sixth and seventh scale degrees). The brightest two of these diminished modes both have a half-diminished tetrad on the tonic, and so they are named the bright and dark half-diminished modes, whereas the darkest has a fully diminished (or [[magical seventh chord|magical seventh]] tetrad) instead. These are sometimes just written bright/dark diminished and magical seventh modes when clear.
**Note: Contains a broken 4/3 chain so it has only 3 4/3s**
||= 22edo Steps ||= 15edo Steps ||= UDP Name || Spelling ||= Other Notes ||
||= 4333243 ||= 3222132 ||= 6|0 v6 || G A B C D Ev F ||=  ||
||= 3433324 ||= 2322213 ||= 5|1 v7 || G Av B C D E Fv ||=  ||
||= 4343332 ||= 3232221 ||= 6|0 ^4^5^6^7 || G A B C^ D^ E^ F^ ||=  ||
||= 2434333 ||= 1323222 ||= 3|3 v2 || G Avv Bv Cv D E F ||=  ||
||= 3243433 ||= 2132322 ||= 2|4 v3 || G Av Bvv Cv Dv E F ||=  ||
||= 3324343 ||= 2213232 ||= 1|5 v4 || G Av Bv Cvv Dv Ev F ||=  ||
||= 3332434 ||= 2221323 ||= 0|6 v5 || G Av Bv Cv Dvv Ev Fv ||=  ||


**MODMOS with 4th note in generator chain flattened: #...###.###**
=== William Lynch's system ===
**Note: Contains a broken 4/3 chain so it has only 3 4/3s**
William Lynch proposed the fun idea of naming modes and MODMOS's of porcupine by various animal names, which are listed as "William's Name" below. He has named these scales as such as he views none of them to be remotely similar to any existing mode name from anywhere. The initial four modes: Porcupine, Chinchilla, Zebra, and Dingo all contain 3/2 from the root while the latter three: Gazelle, Lemur, and Panda lack 3/2 and instead have a triad similar to a diminished triad on the root. In order to remedy this problem, it may be fruitful to use other methods than triadic tertian harmony to build tonal frameworks in porcupine.
||= 22edo Steps ||= 15edo Steps ||= UDP Name || Spelling ||= Other Notes ||
||= 4332433 ||= 3221322 ||= 6|0 v5 || G A B C Dv E F ||=  ||
||= 3433243 ||= 2322132 ||= 5|1 v6 || G Av B C D Ev F ||=  ||
||= 3343324 ||= 2232213 ||= 4|2 v7 || G Av Bv C D E Fv ||=  ||
||= 4334332 ||= 3223221 ||= 6|0 ^5^6^7 || G A B C D^ E^ F^ ||=  ||
||= 2433433 ||= 1322322 ||= 2|4 v2 || G Avv Bv Cv Dv E F ||=  ||
||= 3243343 ||= 2132232 ||= 1|5 v3 || G Av Bvv Cv Dv Ev F ||=  ||
||= 3324334 ||= 2213223 ||= 0|6 v4 || G Av Bv Cvv Dv Ev Fv ||=  ||


&lt;span style="color: #0000ff;"&gt;**MODMOS with 5th note in generator chain flattened: #..####.## Reptiles**&lt;/span&gt;
The scale's nominals can be named by the normal 7-tone alphabet starting on G. This has become somewhat of a standard. Some feel however that given Superpyth uses the same nominals in a contrasting way, it may be beneficial to use an entirely different set of letters for Porcupine. William Lynch's suggestion involves using the old-English alphabet, allowing for both porcupine[8] and porcupine[7] to be notated by leaving out "ð" from the scale.  
**Consists of unbroken chains of 4/3s**
|| Mode Name ||= 22edo Steps ||= 15edo Steps ||= UDP Name || Spelling ||= Other Notes ||
|| Lizard ||= 4324333 ||= 3213222 ||= 6|0 v4 || G A B Cv D E F ||= I, IV, v, vi "mixolydian-like"* ||
|| Iguana ||= 3432433 ||= 2321322 ||= 5|1 v5 || G Av B C Dv E F ||=  ||
|| Serpent ||= 3343243 ||= 2232132 ||= 4|2 v6 || G Av Bv C D Ev F ||= i, III, VI, vii ||
|| Iguana ||= 3334324 ||= 2223213 ||= 3|3 v7 || G Av Bv Cv D E Fv ||= i, ii, IV, VII "dorian-like" ||
|| Chameleon ||= 4333432 ||= 3222321 ||= 6|0 ^6^7 || G A B C D E^ F^ ||= I, ii, iii, V "ionian-like";
8:9:10:11:12:14:15 on the tonic in 15edo as G-A-B-C-D-E^-F^
(but not in 22edo)
Igliashon finds it the "most grounded",
and suggests it as a candidate for "default major" ||
|| Crocodile ||= 2433343 ||= 1322232 ||= 1|5 v2 || G Avv Bv Cv Dv Ev F ||=  ||
|| Turtle ||= 3243334 ||= 2132223 ||= 0|6 v3 || G Av Bvv Cv Dv Ev Fv ||=  ||
* This kind of description is obviously stupid because these porcupine scales are not really like the diatonic modes "mixolydian", "dorian", etc. As always, feel free to edit if you have some better description.


&lt;span style="color: #0000ff;"&gt;**Symmetrical MODMOS with 2nd note in generator chain sharpened or 6th note flattened: #.#####.# Farm Animals** &lt;/span&gt;
Porcupine[8]: b c ð d e f þ æ
**Consists of unbroken chains of 4/3s**
**Has the most evenly-distributed 5-limit triads of all the MODMOSs**
|| Mode Name ||= 22edo Steps ||= 15edo Steps ||= UDP Name #1 ||= UDP Name #2 || Spelling ||= Other Notes ||
|| Horse ||= 4333342 ||= 3222231 ||= 6|0 ^7 ||= (1|5 v1) || G A B C D E F^ ||= I ii° iii iv° V vi vii°
Major with major V chord (most major-sounding major) ||
|| Pig ||= 2433334 ||= 1322223 ||= (5|1 ^1) ||= 0|6 v2 || G Avv Bv Cv Dv Ev Fv ||= i° II iii° iv v° VI vii
Magical seventh ||
|| Sheep ||= 4243333 ||= 3132222 ||= 4|2 ^2 ||= 6|0 v3 || G A Bv C D E F ||= i ii° III iv° v vi° VII
Minor with minor v chord (most minor-sounding minor) ||
|| Cow ||= 3424333 ||= 2313222 ||= 3|3 ^3 ||= 5|1 v4 || G Av B Cv D E F ||= I ii iii° IV v° vi vii°
Major with major IV chord ||
|| Llama ||= 3342433 ||= 2231322 ||= 2|4 ^4 ||= 4|2 v5 || G Av Bv C Dv E F ||= i° II iii iv° V vi° vii
Symmetric diminished ||
|| Goat ||= 3334243 ||= 2223132 ||= 1|5 ^5 ||= 3|3 v6 || G Av Bv Cv D Ev F ||= i ii° III iv v° VI vii°
Minor with minor iv ||
|| Rooster ||= 3333424 ||= 2222313 ||= 0|6 ^6 ||= 2|4 v7 || G Av Bv Cv Dv E Fv ||= i° ii iii° IV v vi° VII
Magical seventh ||


&lt;span style="color: #0000ff;"&gt;**MODMOS with 3rd note in generator chain sharpened: ##.####..# Big Cats**&lt;/span&gt;
Porcupine[7]: b c d e f þ æ with chinchillian mode on "c"  
**Consists of unbroken chains of 4/3s**
|| Mode Name ||= 22edo Steps ||= 15edo Steps ||= UDP Name || Spelling ||= Other Notes ||
|| Lionian ||= 4333423 ||= 3222312 ||= 6|0 ^6 || G A B C D E^ F ||= I, ii, v, VII "mixolydian-like"
8:9:10:11:12:14 on the tonic in 15edo only ||
|| Tigonian ||= 3433342 ||= 2322231 ||= 5|1 ^7 || G Av B C D E F^ ||= I, II, iii, vi ||
|| Cougian ||= 2343334 ||= 1232223 ||= 0|6 v2 v3 || G Avv Bvv Cv Dv Ev Fv ||=  ||
|| Leopardian ||= 4234333 ||= 3123222 ||= 3|3 ^2 || G A Bv Cv D E F ||= i, III, IV, v "dorian-like"
Keenan and Igliashon both find this exceptionally beautiful
and suggest it as a candidate for default "minor" ||
|| Cheetian ||= 3423433 ||= 2312322 ||= 2|4 ^3 || G Av B Cv Dv E F ||=  ||
|| Jaguarian ||= 3342343 ||= 2231232 ||= 1|5 ^4 || G Av Bv C Dv Ev F ||=  ||
|| Pantherian ||= 3334234 ||= 2223123 ||= 0|6 ^5 || G Av Bv Cv D Ev Fv ||= i, iv, VI, VII "aeolian-like" ||


**MODMOS with 4th note in generator chain sharpened: ###.###...#**
pronounced "Be - Ce - Eth - De - E - Eff - Thorn - Ash"
**Note: Contains a broken 4/3 chain so it has only 3 4/3s**
||= 22edo Steps ||= 15edo Steps ||= UDP Name || Spelling ||= Other Notes ||
||= 4334233 ||= 3223122 ||= 6|0 ^5 || G A B C D^ E F ||=  ||
||= 3433423 ||= 2322312 ||= 5|1 ^6 || G Av B C D E^ F ||=  ||
||= 3343342 ||= 2232231 ||= 4|2 ^7 || G Av Bv C D E F^ ||=  ||
||= 2334334 ||= 1223223 ||= 0|6 v2v3v4 || G Avv Bvv Cvv Dv Ev Fv ||=  ||
||= 4233433 ||= 3122322 ||= 2|4 ^2 || G A Bv Cv Dv E F ||=  ||
||= 3423343 ||= 2312232 ||= 1|5 ^3 || G Av B Cv Dv Ev F ||=  ||
||= 3342334 ||= 2231223 ||= 0|6 ^4 || G Av Bv C Dv Ev Fv ||=  ||


**MODMOS with 5th note in generator chain sharpened: ####.##....#**
An alternative suggestion involves using the letters J, K, L, M, N, O, and P for the nominals, replacing A, B, C, D, E, F, and G respectively, such that the bright major mode starts on the note P.
**Note: Contains a broken 4/3 chain so it has only 3 4/3s**
||= 22edo Steps ||= 15edo Steps ||= UDP Name || Spelling ||= Other Notes ||
||= 4342333 ||= 3231222 ||= 6|0 ^4 || G A B C^ D E F ||=  ||
||= 3434233 ||= 2323122 ||= 5|1 ^5 || G Av B C D^ E F ||=  ||
||= 3343423 ||= 2232312 ||= 4|2 ^6 || G Av Bv C D E^ F ||=  ||
||= 3334342 ||= 2223231 ||= 3|3 ^7 || G Av Bv Cv D E F^ ||=  ||
||= 2333434 ||= 1222323 ||= 0|6 v2v3v4v5 || G Avv Bvv Cvv Dvv Ev Fv ||=  ||
||= 4233343 ||= 3122232 ||= 1|5 ^2 || G A Bv Cv Dv Ev F ||=  ||
||= 3423334 ||= 2312223 ||= 0|6 ^3 || G Av B Cv Dv Ev Fv ||=  ||


**MODMOS with 6th note in generator chain sharpened: #####.#.....#**
== The Porcupine[7] MOS ==
**Note: Contains a broken 4/3 chain so it has only 3 4/3s**
{| class="wikitable"
||= 22edo Steps ||= 15edo Steps ||= UDP Name || Spelling ||= Other Notes ||
|-
||= 4423333 ||= 3312222 ||= 6|0 ^3 || G A B^ C D E F ||=   ||
! Functional name
||= 3442333 ||= 2331222 ||= 5|1 ^4 || G Av B C^ D E F ||=   ||
! William's came
||= 3344233 ||= 2233122 ||= 4|2 ^5 || G Av Bv C D^ E F ||=   ||
! style="text-align: center;" | 22edo step pattern
||= 3334423 ||= 2223312 ||= 3|3 ^6 || G Av Bv Cv D E^ F ||=   ||
! style="text-align: center;" | 15edo step pattern
||= 3333442 ||= 2222331 ||= 2|4 ^7 || G Av Bv Cv Dv E F^ ||=   ||
! style="text-align: center;" | UDP name
||= 2333344 ||= 1222233 ||= 0|6 v2v3v4v5v6 || G Avv Bvv Cvv Dvv Evv Fv ||=   ||
! Spelling
||= 4233334 ||= 3122223 ||= 0|6 ^2 || G A Bv Cv Dv Ev Fv ||=   ||
! Alt spelling
! Triad qualities
! style="text-align: center;" | Other notes
!
|-
| Bright major
| Chinchillian
| style="text-align: center;" | 4333333
| style="text-align: center;" | 3222222
| style="text-align: center;" | 6{{pipe}}0
| G A B C D E F
| P J K L M N O
| I iiº iiiº ivº v vi VII
| style="text-align: center;" | Bright, otonal major (VII chord is major)
| [[File:porcupineotonalmajor22edo.mp3]]
|-
| Dark major
| Badgerian
| style="text-align: center;" | 3433333
| style="text-align: center;" | 2322222
| style="text-align: center;" | 5{{pipe}}1
| G Av B C D E F
| P Jv K L M N O
| I II iiiº ivº vº vi vii
| style="text-align: center;" | Darker major (vii is minor)
|
|-
| Bright minor
| Zebrian
| style="text-align: center;" | 3343333
| style="text-align: center;" | 2232222
| style="text-align: center;" | 4{{pipe}}2
| G Av Bv C D E F
| P Jv Kv L M N O
| i II III ivº vº viº vii
| style="text-align: center;" | Bright minor (II is major)
|
|-
| Dark minor (symmetric)
| Dingoian
| style="text-align: center;" | 3334333
| style="text-align: center;" | 2223222
| style="text-align: center;" | 3{{pipe}}3
| G Av Bv Cv D E F
| P Jv Kv Lv M N O
| i ii III IV vº viº viiº
| style="text-align: center;" | Symmetric minor (ii is minor)
| [[File:porcupinesymmetricminor22edo.mp3]]
|-
| Bright (half-)diminished
| Gazellian
| style="text-align: center;" | 3333433
| style="text-align: center;" | 2222322
| style="text-align: center;" | 2{{pipe}}4
| G Av Bv Cv Dv E F
| P Jv Kv Lv Mv N O
| iº ii iii IV V viº viiº
| style="text-align: center;" | Half-Diminished
|  
|-
| Dark (half-)diminished
| Lemurian
| style="text-align: center;" | 3333343
| style="text-align: center;" | 2222232
| style="text-align: center;" | 1{{pipe}}5
| G Av Bv Cv Dv Ev F
| P Jv Kv Lv Mv Nv O
| iº iiº iii iv V VI viiº
| style="text-align: center;" | Half-Diminished
|  
|-
| Magical/diminished seventh
| Pandian
| style="text-align: center;" | 3333334
| style="text-align: center;" | 2222223
| style="text-align: center;" | 0{{pipe}}6
| G Av Bv Cv Dv Ev Fv
| P Jv Kv Lv Mv Nv Ov
| iº iiº iiiº iv v VI VII
| style="text-align: center;" | [[magical seventh chord|Magical seventh]] or diminished seventh mode
|  
|}


**MODMOS with 7th note in generator chain sharpened: ######.......#**
=== Single-alteration MODMOS's ===
**Note: Contains a broken 4/3 chain so it has only 3 4/3s**
'''MODMOS with 1st note in generator chain flattened: #.......######'''
||= 22edo Steps ||= 15edo Steps ||= UDP Name || Spelling ||= Other Notes ||
||= 5233333 ||= 4122222 ||= 6|0 ^2 || G A^ B C D E F ||=  ||
||= 3523333 ||= 2412222 ||= 5|1 ^3 || G Av B^ C D E F ||=  ||
||= 3352333 ||= 2241222 ||= 4|2 ^4 || G Av Bv C^ D E F ||=  ||
||= 3335233 ||= 2224122 ||= 3|3 ^5 || G Av Bv Cv D^ E F ||=  ||
||= 3333523 ||= 2222412 ||= 2|4 ^6 || G Av Bv Cv Dv E^ F ||=  ||
||= 3333352 ||= 2222241 ||= 1|5 ^7 || G Av Bv Cv Dv Ev F^ ||=  ||
||= 2333335 ||= 1222224 ||= 0|6 v2v3v4v5v6v7 || G Avv Bvv Cvv Dvv Evv Fvv ||=  ||


==Notable double-alteration MODMOS's==
'''Note: Contains a broken 4/3 chain so it has only 3 4/3s'''
||= 22edo Steps ||= 15edo Steps ||= UDP Name || Spelling ||= Other Notes ||
||= 4324342 ||= 3213231 ||= 6|0 v4 ^7 || G A B Cv D E F^ || "JI Major" scale a.k.a. Ptolemy/Zarlino ||
||= 4234243 ||= 3123132 ||= 3|3 ^2 v6 || G A Bv Cv D Ev F || "JI Minor" scale ||


=Porcupine[8] and its MODMOS's=  
{| class="wikitable"
All generators below refer to the porcupine[8] chroma-positive generator (the 10/9~11/10~whatever). William Lynch Proposes naming the modes off of sea creatures with Octopus being relevant of the number eight.
|-
! style="text-align: center;" | 22edo steps
! style="text-align: center;" | 15edo steps
! style="text-align: center;" | UDP name
! Spelling
! style="text-align: center;" | Other notes
|-
| style="text-align: center;" | 5333332
| style="text-align: center;" | 4222221
| style="text-align: center;" | 6{{pipe}}0 ^2^3^4^5^6^7
| G A^ B^ C^ D^ E^ F^
| style="text-align: center;" |
|-
| style="text-align: center;" | 2533333
| style="text-align: center;" | 1422222
| style="text-align: center;" | 5{{pipe}}1 v2
| G Avv B C D E F
| style="text-align: center;" |
|-
| style="text-align: center;" | 3253333
| style="text-align: center;" | 2142222
| style="text-align: center;" | 4{{pipe}}2 v3
| G Av Bvv C D E F
| style="text-align: center;" |
|-
| style="text-align: center;" | 3325333
| style="text-align: center;" | 2214222
| style="text-align: center;" | 3{{pipe}}3 v4
| G Av Bv Cvv D E F
| style="text-align: center;" |
|-
| style="text-align: center;" | 3332533
| style="text-align: center;" | 2221422
| style="text-align: center;" | 2{{pipe}}4 v5
| G Av Bv Cv Dvv E F
| style="text-align: center;" |
|-
| style="text-align: center;" | 3333253
| style="text-align: center;" | 2222142
| style="text-align: center;" | 1{{pipe}}5 v6
| G Av Bv Cv Dv Evv F
| style="text-align: center;" |
|-
| style="text-align: center;" | 3333325
| style="text-align: center;" | 2222214
| style="text-align: center;" | 0{{pipe}}6 v7
| G Av Bv Cv Dv Ev Fvv
| style="text-align: center;" |
|}


==The Porcupine[8] MOS==
'''MODMOS with 2nd note in generator chain flattened: #.....#.#####'''
|| Mode Name ||= Step Pattern ||= UDP Name || Spelling ||= Other Notes ||
|| Octopus ||= 33333331 ||= 7|0 || A B C D E F G H ||  ||
|| Mantis ||= 33333313 ||= 6|1 || A B C D E F G Hb ||  ||
|| Dolphin ||= 33333133 ||= 5|2 || A B C D E F Gb Hb ||  ||
|| Crab ||= 33331333 ||= 4|3 || A B C D E Fb Gb Hb ||  ||
|| Tuna ||= 33313333 ||= 3|4 || A B C D Eb Fb Gb Hb ||  ||
|| Salmon ||= 33133333 ||= 2|5 || A B C Db Eb Fb Gb Hb ||  ||
|| Starfish ||= 31333333 ||= 1|6 || A B Cb Db Eb Fb Gb Hb ||  ||
|| Whale ||= 13333333 ||= 0|7 || A Bb Cb Db Eb Fb Gb Hb ||  ||


==Single-alteration MODMOS's==
'''Note: Contains a broken 4/3 chain so it has only 3 4/3s'''
===Alterations by porcupine[8] chroma===
**MODMOS with 2nd note in generator chain flattened:** **#......****#.****######**
||= Step Pattern ||= UDP Name || Spelling || Other Notes ||
||= 15333331 ||= 7|0 b2 || A Bb C D E F G H ||  ||
||= 53333311 ||= 7|0 #2#3#4#5#6#7 || A B# C# D# E# F# G# H ||  ||
||= 33333115 ||= 5|2 b8 || A B C D E F Gb Hbb ||  ||
||= 33331153 ||= 4|3 b7 || A B C D E Fb Gbb Hb ||  ||
||= 33311533 ||= 3|4 b6 || A B C D Eb Fbb Gb Hb ||  ||
||= 33115333 ||= 2|5 b5 || A B C Db Ebb Fb Gb Hb ||  ||
||= 31153333 ||= 1|6 b4 || A B Cb Dbb Eb Fb Gb Hb ||  ||
||= 11533333 ||= 0|7 b3 || A Bb Cbb Db Eb Fb Gb Hb ||  ||


**MODMOS with 3rd note in generator chain flattened:** **#.....****##.****#####**
{| class="wikitable"
||= Step Pattern ||= UDP Name || Spelling || Other Notes ||
|-
||= 31533331 ||= 7|0 b3 || A B Cb D E F G H ||  ||
! style="text-align: center;" | 22edo steps
||= 15333313 ||= 6|1 b2 || A Bb C D E F G Hb ||  ||
! style="text-align: center;" | 15edo steps
||= 53333131 ||= 7|0 #2#3#4#5#6 || A B# C# D# E# F# G H ||  ||
! style="text-align: center;" | UDP name
||= 33331315 ||= 4|3 b8 || A B C D E Fb Gb Hbb ||  ||
! Spelling
||= 33313153 ||= 3|4 b7 || A B C D Eb Fb Gbb Hb ||  ||
! style="text-align: center;" | Other notes
||= 33131533 ||= 2|5 b6 || A B C Db Eb Fbb Gb Hb ||  ||
|-
||= 31315333 ||= 1|6 b5 || A B Cb Db Ebb Fb Gb Hb ||  ||
| style="text-align: center;" | 4333324
||= 13153333 ||= 0|7 b4 || A Bb Cb Dbb Eb Fb Gb Hb ||  ||
| style="text-align: center;" | 3222213
| style="text-align: center;" | 6{{pipe}}0 v7
| G A B C D E Fv
| style="text-align: center;" | 8:9:10:11:12:14 hexad on the tonic,


**MODMOS with 4th note in generator chain flattened:** **#....****##****#.####**
in both 15edo and 22edo as G-A-B-C-D-Fv
||= Step Pattern ||= UDP Name || Spelling || Other Notes ||
|-
||= 33153331 ||= 7|0 b4 || A B C Db E F G H ||   ||
| style="text-align: center;" | 4433332
||= 31533313 ||= 6|1 b3 || A B Cb D E F G Hb ||  ||
| style="text-align: center;" | 3322221
||= 15333133 ||= 5|2 b2 || A Bb C D E F Gb Hb ||   ||
| style="text-align: center;" | 6{{pipe}}0 ^3^4^5^6^7
||= 53331331 ||= 7|0 #2#3#4#5 || A B# C# D# E# F G H ||   ||
| G A B^ C^ D^ E^ F^
||= 33313315 ||= 3|4 b8 || A B C D Eb Fb Gb Hbb ||   ||
| style="text-align: center;" |  
||= 33133153 ||= 2|5 b7 || A B C Db Eb Fb Gbb Hb ||   ||
|-
||= 31331533 ||= 1|6 b6 || A B Cb Db Eb Fbb Gb Hb ||  ||
| style="text-align: center;" | 2443333
||= 13315333 ||= 0|7 b5 || A Bb Cb Db Ebb Fb Gb Hb ||  ||
| style="text-align: center;" | 1332222
| style="text-align: center;" | 4{{pipe}}2 v2
| G Avv Bv C D E F
| style="text-align: center;" |  
|-
| style="text-align: center;" | 3244333
| style="text-align: center;" | 2133222
| style="text-align: center;" | 3{{pipe}}3 v3
| G Av Bvv Cv D E F
| style="text-align: center;" |  
|-
| style="text-align: center;" | 3324433
| style="text-align: center;" | 2213322
| style="text-align: center;" | 2{{pipe}}4 v4
| G Av Bv Cvv Dv E F
| style="text-align: center;" |  
|-
| style="text-align: center;" | 3332443
| style="text-align: center;" | 2221332
| style="text-align: center;" | 1{{pipe}}5 v5
| G Av Bv Cv Dvv Ev F
| style="text-align: center;" |  
|-
| style="text-align: center;" | 3333244
| style="text-align: center;" | 2222133
| style="text-align: center;" | 0{{pipe}}6 v6
| G Av Bv Cv Dv Evv Fv
| style="text-align: center;" |  
|}


**MODMOS with 5th note in generator chain flattened:** **#...****##****##.###**
'''MODMOS with 3rd note in generator chain flattened: #....##.####'''
||= Step Pattern ||= UDP Name || Spelling || Other Notes ||
||= 33315331 ||= 7|0 b5 || A B C D Eb F G H ||  ||
||= 33153313 ||= 6|1 b4 || A B C Db E F G Hb ||  ||
||= 31533133 ||= 5|2 b3 || A B Cb D E F Gb Hb ||  ||
||= 15331333 ||= 4|3 b2 || A Bb C D E Fb Gb Hb ||  ||
||= 53313331 ||= 7|0 #2#3#4 || A B# C# D# E F G H ||  ||
||= 33133315 ||= 2|5 b8 || A B C Db Eb Fb Gb Hbb ||  ||
||= 31333153 ||= 1|6 b7 || A B Cb Db Eb Fb Gbb Hb ||  ||
||= 13331533 ||= 0|7 b6 || A Bb Cb Db Eb Fbb Gb Hb ||  ||


**MODMOS with 6th note in generator chain flattened:** **#..****##****###.##**
'''Note: Contains a broken 4/3 chain so it has only 3 4/3s'''
||= Step Pattern ||= UDP Name || Spelling || Other Notes ||
||= 33331531 ||= 7|0 b6 || A B C D E Fb G H ||  ||
||= 33315313 ||= 6|1 b5 || A B C D Eb F G Hb ||  ||
||= 33153133 ||= 5|2 b4 || A B C Db E F Gb Hb ||  ||
||= 31531333 ||= 4|3 b3 || A B Cb D E Fb Gb Hb ||  ||
||= 15313333 ||= 3|4 b2 || A Bb C D Eb Fb Gb Hb ||  ||
||= 53313331 ||= 7|0 #2#3 || A B# C# D E F G H ||  ||
||= 33133315 ||= 1|6 b8 || A B Cb Db Eb Fb Gb Hbb ||  ||
||= 31333153 ||= 0|7 b7 || A Bb Cb Db Eb Fb Gbb Hb ||  ||


**MODMOS with 7th note in generator chain flattened or 2nd sharpened:** **#.****##****####.#**
{| class="wikitable"
||= Step Pattern ||= UDP Name || Spelling || Other Notes ||
|-
||= 33333151 ||= 7|0 b7 || A B C D E F Gb H ||   ||
! style="text-align: center;" | 22edo steps
||= 33331513 ||= 6|1 b6 || A B C D E Fb G Hb ||   ||
! style="text-align: center;" | 15edo steps
||= 33315133 ||= 5|2 b5 || A B C D Eb F Gb Hb ||   ||
! style="text-align: center;" | UDP name
||= 33151333 ||= 4|3 b4 || A B C Db E Fb Gb Hb ||   ||
! Spelling
||= 31513333 ||= 3|4 b3 || A B Cb D Eb Fb Gb Hb ||   ||
! style="text-align: center;" | Other notes
||= 15133333 ||= 2|5 b2 || A Bb C Db Eb Fb Gb Hb ||   ||
|-
||= 51333331 ||= 7|0 #2 || A B# C D E F G H ||  ||
| style="text-align: center;" | 4333243
||= 13333315 ||= 0|7 b8 || A Bb Cb Db Eb Fb Gb Hbb ||  ||
| style="text-align: center;" | 3222132
| style="text-align: center;" | 6{{pipe}}0 v6
| G A B C D Ev F
| style="text-align: center;" |  
|-
| style="text-align: center;" | 3433324
| style="text-align: center;" | 2322213
| style="text-align: center;" | 5{{pipe}}1 v7
| G Av B C D E Fv
| style="text-align: center;" |  
|-
| style="text-align: center;" | 4343332
| style="text-align: center;" | 3232221
| style="text-align: center;" | 6{{pipe}}0 ^4^5^6^7
| G A B C^ D^ E^ F^
| style="text-align: center;" |  
|-
| style="text-align: center;" | 2434333
| style="text-align: center;" | 1323222
| style="text-align: center;" | 3{{pipe}}3 v2
| G Avv Bv Cv D E F
| style="text-align: center;" |  
|-
| style="text-align: center;" | 3243433
| style="text-align: center;" | 2132322
| style="text-align: center;" | 2{{pipe}}4 v3
| G Av Bvv Cv Dv E F
| style="text-align: center;" |  
|-
| style="text-align: center;" | 3324343
| style="text-align: center;" | 2213232
| style="text-align: center;" | 1{{pipe}}5 v4
| G Av Bv Cvv Dv Ev F
| style="text-align: center;" |  
|-
| style="text-align: center;" | 3332434
| style="text-align: center;" | 2221323
| style="text-align: center;" | 0{{pipe}}6 v5
| G Av Bv Cv Dvv Ev Fv
| style="text-align: center;" |  
|}


**MODMOS with 3rd note in generator chain sharpened:** **##.****#****####..#**
'''MODMOS with 4th note in generator chain flattened: #...###.###'''
||= Step Pattern ||= UDP Name || Spelling || Other Notes ||
||= 35133331 ||= 7|0 #3 || A B C# D E F G H ||  ||
||= 51333313 ||= 6|1 #2 || A B# C D E F G Hb ||  ||
||= 13333135 ||= 0|7 b7b8 || A Bb Cb Db Eb Fb Gbb Hbb ||  ||
||= 33331351 ||= 4|3 #8 || A B C D E Fb Gb H ||  ||
||= 33313513 ||= 3|4 #7 || A B C D Eb Fb G Hb ||  ||
||= 33135133 ||= 2|5 #6 || A B C Db Eb F Gb Hb ||  ||
||= 31351333 ||= 1|6 #5 || A B Cb Db E Fb Gb Hb ||  ||
||= 13513333 ||= 0|7 #4 || A Bb Cb D Eb Fb Gb Hb ||  ||


**MODMOS with 4th note in generator chain sharpened:** **###.****####...#**
'''Note: Contains a broken 4/3 chain so it has only 3 4/3s'''
||= Step Pattern ||= UDP Name || Spelling || Other Notes ||
||= 33513331 ||= 7|0 #4 || A B C D# E F G H ||  ||
||= 35133331 ||= 6|1 #3 || A B C# D E F G Hb ||  ||
||= 51333313 ||= 5|2 #2 || A B# C D E F Gb Hb ||  ||
||= 13333135 ||= 0|7 b6b7b8 || A Bb Cb Db Eb Fbb Gbb Hbb ||  ||
||= 33331351 ||= 3|4 #8 || A B C D Eb Fb Gb H ||  ||
||= 33313513 ||= 2|5 #7 || A B C Db Eb Fb G Hb ||  ||
||= 33135133 ||= 1|6 #6 || A B Cb Db Eb F Gb Hb ||  ||
||= 31351333 ||= 0|7 #5 || A Bb Cb Db E Fb Gb Hb ||  ||


**MODMOS with 5th note in generator chain sharpened:** **####.****###....#**
{| class="wikitable"
||= Step Pattern ||= UDP Name || Spelling || Other Notes ||
|-
||= 33351331 ||= 7|0 #5 || A B C D E# F G H ||   ||
! style="text-align: center;" | 22edo steps
||= 33513331 ||= 6|1 #4 || A B C D# E F G Hb ||   ||
! style="text-align: center;" | 15edo steps
||= 35133313 ||= 5|2 #3 || A B C# D E F Gb Hb ||   ||
! style="text-align: center;" | UDP name
||= 51333133 ||= 4|3 #2 || A B# C D E Fb Gb Hb ||   ||
! Spelling
||= 13331335 ||= 0|7 b5b6b7b8 || A Bb Cb Db Ebb Fbb Gbb Hbb ||   ||
! style="text-align: center;" | Other notes
||= 33313351 ||= 2|5 #8 || A B C Db Eb Fb Gb H ||   ||
|-
||= 33133513 ||= 1|6 #7 || A B Cb Db Eb Fb G Hb ||  ||
| style="text-align: center;" | 4332433
||= 31335133 ||= 0|7 #6 || A Bb Cb Db Eb F Gb Hb ||  ||
| style="text-align: center;" | 3221322
| style="text-align: center;" | 6{{pipe}}0 v5
| G A B C Dv E F
| style="text-align: center;" |  
|-
| style="text-align: center;" | 3433243
| style="text-align: center;" | 2322132
| style="text-align: center;" | 5{{pipe}}1 v6
| G Av B C D Ev F
| style="text-align: center;" |  
|-
| style="text-align: center;" | 3343324
| style="text-align: center;" | 2232213
| style="text-align: center;" | 4{{pipe}}2 v7
| G Av Bv C D E Fv
| style="text-align: center;" |  
|-
| style="text-align: center;" | 4334332
| style="text-align: center;" | 3223221
| style="text-align: center;" | 6{{pipe}}0 ^5^6^7
| G A B C D^ E^ F^
| style="text-align: center;" |  
|-
| style="text-align: center;" | 2433433
| style="text-align: center;" | 1322322
| style="text-align: center;" | 2{{pipe}}4 v2
| G Avv Bv Cv Dv E F
| style="text-align: center;" |  
|-
| style="text-align: center;" | 3243343
| style="text-align: center;" | 2132232
| style="text-align: center;" | 1{{pipe}}5 v3
| G Av Bvv Cv Dv Ev F
| style="text-align: center;" |  
|-
| style="text-align: center;" | 3324334
| style="text-align: center;" | 2213223
| style="text-align: center;" | 0{{pipe}}6 v4
| G Av Bv Cvv Dv Ev Fv
| style="text-align: center;" |  
|}


**MODMOS with 6th note in generator chain sharpened:** **#####.****##.....#**
<span style="color: #0000ff;">'''MODMOS with 5th note in generator chain flattened: #..####.## (melodic major)'''</span>
||= Step Pattern ||= UDP Name || Spelling || Other Notes ||
||= 33335131 ||= 7|0 #6 || A B C D E F# G H ||  ||
||= 33351313 ||= 6|1 #5 || A B C D E# F G Hb ||  ||
||= 33513133 ||= 5|2 #4 || A B C D# E F Gb Hb ||  ||
||= 35131333 ||= 4|3 #3 || A B C# D E Fb Gb Hb ||  ||
||= 51313333 ||= 3|4 #2 || A B# C D Eb Fb Gb Hb ||  ||
||= 13133335 ||= 0|7 b4b5b6b7b8 || A Bb Cb Dbb Ebb Fbb Gbb Hbb ||  ||
||= 31333351 ||= 1|6 #8 || A B Cb Db Eb Fb Gb H ||  ||
||= 13333513 ||= 0|7 #7 || A Bb Cb Db Eb Fb G Hb ||  ||


**MODMOS with 7th note in generator chain sharpened:** **######.****#......#**
'''Consists of unbroken chains of 4/3s'''
||= Step Pattern ||= UDP Name || Spelling || Other Notes ||
||= 33333511 ||= 7|0 #7 || A B C D E F G# H ||  ||
||= 33335113 ||= 6|1 #6 || A B C D E F# G Hb ||  ||
||= 33351133 ||= 5|2 #5 || A B C D E# F Gb Hb ||  ||
||= 33511333 ||= 4|3 #4 || A B C D# E Fb Gb Hb ||  ||
||= 35113333 ||= 3|4 #3 || A B C# D Eb Fb Gb Hb ||  ||
||= 51133333 ||= 2|5 #2 || A B# C Db Eb Fb Gb Hb ||  ||
||= 11333335 ||= 0|7 b3b4b5b6b7b8 || A Bb Cbb Dbb Ebb Fbb Gbb Hbb ||  ||
||= 13333351 ||= 0|7 #8 || A Bb Cb Db Eb Fb Gb H ||  ||
===Alterations by Porcupine[7] chroma===
**MODMOS with 2nd note in generator chain flattened**
||= Step Pattern ||= UDP Name || Spelling ||= Other Notes ||
||= 24333331 ||= 7|0 v2 || A Bv C D E F G H ||  ||
||= 43333312 ||= 6|1 ^2^3^4^5^6^7^8 || A B^ C^ D^ E^ F^ G^ Hb^ ||  ||
||= 33333124 ||= 5|2 v8 || A B C D E F Gb Hbv ||  ||
||= 33331243 ||= 4|3 v7 || A B C D E Fb Gbv Hb ||  ||
||= 33312433 ||= 3|4 v6 || A B C D Eb Fbv Gb Hb ||  ||
||= 33124333 ||= 2|5 v5 || A B C Db Ebv Fb Gb Hb ||  ||
||= 31243333 ||= 1|6 v4 || A B Cb Dbv Eb Fb Gb Hb ||  ||
||= 12433333 ||= 0|7 v3 || A Bb Cbv Db Eb Fb Gb Hb ||  ||


**MODMOS with 3rd note in generator chain flattened**
{| class="wikitable"
||= Step Pattern ||= UDP Name || Spelling ||= Other Notes ||
|-
||= 32433331 ||= 7|0 v3 || A B Cv D E F G H ||   ||
! Functional Name
||= 24333313 ||= 6|1 v2 || A Bv C D E F G Hb ||  ||
! William's Name (repltiles)
||= 43333132 ||= 5|2 ^2^3^4^5^6^7^8 || A B^ C^ D^ E^ F^ Gb^ Hb^ ||   ||
! style="text-align: center;" | 22edo steps
||= 33331324 ||= 4|3 v8 || A B C D E Fb Gb Hbv ||  ||
! style="text-align: center;" | 15edo steps
||= 33313243 ||= 3|4 v7 || A B C D Eb Fb Gbv Hb ||   ||
! style="text-align: center;" | UDP name
||= 33132433 ||= 2|5 v6 || A B C Db Eb Fbv Gb Hb ||  ||
! Spelling
||= 31324333 ||= 1|6 v5 || A B Cb Db Ebv Fb Gb Hb ||   ||
! style="text-align: center;" | Other notes
||= 13243333 ||= 0|7 v4 || A Bb Cb Dbv Eb Fb Gb Hb ||  ||
|-
| Bright major v4
| Lizard
| style="text-align: center;" | 4324333
| style="text-align: center;" | 3213222
| style="text-align: center;" | 6{{pipe}}0 v4
| G A B Cv D E F
| style="text-align: center;" | I, IV, v, vi "mixolydian-like"*
|-
| Dark major v5
| Iguana
| style="text-align: center;" | 3432433
| style="text-align: center;" | 2321322
| style="text-align: center;" | 5{{pipe}}1 v5
| G Av B C Dv E F
| style="text-align: center;" |  
|-
| Bright minor v6
| Serpent
| style="text-align: center;" | 3343243
| style="text-align: center;" | 2232132
| style="text-align: center;" | 4{{pipe}}2 v6
| G Av Bv C D Ev F
| style="text-align: center;" | i, III, VI, vii
|-
| Dark minor v7
| Iguana
| style="text-align: center;" | 3334324
| style="text-align: center;" | 2223213
| style="text-align: center;" | 3{{pipe}}3 v7
| G Av Bv Cv D E Fv
| style="text-align: center;" | i, ii, IV, VII "dorian-like"
|-
| Bright major ^6^7
(melodic major)
| Chameleon
| style="text-align: center;" | 4333432
| style="text-align: center;" | 3222321
| style="text-align: center;" | 6{{pipe}}0 ^6^7
| G A B C D E^ F^
| style="text-align: center;" | I, ii, iii, V "ionian-like";


**MODMOS with 4th note in generator chain flattened**
8:9:10:11:12:14:15 on the tonic in 15edo as G-A-B-C-D-E^-F^
||= Step Pattern ||= UDP Name || Spelling ||= Other Notes ||
||= 33243331 ||= 7|0 v4 || A B C Dv E F G H ||  ||
||= 32433313 ||= 6|1 v3 || A B Cv D E F G Hb ||  ||
||= 24333133 ||= 5|2 v2 || A Bv C D E F Gb Hb ||  ||
||= 43331332 ||= 4|3 ^2^3^4^5^6^7^8 || A B^ C^ D^ E^ Fb^ Gb^ Hb^ ||  ||
||= 33313324 ||= 3|4 v8 || A B C D Eb Fb Gb Hbv ||  ||
||= 33133243 ||= 2|5 v7 || A B C Db Eb Fb Gbv Hb ||  ||
||= 31332433 ||= 1|6 v6 || A B Cb Db Eb Fbv Gb Hb ||  ||
||= 13324333 ||= 0|7 v5 || A Bb Cb Db Ebv Fb Gb Hb ||  ||


**MODMOS with 5th note in generator chain flattened**
(but not in 22edo)
||= Step Pattern ||= UDP Name || Spelling ||= Other Notes ||
||= 33324331 ||= 7|0 v5 || A B C D Ev F G H ||  ||
||= 33243313 ||= 6|1 v4 || A B C Dv E F G Hb ||  ||
||= 32433133 ||= 5|2 v3 || A B Cv D E F Gb Hb ||  ||
||= 24331333 ||= 4|3 v2 || A Bv C D E Fb Gb Hb ||  ||
||= 43313332 ||= 3|4 ^2^3^4^5^6^7^8 || A B^ C^ D^ Eb^ Fb^ Gb^ Hb^ ||  ||
||= 33133324 ||= 2|5 v8 || A B C Db Eb Fb Gb Hbv ||  ||
||= 31333243 ||= 1|6 v7 || A B Cb Db Eb Fb Gbv Hb ||  ||
||= 13332433 ||= 0|7 v6 || A Bb Cb Db Eb Fbv Gb Hb ||  ||


**MODMOS with 6th note in generator chain flattened**
Igliashon finds it the "most grounded",
||= Step Pattern ||= UDP Name || Spelling ||= Other Notes ||
||= 33332431 ||= 7|0 v6 || A B C D E Fv G H ||  ||
||= 33324313 ||= 6|1 v5 || A B C D Ev F G Hb ||  ||
||= 33243133 ||= 5|2 v4 || A B C Dv E F Gb Hb ||  ||
||= 32431333 ||= 4|3 v3 || A B Cv D E Fb Gb Hb ||  ||
||= 24313333 ||= 3|4 v2 || A Bv C D Eb Fb Gb Hb ||  ||
||= 43133332 ||= 2|5 ^2^3^4^5^6^7^8 || A B^ C^ Db^ Eb^ Fb^ Gb^ Hb^ ||  ||
||= 31333324 ||= 1|6 v8 || A B Cb Db Eb Fb Gb Hbv ||  ||
||= 13333243 ||= 0|7 v7 || A Bb Cb Db Eb Fb Gbv Hb ||  ||


**MODMOS with 7th note in generator chain flattened**
and suggests it as a candidate for "default major"
||= Step Pattern ||= UDP Name || Spelling ||= Other Notes ||
|-
||= 33333241 ||= 7|0 v7 || A B C D E F Gv H ||  ||
| Dark (half-)diminished v2
||= 33332413 ||= 6|1 v6 || A B C D E Fv G Hb ||  ||
| Crocodile
||= 33324133 ||= 5|2 v5 || A B C D Ev F Gb Hb ||  ||
| style="text-align: center;" | 2433343
||= 33241333 ||= 4|3 v4 || A B C Dv E Fb Gb Hb ||  ||
| style="text-align: center;" | 1322232
||= 32413333 ||= 3|4 v3 || A B Cv D Eb Fb Gb Hb ||  ||
| style="text-align: center;" | 1{{pipe}}5 v2
||= 24133333 ||= 2|5 v2 || A Bv C Db Eb Fb Gb Hb ||  ||
| G Avv Bv Cv Dv Ev F
||= 41333332 ||= 1|6 ^2^3^4^5^6^7^8 || A B^ Cb^ Db^ Eb^ Fb^ Gb^ Hb^ ||  ||
| style="text-align: center;" |  
||= 13333324 ||= 0|7 v8 || A Bb Cb Db Eb Fb Gb Hbv ||  ||
|-
| Magical seventh v3
| Turtle
| style="text-align: center;" | 3243334
| style="text-align: center;" | 2132223
| style="text-align: center;" | 0{{pipe}}6 v3
| G Av Bvv Cv Dv Ev Fv
| style="text-align: center;" |  
|}
<ul><li>This kind of description is obviously stupid because these porcupine scales are not really like the diatonic modes "mixolydian", "dorian", etc. As always, feel free to edit if you have some better description.</li></ul>


**MODMOS with 8th note in generator chain flattened**
<span style="color: #0000ff;">'''Symmetrical MODMOS with 2nd note in generator chain sharpened or 6th note flattened: #.#####.# (harmonic)'''</span>
||= Step Pattern ||= UDP Name || Spelling ||= Other Notes ||
||= 33333322 ||= 7|0 v8 || A B C D E F G Hv ||  ||
||= 33333223 ||= 6|1 v7 || A B C D E F Gv Hb ||  ||
||= 33332233 ||= 5|2 v6 || A B C D E Fv Gb Hb ||  ||
||= 33322333 ||= 4|3 v5 || A B C D Ev Fb Gb Hb ||  ||
||= 33223333 ||= 3|4 v4 || A B C Dv Eb Fb Gb Hb ||  ||
||= 32233333 ||= 2|5 v3 || A B Cv Db Eb Fb Gb Hb ||  ||
||= 22333333 ||= 1|6 v2 || A Bv Cb Db Eb Fb Gb Hb ||  ||
||= 23333332 ||= 0|7 ^2^3^4^5^6^7^8 || A Bb^ Cb^ Db^ Eb^ Fb^ Gb^ Hb^ ||  ||


**MODMOS with 1st note in generator chain sharpened (in 22edo this gives same modes as flattening 8th note)**
'''Consists of unbroken chains of 4/3s'''
||= Step Pattern ||= UDP Name || Spelling ||= Other Notes ||
||= 23333332 ||= 7|0 v2v3v4v5v6v7v8 || A Bv Cv Dv Ev Fv Gv Hv ||  ||
||= 33333322 ||= 6|1 ^8 || A B C D E F G Hb^ ||  ||
||= 33333223 ||= 5|2 ^7 || A B C D E F Gb^ Hb ||  ||
||= 33332233 ||= 4|3 ^6 || A B C D E Fb^ Gb Hb ||  ||
||= 33322333 ||= 3|4 ^5 || A B C D Eb^ Fb Gb Hb ||  ||
||= 33223333 ||= 2|5 ^4 || A B C Db^ Eb Fb Gb Hb ||  ||
||= 32233333 ||= 1|6 ^3 || A B Cb^ Db Eb Fb Gb Hb ||  ||
||= 22333333 ||= 0|7 ^2 || A Bb^ Cb Db Eb Fb Gb Hb ||  ||


**MODMOS with 2nd note in generator chain sharpened**
'''Has the most evenly-distributed 5-limit triads of all the MODMOSs'''
||= Step Pattern ||= UDP Name || Spelling ||= Other Notes ||
||= 42333331 ||= 7|0 ^2 || A B^ C D E F G H ||  ||
||= 23333314 ||= 6|1 v2v3v4v5v6v7v8 || A Bv Cv Dv Ev Fv Gv Hbv ||  ||
||= 33333142 ||= 5|2 ^8 || A B C D E F Gb Hb^ ||  ||
||= 33331423 ||= 4|3 ^7 || A B C D E Fb Gb^ Hb ||  ||
||= 33314233 ||= 3|4 ^6 || A B C D Eb Fb^ Gb Hb ||  ||
||= 33142333 ||= 2|5 ^5 || A B C Db Eb^ Fb Gb Hb ||  ||
||= 31423333 ||= 1|6 ^4 || A B Cb Db^ Eb Fb Gb Hb ||  ||
||= 14233333 ||= 0|7 ^3 || A Bb Cb^ Db Eb Fb Gb Hb ||  ||


**MODMOS with 3rd note in generator chain sharpened**
{| class="wikitable"
||= Step Pattern ||= UDP Name || Spelling ||= Other Notes ||
|-
||= 34233331 ||= 7|0 ^3 || A B C^ D E F G H ||  ||
! Functional Name
||= 42333313 ||= 6|1^2 || A B^ C D E F G Hb ||  ||
! William's Name (Farm animals)
||= 23333134 ||= 5|2 v2v3v4v5v6v7v8 || A Bv Cv Dv Ev Fv Gbv Hbv ||  ||
! style="text-align: center;" | 22edo steps
||= 33331342 ||= 4|3 ^8 || A B C D E Fb Gb Hb^ ||  ||
! style="text-align: center;" | 15edo steps
||= 33313423 ||= 3|4 ^7 || A B C D Eb Fb Gb^ Hb ||  ||
! style="text-align: center;" | UDP name #1
||= 33134233 ||= 2|5 ^6 || A B C Db Eb Fb^ Gb Hb ||  ||
! style="text-align: center;" | UDP name #2
||= 31342333 ||= 1|6 ^5 || A B Cb Db Eb^ Fb Gb Hb ||  ||
! Spelling
||= 13423333 ||= 0|7 ^4 || A Bb Cb Db^ Eb Fb Gb Hb ||  ||
! style="text-align: center;" | Other notes
|-
| Bright major ^7
(harmonic major)
| Horse
| style="text-align: center;" | 4333342
| style="text-align: center;" | 3222231
| style="text-align: center;" | 6{{pipe}}0 ^7
| style="text-align: center;" | (1{{pipe}}5 v1)
| G A B C D E F^
| style="text-align: center;" | I ii° iii iv° V vi vii°


**MODMOS with 4th note in generator chain sharpened**
Major with major V chord (most major-sounding major)
||= Step Pattern ||= UDP Name || Spelling ||= Other Notes ||
|-
||= 33423331 ||= 7|0 ^4 || A B C D^ E F G H ||  ||
| Magical seventh v2
||= 34233313 ||= 6|1^3 || A B C^ D E F G Hb ||  ||
| Pig
||= 42333133 ||= 5|2 ^2 || A B^ C D E F Gb Hb ||  ||
| style="text-align: center;" | 2433334
||= 23331334 ||= 4|3 v2v3v4v5v6v7v8 || A Bv Cv Dv Ev Fbv Gbv Hbv ||  ||
| style="text-align: center;" | 1322223
||= 33313342 ||= 3|4 ^8 || A B C D Eb Fb Gb Hb^ ||  ||
| style="text-align: center;" | (5{{pipe}}1 ^1)
||= 33133423 ||= 2|5 ^7 || A B C Db Eb Fb Gb^ Hb ||  ||
| style="text-align: center;" | 0{{pipe}}6 v2
||= 31334233 ||= 1|6 ^6 || A B Cb Db Eb Fb^ Gb Hb ||  ||
| G Avv Bv Cv Dv Ev Fv
||= 13342333 ||= 0|7 ^5 || A Bb Cb Db Eb^ Fb Gb Hb ||  ||
| style="text-align: center;" | i° II iii° iv v° VI vii


**MODMOS with 5th note in generator chain sharpened**
Magical seventh
||= Step Pattern ||= UDP Name || Spelling ||= Other Notes ||
|-
||= 33342331 ||= 7|0 ^5 || A B C D E^ F G H ||  ||
| Bright minor ^2
||= 33423313 ||= 6|1^4 || A B C D^ E F G Hb ||  ||
(harmonic minor)
||= 34233133 ||= 5|2 ^3 || A B C^ D E F Gb Hb ||  ||
| Sheep
||= 42331333 ||= 4|3 ^2 || A B^ C D E Fb Gb Hb ||  ||
| style="text-align: center;" | 4243333
||= 23313334 ||= 3|4 v2v3v4v5v6v7v8 || A Bv Cv Dv Ebv Fbv Gbv Hbv ||  ||
| style="text-align: center;" | 3132222
||= 33133342 ||= 2|5 ^8 || A B C Db Eb Fb Gb Hb^ ||  ||
| style="text-align: center;" | 4{{pipe}}2 ^2
||= 31333423 ||= 1|6 ^7 || A B Cb Db Eb Fb Gb^ Hb ||  ||
| style="text-align: center;" | 6{{pipe}}0 v3
||= 13334233 ||= 0|7 ^6 || A Bb Cb Db Eb Fb^ Gb Hb ||  ||
| G A Bv C D E F
| style="text-align: center;" | i ii° III iv° v vi° VII


**MODMOS with 6th note in generator chain sharpened**
Minor with minor v chord (most minor-sounding minor)
||= Step Pattern ||= UDP Name || Spelling ||= Other Notes ||
|-
||= 33334231 ||= 7|0 ^6 || A B C D E F^ G H ||  ||
| Dark major v4
||= 33342313 ||= 6|1 ^5 || A B C D E^ F G Hb ||  ||
| Cow
||= 33423133 ||= 5|2 ^4 || A B C D^ E F Gb Hb ||  ||
| style="text-align: center;" | 3424333
||= 34231333 ||= 4|3 ^3 || A B C^ D E Fb Gb Hb ||  ||
| style="text-align: center;" | 2313222
||= 42313333 ||= 3|4 ^2 || A B^ C D Eb Fb Gb Hb ||  ||
| style="text-align: center;" | 3{{pipe}}3 ^3
||= 23133334 ||= 2|5 v2v3v4v5v6v7v8 || A Bv Cv Dbv Ebv Fbv Gbv Hbv ||  ||
| style="text-align: center;" | 5{{pipe}}1 v4
||= 31333342 ||= 1|6 ^8 || A B Cb Db Eb Fb Gb Hb^ ||  ||
| G Av B Cv D E F
||= 13333423 ||= 0|7 ^7 || A Bb Cb Db Eb Fb Gb^ Hb ||  ||
| style="text-align: center;" | I ii iii° IV v° vi vii°


**MODMOS with 7th note in generator chain sharpened**
Major with major IV chord
||= Step Pattern ||= UDP Name || Spelling ||= Other Notes ||
|-
||= 33333421 ||= 7|0 ^7 || A B C D E F G^ H ||  ||
| Symmetric half-diminished
||= 33334213 ||= 6|1 ^6 || A B C D E F^ G Hb ||  ||
| Llama
||= 33342133 ||= 5|2 ^5 || A B C D E^ F Gb Hb ||  ||
| style="text-align: center;" | 3342433
||= 33421333 ||= 4|3 ^4 || A B C D^ E Fb Gb Hb ||  ||
| style="text-align: center;" | 2231322
||= 34213333 ||= 3|4 ^3 || A B C^ D Eb Fb Gb Hb ||  ||
| style="text-align: center;" | 2{{pipe}}4 ^4
||= 42133333 ||= 2|5 ^2 || A B^ C Db Eb Fb Gb Hb ||  ||
| style="text-align: center;" | 4{{pipe}}2 v5
||= 21333334 ||= 1|6 v2v3v4v5v6v7v8 || A Bv Cbv Dbv Ebv Fbv Gbv Hbv ||  ||
| G Av Bv C Dv E F
||= 13333342 ||= 0|7 ^8 || A Bb Cb Db Eb Fb Gb Hb^ ||  ||</pre></div>
| style="text-align: center;" | i° II iii iv° V vi° vii
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Porcupine Temperament Modal Harmony&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:26:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Intro To Porcupine"&gt;Intro To Porcupine&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Brief Intro to Modal Harmony and MODMOS's"&gt;Brief Intro to Modal Harmony and MODMOS's&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Reasons Why Porcupine Will Make for The Best Modal Harmony Ever"&gt;Reasons Why Porcupine Will Make for The Best Modal Harmony Ever&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Porcupine[7] and its MODMOSs"&gt;Porcupine[7] and its MODMOSs&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Porcupine[7] and its MODMOSs-The Porcupine[7] MOS"&gt;The Porcupine[7] MOS&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Porcupine[7] and its MODMOSs-Single-alteration MODMOS's"&gt;Single-alteration MODMOS's&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;!-- ws:start:WikiTextTocRule:33: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Porcupine[7] and its MODMOSs-Notable double-alteration MODMOS's"&gt;Notable double-alteration MODMOS's&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Porcupine[8] and its MODMOS's"&gt;Porcupine[8] and its MODMOS's&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Porcupine[8] and its MODMOS's-The Porcupine[8] MOS"&gt;The Porcupine[8] MOS&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Porcupine[8] and its MODMOS's-Single-alteration MODMOS's"&gt;Single-alteration MODMOS's&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Porcupine[8] and its MODMOS's-Single-alteration MODMOS's-Alterations by porcupine[8] chroma"&gt;Alterations by porcupine[8] chroma&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;!-- ws:start:WikiTextTocRule:38: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Porcupine[8] and its MODMOS's-Single-alteration MODMOS's-Alterations by Porcupine[7] chroma"&gt;Alterations by Porcupine[7] chroma&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:38 --&gt;&lt;!-- ws:start:WikiTextTocRule:39: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:39 --&gt;&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Intro To Porcupine"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Intro To &lt;a class="wiki_link" href="/Porcupine"&gt;Porcupine&lt;/a&gt;&lt;/h1&gt;
Porcupine is significant as a 5-limit temperament because it is the only 5-limit temperament other than meantone which possesses a 7-note MOS scale that is well-supplied with 5-limit major and minor triads (specifically, it has two of each of them). What is perhaps more significant about it is how naturally it extends those triads to involve the 11th harmonic; for instance, the first five consecutive notes of the Lssssss mode approximate the consecutive harmonics 8:9:10:11:12. This makes it a prime candidate for using extended JI-style harmonies in a compact and intuitive scale structure.&lt;br /&gt;
&lt;br /&gt;
It is also significant because it is supported by both &lt;a class="wiki_link" href="/15edo" target="_blank"&gt;15edo&lt;/a&gt; and &lt;a class="wiki_link" href="/22edo" target="_blank"&gt;22edo&lt;/a&gt;, the smallest ETs which improve on the 11-limit damage of &lt;a class="wiki_link" href="/12edo" target="_blank"&gt;12edo&lt;/a&gt; (other than &lt;a class="wiki_link" href="/19edo" target="_blank"&gt;19edo&lt;/a&gt;). In those ETs, Porcupine is an excellent candidate for providing a 7-nominal notational basis and 7-interval-class categorical framework for those ETs (which is important because it allows 5-limit major and minor triads to share a triad class, in keeping with common-practice conventions). Or, in other words, if you want to use 15edo or 22edo in such a way that allows you to think of 5/4 and 6/5 as types of &amp;quot;third&amp;quot;, and 4/3 and 3/2 as types of &amp;quot;fifth&amp;quot;, thinking of those ETs in terms of porcupine temperament is the ideal conceptual approach. &lt;em&gt;(To be continued...)&lt;/em&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Brief Intro to Modal Harmony and MODMOS's"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Brief Intro to Modal Harmony and MODMOS's&lt;/h1&gt;
Porcupine is a temperament completely capable of diverse harmony. Using it's MOS in conjunction with it's modmos will allow for some very diverse chordal movement that will still be tonally solid. Porcupine mode and modmos names are based on animal names because none of the scales remotely are similar to any existing mode name from anywhere. The initial four modes: Porcupine, Chinchilla, Zebra, and Dog all contain 3/2 from the root while the latter three: Gazette, Lemur, and Panda lack 3/2 and instead have a triad similar to a diminished triad on the root. In order to remedy this problem, it may be fruitful to use other methods than triadic tertian harmony to build tonal frameworks in porcupine.&lt;br /&gt;
&lt;br /&gt;
Because the generator of porcupine is 9/8, secondual harmony tends to work quite well. William lynch considers varying subsets of 8:9:10:11:12 to work really well for building harmonic movement in porcupine. In addition, the second inversion which produces chords of stacked sevenths of varying sizes, also works well as an additional sonority to create better voice leading and variety. If the mode position of porcupine contains no 3/2 from the root, then a chord without 3/2 is played on the root. &lt;br /&gt;
&lt;br /&gt;
The Modmos of porcupine can be used in conjunction with the regular mos in order to build powerful tonal movement. While each useful modmos has it's own distinct name, they most likely will be useful to use as a particular function in each porcupine mode. They can also be used stand alone but little is known about the very complex system of tonality.&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Reasons Why Porcupine Will Make for The Best Modal Harmony Ever"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Reasons Why Porcupine Will Make for The Best Modal Harmony Ever&lt;/h1&gt;
The 7-note MOS of porcupine is great, but it lumps all the consonant chords together at one end of the scale (see below). It also fails to contain a complete 11-limit otonal hexad (4:5:6:7:9:11), even though porcupine is not excessively complex in the 11-limit. Thankfully, unlike in meantone[7] where the MODMOSs all reduce the number of consonant triads available, there are several MODMOSs of porcupine that contain an equal or greater number of consonant triads to the MOS (these are highlighted in blue text below). These MODMOSs also conveniently alter the distribution of triads within the scale, providing much-needed variety of possible chord progessions. Even better, some single-alteration MODMOSs make at least one full 11-limit hexad available, meaning 6 of the 7 notes of the scale can be sounded simultaneously and produce a consonant otonal harmony. The fact that porcupine temperament provides not just one 7-note scale but several that are equally-rich in harmonic resources makes it extremely fertile for modal harmony.&lt;br /&gt;
&lt;em&gt;(To be continued...)&lt;/em&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Porcupine[7] and its MODMOSs"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Porcupine[7] and its MODMOSs&lt;/h1&gt;
&lt;br /&gt;
The below mode names are given in &lt;a class="wiki_link" href="/Modal%20UDP%20Notation"&gt;UDP notation&lt;/a&gt;. For porcupine[7], the chroma-aligned generator is the 9/5, or the 11/6 if you prefer. All generators below refer to this generator, NOT the 10/9 one. For an explanation of the spellings, see &lt;a class="wiki_link" href="/Porcupine%20Notation"&gt;Porcupine Notation&lt;/a&gt;. William Lynch proposed the fun idea of naming modes of porcupine by various animal names.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Porcupine[7] and its MODMOSs-The Porcupine[7] MOS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;&lt;strong&gt;The Porcupine[7] MOS&lt;/strong&gt;&lt;/h2&gt;


&lt;table class="wiki_table"&gt;
Symmetric diminished
    &lt;tr&gt;
|-
        &lt;td&gt;Mode Name&lt;br /&gt;
| Dark minor v6
&lt;/td&gt;
| Goat
        &lt;td style="text-align: center;"&gt;22edo Step Pattern&lt;br /&gt;
| style="text-align: center;" | 3334243
&lt;/td&gt;
| style="text-align: center;" | 2223132
        &lt;td style="text-align: center;"&gt;15edo Step Pattern&lt;br /&gt;
| style="text-align: center;" | 1{{pipe}}5 ^5
&lt;/td&gt;
| style="text-align: center;" | 3{{pipe}}3 v6
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
| G Av Bv Cv D Ev F
&lt;/td&gt;
| style="text-align: center;" | i ii° III iv v° VI vii°
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Triad Qualities&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Chinchillian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4333333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3222222&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G A B C D E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;I iiº iiiº ivº v vi VII&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bright, otonal major (VII chord is major)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/porcupineotonalmajor22edo.mp3?h=20&amp;amp;w=240&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;porcupineotonalmajor22edo.mp3&amp;amp;quot; width=&amp;amp;quot;240&amp;amp;quot; height=&amp;amp;quot;20&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;20&amp;quot; width=&amp;quot;240&amp;quot;/&amp;gt; --&gt;&lt;embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Fporcupineotonalmajor22edo.mp3?file_extension=mp3&amp;autostart=false&amp;repeat=false&amp;showdigits=true&amp;showfsbutton=false&amp;width=240&amp;height=20"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Badgerian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3433333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2322222&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av B C D E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;I II iiiº ivº vº vi vii&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Darker major (vii is minor)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Zebrian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3343333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2232222&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv C D E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;i II III ivº vº viº vii&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bright minor (II is major)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Dingoian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3334333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2223222&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv Cv D E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;i ii III IV vº viº viiº&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Symmetric minor (ii is minor)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;!-- ws:start:WikiTextMediaRule:1:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/porcupinesymmetricminor22edo.mp3?h=20&amp;amp;w=240&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;porcupinesymmetricminor22edo.mp3&amp;amp;quot; width=&amp;amp;quot;240&amp;amp;quot; height=&amp;amp;quot;20&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;20&amp;quot; width=&amp;quot;240&amp;quot;/&amp;gt; --&gt;&lt;embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252Fporcupinesymmetricminor22edo.mp3?file_extension=mp3&amp;autostart=false&amp;repeat=false&amp;showdigits=true&amp;showfsbutton=false&amp;width=240&amp;height=20"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:1 --&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Gazettian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3333433&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2222322&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv Cv Dv E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;iº ii iii IV V viº viiº&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Diminished&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Lemurian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3333343&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2222232&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv Cv Dv Ev F&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;iº iiº iii iv V VI viiº&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Diminished&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Pandian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3333334&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2222223&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv Cv Dv Ev Fv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;iº iiº iiiº iv v VI VII&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;a class="wiki_link" href="/magical%20seventh%20chord"&gt;Magical seventh&lt;/a&gt; mode&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
Minor with minor iv
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Porcupine[7] and its MODMOSs-Single-alteration MODMOS's"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Single-alteration MODMOS's&lt;/h2&gt;
|-
&lt;strong&gt;MODMOS with 1st note in generator chain flattened: #.......######&lt;/strong&gt;&lt;br /&gt;
| Magical seventh ^6
&lt;strong&gt;Note: Contains a broken 4/3 chain so it has only 3 4/3s&lt;/strong&gt;&lt;br /&gt;
| Rooster
| style="text-align: center;" | 3333424
| style="text-align: center;" | 2222313
| style="text-align: center;" | 0{{pipe}}6 ^6
| style="text-align: center;" | 2{{pipe}}4 v7
| G Av Bv Cv Dv E Fv
| style="text-align: center;" | i° ii iii° IV v vi° VII


Magical seventh
|}


&lt;table class="wiki_table"&gt;
<span style="color: #0000ff;">'''MODMOS with 3rd note in generator chain sharpened: ##.####..# (melodic minor)'''</span>
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;22edo Steps&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;15edo Steps&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;5333332&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4222221&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|0 ^2^3^4^5^6^7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G A^ B^ C^ D^ E^ F^&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;2533333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1422222&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|1 v2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Avv B C D E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3253333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2142222&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|2 v3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bvv C D E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3325333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2214222&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|3 v4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv Cvv D E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3332533&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2221422&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|4 v5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv Cv Dvv E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3333253&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2222142&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|5 v6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv Cv Dv Evv F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3333325&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2222214&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|6 v7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv Cv Dv Ev Fvv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
'''Consists of unbroken chains of 4/3s'''
&lt;strong&gt;MODMOS with 2nd note in generator chain flattened: #.....#.#####&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;Note: Contains a broken 4/3 chain so it has only 3 4/3s&lt;/strong&gt;&lt;br /&gt;


{| class="wikitable"
|-
! Functional Name
! William's Name (big cats)
! style="text-align: center;" | 22edo steps
! style="text-align: center;" | 15edo steps
! style="text-align: center;" | UDP name #1
! style="text-align: center;" | UDP name #2
! Spelling
! style="text-align: center;" | Other notes
|-
| Bright major ^6
| Lionian
| style="text-align: center;" | 4333423
| style="text-align: center;" | 3222312
| style="text-align: center;" | 6{{pipe}}0 ^6
| style="text-align: center;" | (2{{pipe}}4 v1v7)
| G A B C D E^ F
| style="text-align: center;" | I, ii, v, VII "mixolydian-like"


&lt;table class="wiki_table"&gt;
8:9:10:11:12:14 on the tonic in 15edo only
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;22edo Steps&lt;br /&gt;
| Dark major ^7
&lt;/td&gt;
| Tigonian
        &lt;td style="text-align: center;"&gt;15edo Steps&lt;br /&gt;
| style="text-align: center;" | 3433342
&lt;/td&gt;
| style="text-align: center;" | 2322231
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
| style="text-align: center;" | 5{{pipe}}1 ^7
&lt;/td&gt;
| style="text-align: center;" | (1{{pipe}}5 v1v2)
        &lt;td&gt;Spelling&lt;br /&gt;
| G Av B C D E F^
&lt;/td&gt;
| style="text-align: center;" | I, II, iii, vi
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
|-
&lt;/td&gt;
| Bright minor ^1
    &lt;/tr&gt;
| Cougian
    &lt;tr&gt;
| style="text-align: center;" | 2343334
        &lt;td style="text-align: center;"&gt;4333324&lt;br /&gt;
| style="text-align: center;" | 1232223
&lt;/td&gt;
| style="text-align: center;" | (4{{pipe}}2 ^1)
        &lt;td style="text-align: center;"&gt;3222213&lt;br /&gt;
| style="text-align: center;" | 0{{pipe}}6 v2v3
&lt;/td&gt;
| G Avv Bvv Cv Dv Ev Fv
        &lt;td style="text-align: center;"&gt;6|0 v7&lt;br /&gt;
| style="text-align: center;" |
&lt;/td&gt;
|-
        &lt;td&gt;G A B C D E Fv&lt;br /&gt;
| Dark minor ^2
&lt;/td&gt;
(melodic minor)
        &lt;td style="text-align: center;"&gt;8:9:10:11:12:14 hexad on the tonic,&lt;br /&gt;
| Leopardian
in both 15edo and 22edo as G-A-B-C-D-Fv&lt;br /&gt;
| style="text-align: center;" | 4234333
&lt;/td&gt;
| style="text-align: center;" | 3123222
    &lt;/tr&gt;
| style="text-align: center;" | 3{{pipe}}3 ^2
    &lt;tr&gt;
| style="text-align: center;" | 6{{pipe}}0 v3v4
        &lt;td style="text-align: center;"&gt;4433332&lt;br /&gt;
| G A Bv Cv D E F
&lt;/td&gt;
| style="text-align: center;" | i, III, IV, v "dorian-like"
        &lt;td style="text-align: center;"&gt;3322221&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|0 ^3^4^5^6^7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G A B^ C^ D^ E^ F^&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;2443333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1332222&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|2 v2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Avv Bv C D E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3244333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2133222&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|3 v3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bvv Cv D E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3324433&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2213322&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|4 v4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv Cvv Dv E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3332443&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2221332&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|5 v5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv Cv Dvv Ev F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3333244&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2222133&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|6 v6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv Cv Dv Evv Fv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
Keenan and Igliashon both find this exceptionally beautiful
&lt;strong&gt;MODMOS with 3rd note in generator chain flattened: #....##.####&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;Note: Contains a broken 4/3 chain so it has only 3 4/3s&lt;/strong&gt;&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;22edo Steps&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;15edo Steps&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;4333243&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3222132&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|0 v6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G A B C D Ev F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3433324&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2322213&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|1 v7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av B C D E Fv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;4343332&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3232221&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|0 ^4^5^6^7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G A B C^ D^ E^ F^&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;2434333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1323222&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|3 v2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Avv Bv Cv D E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3243433&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2132322&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|4 v3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bvv Cv Dv E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3324343&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2213232&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|5 v4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv Cvv Dv Ev F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3332434&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2221323&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|6 v5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv Cv Dvv Ev Fv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;strong&gt;MODMOS with 4th note in generator chain flattened: #...###.###&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;Note: Contains a broken 4/3 chain so it has only 3 4/3s&lt;/strong&gt;&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;22edo Steps&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;15edo Steps&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;4332433&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3221322&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|0 v5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G A B C Dv E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3433243&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2322132&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|1 v6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av B C D Ev F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3343324&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2232213&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|2 v7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv C D E Fv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;4334332&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3223221&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|0 ^5^6^7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G A B C D^ E^ F^&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;2433433&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1322322&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|4 v2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Avv Bv Cv Dv E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3243343&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2132232&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|5 v3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bvv Cv Dv Ev F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3324334&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2213223&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|6 v4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv Cvv Dv Ev Fv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;span style="color: #0000ff;"&gt;&lt;strong&gt;MODMOS with 5th note in generator chain flattened: #..####.## Reptiles&lt;/strong&gt;&lt;/span&gt;&lt;br /&gt;
&lt;strong&gt;Consists of unbroken chains of 4/3s&lt;/strong&gt;&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;Mode Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;22edo Steps&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;15edo Steps&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Lizard&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4324333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3213222&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|0 v4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G A B Cv D E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;I, IV, v, vi &amp;quot;mixolydian-like&amp;quot;*&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Iguana&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3432433&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2321322&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|1 v5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av B C Dv E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Serpent&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3343243&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2232132&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|2 v6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv C D Ev F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;i, III, VI, vii&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Iguana&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3334324&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2223213&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|3 v7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv Cv D E Fv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;i, ii, IV, VII &amp;quot;dorian-like&amp;quot;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Chameleon&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4333432&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3222321&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|0 ^6^7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G A B C D E^ F^&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;I, ii, iii, V &amp;quot;ionian-like&amp;quot;;&lt;br /&gt;
8:9:10:11:12:14:15 on the tonic in 15edo as G-A-B-C-D-E^-F^&lt;br /&gt;
(but not in 22edo)&lt;br /&gt;
Igliashon finds it the &amp;quot;most grounded&amp;quot;,&lt;br /&gt;
and suggests it as a candidate for &amp;quot;default major&amp;quot;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Crocodile&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2433343&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1322232&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|5 v2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Avv Bv Cv Dv Ev F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Turtle&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3243334&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2132223&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|6 v3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bvv Cv Dv Ev Fv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;ul&gt;&lt;li&gt;This kind of description is obviously stupid because these porcupine scales are not really like the diatonic modes &amp;quot;mixolydian&amp;quot;, &amp;quot;dorian&amp;quot;, etc. As always, feel free to edit if you have some better description.&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;span style="color: #0000ff;"&gt;&lt;strong&gt;Symmetrical MODMOS with 2nd note in generator chain sharpened or 6th note flattened: #.#####.# Farm Animals&lt;/strong&gt; &lt;/span&gt;&lt;br /&gt;
&lt;strong&gt;Consists of unbroken chains of 4/3s&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;Has the most evenly-distributed 5-limit triads of all the MODMOSs&lt;/strong&gt;&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;Mode Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;22edo Steps&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;15edo Steps&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name #1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name #2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Horse&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4333342&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3222231&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|0 ^7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;(1|5 v1)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G A B C D E F^&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;I ii° iii iv° V vi vii°&lt;br /&gt;
Major with major V chord (most major-sounding major)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Pig&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2433334&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1322223&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;(5|1 ^1)&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|6 v2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Avv Bv Cv Dv Ev Fv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;i° II iii° iv v° VI vii&lt;br /&gt;
Magical seventh&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Sheep&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4243333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3132222&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|2 ^2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|0 v3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G A Bv C D E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;i ii° III iv° v vi° VII&lt;br /&gt;
Minor with minor v chord (most minor-sounding minor)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Cow&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3424333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2313222&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|3 ^3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|1 v4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av B Cv D E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;I ii iii° IV v° vi vii°&lt;br /&gt;
Major with major IV chord&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Llama&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3342433&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2231322&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|4 ^4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|2 v5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv C Dv E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;i° II iii iv° V vi° vii&lt;br /&gt;
Symmetric diminished&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Goat&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3334243&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2223132&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|5 ^5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|3 v6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv Cv D Ev F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;i ii° III iv v° VI vii°&lt;br /&gt;
Minor with minor iv&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Rooster&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3333424&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2222313&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|6 ^6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|4 v7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv Cv Dv E Fv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;i° ii iii° IV v vi° VII&lt;br /&gt;
Magical seventh&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;span style="color: #0000ff;"&gt;&lt;strong&gt;MODMOS with 3rd note in generator chain sharpened: ##.####..# Big Cats&lt;/strong&gt;&lt;/span&gt;&lt;br /&gt;
&lt;strong&gt;Consists of unbroken chains of 4/3s&lt;/strong&gt;&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;Mode Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;22edo Steps&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;15edo Steps&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Lionian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4333423&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3222312&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|0 ^6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G A B C D E^ F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;I, ii, v, VII &amp;quot;mixolydian-like&amp;quot;&lt;br /&gt;
8:9:10:11:12:14 on the tonic in 15edo only&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Tigonian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3433342&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2322231&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|1 ^7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av B C D E F^&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;I, II, iii, vi&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Cougian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2343334&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1232223&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|6 v2 v3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Avv Bvv Cv Dv Ev Fv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Leopardian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4234333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3123222&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|3 ^2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G A Bv Cv D E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;i, III, IV, v &amp;quot;dorian-like&amp;quot;&lt;br /&gt;
Keenan and Igliashon both find this exceptionally beautiful&lt;br /&gt;
and suggest it as a candidate for default &amp;quot;minor&amp;quot;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Cheetian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3423433&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2312322&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|4 ^3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av B Cv Dv E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Jaguarian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3342343&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2231232&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|5 ^4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv C Dv Ev F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Pantherian&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3334234&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2223123&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|6 ^5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv Cv D Ev Fv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;i, iv, VI, VII &amp;quot;aeolian-like&amp;quot;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;strong&gt;MODMOS with 4th note in generator chain sharpened: ###.###...#&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;Note: Contains a broken 4/3 chain so it has only 3 4/3s&lt;/strong&gt;&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;22edo Steps&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;15edo Steps&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;4334233&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3223122&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|0 ^5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G A B C D^ E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3433423&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2322312&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|1 ^6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av B C D E^ F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3343342&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2232231&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|2 ^7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv C D E F^&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;2334334&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1223223&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|6 v2v3v4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Avv Bvv Cvv Dv Ev Fv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;4233433&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3122322&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|4 ^2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G A Bv Cv Dv E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3423343&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2312232&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|5 ^3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av B Cv Dv Ev F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3342334&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2231223&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|6 ^4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv C Dv Ev Fv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;strong&gt;MODMOS with 5th note in generator chain sharpened: ####.##....#&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;Note: Contains a broken 4/3 chain so it has only 3 4/3s&lt;/strong&gt;&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;22edo Steps&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;15edo Steps&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;4342333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3231222&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|0 ^4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G A B C^ D E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3434233&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2323122&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|1 ^5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av B C D^ E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3343423&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2232312&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|2 ^6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv C D E^ F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3334342&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2223231&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|3 ^7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv Cv D E F^&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;2333434&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1222323&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|6 v2v3v4v5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Avv Bvv Cvv Dvv Ev Fv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;4233343&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3122232&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|5 ^2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G A Bv Cv Dv Ev F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3423334&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2312223&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|6 ^3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av B Cv Dv Ev Fv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;strong&gt;MODMOS with 6th note in generator chain sharpened: #####.#.....#&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;Note: Contains a broken 4/3 chain so it has only 3 4/3s&lt;/strong&gt;&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;22edo Steps&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;15edo Steps&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;4423333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3312222&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|0 ^3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G A B^ C D E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3442333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2331222&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|1 ^4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av B C^ D E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3344233&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2233122&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|2 ^5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv C D^ E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3334423&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2223312&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|3 ^6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv Cv D E^ F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3333442&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2222331&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|4 ^7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv Cv Dv E F^&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;2333344&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1222233&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|6 v2v3v4v5v6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Avv Bvv Cvv Dvv Evv Fv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;4233334&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3122223&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|6 ^2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G A Bv Cv Dv Ev Fv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;strong&gt;MODMOS with 7th note in generator chain sharpened: ######.......#&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;Note: Contains a broken 4/3 chain so it has only 3 4/3s&lt;/strong&gt;&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;22edo Steps&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;15edo Steps&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;5233333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4122222&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|0 ^2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G A^ B C D E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3523333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2412222&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|1 ^3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av B^ C D E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3352333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2241222&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|2 ^4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv C^ D E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3335233&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2224122&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|3 ^5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv Cv D^ E F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3333523&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2222412&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|4 ^6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv Cv Dv E^ F&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3333352&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2222241&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|5 ^7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Av Bv Cv Dv Ev F^&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;2333335&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1222224&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|6 v2v3v4v5v6v7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G Avv Bvv Cvv Dvv Evv Fvv&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Porcupine[7] and its MODMOSs-Notable double-alteration MODMOS's"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Notable double-alteration MODMOS's&lt;/h2&gt;
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;22edo Steps&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;15edo Steps&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;4324342&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3213231&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|0 v4 ^7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G A B Cv D E F^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&amp;quot;JI Major&amp;quot; scale a.k.a. Ptolemy/Zarlino&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;4234243&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3123132&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|3 ^2 v6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;G A Bv Cv D Ev F&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&amp;quot;JI Minor&amp;quot; scale&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
and suggest it as a candidate for default "minor"
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Porcupine[8] and its MODMOS's"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Porcupine[8] and its MODMOS's&lt;/h1&gt;
|-
All generators below refer to the porcupine[8] chroma-positive generator (the 10/9~11/10~whatever). William Lynch Proposes naming the modes off of sea creatures with Octopus being relevant of the number eight.&lt;br /&gt;
| Bright (half-)diminished ^3
&lt;br /&gt;
| Cheetian
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Porcupine[8] and its MODMOS's-The Porcupine[8] MOS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;The Porcupine[8] MOS&lt;/h2&gt;
| style="text-align: center;" | 3423433
| style="text-align: center;" | 2312322
| style="text-align: center;" | 2{{pipe}}4 ^3
| style="text-align: center;" | 5{{pipe}}1 v4v5
| G Av B Cv Dv E F
| style="text-align: center;" |
|-
| Dark (half-)diminished ^4
| Jaguarian
| style="text-align: center;" | 3342343
| style="text-align: center;" | 2231232
| style="text-align: center;" | 1{{pipe}}5 ^4
| style="text-align: center;" | 4{{pipe}}2 v5v6
| G Av Bv C Dv Ev F
| style="text-align: center;" |
|-
| Dark minor v6 v7
| Pantherian
| style="text-align: center;" | 3334234
| style="text-align: center;" | 2223123
| style="text-align: center;" | 0{{pipe}}6 ^5
| style="text-align: center;" | 3{{pipe}}3 v6v7
| G Av Bv Cv D Ev Fv
| style="text-align: center;" | i, iv, VI, VII "aeolian-like"
|}


&lt;table class="wiki_table"&gt;
'''MODMOS with 4th note in generator chain sharpened: ###.###...#'''
    &lt;tr&gt;
        &lt;td&gt;Mode Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Octopus&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;33333331&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7|0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D E F G H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Mantis&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;33333313&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D E F G Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Dolphin&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;33333133&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D E F Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Crab&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;33331333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D E Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Tuna&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;33313333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Salmon&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;33133333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C Db Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Starfish&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;31333333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb Db Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Whale&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;13333333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb Db Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
'''Note: Contains a broken 4/3 chain so it has only 3 4/3s'''
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Porcupine[8] and its MODMOS's-Single-alteration MODMOS's"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Single-alteration MODMOS's&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc10"&gt;&lt;a name="Porcupine[8] and its MODMOS's-Single-alteration MODMOS's-Alterations by porcupine[8] chroma"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Alterations by porcupine[8] chroma&lt;/h3&gt;
&lt;strong&gt;MODMOS with 2nd note in generator chain flattened:&lt;/strong&gt; &lt;strong&gt;#......&lt;/strong&gt;&lt;strong&gt;#.&lt;/strong&gt;&lt;strong&gt;######&lt;/strong&gt;&lt;br /&gt;


{| class="wikitable"
|-
! style="text-align: center;" | 22edo steps
! style="text-align: center;" | 15edo steps
! style="text-align: center;" | UDP name
! Spelling
! style="text-align: center;" | Other notes
|-
| style="text-align: center;" | 4334233
| style="text-align: center;" | 3223122
| style="text-align: center;" | 6{{pipe}}0 ^5
| G A B C D^ E F
| style="text-align: center;" |
|-
| style="text-align: center;" | 3433423
| style="text-align: center;" | 2322312
| style="text-align: center;" | 5{{pipe}}1 ^6
| G Av B C D E^ F
| style="text-align: center;" |
|-
| style="text-align: center;" | 3343342
| style="text-align: center;" | 2232231
| style="text-align: center;" | 4{{pipe}}2 ^7
| G Av Bv C D E F^
| style="text-align: center;" |
|-
| style="text-align: center;" | 2334334
| style="text-align: center;" | 1223223
| style="text-align: center;" | 0{{pipe}}6 v2v3v4
| G Avv Bvv Cvv Dv Ev Fv
| style="text-align: center;" |
|-
| style="text-align: center;" | 4233433
| style="text-align: center;" | 3122322
| style="text-align: center;" | 2{{pipe}}4 ^2
| G A Bv Cv Dv E F
| style="text-align: center;" |
|-
| style="text-align: center;" | 3423343
| style="text-align: center;" | 2312232
| style="text-align: center;" | 1{{pipe}}5 ^3
| G Av B Cv Dv Ev F
| style="text-align: center;" |
|-
| style="text-align: center;" | 3342334
| style="text-align: center;" | 2231223
| style="text-align: center;" | 0{{pipe}}6 ^4
| G Av Bv C Dv Ev Fv
| style="text-align: center;" |
|}


&lt;table class="wiki_table"&gt;
'''MODMOS with 5th note in generator chain sharpened: ####.##....#'''
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;15333331&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7|0 b2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb C D E F G H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;53333311&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7|0 #2#3#4#5#6#7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B# C# D# E# F# G# H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33333115&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|2 b8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D E F Gb Hbb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33331153&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|3 b7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D E Fb Gbb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33311533&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|4 b6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D Eb Fbb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33115333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|5 b5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C Db Ebb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31153333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|6 b4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb Dbb Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;11533333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 b3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cbb Db Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
'''Note: Contains a broken 4/3 chain so it has only 3 4/3s'''
&lt;strong&gt;MODMOS with 3rd note in generator chain flattened:&lt;/strong&gt; &lt;strong&gt;#.....&lt;/strong&gt;&lt;strong&gt;##.&lt;/strong&gt;&lt;strong&gt;#####&lt;/strong&gt;&lt;br /&gt;


{| class="wikitable"
|-
! style="text-align: center;" | 22edo steps
! style="text-align: center;" | 15edo steps
! style="text-align: center;" | UDP name
! Spelling
! style="text-align: center;" | Other notes
|-
| style="text-align: center;" | 4342333
| style="text-align: center;" | 3231222
| style="text-align: center;" | 6{{pipe}}0 ^4
| G A B C^ D E F
| style="text-align: center;" |
|-
| style="text-align: center;" | 3434233
| style="text-align: center;" | 2323122
| style="text-align: center;" | 5{{pipe}}1 ^5
| G Av B C D^ E F
| style="text-align: center;" |
|-
| style="text-align: center;" | 3343423
| style="text-align: center;" | 2232312
| style="text-align: center;" | 4{{pipe}}2 ^6
| G Av Bv C D E^ F
| style="text-align: center;" |
|-
| style="text-align: center;" | 3334342
| style="text-align: center;" | 2223231
| style="text-align: center;" | 3{{pipe}}3 ^7
| G Av Bv Cv D E F^
| style="text-align: center;" |
|-
| style="text-align: center;" | 2333434
| style="text-align: center;" | 1222323
| style="text-align: center;" | 0{{pipe}}6 v2v3v4v5
| G Avv Bvv Cvv Dvv Ev Fv
| style="text-align: center;" |
|-
| style="text-align: center;" | 4233343
| style="text-align: center;" | 3122232
| style="text-align: center;" | 1{{pipe}}5 ^2
| G A Bv Cv Dv Ev F
| style="text-align: center;" |
|-
| style="text-align: center;" | 3423334
| style="text-align: center;" | 2312223
| style="text-align: center;" | 0{{pipe}}6 ^3
| G Av B Cv Dv Ev Fv
| style="text-align: center;" |
|}


&lt;table class="wiki_table"&gt;
'''MODMOS with 6th note in generator chain sharpened: #####.#.....#'''
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31533331&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7|0 b3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb D E F G H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;15333313&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|1 b2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb C D E F G Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;53333131&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7|0 #2#3#4#5#6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B# C# D# E# F# G H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33331315&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|3 b8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D E Fb Gb Hbb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33313153&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|4 b7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D Eb Fb Gbb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33131533&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|5 b6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C Db Eb Fbb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31315333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|6 b5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb Db Ebb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13153333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 b4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb Dbb Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
'''Note: Contains a broken 4/3 chain so it has only 3 4/3s'''
&lt;strong&gt;MODMOS with 4th note in generator chain flattened:&lt;/strong&gt; &lt;strong&gt;#....&lt;/strong&gt;&lt;strong&gt;##&lt;/strong&gt;&lt;strong&gt;#.####&lt;/strong&gt;&lt;br /&gt;


{| class="wikitable"
|-
! style="text-align: center;" | 22edo steps
! style="text-align: center;" | 15edo steps
! style="text-align: center;" | UDP name
! Spelling
! style="text-align: center;" | Other notes
|-
| style="text-align: center;" | 4423333
| style="text-align: center;" | 3312222
| style="text-align: center;" | 6{{pipe}}0 ^3
| G A B^ C D E F
| style="text-align: center;" |
|-
| style="text-align: center;" | 3442333
| style="text-align: center;" | 2331222
| style="text-align: center;" | 5{{pipe}}1 ^4
| G Av B C^ D E F
| style="text-align: center;" |
|-
| style="text-align: center;" | 3344233
| style="text-align: center;" | 2233122
| style="text-align: center;" | 4{{pipe}}2 ^5
| G Av Bv C D^ E F
| style="text-align: center;" |
|-
| style="text-align: center;" | 3334423
| style="text-align: center;" | 2223312
| style="text-align: center;" | 3{{pipe}}3 ^6
| G Av Bv Cv D E^ F
| style="text-align: center;" |
|-
| style="text-align: center;" | 3333442
| style="text-align: center;" | 2222331
| style="text-align: center;" | 2{{pipe}}4 ^7
| G Av Bv Cv Dv E F^
| style="text-align: center;" |
|-
| style="text-align: center;" | 2333344
| style="text-align: center;" | 1222233
| style="text-align: center;" | 0{{pipe}}6 v2v3v4v5v6
| G Avv Bvv Cvv Dvv Evv Fv
| style="text-align: center;" |
|-
| style="text-align: center;" | 4233334
| style="text-align: center;" | 3122223
| style="text-align: center;" | 0{{pipe}}6 ^2
| G A Bv Cv Dv Ev Fv
| style="text-align: center;" |
|}


&lt;table class="wiki_table"&gt;
'''MODMOS with 7th note in generator chain sharpened: ######.......#'''
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33153331&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7|0 b4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C Db E F G H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31533313&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|1 b3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb D E F G Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;15333133&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|2 b2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb C D E F Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;53331331&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7|0 #2#3#4#5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B# C# D# E# F G H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33313315&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|4 b8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D Eb Fb Gb Hbb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33133153&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|5 b7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C Db Eb Fb Gbb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31331533&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|6 b6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb Db Eb Fbb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13315333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 b5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb Db Ebb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
'''Note: Contains a broken 4/3 chain so it has only 3 4/3s'''
&lt;strong&gt;MODMOS with 5th note in generator chain flattened:&lt;/strong&gt; &lt;strong&gt;#...&lt;/strong&gt;&lt;strong&gt;##&lt;/strong&gt;&lt;strong&gt;##.###&lt;/strong&gt;&lt;br /&gt;


{| class="wikitable"
|-
! style="text-align: center;" | 22edo steps
! style="text-align: center;" | 15edo steps
! style="text-align: center;" | UDP name
! Spelling
! style="text-align: center;" | Other notes
|-
| style="text-align: center;" | 5233333
| style="text-align: center;" | 4122222
| style="text-align: center;" | 6{{pipe}}0 ^2
| G A^ B C D E F
| style="text-align: center;" |
|-
| style="text-align: center;" | 3523333
| style="text-align: center;" | 2412222
| style="text-align: center;" | 5{{pipe}}1 ^3
| G Av B^ C D E F
| style="text-align: center;" |
|-
| style="text-align: center;" | 3352333
| style="text-align: center;" | 2241222
| style="text-align: center;" | 4{{pipe}}2 ^4
| G Av Bv C^ D E F
| style="text-align: center;" |
|-
| style="text-align: center;" | 3335233
| style="text-align: center;" | 2224122
| style="text-align: center;" | 3{{pipe}}3 ^5
| G Av Bv Cv D^ E F
| style="text-align: center;" |
|-
| style="text-align: center;" | 3333523
| style="text-align: center;" | 2222412
| style="text-align: center;" | 2{{pipe}}4 ^6
| G Av Bv Cv Dv E^ F
| style="text-align: center;" |
|-
| style="text-align: center;" | 3333352
| style="text-align: center;" | 2222241
| style="text-align: center;" | 1{{pipe}}5 ^7
| G Av Bv Cv Dv Ev F^
| style="text-align: center;" |
|-
| style="text-align: center;" | 2333335
| style="text-align: center;" | 1222224
| style="text-align: center;" | 0{{pipe}}6 v2v3v4v5v6v7
| G Avv Bvv Cvv Dvv Evv Fvv
| style="text-align: center;" |
|}


&lt;table class="wiki_table"&gt;
=== Notable double-alteration MODMOS's ===
    &lt;tr&gt;
{| class="wikitable"
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
|-
&lt;/td&gt;
! style="text-align: center;" | 22edo steps
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
! style="text-align: center;" | 15edo steps
&lt;/td&gt;
! style="text-align: center;" | UDP name
        &lt;td&gt;Spelling&lt;br /&gt;
! Spelling
&lt;/td&gt;
! style="text-align: center;" | Other notes
        &lt;td&gt;Other Notes&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 4324342
    &lt;/tr&gt;
| style="text-align: center;" | 3213231
    &lt;tr&gt;
| style="text-align: center;" | 6{{pipe}}0 v4 ^7
        &lt;td style="text-align: center;"&gt;33315331&lt;br /&gt;
| G A B Cv D E F^
&lt;/td&gt;
| "JI Major" scale a.k.a. Ptolemy/Zarlino
        &lt;td style="text-align: center;"&gt;7|0 b5&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 4234243
        &lt;td&gt;A B C D Eb F G H&lt;br /&gt;
| style="text-align: center;" | 3123132
&lt;/td&gt;
| style="text-align: center;" | 3{{pipe}}3 ^2 v6
        &lt;td&gt;&lt;br /&gt;
| G A Bv Cv D Ev F
&lt;/td&gt;
| "JI Minor" scale
    &lt;/tr&gt;
|}
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33153313&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|1 b4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C Db E F G Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31533133&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|2 b3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb D E F Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;15331333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|3 b2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb C D E Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;53313331&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7|0 #2#3#4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B# C# D# E F G H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33133315&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|5 b8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C Db Eb Fb Gb Hbb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31333153&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|6 b7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb Db Eb Fb Gbb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13331533&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 b6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb Db Eb Fbb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
== Porcupine[8] and its MODMOS's ==
&lt;strong&gt;MODMOS with 6th note in generator chain flattened:&lt;/strong&gt; &lt;strong&gt;#..&lt;/strong&gt;&lt;strong&gt;##&lt;/strong&gt;&lt;strong&gt;###.##&lt;/strong&gt;&lt;br /&gt;
All generators below refer to the porcupine[8] bright generator (the 10/9~11/10~whatever).


Similarly to Porcupine[7], William Lynch has proposed naming the modes off of sea creatures, with Octopus being relevant to the number eight.


&lt;table class="wiki_table"&gt;
Functional mode names are proposed based on the 3-step triads, which may be augmented (~9:12:16), major (~3:4:5) or minor (~12:15:20). However, it can also useful to look at a different functional system in which the octatonic MOS modes extend the heptatonic ones by adding one extra note.
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33331531&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7|0 b6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D E Fb G H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33315313&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|1 b5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D Eb F G Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33153133&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|2 b4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C Db E F Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31531333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|3 b3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb D E Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;15313333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|4 b2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb C D Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;53313331&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7|0 #2#3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B# C# D E F G H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33133315&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|6 b8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb Db Eb Fb Gb Hbb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31333153&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 b7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb Db Eb Fb Gbb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
=== The Porcupine[8] MOS ===
&lt;strong&gt;MODMOS with 7th note in generator chain flattened or 2nd sharpened:&lt;/strong&gt; &lt;strong&gt;#.&lt;/strong&gt;&lt;strong&gt;##&lt;/strong&gt;&lt;strong&gt;####.#&lt;/strong&gt;&lt;br /&gt;
{| class="wikitable"
|-
! Functional Name
! William's Name
! style="text-align: center;" | Step pattern
! style="text-align: center;" | UDP name
! Traditional Spelling
! Triad qualities (3-step triads)
! style="text-align: center;" | Other notes
|-
| Bright augmented
| Octopus
| style="text-align: center;" | 33333331
| style="text-align: center;" | 7{{pipe}}0
| A B C D E F G H
| I+ II+ III IV V vi vii viii
|
|-
| Dark augmented
| Mantis
| style="text-align: center;" | 33333313
| style="text-align: center;" | 6{{pipe}}1
| A B C D E F G Hb
| I+ II III IV v vi vii VIII+
|
|-
| Bright major
| Dolphin
| style="text-align: center;" | 33333133
| style="text-align: center;" | 5{{pipe}}2
| A B C D E F Gb Hb
| I II III iv v vi VII+ VIII+
|
|-
| Middle major
| Crab
| style="text-align: center;" | 33331333
| style="text-align: center;" | 4{{pipe}}3
| A B C D E Fb Gb Hb
| I II iii iv v VI+ VII+ VII
| 10:12:15 on the tonic
Has both 4/3 and 3/2
|-
| Dark major
| Tuna
| style="text-align: center;" | 33313333
| style="text-align: center;" | 3{{pipe}}4
| A B C D Eb Fb Gb Hb
| I ii iii iv V+ VI+ VII VIII
| 10:12:15 on the tonic
Has both 4/3 and 3/2
|-
| Bright minor
| Salmon
| style="text-align: center;" | 33133333
| style="text-align: center;" | 2{{pipe}}5
| A B C Db Eb Fb Gb Hb
| i ii iii IV+ V+ VI VII VIII
| 8:10:11:12 and 10:12:15 on the tonic
|-
| Middle minor
| Starfish
| style="text-align: center;" | 31333333
| style="text-align: center;" | 1{{pipe}}6
| A B Cb Db Eb Fb Gb Hb
| i ii III+ IV+ V VI VII viii
| 8:9:10:11:12 on the tonic
|-
| Dark minor
| Whale
| style="text-align: center;" | 13333333
| style="text-align: center;" | 0{{pipe}}7
| A Bb Cb Db Eb Fb Gb Hb
| i II+ III+ IV V VI vii viii
| 8:9:10:11:12 on the tonic
|}


=== Single-alteration MODMOSes ===
==== Alterations by Porcupine[8] chroma ====
'''MODMOS with 2nd note in generator chain flattened:''' '''#......''''''#.''''''######'''


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
! style="text-align: center;" | Step pattern
&lt;/td&gt;
! style="text-align: center;" | UDP name
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
! Spelling
&lt;/td&gt;
! Other Notes
        &lt;td&gt;Spelling&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 15333331
        &lt;td&gt;Other Notes&lt;br /&gt;
| style="text-align: center;" | 7{{pipe}}0 b2
&lt;/td&gt;
| A Bb C D E F G H
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;33333151&lt;br /&gt;
| style="text-align: center;" | 53333311
&lt;/td&gt;
| style="text-align: center;" | 7{{pipe}}0 #2#3#4#5#6#7
        &lt;td style="text-align: center;"&gt;7|0 b7&lt;br /&gt;
| A B# C# D# E# F# G# H
&lt;/td&gt;
|
        &lt;td&gt;A B C D E F Gb H&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 33333115
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 5{{pipe}}2 b8
&lt;/td&gt;
| A B C D E F Gb Hbb
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;33331513&lt;br /&gt;
| style="text-align: center;" | 33331153
&lt;/td&gt;
| style="text-align: center;" | 4{{pipe}}3 b7
        &lt;td style="text-align: center;"&gt;6|1 b6&lt;br /&gt;
| A B C D E Fb Gbb Hb
&lt;/td&gt;
|
        &lt;td&gt;A B C D E Fb G Hb&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 33311533
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 3{{pipe}}4 b6
&lt;/td&gt;
| A B C D Eb Fbb Gb Hb
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;33315133&lt;br /&gt;
| style="text-align: center;" | 33115333
&lt;/td&gt;
| style="text-align: center;" | 2{{pipe}}5 b5
        &lt;td style="text-align: center;"&gt;5|2 b5&lt;br /&gt;
| A B C Db Ebb Fb Gb Hb
&lt;/td&gt;
|
        &lt;td&gt;A B C D Eb F Gb Hb&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 31153333
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 1{{pipe}}6 b4
&lt;/td&gt;
| A B Cb Dbb Eb Fb Gb Hb
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;33151333&lt;br /&gt;
| style="text-align: center;" | 11533333
&lt;/td&gt;
| style="text-align: center;" | 0{{pipe}}7 b3
        &lt;td style="text-align: center;"&gt;4|3 b4&lt;br /&gt;
| A Bb Cbb Db Eb Fb Gb Hb
&lt;/td&gt;
|
        &lt;td&gt;A B C Db E Fb Gb Hb&lt;br /&gt;
|}
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31513333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|4 b3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb D Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;15133333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|5 b2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb C Db Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;51333331&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7|0 #2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B# C D E F G H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13333315&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 b8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb Db Eb Fb Gb Hbb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
'''MODMOS with 3rd note in generator chain flattened:''' '''#.....''''''##.''''''#####'''
&lt;strong&gt;MODMOS with 3rd note in generator chain sharpened:&lt;/strong&gt; &lt;strong&gt;##.&lt;/strong&gt;&lt;strong&gt;#&lt;/strong&gt;&lt;strong&gt;####..#&lt;/strong&gt;&lt;br /&gt;


{| class="wikitable"
|-
! style="text-align: center;" | Step pattern
! style="text-align: center;" | UDP name
! Spelling
! Other Notes
|-
| style="text-align: center;" | 31533331
| style="text-align: center;" | 7{{pipe}}0 b3
| A B Cb D E F G H
|
|-
| style="text-align: center;" | 15333313
| style="text-align: center;" | 6{{pipe}}1 b2
| A Bb C D E F G Hb
|
|-
| style="text-align: center;" | 53333131
| style="text-align: center;" | 7{{pipe}}0 #2#3#4#5#6
| A B# C# D# E# F# G H
|
|-
| style="text-align: center;" | 33331315
| style="text-align: center;" | 4{{pipe}}3 b8
| A B C D E Fb Gb Hbb
|
|-
| style="text-align: center;" | 33313153
| style="text-align: center;" | 3{{pipe}}4 b7
| A B C D Eb Fb Gbb Hb
|
|-
| style="text-align: center;" | 33131533
| style="text-align: center;" | 2{{pipe}}5 b6
| A B C Db Eb Fbb Gb Hb
|
|-
| style="text-align: center;" | 31315333
| style="text-align: center;" | 1{{pipe}}6 b5
| A B Cb Db Ebb Fb Gb Hb
|
|-
| style="text-align: center;" | 13153333
| style="text-align: center;" | 0{{pipe}}7 b4
| A Bb Cb Dbb Eb Fb Gb Hb
|
|}


&lt;table class="wiki_table"&gt;
'''MODMOS with 4th note in generator chain flattened:''' '''#....''''''##''''''#.####'''
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;35133331&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7|0 #3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C# D E F G H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;51333313&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|1 #2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B# C D E F G Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13333135&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 b7b8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb Db Eb Fb Gbb Hbb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33331351&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|3 #8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D E Fb Gb H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33313513&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|4 #7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D Eb Fb G Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33135133&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|5 #6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C Db Eb F Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31351333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|6 #5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb Db E Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13513333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 #4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb D Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
{| class="wikitable"
&lt;strong&gt;MODMOS with 4th note in generator chain sharpened:&lt;/strong&gt; &lt;strong&gt;###.&lt;/strong&gt;&lt;strong&gt;####...#&lt;/strong&gt;&lt;br /&gt;
|-
! style="text-align: center;" | Step pattern
! style="text-align: center;" | UDP name
! Spelling
! Other Notes
|-
| style="text-align: center;" | 33153331
| style="text-align: center;" | 7{{pipe}}0 b4
| A B C Db E F G H
|
|-
| style="text-align: center;" | 31533313
| style="text-align: center;" | 6{{pipe}}1 b3
| A B Cb D E F G Hb
|
|-
| style="text-align: center;" | 15333133
| style="text-align: center;" | 5{{pipe}}2 b2
| A Bb C D E F Gb Hb
|
|-
| style="text-align: center;" | 53331331
| style="text-align: center;" | 7{{pipe}}0 #2#3#4#5
| A B# C# D# E# F G H
|
|-
| style="text-align: center;" | 33313315
| style="text-align: center;" | 3{{pipe}}4 b8
| A B C D Eb Fb Gb Hbb
|
|-
| style="text-align: center;" | 33133153
| style="text-align: center;" | 2{{pipe}}5 b7
| A B C Db Eb Fb Gbb Hb
|
|-
| style="text-align: center;" | 31331533
| style="text-align: center;" | 1{{pipe}}6 b6
| A B Cb Db Eb Fbb Gb Hb
|
|-
| style="text-align: center;" | 13315333
| style="text-align: center;" | 0{{pipe}}7 b5
| A Bb Cb Db Ebb Fb Gb Hb
|
|}


'''MODMOS with 5th note in generator chain flattened:''' '''#...''''''##''''''##.###'''


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
! style="text-align: center;" | Step pattern
&lt;/td&gt;
! style="text-align: center;" | UDP name
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
! Spelling
&lt;/td&gt;
! Other Notes
        &lt;td&gt;Spelling&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 33315331
        &lt;td&gt;Other Notes&lt;br /&gt;
| style="text-align: center;" | 7{{pipe}}0 b5
&lt;/td&gt;
| A B C D Eb F G H
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;33513331&lt;br /&gt;
| style="text-align: center;" | 33153313
&lt;/td&gt;
| style="text-align: center;" | 6{{pipe}}1 b4
        &lt;td style="text-align: center;"&gt;7|0 #4&lt;br /&gt;
| A B C Db E F G Hb
&lt;/td&gt;
|
        &lt;td&gt;A B C D# E F G H&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 31533133
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 5{{pipe}}2 b3
&lt;/td&gt;
| A B Cb D E F Gb Hb
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;35133331&lt;br /&gt;
| style="text-align: center;" | 15331333
&lt;/td&gt;
| style="text-align: center;" | 4{{pipe}}3 b2
        &lt;td style="text-align: center;"&gt;6|1 #3&lt;br /&gt;
| A Bb C D E Fb Gb Hb
&lt;/td&gt;
|
        &lt;td&gt;A B C# D E F G Hb&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 53313331
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 7{{pipe}}0 #2#3#4
&lt;/td&gt;
| A B# C# D# E F G H
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;51333313&lt;br /&gt;
| style="text-align: center;" | 33133315
&lt;/td&gt;
| style="text-align: center;" | 2{{pipe}}5 b8
        &lt;td style="text-align: center;"&gt;5|2 #2&lt;br /&gt;
| A B C Db Eb Fb Gb Hbb
&lt;/td&gt;
|
        &lt;td&gt;A B# C D E F Gb Hb&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 31333153
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 1{{pipe}}6 b7
&lt;/td&gt;
| A B Cb Db Eb Fb Gbb Hb
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;13333135&lt;br /&gt;
| style="text-align: center;" | 13331533
&lt;/td&gt;
| style="text-align: center;" | 0{{pipe}}7 b6
        &lt;td style="text-align: center;"&gt;0|7 b6b7b8&lt;br /&gt;
| A Bb Cb Db Eb Fbb Gb Hb
&lt;/td&gt;
|
        &lt;td&gt;A Bb Cb Db Eb Fbb Gbb Hbb&lt;br /&gt;
|}
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33331351&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|4 #8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D Eb Fb Gb H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33313513&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|5 #7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C Db Eb Fb G Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33135133&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|6 #6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb Db Eb F Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31351333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 #5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb Db E Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
'''MODMOS with 6th note in generator chain flattened:''' '''#..''''''##''''''###.##'''
&lt;strong&gt;MODMOS with 5th note in generator chain sharpened:&lt;/strong&gt; &lt;strong&gt;####.&lt;/strong&gt;&lt;strong&gt;###....#&lt;/strong&gt;&lt;br /&gt;


{| class="wikitable"
|-
! Functional name
! style="text-align: center;" | Step pattern
! style="text-align: center;" | UDP name #1
! style="text-align: center;" | UDP name #2
! Spelling
! Triad qualities (3-step triads)
! Other Notes
|-
| Bright augmented b6
| style="text-align: center;" | 33331531
| style="text-align: center;" | 7{{pipe}}0 b6
| style="text-align: center;" | 4{{pipe}}3 #7#8
| A B C D E Fb G H
| I+ II+ iii IV V VI+ vii viiiº
| 10:12:15 on tonic
|-
| Dark augmented b5
| style="text-align: center;" | 33315313
| style="text-align: center;" | 6{{pipe}}1 b5
| style="text-align: center;" | 3{{pipe}}4 #6#7
| A B C D Eb F G Hb
| I+ ii III IV V+ vi viiº VIII+
|
|-
| Bright minor #5#6
| style="text-align: center;" | 33153133
| style="text-align: center;" | 5{{pipe}}2 b4
| style="text-align: center;" | 2{{pipe}}5 #5#6
| A B C Db E F Gb Hb
| i II III IV+ v viº VII+ VIII+
|
|-
| Middle major b3
| style="text-align: center;" | 31531333
| style="text-align: center;" | 4{{pipe}}3 b3
| style="text-align: center;" | 1{{pipe}}6 #4#5
| A B Cb D E Fb Gb Hb
| I II III+ iv vº VI+ VII+ viii
| Has both 4/3 and 3/2
|-
| Dark major b2
| style="text-align: center;" | 15313333
| style="text-align: center;" | 3{{pipe}}4 b2
| style="text-align: center;" | 0{{pipe}}7 #3#4
| A Bb C D Eb Fb Gb Hb
| I III+ iii ivº V+ VI+ vii VIII
| 10:12:15 on the tonic
Has both 4/3 and 3/2
|-
| Bright augmented #2#3
| style="text-align: center;" | 53313331
| style="text-align: center;" |
| style="text-align: center;" | 7{{pipe}}0 #2#3
| A B# C# D E F G H
| I+ ii iiiº IV+ V+ vi VII VIII+
|
|-
| Middle minor b8
| style="text-align: center;" | 33133315
| style="text-align: center;" | 2{{pipe}}5 b8
|
| A B Cb Db Eb Fb Gb Hbb
| i iiº III+ IV+ v VI VII+ VIII+
| 8:9:10:11:12 on the tonic
|-
| Bright diminished
| style="text-align: center;" | 31333153
| style="text-align: center;" | 1{{pipe}}6 b7
|
| A Bb Cb Db Eb Fb Gbb Hb
| iº II+ III+ iv V VI+ VII+ viii
| 8:9:10:11:12 on the tonic
|}


&lt;table class="wiki_table"&gt;
'''MODMOS with 7th note in generator chain flattened or 2nd sharpened:''' '''#.''''''##''''''####.#'''
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33351331&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7|0 #5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D E# F G H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33513331&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|1 #4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D# E F G Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;35133313&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|2 #3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C# D E F Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;51333133&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|3 #2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B# C D E Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13331335&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 b5b6b7b8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb Db Ebb Fbb Gbb Hbb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33313351&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|5 #8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C Db Eb Fb Gb H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33133513&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|6 #7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb Db Eb Fb G Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31335133&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 #6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb Db Eb F Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
{| class="wikitable"
&lt;strong&gt;MODMOS with 6th note in generator chain sharpened:&lt;/strong&gt; &lt;strong&gt;#####.&lt;/strong&gt;&lt;strong&gt;##.....#&lt;/strong&gt;&lt;br /&gt;
|-
! Functional name
! style="text-align: center;" | Step pattern
! style="text-align: center;" | UDP name #1
! style="text-align: center;" | UDP name #2
! Spelling
! Triad qualities (3-step triads)
! Other Notes
|-
| Bright major #8
| style="text-align: center;" | 33333151
| style="text-align: center;" | 7{{pipe}}0 b7
| style="text-align: center;" | 5{{pipe}}2 #8
| A B C D E F Gb H
| I II+ III iv V vi VII+ viii
| Brightest major with all consonant 3-step triads


Major triads on 1/1, 6/5, 36/25 (with roots on 4/3, 8/5, 48/25)


&lt;table class="wiki_table"&gt;
Minor triads on 4/3, 8/5, 48/25 (with roots on 10/9, 4/3, 8/5)
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
| Dark augmented b6
&lt;/td&gt;
| style="text-align: center;" | 33331513
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
| style="text-align: center;" | 6{{pipe}}1 b6
&lt;/td&gt;
| style="text-align: center;" | 4{{pipe}}3 #7
        &lt;td&gt;Spelling&lt;br /&gt;
| A B C D E Fb G Hb
&lt;/td&gt;
| I+ II iii IV v VI+ vii VIII
        &lt;td&gt;Other Notes&lt;br /&gt;
| 10:12:15 on the tonic
&lt;/td&gt;
Has both 4/3 and 3/2
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| Bright major b5, Dark major #6
        &lt;td style="text-align: center;"&gt;33335131&lt;br /&gt;
| style="text-align: center;" | 33315133
&lt;/td&gt;
| style="text-align: center;" | 5{{pipe}}2 b5
        &lt;td style="text-align: center;"&gt;7|0 #6&lt;br /&gt;
| style="text-align: center;" | 3{{pipe}}4 #6
&lt;/td&gt;
| A B C D Eb F Gb Hb
        &lt;td&gt;A B C D E F# G H&lt;br /&gt;
| I ii III iv V+ vi VII VIII+
&lt;/td&gt;
| Major triads on 1/1, 6/5, 5/3 (with roots on 4/3, 8/5, 10/9)
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33351313&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|1 #5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D E# F G Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33513133&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|2 #4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D# E F Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;35131333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|3 #3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C# D E Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;51313333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|4 #2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B# C D Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13133335&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 b4b5b6b7b8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb Dbb Ebb Fbb Gbb Hbb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31333351&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|6 #8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb Db Eb Fb Gb H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13333513&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 #7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb Db Eb Fb G Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
Minor triads on 10/9, 4/3, 8/5 (with roots on 9/5, 10/9, 4/3)
&lt;strong&gt;MODMOS with 7th note in generator chain sharpened:&lt;/strong&gt; &lt;strong&gt;######.&lt;/strong&gt;&lt;strong&gt;#......#&lt;/strong&gt;&lt;br /&gt;
|-
| Bright minor #5
| style="text-align: center;" | 33151333
| style="text-align: center;" | 4{{pipe}}3 b4
| style="text-align: center;" | 2{{pipe}}5 #5
| A B C Db E Fb Gb Hb
| i II iii IV+ v VI VII+ VIII
| Brightest minor with all consonant 3-step triads
Major triads on 10/9, 3/2, 9/5 (with roots on 36/25, 1/1, 6/5)


Minor triads on 1/1, 6/5, 36/25 (with roots on 5/3, 1/1, 6/5)
|-
| Dark major v3
| style="text-align: center;" | 31513333
| style="text-align: center;" | 3{{pipe}}4 b3
| style="text-align: center;" | 1{{pipe}}6 #4
| A B Cb D Eb Fb Gb Hb
| I ii III+ iv V VI+ VII viii
| Major triads on 1/1, 25/18, 5/3 (with roots on 4/3, 9/5, 10/9)


&lt;table class="wiki_table"&gt;
Minor triads on 10/9, 4/3, 9/5 (with roots on 9/5, 10/9, 3/2)
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33333511&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7|0 #7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D E F G# H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33335113&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|1 #6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D E F# G Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33351133&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|2 #5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D E# F Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33511333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|3 #4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D# E Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;35113333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|4 #3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C# D Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;51133333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|5 #2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B# C Db Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;11333335&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 b3b4b5b6b7b8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cbb Dbb Ebb Fbb Gbb Hbb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13333351&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 #8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb Db Eb Fb Gb H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc11"&gt;&lt;a name="Porcupine[8] and its MODMOS's-Single-alteration MODMOS's-Alterations by Porcupine[7] chroma"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Alterations by Porcupine[7] chroma&lt;/h3&gt;
Has both 4/3 and 3/2
&lt;strong&gt;MODMOS with 2nd note in generator chain flattened&lt;/strong&gt;&lt;br /&gt;
|-
| Bright minor b2, Dark minor #3
| style="text-align: center;" | 15133333
| style="text-align: center;" | 2{{pipe}}5 b2
| style="text-align: center;" | 0{{pipe}}7 #3
| A Bb C Db Eb Fb Gb Hb
| i II+ iii IV V+ VI vii VIII
| 8:10:11:12 and 10:12:15 on the tonic
Major triads on 5/4, 3/2, 9/5 (with roots on 5/3, 1/1, 6/5)


Minor triads on 1/1, 6/5, 5/3 (with roots on 5/3, 1/1, 25/18)
|-
| Bright augmented #2
| style="text-align: center;" | 51333331
| style="text-align: center;" |
| style="text-align: center;" | 7{{pipe}}0 #2
| A B# C D E F G H
| I+ ii III IV+ V vi VII viii
| Brightest mode with all consonant 3-step triads
|-
| Dark minor b8
| style="text-align: center;" | 13333315
| style="text-align: center;" | 0{{pipe}}7 b8
|
| A Bb Cb Db Eb Fb Gb Hbb
| i II III+ IV v VI vii VIII+
| Darkest mode/minor with all consonant 3-step triads
8:9:10:11:12 on the tonic (8:9:10:11:12:14 in 15edo)


&lt;table class="wiki_table"&gt;
Major triads on 25/24, 5/4, 3/2 (with roots on 25/18, 5/3, 1/1)
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;24333331&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7|0 v2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bv C D E F G H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;43333312&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|1 ^2^3^4^5^6^7^8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B^ C^ D^ E^ F^ G^ Hb^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33333124&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|2 v8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D E F Gb Hbv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33331243&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|3 v7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D E Fb Gbv Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33312433&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|4 v6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D Eb Fbv Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33124333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|5 v5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C Db Ebv Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31243333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|6 v4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb Dbv Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;12433333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 v3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cbv Db Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
Minor triads on 1/1, 25/18, 5/3 (with roots on 5/3, 9/8, 25/18)
&lt;strong&gt;MODMOS with 3rd note in generator chain flattened&lt;/strong&gt;&lt;br /&gt;
|}


'''MODMOS with 3rd note in generator chain sharpened:''' '''##.''''''#''''''####..#'''


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
! Functional name
&lt;/td&gt;
! style="text-align: center;" | Step pattern
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
! style="text-align: center;" | UDP name #1
&lt;/td&gt;
! style="text-align: center;" | UDP name #2
        &lt;td&gt;Spelling&lt;br /&gt;
! Spelling
&lt;/td&gt;
! Triad qualities (3-step triads)
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
! Other Notes
&lt;/td&gt;
|-
    &lt;/tr&gt;
| Bright augmented #3
    &lt;tr&gt;
| style="text-align: center;" | 35133331
        &lt;td style="text-align: center;"&gt;32433331&lt;br /&gt;
| style="text-align: center;" | 7{{pipe}}0 #3
&lt;/td&gt;
|
        &lt;td style="text-align: center;"&gt;7|0 v3&lt;br /&gt;
| A B C# D E F G H
&lt;/td&gt;
| I+ II+ iiiº IV V+ vi vii VIII
        &lt;td&gt;A B Cv D E F G H&lt;br /&gt;
|
&lt;/td&gt;
|-
        &lt;td&gt;&lt;br /&gt;
| Dark augmented #2
&lt;/td&gt;
| style="text-align: center;" | 51333313
    &lt;/tr&gt;
| style="text-align: center;" | 6{{pipe}}1 #2
    &lt;tr&gt;
|
        &lt;td style="text-align: center;"&gt;24333313&lt;br /&gt;
| A B# C D E F G Hb
&lt;/td&gt;
| I+ iiº III IV+ v vi VII VIII+
        &lt;td style="text-align: center;"&gt;6|1 v2&lt;br /&gt;
|
&lt;/td&gt;
|-
        &lt;td&gt;A Bv C D E F G Hb&lt;br /&gt;
| Dark diminished
&lt;/td&gt;
| style="text-align: center;" | 13333135
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" |
&lt;/td&gt;
| style="text-align: center;" | 0{{pipe}}7 b7b8
    &lt;/tr&gt;
| A Bb Cb Db Eb Fb Gbb Hbb
    &lt;tr&gt;
| iº II III+ iv v VI VII+ VIII+
        &lt;td style="text-align: center;"&gt;43333132&lt;br /&gt;
| 8:9:10:11:12 on the tonic
&lt;/td&gt;
8:9:10:11:12:14 on the tonic in 15edo
        &lt;td style="text-align: center;"&gt;5|2 ^2^3^4^5^6^7^8&lt;br /&gt;
|-
&lt;/td&gt;
| Middle major #8
        &lt;td&gt;A B^ C^ D^ E^ F^ Gb^ Hb^&lt;br /&gt;
| style="text-align: center;" | 33331351
&lt;/td&gt;
| style="text-align: center;" | 4{{pipe}}3 #8
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 7{{pipe}}0 b6b7
&lt;/td&gt;
| A B C D E Fb Gb H
    &lt;/tr&gt;
| I II+ iii iv V VI+ VII+ viiiº
    &lt;tr&gt;
| 10:12:15 on the tonic
        &lt;td style="text-align: center;"&gt;33331324&lt;br /&gt;
Has both 4/3 and 3/2
&lt;/td&gt;
|-
        &lt;td style="text-align: center;"&gt;4|3 v8&lt;br /&gt;
| Dark augmented b5b6
&lt;/td&gt;
| style="text-align: center;" | 33313513
        &lt;td&gt;A B C D E Fb Gb Hbv&lt;br /&gt;
| style="text-align: center;" | 3{{pipe}}4 #7
&lt;/td&gt;
| style="text-align: center;" | 6{{pipe}}1 b5b6
        &lt;td&gt;&lt;br /&gt;
| A B C D Eb Fb G Hb
&lt;/td&gt;
| I+ ii iii IV V+ VI+ viiº VIII
    &lt;/tr&gt;
| 10:12:15 on the tonic
    &lt;tr&gt;
Has both 4/3 and 3/2
        &lt;td style="text-align: center;"&gt;33313243&lt;br /&gt;
|-
&lt;/td&gt;
| Bright minor #6
        &lt;td style="text-align: center;"&gt;3|4 v7&lt;br /&gt;
| style="text-align: center;" | 33135133
&lt;/td&gt;
| style="text-align: center;" | 2{{pipe}}5 #6
        &lt;td&gt;A B C D Eb Fb Gbv Hb&lt;br /&gt;
| style="text-align: center;" | 5{{pipe}}2 b4b5
&lt;/td&gt;
| A B C Db Eb F Gb Hb
        &lt;td&gt;&lt;br /&gt;
| i ii III IV+ V+ viº VII VIII+
&lt;/td&gt;
|
    &lt;/tr&gt;
|-
    &lt;tr&gt;
| Middle minor #5
        &lt;td style="text-align: center;"&gt;33132433&lt;br /&gt;
| style="text-align: center;" | 31351333
&lt;/td&gt;
| style="text-align: center;" | 1{{pipe}}6 #5
        &lt;td style="text-align: center;"&gt;2|5 v6&lt;br /&gt;
| style="text-align: center;" | 4{{pipe}}3 b3b4
&lt;/td&gt;
| A B Cb Db E Fb Gb Hb
        &lt;td&gt;A B C Db Eb Fbv Gb Hb&lt;br /&gt;
| i II III+ IV+ vº VI VII+ viii
&lt;/td&gt;
| 8:9:10:12 on the tonic
        &lt;td&gt;&lt;br /&gt;
|-
&lt;/td&gt;
| Dark major b2b3
    &lt;/tr&gt;
| style="text-align: center;" | 13513333
    &lt;tr&gt;
| style="text-align: center;" | 0{{pipe}}7 #4
        &lt;td style="text-align: center;"&gt;31324333&lt;br /&gt;
| style="text-align: center;" | 3{{pipe}}4 b2b3
&lt;/td&gt;
| A Bb Cb D Eb Fb Gb Hb
        &lt;td style="text-align: center;"&gt;1|6 v5&lt;br /&gt;
| I II+ III+ ivº V VI+ vii viii
&lt;/td&gt;
| Has both 4/3 and 3/2
        &lt;td&gt;A B Cb Db Ebv Fb Gb Hb&lt;br /&gt;
|}
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13243333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 v4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb Dbv Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
'''MODMOS with 4th note in generator chain sharpened:''' '''###.''''''####...#'''
&lt;strong&gt;MODMOS with 4th note in generator chain flattened&lt;/strong&gt;&lt;br /&gt;


{| class="wikitable"
|-
! style="text-align: center;" | Step pattern
! style="text-align: center;" | UDP name
! Spelling
! Other Notes
|-
| style="text-align: center;" | 33513331
| style="text-align: center;" | 7{{pipe}}0 #4
| A B C D# E F G H
|
|-
| style="text-align: center;" | 35133331
| style="text-align: center;" | 6{{pipe}}1 #3
| A B C# D E F G Hb
|
|-
| style="text-align: center;" | 51333313
| style="text-align: center;" | 5{{pipe}}2 #2
| A B# C D E F Gb Hb
|
|-
| style="text-align: center;" | 13333135
| style="text-align: center;" | 0{{pipe}}7 b6b7b8
| A Bb Cb Db Eb Fbb Gbb Hbb
|
|-
| style="text-align: center;" | 33331351
| style="text-align: center;" | 3{{pipe}}4 #8
| A B C D Eb Fb Gb H
|
|-
| style="text-align: center;" | 33313513
| style="text-align: center;" | 2{{pipe}}5 #7
| A B C Db Eb Fb G Hb
|
|-
| style="text-align: center;" | 33135133
| style="text-align: center;" | 1{{pipe}}6 #6
| A B Cb Db Eb F Gb Hb
|
|-
| style="text-align: center;" | 31351333
| style="text-align: center;" | 0{{pipe}}7 #5
| A Bb Cb Db E Fb Gb Hb
|
|}


&lt;table class="wiki_table"&gt;
'''MODMOS with 5th note in generator chain sharpened:''' '''####.''''''###....#'''
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33243331&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7|0 v4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C Dv E F G H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;32433313&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|1 v3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cv D E F G Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;24333133&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|2 v2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bv C D E F Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;43331332&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|3 ^2^3^4^5^6^7^8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B^ C^ D^ E^ Fb^ Gb^ Hb^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33313324&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|4 v8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D Eb Fb Gb Hbv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33133243&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|5 v7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C Db Eb Fb Gbv Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31332433&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|6 v6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb Db Eb Fbv Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13324333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 v5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb Db Ebv Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
{| class="wikitable"
&lt;strong&gt;MODMOS with 5th note in generator chain flattened&lt;/strong&gt;&lt;br /&gt;
|-
! style="text-align: center;" | Step pattern
! style="text-align: center;" | UDP name
! Spelling
! Other Notes
|-
| style="text-align: center;" | 33351331
| style="text-align: center;" | 7{{pipe}}0 #5
| A B C D E# F G H
|
|-
| style="text-align: center;" | 33513331
| style="text-align: center;" | 6{{pipe}}1 #4
| A B C D# E F G Hb
|
|-
| style="text-align: center;" | 35133313
| style="text-align: center;" | 5{{pipe}}2 #3
| A B C# D E F Gb Hb
|
|-
| style="text-align: center;" | 51333133
| style="text-align: center;" | 4{{pipe}}3 #2
| A B# C D E Fb Gb Hb
|
|-
| style="text-align: center;" | 13331335
| style="text-align: center;" | 0{{pipe}}7 b5b6b7b8
| A Bb Cb Db Ebb Fbb Gbb Hbb
|
|-
| style="text-align: center;" | 33313351
| style="text-align: center;" | 2{{pipe}}5 #8
| A B C Db Eb Fb Gb H
|
|-
| style="text-align: center;" | 33133513
| style="text-align: center;" | 1{{pipe}}6 #7
| A B Cb Db Eb Fb G Hb
|
|-
| style="text-align: center;" | 31335133
| style="text-align: center;" | 0{{pipe}}7 #6
| A Bb Cb Db Eb F Gb Hb
|
|}


'''MODMOS with 6th note in generator chain sharpened:''' '''#####.''''''##.....#'''


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
! style="text-align: center;" | Step pattern
&lt;/td&gt;
! style="text-align: center;" | UDP name
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
! Spelling
&lt;/td&gt;
! Other Notes
        &lt;td&gt;Spelling&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 33335131
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
| style="text-align: center;" | 7{{pipe}}0 #6
&lt;/td&gt;
| A B C D E F# G H
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;33324331&lt;br /&gt;
| style="text-align: center;" | 33351313
&lt;/td&gt;
| style="text-align: center;" | 6{{pipe}}1 #5
        &lt;td style="text-align: center;"&gt;7|0 v5&lt;br /&gt;
| A B C D E# F G Hb
&lt;/td&gt;
|
        &lt;td&gt;A B C D Ev F G H&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 33513133
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 5{{pipe}}2 #4
&lt;/td&gt;
| A B C D# E F Gb Hb
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;33243313&lt;br /&gt;
| style="text-align: center;" | 35131333
&lt;/td&gt;
| style="text-align: center;" | 4{{pipe}}3 #3
        &lt;td style="text-align: center;"&gt;6|1 v4&lt;br /&gt;
| A B C# D E Fb Gb Hb
&lt;/td&gt;
|
        &lt;td&gt;A B C Dv E F G Hb&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 51313333
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 3{{pipe}}4 #2
&lt;/td&gt;
| A B# C D Eb Fb Gb Hb
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;32433133&lt;br /&gt;
| style="text-align: center;" | 13133335
&lt;/td&gt;
| style="text-align: center;" | 0{{pipe}}7 b4b5b6b7b8
        &lt;td style="text-align: center;"&gt;5|2 v3&lt;br /&gt;
| A Bb Cb Dbb Ebb Fbb Gbb Hbb
&lt;/td&gt;
|
        &lt;td&gt;A B Cv D E F Gb Hb&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 31333351
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 1{{pipe}}6 #8
&lt;/td&gt;
| A B Cb Db Eb Fb Gb H
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;24331333&lt;br /&gt;
| style="text-align: center;" | 13333513
&lt;/td&gt;
| style="text-align: center;" | 0{{pipe}}7 #7
        &lt;td style="text-align: center;"&gt;4|3 v2&lt;br /&gt;
| A Bb Cb Db Eb Fb G Hb
&lt;/td&gt;
|
        &lt;td&gt;A Bv C D E Fb Gb Hb&lt;br /&gt;
|}
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;43313332&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|4 ^2^3^4^5^6^7^8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B^ C^ D^ Eb^ Fb^ Gb^ Hb^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33133324&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|5 v8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C Db Eb Fb Gb Hbv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31333243&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|6 v7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb Db Eb Fb Gbv Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13332433&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 v6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb Db Eb Fbv Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
'''MODMOS with 7th note in generator chain sharpened:''' '''######.''''''#......#'''
&lt;strong&gt;MODMOS with 6th note in generator chain flattened&lt;/strong&gt;&lt;br /&gt;


{| class="wikitable"
|-
! style="text-align: center;" | Step pattern
! style="text-align: center;" | UDP name
! Spelling
! Other Notes
|-
| style="text-align: center;" | 33333511
| style="text-align: center;" | 7{{pipe}}0 #7
| A B C D E F G# H
|
|-
| style="text-align: center;" | 33335113
| style="text-align: center;" | 6{{pipe}}1 #6
| A B C D E F# G Hb
|
|-
| style="text-align: center;" | 33351133
| style="text-align: center;" | 5{{pipe}}2 #5
| A B C D E# F Gb Hb
|
|-
| style="text-align: center;" | 33511333
| style="text-align: center;" | 4{{pipe}}3 #4
| A B C D# E Fb Gb Hb
|
|-
| style="text-align: center;" | 35113333
| style="text-align: center;" | 3{{pipe}}4 #3
| A B C# D Eb Fb Gb Hb
|
|-
| style="text-align: center;" | 51133333
| style="text-align: center;" | 2{{pipe}}5 #2
| A B# C Db Eb Fb Gb Hb
|
|-
| style="text-align: center;" | 11333335
| style="text-align: center;" | 0{{pipe}}7 b3b4b5b6b7b8
| A Bb Cbb Dbb Ebb Fbb Gbb Hbb
|
|-
| style="text-align: center;" | 13333351
| style="text-align: center;" | 0{{pipe}}7 #8
| A Bb Cb Db Eb Fb Gb H
|
|}


&lt;table class="wiki_table"&gt;
==== Alterations by Porcupine[7] chroma ====
    &lt;tr&gt;
'''MODMOS with 2nd note in generator chain flattened'''
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33332431&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7|0 v6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D E Fv G H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33324313&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|1 v5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D Ev F G Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33243133&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|2 v4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C Dv E F Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;32431333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|3 v3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cv D E Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;24313333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|4 v2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bv C D Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;43133332&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|5 ^2^3^4^5^6^7^8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B^ C^ Db^ Eb^ Fb^ Gb^ Hb^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31333324&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|6 v8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb Db Eb Fb Gb Hbv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13333243&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 v7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb Db Eb Fb Gbv Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
{| class="wikitable"
&lt;strong&gt;MODMOS with 7th note in generator chain flattened&lt;/strong&gt;&lt;br /&gt;
|-
! style="text-align: center;" | Step pattern
! style="text-align: center;" | UDP name
! Spelling
! style="text-align: center;" | Other notes
|-
| style="text-align: center;" | 24333331
| style="text-align: center;" | 7{{pipe}}0 v2
| A Bv C D E F G H
|
|-
| style="text-align: center;" | 43333312
| style="text-align: center;" | 6{{pipe}}1 ^2^3^4^5^6^7^8
| A B^ C^ D^ E^ F^ G^ Hb^
|
|-
| style="text-align: center;" | 33333124
| style="text-align: center;" | 5{{pipe}}2 v8
| A B C D E F Gb Hbv
|
|-
| style="text-align: center;" | 33331243
| style="text-align: center;" | 4{{pipe}}3 v7
| A B C D E Fb Gbv Hb
|
|-
| style="text-align: center;" | 33312433
| style="text-align: center;" | 3{{pipe}}4 v6
| A B C D Eb Fbv Gb Hb
|
|-
| style="text-align: center;" | 33124333
| style="text-align: center;" | 2{{pipe}}5 v5
| A B C Db Ebv Fb Gb Hb
|
|-
| style="text-align: center;" | 31243333
| style="text-align: center;" | 1{{pipe}}6 v4
| A B Cb Dbv Eb Fb Gb Hb
|
|-
| style="text-align: center;" | 12433333
| style="text-align: center;" | 0{{pipe}}7 v3
| A Bb Cbv Db Eb Fb Gb Hb
|
|}


'''MODMOS with 3rd note in generator chain flattened'''


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
! style="text-align: center;" | Step pattern
&lt;/td&gt;
! style="text-align: center;" | UDP name
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
! Spelling
&lt;/td&gt;
! style="text-align: center;" | Other notes
        &lt;td&gt;Spelling&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 32433331
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
| style="text-align: center;" | 7{{pipe}}0 v3
&lt;/td&gt;
| A B Cv D E F G H
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;33333241&lt;br /&gt;
| style="text-align: center;" | 24333313
&lt;/td&gt;
| style="text-align: center;" | 6{{pipe}}1 v2
        &lt;td style="text-align: center;"&gt;7|0 v7&lt;br /&gt;
| A Bv C D E F G Hb
&lt;/td&gt;
|
        &lt;td&gt;A B C D E F Gv H&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 43333132
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 5{{pipe}}2 ^2^3^4^5^6^7^8
&lt;/td&gt;
| A B^ C^ D^ E^ F^ Gb^ Hb^
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;33332413&lt;br /&gt;
| style="text-align: center;" | 33331324
&lt;/td&gt;
| style="text-align: center;" | 4{{pipe}}3 v8
        &lt;td style="text-align: center;"&gt;6|1 v6&lt;br /&gt;
| A B C D E Fb Gb Hbv
&lt;/td&gt;
|
        &lt;td&gt;A B C D E Fv G Hb&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 33313243
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 3{{pipe}}4 v7
&lt;/td&gt;
| A B C D Eb Fb Gbv Hb
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;33324133&lt;br /&gt;
| style="text-align: center;" | 33132433
&lt;/td&gt;
| style="text-align: center;" | 2{{pipe}}5 v6
        &lt;td style="text-align: center;"&gt;5|2 v5&lt;br /&gt;
| A B C Db Eb Fbv Gb Hb
&lt;/td&gt;
|
        &lt;td&gt;A B C D Ev F Gb Hb&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 31324333
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 1{{pipe}}6 v5
&lt;/td&gt;
| A B Cb Db Ebv Fb Gb Hb
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;33241333&lt;br /&gt;
| style="text-align: center;" | 13243333
&lt;/td&gt;
| style="text-align: center;" | 0{{pipe}}7 v4
        &lt;td style="text-align: center;"&gt;4|3 v4&lt;br /&gt;
| A Bb Cb Dbv Eb Fb Gb Hb
&lt;/td&gt;
|
        &lt;td&gt;A B C Dv E Fb Gb Hb&lt;br /&gt;
|}
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;32413333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|4 v3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cv D Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;24133333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|5 v2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bv C Db Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;41333332&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|6 ^2^3^4^5^6^7^8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B^ Cb^ Db^ Eb^ Fb^ Gb^ Hb^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13333324&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 v8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb Db Eb Fb Gb Hbv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
'''MODMOS with 4th note in generator chain flattened'''
&lt;strong&gt;MODMOS with 8th note in generator chain flattened&lt;/strong&gt;&lt;br /&gt;


{| class="wikitable"
|-
! style="text-align: center;" | Step pattern
! style="text-align: center;" | UDP name
! Spelling
! style="text-align: center;" | Other notes
|-
| style="text-align: center;" | 33243331
| style="text-align: center;" | 7{{pipe}}0 v4
| A B C Dv E F G H
|
|-
| style="text-align: center;" | 32433313
| style="text-align: center;" | 6{{pipe}}1 v3
| A B Cv D E F G Hb
|
|-
| style="text-align: center;" | 24333133
| style="text-align: center;" | 5{{pipe}}2 v2
| A Bv C D E F Gb Hb
|
|-
| style="text-align: center;" | 43331332
| style="text-align: center;" | 4{{pipe}}3 ^2^3^4^5^6^7^8
| A B^ C^ D^ E^ Fb^ Gb^ Hb^
|
|-
| style="text-align: center;" | 33313324
| style="text-align: center;" | 3{{pipe}}4 v8
| A B C D Eb Fb Gb Hbv
|
|-
| style="text-align: center;" | 33133243
| style="text-align: center;" | 2{{pipe}}5 v7
| A B C Db Eb Fb Gbv Hb
|
|-
| style="text-align: center;" | 31332433
| style="text-align: center;" | 1{{pipe}}6 v6
| A B Cb Db Eb Fbv Gb Hb
|
|-
| style="text-align: center;" | 13324333
| style="text-align: center;" | 0{{pipe}}7 v5
| A Bb Cb Db Ebv Fb Gb Hb
|
|}


&lt;table class="wiki_table"&gt;
'''MODMOS with 5th note in generator chain flattened'''
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33333322&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7|0 v8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D E F G Hv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33333223&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|1 v7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D E F Gv Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33332233&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|2 v6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D E Fv Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33322333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|3 v5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D Ev Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33223333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|4 v4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C Dv Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;32233333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|5 v3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cv Db Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;22333333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|6 v2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bv Cb Db Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;23333332&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 ^2^3^4^5^6^7^8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb^ Cb^ Db^ Eb^ Fb^ Gb^ Hb^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
{| class="wikitable"
&lt;strong&gt;MODMOS with 1st note in generator chain sharpened (in 22edo this gives same modes as flattening 8th note)&lt;/strong&gt;&lt;br /&gt;
|-
! style="text-align: center;" | Step pattern
! style="text-align: center;" | UDP name
! Spelling
! style="text-align: center;" | Other notes
|-
| style="text-align: center;" | 33324331
| style="text-align: center;" | 7{{pipe}}0 v5
| A B C D Ev F G H
|
|-
| style="text-align: center;" | 33243313
| style="text-align: center;" | 6{{pipe}}1 v4
| A B C Dv E F G Hb
|
|-
| style="text-align: center;" | 32433133
| style="text-align: center;" | 5{{pipe}}2 v3
| A B Cv D E F Gb Hb
|
|-
| style="text-align: center;" | 24331333
| style="text-align: center;" | 4{{pipe}}3 v2
| A Bv C D E Fb Gb Hb
|
|-
| style="text-align: center;" | 43313332
| style="text-align: center;" | 3{{pipe}}4 ^2^3^4^5^6^7^8
| A B^ C^ D^ Eb^ Fb^ Gb^ Hb^
|
|-
| style="text-align: center;" | 33133324
| style="text-align: center;" | 2{{pipe}}5 v8
| A B C Db Eb Fb Gb Hbv
|
|-
| style="text-align: center;" | 31333243
| style="text-align: center;" | 1{{pipe}}6 v7
| A B Cb Db Eb Fb Gbv Hb
|
|-
| style="text-align: center;" | 13332433
| style="text-align: center;" | 0{{pipe}}7 v6
| A Bb Cb Db Eb Fbv Gb Hb
|
|}


'''MODMOS with 6th note in generator chain flattened'''


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
! style="text-align: center;" | Step pattern
&lt;/td&gt;
! style="text-align: center;" | UDP name
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
! Spelling
&lt;/td&gt;
! style="text-align: center;" | Other notes
        &lt;td&gt;Spelling&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 33332431
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
| style="text-align: center;" | 7{{pipe}}0 v6
&lt;/td&gt;
| A B C D E Fv G H
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;23333332&lt;br /&gt;
| style="text-align: center;" | 33324313
&lt;/td&gt;
| style="text-align: center;" | 6{{pipe}}1 v5
        &lt;td style="text-align: center;"&gt;7|0 v2v3v4v5v6v7v8&lt;br /&gt;
| A B C D Ev F G Hb
&lt;/td&gt;
|
        &lt;td&gt;A Bv Cv Dv Ev Fv Gv Hv&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 33243133
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 5{{pipe}}2 v4
&lt;/td&gt;
| A B C Dv E F Gb Hb
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;33333322&lt;br /&gt;
| style="text-align: center;" | 32431333
&lt;/td&gt;
| style="text-align: center;" | 4{{pipe}}3 v3
        &lt;td style="text-align: center;"&gt;6|1 ^8&lt;br /&gt;
| A B Cv D E Fb Gb Hb
&lt;/td&gt;
|
        &lt;td&gt;A B C D E F G Hb^&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 24313333
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 3{{pipe}}4 v2
&lt;/td&gt;
| A Bv C D Eb Fb Gb Hb
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;33333223&lt;br /&gt;
| style="text-align: center;" | 43133332
&lt;/td&gt;
| style="text-align: center;" | 2{{pipe}}5 ^2^3^4^5^6^7^8
        &lt;td style="text-align: center;"&gt;5|2 ^7&lt;br /&gt;
| A B^ C^ Db^ Eb^ Fb^ Gb^ Hb^
&lt;/td&gt;
|
        &lt;td&gt;A B C D E F Gb^ Hb&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 31333324
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 1{{pipe}}6 v8
&lt;/td&gt;
| A B Cb Db Eb Fb Gb Hbv
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;33332233&lt;br /&gt;
| style="text-align: center;" | 13333243
&lt;/td&gt;
| style="text-align: center;" | 0{{pipe}}7 v7
        &lt;td style="text-align: center;"&gt;4|3 ^6&lt;br /&gt;
| A Bb Cb Db Eb Fb Gbv Hb
&lt;/td&gt;
|
        &lt;td&gt;A B C D E Fb^ Gb Hb&lt;br /&gt;
|}
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33322333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|4 ^5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D Eb^ Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33223333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|5 ^4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C Db^ Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;32233333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|6 ^3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb^ Db Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;22333333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 ^2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb^ Cb Db Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
'''MODMOS with 7th note in generator chain flattened'''
&lt;strong&gt;MODMOS with 2nd note in generator chain sharpened&lt;/strong&gt;&lt;br /&gt;


{| class="wikitable"
|-
! style="text-align: center;" | Step pattern
! style="text-align: center;" | UDP name
! Spelling
! style="text-align: center;" | Other notes
|-
| style="text-align: center;" | 33333241
| style="text-align: center;" | 7{{pipe}}0 v7
| A B C D E F Gv H
|
|-
| style="text-align: center;" | 33332413
| style="text-align: center;" | 6{{pipe}}1 v6
| A B C D E Fv G Hb
|
|-
| style="text-align: center;" | 33324133
| style="text-align: center;" | 5{{pipe}}2 v5
| A B C D Ev F Gb Hb
|
|-
| style="text-align: center;" | 33241333
| style="text-align: center;" | 4{{pipe}}3 v4
| A B C Dv E Fb Gb Hb
|
|-
| style="text-align: center;" | 32413333
| style="text-align: center;" | 3{{pipe}}4 v3
| A B Cv D Eb Fb Gb Hb
|
|-
| style="text-align: center;" | 24133333
| style="text-align: center;" | 2{{pipe}}5 v2
| A Bv C Db Eb Fb Gb Hb
|
|-
| style="text-align: center;" | 41333332
| style="text-align: center;" | 1{{pipe}}6 ^2^3^4^5^6^7^8
| A B^ Cb^ Db^ Eb^ Fb^ Gb^ Hb^
|
|-
| style="text-align: center;" | 13333324
| style="text-align: center;" | 0{{pipe}}7 v8
| A Bb Cb Db Eb Fb Gb Hbv
|
|}


&lt;table class="wiki_table"&gt;
'''MODMOS with 8th note in generator chain flattened'''
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;42333331&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7|0 ^2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B^ C D E F G H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;23333314&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|1 v2v3v4v5v6v7v8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bv Cv Dv Ev Fv Gv Hbv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33333142&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|2 ^8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D E F Gb Hb^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33331423&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|3 ^7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D E Fb Gb^ Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33314233&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|4 ^6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D Eb Fb^ Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33142333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|5 ^5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C Db Eb^ Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31423333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|6 ^4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb Db^ Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;14233333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 ^3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb^ Db Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
{| class="wikitable"
&lt;strong&gt;MODMOS with 3rd note in generator chain sharpened&lt;/strong&gt;&lt;br /&gt;
|-
! style="text-align: center;" | Step pattern
! style="text-align: center;" | UDP name
! Spelling
! style="text-align: center;" | Other notes
|-
| style="text-align: center;" | 33333322
| style="text-align: center;" | 7{{pipe}}0 v8
| A B C D E F G Hv
|
|-
| style="text-align: center;" | 33333223
| style="text-align: center;" | 6{{pipe}}1 v7
| A B C D E F Gv Hb
|
|-
| style="text-align: center;" | 33332233
| style="text-align: center;" | 5{{pipe}}2 v6
| A B C D E Fv Gb Hb
|
|-
| style="text-align: center;" | 33322333
| style="text-align: center;" | 4{{pipe}}3 v5
| A B C D Ev Fb Gb Hb
|
|-
| style="text-align: center;" | 33223333
| style="text-align: center;" | 3{{pipe}}4 v4
| A B C Dv Eb Fb Gb Hb
|
|-
| style="text-align: center;" | 32233333
| style="text-align: center;" | 2{{pipe}}5 v3
| A B Cv Db Eb Fb Gb Hb
|
|-
| style="text-align: center;" | 22333333
| style="text-align: center;" | 1{{pipe}}6 v2
| A Bv Cb Db Eb Fb Gb Hb
|
|-
| style="text-align: center;" | 23333332
| style="text-align: center;" | 0{{pipe}}7 ^2^3^4^5^6^7^8
| A Bb^ Cb^ Db^ Eb^ Fb^ Gb^ Hb^
|
|}


'''MODMOS with 1st note in generator chain sharpened (in 22edo this gives same modes as flattening 8th note)'''


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
! style="text-align: center;" | Step pattern
&lt;/td&gt;
! style="text-align: center;" | UDP name
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
! Spelling
&lt;/td&gt;
! style="text-align: center;" | Other notes
        &lt;td&gt;Spelling&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 23333332
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
| style="text-align: center;" | 7{{pipe}}0 v2v3v4v5v6v7v8
&lt;/td&gt;
| A Bv Cv Dv Ev Fv Gv Hv
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;34233331&lt;br /&gt;
| style="text-align: center;" | 33333322
&lt;/td&gt;
| style="text-align: center;" | 6{{pipe}}1 ^8
        &lt;td style="text-align: center;"&gt;7|0 ^3&lt;br /&gt;
| A B C D E F G Hb^
&lt;/td&gt;
|
        &lt;td&gt;A B C^ D E F G H&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 33333223
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 5{{pipe}}2 ^7
&lt;/td&gt;
| A B C D E F Gb^ Hb
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;42333313&lt;br /&gt;
| style="text-align: center;" | 33332233
&lt;/td&gt;
| style="text-align: center;" | 4{{pipe}}3 ^6
        &lt;td style="text-align: center;"&gt;6|1^2&lt;br /&gt;
| A B C D E Fb^ Gb Hb
&lt;/td&gt;
|
        &lt;td&gt;A B^ C D E F G Hb&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 33322333
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 3{{pipe}}4 ^5
&lt;/td&gt;
| A B C D Eb^ Fb Gb Hb
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;23333134&lt;br /&gt;
| style="text-align: center;" | 33223333
&lt;/td&gt;
| style="text-align: center;" | 2{{pipe}}5 ^4
        &lt;td style="text-align: center;"&gt;5|2 v2v3v4v5v6v7v8&lt;br /&gt;
| A B C Db^ Eb Fb Gb Hb
&lt;/td&gt;
|
        &lt;td&gt;A Bv Cv Dv Ev Fv Gbv Hbv&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 32233333
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 1{{pipe}}6 ^3
&lt;/td&gt;
| A B Cb^ Db Eb Fb Gb Hb
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;33331342&lt;br /&gt;
| style="text-align: center;" | 22333333
&lt;/td&gt;
| style="text-align: center;" | 0{{pipe}}7 ^2
        &lt;td style="text-align: center;"&gt;4|3 ^8&lt;br /&gt;
| A Bb^ Cb Db Eb Fb Gb Hb
&lt;/td&gt;
|
        &lt;td&gt;A B C D E Fb Gb Hb^&lt;br /&gt;
|}
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33313423&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|4 ^7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D Eb Fb Gb^ Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33134233&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|5 ^6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C Db Eb Fb^ Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31342333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|6 ^5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb Db Eb^ Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13423333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 ^4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb Db^ Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
'''MODMOS with 2nd note in generator chain sharpened'''
&lt;strong&gt;MODMOS with 4th note in generator chain sharpened&lt;/strong&gt;&lt;br /&gt;


{| class="wikitable"
|-
! style="text-align: center;" | Step pattern
! style="text-align: center;" | UDP name
! Spelling
! style="text-align: center;" | Other notes
|-
| style="text-align: center;" | 42333331
| style="text-align: center;" | 7{{pipe}}0 ^2
| A B^ C D E F G H
|
|-
| style="text-align: center;" | 23333314
| style="text-align: center;" | 6{{pipe}}1 v2v3v4v5v6v7v8
| A Bv Cv Dv Ev Fv Gv Hbv
|
|-
| style="text-align: center;" | 33333142
| style="text-align: center;" | 5{{pipe}}2 ^8
| A B C D E F Gb Hb^
|
|-
| style="text-align: center;" | 33331423
| style="text-align: center;" | 4{{pipe}}3 ^7
| A B C D E Fb Gb^ Hb
|
|-
| style="text-align: center;" | 33314233
| style="text-align: center;" | 3{{pipe}}4 ^6
| A B C D Eb Fb^ Gb Hb
|
|-
| style="text-align: center;" | 33142333
| style="text-align: center;" | 2{{pipe}}5 ^5
| A B C Db Eb^ Fb Gb Hb
|
|-
| style="text-align: center;" | 31423333
| style="text-align: center;" | 1{{pipe}}6 ^4
| A B Cb Db^ Eb Fb Gb Hb
|
|-
| style="text-align: center;" | 14233333
| style="text-align: center;" | 0{{pipe}}7 ^3
| A Bb Cb^ Db Eb Fb Gb Hb
|
|}


&lt;table class="wiki_table"&gt;
'''MODMOS with 3rd note in generator chain sharpened'''
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33423331&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7|0 ^4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D^ E F G H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;34233313&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|1^3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C^ D E F G Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;42333133&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|2 ^2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B^ C D E F Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;23331334&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|3 v2v3v4v5v6v7v8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bv Cv Dv Ev Fbv Gbv Hbv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33313342&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|4 ^8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D Eb Fb Gb Hb^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33133423&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|5 ^7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C Db Eb Fb Gb^ Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31334233&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|6 ^6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb Db Eb Fb^ Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13342333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 ^5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb Db Eb^ Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
{| class="wikitable"
&lt;strong&gt;MODMOS with 5th note in generator chain sharpened&lt;/strong&gt;&lt;br /&gt;
|-
! style="text-align: center;" | Step pattern
! style="text-align: center;" | UDP name
! Spelling
! style="text-align: center;" | Other notes
|-
| style="text-align: center;" | 34233331
| style="text-align: center;" | 7{{pipe}}0 ^3
| A B C^ D E F G H
|
|-
| style="text-align: center;" | 42333313
| style="text-align: center;" | 6{{pipe}}1^2
| A B^ C D E F G Hb
|
|-
| style="text-align: center;" | 23333134
| style="text-align: center;" | 5{{pipe}}2 v2v3v4v5v6v7v8
| A Bv Cv Dv Ev Fv Gbv Hbv
|
|-
| style="text-align: center;" | 33331342
| style="text-align: center;" | 4{{pipe}}3 ^8
| A B C D E Fb Gb Hb^
|
|-
| style="text-align: center;" | 33313423
| style="text-align: center;" | 3{{pipe}}4 ^7
| A B C D Eb Fb Gb^ Hb
|
|-
| style="text-align: center;" | 33134233
| style="text-align: center;" | 2{{pipe}}5 ^6
| A B C Db Eb Fb^ Gb Hb
|
|-
| style="text-align: center;" | 31342333
| style="text-align: center;" | 1{{pipe}}6 ^5
| A B Cb Db Eb^ Fb Gb Hb
|
|-
| style="text-align: center;" | 13423333
| style="text-align: center;" | 0{{pipe}}7 ^4
| A Bb Cb Db^ Eb Fb Gb Hb
|
|}


'''MODMOS with 4th note in generator chain sharpened'''


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
! style="text-align: center;" | Step pattern
&lt;/td&gt;
! style="text-align: center;" | UDP name
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
! Spelling
&lt;/td&gt;
! style="text-align: center;" | Other notes
        &lt;td&gt;Spelling&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 33423331
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
| style="text-align: center;" | 7{{pipe}}0 ^4
&lt;/td&gt;
| A B C D^ E F G H
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;33342331&lt;br /&gt;
| style="text-align: center;" | 34233313
&lt;/td&gt;
| style="text-align: center;" | 6{{pipe}}1^3
        &lt;td style="text-align: center;"&gt;7|0 ^5&lt;br /&gt;
| A B C^ D E F G Hb
&lt;/td&gt;
|
        &lt;td&gt;A B C D E^ F G H&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 42333133
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 5{{pipe}}2 ^2
&lt;/td&gt;
| A B^ C D E F Gb Hb
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;33423313&lt;br /&gt;
| style="text-align: center;" | 23331334
&lt;/td&gt;
| style="text-align: center;" | 4{{pipe}}3 v2v3v4v5v6v7v8
        &lt;td style="text-align: center;"&gt;6|1^4&lt;br /&gt;
| A Bv Cv Dv Ev Fbv Gbv Hbv
&lt;/td&gt;
|
        &lt;td&gt;A B C D^ E F G Hb&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 33313342
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 3{{pipe}}4 ^8
&lt;/td&gt;
| A B C D Eb Fb Gb Hb^
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;34233133&lt;br /&gt;
| style="text-align: center;" | 33133423
&lt;/td&gt;
| style="text-align: center;" | 2{{pipe}}5 ^7
        &lt;td style="text-align: center;"&gt;5|2 ^3&lt;br /&gt;
| A B C Db Eb Fb Gb^ Hb
&lt;/td&gt;
|
        &lt;td&gt;A B C^ D E F Gb Hb&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 31334233
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 1{{pipe}}6 ^6
&lt;/td&gt;
| A B Cb Db Eb Fb^ Gb Hb
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;42331333&lt;br /&gt;
| style="text-align: center;" | 13342333
&lt;/td&gt;
| style="text-align: center;" | 0{{pipe}}7 ^5
        &lt;td style="text-align: center;"&gt;4|3 ^2&lt;br /&gt;
| A Bb Cb Db Eb^ Fb Gb Hb
&lt;/td&gt;
|
        &lt;td&gt;A B^ C D E Fb Gb Hb&lt;br /&gt;
|}
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;23313334&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|4 v2v3v4v5v6v7v8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bv Cv Dv Ebv Fbv Gbv Hbv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33133342&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|5 ^8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C Db Eb Fb Gb Hb^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31333423&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|6 ^7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb Db Eb Fb Gb^ Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13334233&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 ^6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb Db Eb Fb^ Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
'''MODMOS with 5th note in generator chain sharpened'''
&lt;strong&gt;MODMOS with 6th note in generator chain sharpened&lt;/strong&gt;&lt;br /&gt;


{| class="wikitable"
|-
! style="text-align: center;" | Step pattern
! style="text-align: center;" | UDP name
! Spelling
! style="text-align: center;" | Other notes
|-
| style="text-align: center;" | 33342331
| style="text-align: center;" | 7{{pipe}}0 ^5
| A B C D E^ F G H
|
|-
| style="text-align: center;" | 33423313
| style="text-align: center;" | 6{{pipe}}1^4
| A B C D^ E F G Hb
|
|-
| style="text-align: center;" | 34233133
| style="text-align: center;" | 5{{pipe}}2 ^3
| A B C^ D E F Gb Hb
|
|-
| style="text-align: center;" | 42331333
| style="text-align: center;" | 4{{pipe}}3 ^2
| A B^ C D E Fb Gb Hb
|
|-
| style="text-align: center;" | 23313334
| style="text-align: center;" | 3{{pipe}}4 v2v3v4v5v6v7v8
| A Bv Cv Dv Ebv Fbv Gbv Hbv
|
|-
| style="text-align: center;" | 33133342
| style="text-align: center;" | 2{{pipe}}5 ^8
| A B C Db Eb Fb Gb Hb^
|
|-
| style="text-align: center;" | 31333423
| style="text-align: center;" | 1{{pipe}}6 ^7
| A B Cb Db Eb Fb Gb^ Hb
|
|-
| style="text-align: center;" | 13334233
| style="text-align: center;" | 0{{pipe}}7 ^6
| A Bb Cb Db Eb Fb^ Gb Hb
|
|}


&lt;table class="wiki_table"&gt;
'''MODMOS with 6th note in generator chain sharpened'''
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Spelling&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33334231&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7|0 ^6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D E F^ G H&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33342313&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6|1 ^5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D E^ F G Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33423133&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5|2 ^4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C D^ E F Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;34231333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4|3 ^3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C^ D E Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;42313333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|4 ^2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B^ C D Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;23133334&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|5 v2v3v4v5v6v7v8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bv Cv Dbv Ebv Fbv Gbv Hbv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31333342&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|6 ^8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B Cb Db Eb Fb Gb Hb^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13333423&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 ^7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb Db Eb Fb Gb^ Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
{| class="wikitable"
&lt;strong&gt;MODMOS with 7th note in generator chain sharpened&lt;/strong&gt;&lt;br /&gt;
|-
! style="text-align: center;" | Step pattern
! style="text-align: center;" | UDP name
! Spelling
! style="text-align: center;" | Other notes
|-
| style="text-align: center;" | 33334231
| style="text-align: center;" | 7{{pipe}}0 ^6
| A B C D E F^ G H
|
|-
| style="text-align: center;" | 33342313
| style="text-align: center;" | 6{{pipe}}1 ^5
| A B C D E^ F G Hb
|
|-
| style="text-align: center;" | 33423133
| style="text-align: center;" | 5{{pipe}}2 ^4
| A B C D^ E F Gb Hb
|
|-
| style="text-align: center;" | 34231333
| style="text-align: center;" | 4{{pipe}}3 ^3
| A B C^ D E Fb Gb Hb
|
|-
| style="text-align: center;" | 42313333
| style="text-align: center;" | 3{{pipe}}4 ^2
| A B^ C D Eb Fb Gb Hb
|
|-
| style="text-align: center;" | 23133334
| style="text-align: center;" | 2{{pipe}}5 v2v3v4v5v6v7v8
| A Bv Cv Dbv Ebv Fbv Gbv Hbv
|
|-
| style="text-align: center;" | 31333342
| style="text-align: center;" | 1{{pipe}}6 ^8
| A B Cb Db Eb Fb Gb Hb^
|
|-
| style="text-align: center;" | 13333423
| style="text-align: center;" | 0{{pipe}}7 ^7
| A Bb Cb Db Eb Fb Gb^ Hb
|
|}


'''MODMOS with 7th note in generator chain sharpened'''


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;Step Pattern&lt;br /&gt;
! style="text-align: center;" | Step pattern
&lt;/td&gt;
! style="text-align: center;" | UDP name
        &lt;td style="text-align: center;"&gt;UDP Name&lt;br /&gt;
! Spelling
&lt;/td&gt;
! style="text-align: center;" | Other notes
        &lt;td&gt;Spelling&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 33333421
        &lt;td style="text-align: center;"&gt;Other Notes&lt;br /&gt;
| style="text-align: center;" | 7{{pipe}}0 ^7
&lt;/td&gt;
| A B C D E F G^ H
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;33333421&lt;br /&gt;
| style="text-align: center;" | 33334213
&lt;/td&gt;
| style="text-align: center;" | 6{{pipe}}1 ^6
        &lt;td style="text-align: center;"&gt;7|0 ^7&lt;br /&gt;
| A B C D E F^ G Hb
&lt;/td&gt;
|
        &lt;td&gt;A B C D E F G^ H&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 33342133
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 5{{pipe}}2 ^5
&lt;/td&gt;
| A B C D E^ F Gb Hb
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;33334213&lt;br /&gt;
| style="text-align: center;" | 33421333
&lt;/td&gt;
| style="text-align: center;" | 4{{pipe}}3 ^4
        &lt;td style="text-align: center;"&gt;6|1 ^6&lt;br /&gt;
| A B C D^ E Fb Gb Hb
&lt;/td&gt;
|
        &lt;td&gt;A B C D E F^ G Hb&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 34213333
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 3{{pipe}}4 ^3
&lt;/td&gt;
| A B C^ D Eb Fb Gb Hb
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;33342133&lt;br /&gt;
| style="text-align: center;" | 42133333
&lt;/td&gt;
| style="text-align: center;" | 2{{pipe}}5 ^2
        &lt;td style="text-align: center;"&gt;5|2 ^5&lt;br /&gt;
| A B^ C Db Eb Fb Gb Hb
&lt;/td&gt;
|
        &lt;td&gt;A B C D E^ F Gb Hb&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align: center;" | 21333334
        &lt;td&gt;&lt;br /&gt;
| style="text-align: center;" | 1{{pipe}}6 v2v3v4v5v6v7v8
&lt;/td&gt;
| A Bv Cbv Dbv Ebv Fbv Gbv Hbv
    &lt;/tr&gt;
|
    &lt;tr&gt;
|-
        &lt;td style="text-align: center;"&gt;33421333&lt;br /&gt;
| style="text-align: center;" | 13333342
&lt;/td&gt;
| style="text-align: center;" | 0{{pipe}}7 ^8
        &lt;td style="text-align: center;"&gt;4|3 ^4&lt;br /&gt;
| A Bb Cb Db Eb Fb Gb Hb^
&lt;/td&gt;
|
        &lt;td&gt;A B C D^ E Fb Gb Hb&lt;br /&gt;
|}
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;34213333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3|4 ^3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B C^ D Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;42133333&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2|5 ^2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A B^ C Db Eb Fb Gb Hb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;21333334&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1|6 v2v3v4v5v6v7v8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bv Cbv Dbv Ebv Fbv Gbv Hbv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13333342&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0|7 ^8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;A Bb Cb Db Eb Fb Gb Hb^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
[[Category:Porcupine]]
[[Category:modes]]

Latest revision as of 15:56, 16 May 2025

Porcupine is a temperament splitting 4/3 into three equal parts representing 10/9 and 27/25, so that two steps represent 6/5. This results in a slightly flat 4/3 and a slightly sharp 6/5, meaning that 5/4 is accurately tuned.

Porcupine scales

Todo: rework

Explain in a non-MOS-centric way

Porcupine is one of the few reasonably good 5-limit temperaments, alongside meantone, which possesses a 7-note MOS scale ("porcupine[7]" or "onyx") that is well-supplied with 5-limit major and minor triads (specifically, it has two of each of them). What is perhaps more significant about it is how naturally it extends those triads to involve the 11th harmonic; for instance, the first five consecutive notes of the Lssssss mode approximate the consecutive harmonics 8:9:10:11:12. This makes it a prime candidate for using extended JI-style harmonies in a compact and intuitive scale structure.

It is also significant because it is supported by both 15edo and 22edo, the smallest ETs which improve on the 11-limit damage of 12edo (other than 19edo). In those edos, porcupine is an excellent candidate for providing a 7-nominal notational basis and 7-interval-class categorical framework. This is important, because if you want to use 15edo (or to a lesser extent, 22edo) in a somewhat "heptatonic" fashion, where 5/4 and 6/5 are types of "thirds", 3/2 is a type of "fifth," and 5-limit major and minor triads share the same "1 – 3 – 5" triad shape, thinking of those ETs in terms of porcupine temperament is, in a certain sense, the natural approach. This most transparently leads to notation systems based upon porcupine[7], but 15edo and 22edo also contain a zarlino scale which can be naturally interpreted as a porcupine scale (what this means for zarlino is that the three sizes of step are equidistant). In fact, *any* heptatonic scale in 15edo or 22edo can be viewed as a MODMOS of porcupine[7].

In summary:

  1. Porcupine is the simplest 5-limit temperament that has less tuning error than 12edo which 12edo does not support.
  2. In a temperament search of 5-limit temperaments, using the standard search parameter of 5 ¢ of error, porcupine is the first temperament in the results that is not supported by 12.

Porcupine remains the "best" such temperament in the 5-limit even if the maximum error is relaxed somewhat. While mavila eventually supersedes it due to being simpler, mavila's accuracy is much lower as its fifths are extremely flat (670 – 680 ¢).

Brief intro to modal harmony and MODMOSes

Porcupine is a temperament completely capable of diverse harmony. Its MOS and its MODMOS scales (including zarlino) allow for some very diverse chordal movement that will still be tonally solid.

Because the generator of porcupine is simultaneously 10/9, 11/10, and 12/11, a chord made up of consecutive generators approximates 9:10:11:12; since -6 generators approximates 9/8, the chord 8:9:10:11:12 can be approximated by a series of consecutive 2nds in porcupine[7]. Varying subsets of 8:9:10:11:12 provide fruitful ground for building harmonic movement in porcupine. Additionally, chords of stacked sevenths of varying sizes may be used to improve voice leading and add variety. Chords without a 'fifth' are recommended for use on the root for modes without a 3/2 from the root. Further, quartal triads, tetrads, and pentads are available in more variety than in Meantone, and make good use of Porcupine's 11-limit consonances.

Stacked 3-step triads may be employed in Porcupine[8] and it's MODMOS, comprising in their root position three 3:4:5 triads (second inversion major triad) as major 3-step, minor 3-step: major[8] triad; three 15:20:24 triads (first inversion minor triad) as minor 3-step, major 3-step: minor[8] triad; and two 9:12:16 triads (second inversion suspended triad) as major 3-step, major 3-step: augmented[8] triad. At least one MODMOS of Porcupine[8] contains the same number of major and minor triads as the MOS, but more spread out across the scale, similar to Porcupine[7] MODMOS.

The MODMOS scales of porcupine can be used in conjunction with the regular MOS in order to build powerful tonal movement. While each useful MODMOS has its own distinct name, they most likely will be useful to use as a particular function in each porcupine mode. They can also be used stand alone but little is known about the very complex system of tonality.

Porcupine[7] is great, but it lumps all the consonant chords together at one end of the scale (see below). It also fails to contain a complete 11-limit otonal hexad (4:5:6:7:9:11), even though porcupine is not excessively complex in the 11-limit. Thankfully, unlike in meantone[7] where the MODMOSs all reduce the number of consonant triads available, there are several MODMOSs of porcupine that contain an equal or greater number of consonant triads to the MOS (these are highlighted in blue text below). These MODMOSs also conveniently alter the distribution of triads within the scale, providing much-needed variety of possible chord progressions. Even better, some single-alteration MODMOSs make at least one full 11-limit hexad available, meaning 6 of the 7 notes of the scale can be sounded simultaneously and produce a consonant otonal harmony. The fact that porcupine temperament provides not just one 7-note scale but several that are equally-rich in harmonic resources makes it extremely fertile for modal harmony.

Porcupine[7] and its MODMOSes

The below mode names are given in UDP notation. For porcupine[7], the bright generator is the 9/5, or the 11/6 if you prefer. All generators below refer to this generator, NOT the 10/9 one. For an explanation of the spellings, see Porcupine Notation.

The functional names are pretty straightforward: there are two major modes, one bright and one dark (differing in the second scale degree), two similarly-named minor modes (differing in the fourth scale degree), and then three modes with a diminished triad on the tonic (differing in the sixth and seventh scale degrees). The brightest two of these diminished modes both have a half-diminished tetrad on the tonic, and so they are named the bright and dark half-diminished modes, whereas the darkest has a fully diminished (or magical seventh tetrad) instead. These are sometimes just written bright/dark diminished and magical seventh modes when clear.

William Lynch's system

William Lynch proposed the fun idea of naming modes and MODMOS's of porcupine by various animal names, which are listed as "William's Name" below. He has named these scales as such as he views none of them to be remotely similar to any existing mode name from anywhere. The initial four modes: Porcupine, Chinchilla, Zebra, and Dingo all contain 3/2 from the root while the latter three: Gazelle, Lemur, and Panda lack 3/2 and instead have a triad similar to a diminished triad on the root. In order to remedy this problem, it may be fruitful to use other methods than triadic tertian harmony to build tonal frameworks in porcupine.

The scale's nominals can be named by the normal 7-tone alphabet starting on G. This has become somewhat of a standard. Some feel however that given Superpyth uses the same nominals in a contrasting way, it may be beneficial to use an entirely different set of letters for Porcupine. William Lynch's suggestion involves using the old-English alphabet, allowing for both porcupine[8] and porcupine[7] to be notated by leaving out "ð" from the scale.

Porcupine[8]: b c ð d e f þ æ

Porcupine[7]: b c d e f þ æ with chinchillian mode on "c"

pronounced "Be - Ce - Eth - De - E - Eff - Thorn - Ash"

An alternative suggestion involves using the letters J, K, L, M, N, O, and P for the nominals, replacing A, B, C, D, E, F, and G respectively, such that the bright major mode starts on the note P.

The Porcupine[7] MOS

Functional name William's came 22edo step pattern 15edo step pattern UDP name Spelling Alt spelling Triad qualities Other notes
Bright major Chinchillian 4333333 3222222 6|0 G A B C D E F P J K L M N O I iiº iiiº ivº v vi VII Bright, otonal major (VII chord is major)
Dark major Badgerian 3433333 2322222 5|1 G Av B C D E F P Jv K L M N O I II iiiº ivº vº vi vii Darker major (vii is minor)
Bright minor Zebrian 3343333 2232222 4|2 G Av Bv C D E F P Jv Kv L M N O i II III ivº vº viº vii Bright minor (II is major)
Dark minor (symmetric) Dingoian 3334333 2223222 3|3 G Av Bv Cv D E F P Jv Kv Lv M N O i ii III IV vº viº viiº Symmetric minor (ii is minor)
Bright (half-)diminished Gazellian 3333433 2222322 2|4 G Av Bv Cv Dv E F P Jv Kv Lv Mv N O iº ii iii IV V viº viiº Half-Diminished
Dark (half-)diminished Lemurian 3333343 2222232 1|5 G Av Bv Cv Dv Ev F P Jv Kv Lv Mv Nv O iº iiº iii iv V VI viiº Half-Diminished
Magical/diminished seventh Pandian 3333334 2222223 0|6 G Av Bv Cv Dv Ev Fv P Jv Kv Lv Mv Nv Ov iº iiº iiiº iv v VI VII Magical seventh or diminished seventh mode

Single-alteration MODMOS's

MODMOS with 1st note in generator chain flattened: #.......######

Note: Contains a broken 4/3 chain so it has only 3 4/3s

22edo steps 15edo steps UDP name Spelling Other notes
5333332 4222221 6|0 ^2^3^4^5^6^7 G A^ B^ C^ D^ E^ F^
2533333 1422222 5|1 v2 G Avv B C D E F
3253333 2142222 4|2 v3 G Av Bvv C D E F
3325333 2214222 3|3 v4 G Av Bv Cvv D E F
3332533 2221422 2|4 v5 G Av Bv Cv Dvv E F
3333253 2222142 1|5 v6 G Av Bv Cv Dv Evv F
3333325 2222214 0|6 v7 G Av Bv Cv Dv Ev Fvv

MODMOS with 2nd note in generator chain flattened: #.....#.#####

Note: Contains a broken 4/3 chain so it has only 3 4/3s

22edo steps 15edo steps UDP name Spelling Other notes
4333324 3222213 6|0 v7 G A B C D E Fv 8:9:10:11:12:14 hexad on the tonic,

in both 15edo and 22edo as G-A-B-C-D-Fv

4433332 3322221 6|0 ^3^4^5^6^7 G A B^ C^ D^ E^ F^
2443333 1332222 4|2 v2 G Avv Bv C D E F
3244333 2133222 3|3 v3 G Av Bvv Cv D E F
3324433 2213322 2|4 v4 G Av Bv Cvv Dv E F
3332443 2221332 1|5 v5 G Av Bv Cv Dvv Ev F
3333244 2222133 0|6 v6 G Av Bv Cv Dv Evv Fv

MODMOS with 3rd note in generator chain flattened: #....##.####

Note: Contains a broken 4/3 chain so it has only 3 4/3s

22edo steps 15edo steps UDP name Spelling Other notes
4333243 3222132 6|0 v6 G A B C D Ev F
3433324 2322213 5|1 v7 G Av B C D E Fv
4343332 3232221 6|0 ^4^5^6^7 G A B C^ D^ E^ F^
2434333 1323222 3|3 v2 G Avv Bv Cv D E F
3243433 2132322 2|4 v3 G Av Bvv Cv Dv E F
3324343 2213232 1|5 v4 G Av Bv Cvv Dv Ev F
3332434 2221323 0|6 v5 G Av Bv Cv Dvv Ev Fv

MODMOS with 4th note in generator chain flattened: #...###.###

Note: Contains a broken 4/3 chain so it has only 3 4/3s

22edo steps 15edo steps UDP name Spelling Other notes
4332433 3221322 6|0 v5 G A B C Dv E F
3433243 2322132 5|1 v6 G Av B C D Ev F
3343324 2232213 4|2 v7 G Av Bv C D E Fv
4334332 3223221 6|0 ^5^6^7 G A B C D^ E^ F^
2433433 1322322 2|4 v2 G Avv Bv Cv Dv E F
3243343 2132232 1|5 v3 G Av Bvv Cv Dv Ev F
3324334 2213223 0|6 v4 G Av Bv Cvv Dv Ev Fv

MODMOS with 5th note in generator chain flattened: #..####.## (melodic major)

Consists of unbroken chains of 4/3s

Functional Name William's Name (repltiles) 22edo steps 15edo steps UDP name Spelling Other notes
Bright major v4 Lizard 4324333 3213222 6|0 v4 G A B Cv D E F I, IV, v, vi "mixolydian-like"*
Dark major v5 Iguana 3432433 2321322 5|1 v5 G Av B C Dv E F
Bright minor v6 Serpent 3343243 2232132 4|2 v6 G Av Bv C D Ev F i, III, VI, vii
Dark minor v7 Iguana 3334324 2223213 3|3 v7 G Av Bv Cv D E Fv i, ii, IV, VII "dorian-like"
Bright major ^6^7

(melodic major)

Chameleon 4333432 3222321 6|0 ^6^7 G A B C D E^ F^ I, ii, iii, V "ionian-like";

8:9:10:11:12:14:15 on the tonic in 15edo as G-A-B-C-D-E^-F^

(but not in 22edo)

Igliashon finds it the "most grounded",

and suggests it as a candidate for "default major"

Dark (half-)diminished v2 Crocodile 2433343 1322232 1|5 v2 G Avv Bv Cv Dv Ev F
Magical seventh v3 Turtle 3243334 2132223 0|6 v3 G Av Bvv Cv Dv Ev Fv
  • This kind of description is obviously stupid because these porcupine scales are not really like the diatonic modes "mixolydian", "dorian", etc. As always, feel free to edit if you have some better description.

Symmetrical MODMOS with 2nd note in generator chain sharpened or 6th note flattened: #.#####.# (harmonic)

Consists of unbroken chains of 4/3s

Has the most evenly-distributed 5-limit triads of all the MODMOSs

Functional Name William's Name (Farm animals) 22edo steps 15edo steps UDP name #1 UDP name #2 Spelling Other notes
Bright major ^7

(harmonic major)

Horse 4333342 3222231 6|0 ^7 (1|5 v1) G A B C D E F^ I ii° iii iv° V vi vii°

Major with major V chord (most major-sounding major)

Magical seventh v2 Pig 2433334 1322223 (5|1 ^1) 0|6 v2 G Avv Bv Cv Dv Ev Fv i° II iii° iv v° VI vii

Magical seventh

Bright minor ^2

(harmonic minor)

Sheep 4243333 3132222 4|2 ^2 6|0 v3 G A Bv C D E F i ii° III iv° v vi° VII

Minor with minor v chord (most minor-sounding minor)

Dark major v4 Cow 3424333 2313222 3|3 ^3 5|1 v4 G Av B Cv D E F I ii iii° IV v° vi vii°

Major with major IV chord

Symmetric half-diminished Llama 3342433 2231322 2|4 ^4 4|2 v5 G Av Bv C Dv E F i° II iii iv° V vi° vii

Symmetric diminished

Dark minor v6 Goat 3334243 2223132 1|5 ^5 3|3 v6 G Av Bv Cv D Ev F i ii° III iv v° VI vii°

Minor with minor iv

Magical seventh ^6 Rooster 3333424 2222313 0|6 ^6 2|4 v7 G Av Bv Cv Dv E Fv i° ii iii° IV v vi° VII

Magical seventh

MODMOS with 3rd note in generator chain sharpened: ##.####..# (melodic minor)

Consists of unbroken chains of 4/3s

Functional Name William's Name (big cats) 22edo steps 15edo steps UDP name #1 UDP name #2 Spelling Other notes
Bright major ^6 Lionian 4333423 3222312 6|0 ^6 (2|4 v1v7) G A B C D E^ F I, ii, v, VII "mixolydian-like"

8:9:10:11:12:14 on the tonic in 15edo only

Dark major ^7 Tigonian 3433342 2322231 5|1 ^7 (1|5 v1v2) G Av B C D E F^ I, II, iii, vi
Bright minor ^1 Cougian 2343334 1232223 (4|2 ^1) 0|6 v2v3 G Avv Bvv Cv Dv Ev Fv
Dark minor ^2

(melodic minor)

Leopardian 4234333 3123222 3|3 ^2 6|0 v3v4 G A Bv Cv D E F i, III, IV, v "dorian-like"

Keenan and Igliashon both find this exceptionally beautiful

and suggest it as a candidate for default "minor"

Bright (half-)diminished ^3 Cheetian 3423433 2312322 2|4 ^3 5|1 v4v5 G Av B Cv Dv E F
Dark (half-)diminished ^4 Jaguarian 3342343 2231232 1|5 ^4 4|2 v5v6 G Av Bv C Dv Ev F
Dark minor v6 v7 Pantherian 3334234 2223123 0|6 ^5 3|3 v6v7 G Av Bv Cv D Ev Fv i, iv, VI, VII "aeolian-like"

MODMOS with 4th note in generator chain sharpened: ###.###...#

Note: Contains a broken 4/3 chain so it has only 3 4/3s

22edo steps 15edo steps UDP name Spelling Other notes
4334233 3223122 6|0 ^5 G A B C D^ E F
3433423 2322312 5|1 ^6 G Av B C D E^ F
3343342 2232231 4|2 ^7 G Av Bv C D E F^
2334334 1223223 0|6 v2v3v4 G Avv Bvv Cvv Dv Ev Fv
4233433 3122322 2|4 ^2 G A Bv Cv Dv E F
3423343 2312232 1|5 ^3 G Av B Cv Dv Ev F
3342334 2231223 0|6 ^4 G Av Bv C Dv Ev Fv

MODMOS with 5th note in generator chain sharpened: ####.##....#

Note: Contains a broken 4/3 chain so it has only 3 4/3s

22edo steps 15edo steps UDP name Spelling Other notes
4342333 3231222 6|0 ^4 G A B C^ D E F
3434233 2323122 5|1 ^5 G Av B C D^ E F
3343423 2232312 4|2 ^6 G Av Bv C D E^ F
3334342 2223231 3|3 ^7 G Av Bv Cv D E F^
2333434 1222323 0|6 v2v3v4v5 G Avv Bvv Cvv Dvv Ev Fv
4233343 3122232 1|5 ^2 G A Bv Cv Dv Ev F
3423334 2312223 0|6 ^3 G Av B Cv Dv Ev Fv

MODMOS with 6th note in generator chain sharpened: #####.#.....#

Note: Contains a broken 4/3 chain so it has only 3 4/3s

22edo steps 15edo steps UDP name Spelling Other notes
4423333 3312222 6|0 ^3 G A B^ C D E F
3442333 2331222 5|1 ^4 G Av B C^ D E F
3344233 2233122 4|2 ^5 G Av Bv C D^ E F
3334423 2223312 3|3 ^6 G Av Bv Cv D E^ F
3333442 2222331 2|4 ^7 G Av Bv Cv Dv E F^
2333344 1222233 0|6 v2v3v4v5v6 G Avv Bvv Cvv Dvv Evv Fv
4233334 3122223 0|6 ^2 G A Bv Cv Dv Ev Fv

MODMOS with 7th note in generator chain sharpened: ######.......#

Note: Contains a broken 4/3 chain so it has only 3 4/3s

22edo steps 15edo steps UDP name Spelling Other notes
5233333 4122222 6|0 ^2 G A^ B C D E F
3523333 2412222 5|1 ^3 G Av B^ C D E F
3352333 2241222 4|2 ^4 G Av Bv C^ D E F
3335233 2224122 3|3 ^5 G Av Bv Cv D^ E F
3333523 2222412 2|4 ^6 G Av Bv Cv Dv E^ F
3333352 2222241 1|5 ^7 G Av Bv Cv Dv Ev F^
2333335 1222224 0|6 v2v3v4v5v6v7 G Avv Bvv Cvv Dvv Evv Fvv

Notable double-alteration MODMOS's

22edo steps 15edo steps UDP name Spelling Other notes
4324342 3213231 6|0 v4 ^7 G A B Cv D E F^ "JI Major" scale a.k.a. Ptolemy/Zarlino
4234243 3123132 3|3 ^2 v6 G A Bv Cv D Ev F "JI Minor" scale

Porcupine[8] and its MODMOS's

All generators below refer to the porcupine[8] bright generator (the 10/9~11/10~whatever).

Similarly to Porcupine[7], William Lynch has proposed naming the modes off of sea creatures, with Octopus being relevant to the number eight.

Functional mode names are proposed based on the 3-step triads, which may be augmented (~9:12:16), major (~3:4:5) or minor (~12:15:20). However, it can also useful to look at a different functional system in which the octatonic MOS modes extend the heptatonic ones by adding one extra note.

The Porcupine[8] MOS

Functional Name William's Name Step pattern UDP name Traditional Spelling Triad qualities (3-step triads) Other notes
Bright augmented Octopus 33333331 7|0 A B C D E F G H I+ II+ III IV V vi vii viii
Dark augmented Mantis 33333313 6|1 A B C D E F G Hb I+ II III IV v vi vii VIII+
Bright major Dolphin 33333133 5|2 A B C D E F Gb Hb I II III iv v vi VII+ VIII+
Middle major Crab 33331333 4|3 A B C D E Fb Gb Hb I II iii iv v VI+ VII+ VII 10:12:15 on the tonic

Has both 4/3 and 3/2

Dark major Tuna 33313333 3|4 A B C D Eb Fb Gb Hb I ii iii iv V+ VI+ VII VIII 10:12:15 on the tonic

Has both 4/3 and 3/2

Bright minor Salmon 33133333 2|5 A B C Db Eb Fb Gb Hb i ii iii IV+ V+ VI VII VIII 8:10:11:12 and 10:12:15 on the tonic
Middle minor Starfish 31333333 1|6 A B Cb Db Eb Fb Gb Hb i ii III+ IV+ V VI VII viii 8:9:10:11:12 on the tonic
Dark minor Whale 13333333 0|7 A Bb Cb Db Eb Fb Gb Hb i II+ III+ IV V VI vii viii 8:9:10:11:12 on the tonic

Single-alteration MODMOSes

Alterations by Porcupine[8] chroma

MODMOS with 2nd note in generator chain flattened: #......'#.'######

Step pattern UDP name Spelling Other Notes
15333331 7|0 b2 A Bb C D E F G H
53333311 7|0 #2#3#4#5#6#7 A B# C# D# E# F# G# H
33333115 5|2 b8 A B C D E F Gb Hbb
33331153 4|3 b7 A B C D E Fb Gbb Hb
33311533 3|4 b6 A B C D Eb Fbb Gb Hb
33115333 2|5 b5 A B C Db Ebb Fb Gb Hb
31153333 1|6 b4 A B Cb Dbb Eb Fb Gb Hb
11533333 0|7 b3 A Bb Cbb Db Eb Fb Gb Hb

MODMOS with 3rd note in generator chain flattened: #.....'##.'#####

Step pattern UDP name Spelling Other Notes
31533331 7|0 b3 A B Cb D E F G H
15333313 6|1 b2 A Bb C D E F G Hb
53333131 7|0 #2#3#4#5#6 A B# C# D# E# F# G H
33331315 4|3 b8 A B C D E Fb Gb Hbb
33313153 3|4 b7 A B C D Eb Fb Gbb Hb
33131533 2|5 b6 A B C Db Eb Fbb Gb Hb
31315333 1|6 b5 A B Cb Db Ebb Fb Gb Hb
13153333 0|7 b4 A Bb Cb Dbb Eb Fb Gb Hb

MODMOS with 4th note in generator chain flattened: #....'##'#.####

Step pattern UDP name Spelling Other Notes
33153331 7|0 b4 A B C Db E F G H
31533313 6|1 b3 A B Cb D E F G Hb
15333133 5|2 b2 A Bb C D E F Gb Hb
53331331 7|0 #2#3#4#5 A B# C# D# E# F G H
33313315 3|4 b8 A B C D Eb Fb Gb Hbb
33133153 2|5 b7 A B C Db Eb Fb Gbb Hb
31331533 1|6 b6 A B Cb Db Eb Fbb Gb Hb
13315333 0|7 b5 A Bb Cb Db Ebb Fb Gb Hb

MODMOS with 5th note in generator chain flattened: #...'##'##.###

Step pattern UDP name Spelling Other Notes
33315331 7|0 b5 A B C D Eb F G H
33153313 6|1 b4 A B C Db E F G Hb
31533133 5|2 b3 A B Cb D E F Gb Hb
15331333 4|3 b2 A Bb C D E Fb Gb Hb
53313331 7|0 #2#3#4 A B# C# D# E F G H
33133315 2|5 b8 A B C Db Eb Fb Gb Hbb
31333153 1|6 b7 A B Cb Db Eb Fb Gbb Hb
13331533 0|7 b6 A Bb Cb Db Eb Fbb Gb Hb

MODMOS with 6th note in generator chain flattened: #..'##'###.##

Functional name Step pattern UDP name #1 UDP name #2 Spelling Triad qualities (3-step triads) Other Notes
Bright augmented b6 33331531 7|0 b6 4|3 #7#8 A B C D E Fb G H I+ II+ iii IV V VI+ vii viiiº 10:12:15 on tonic
Dark augmented b5 33315313 6|1 b5 3|4 #6#7 A B C D Eb F G Hb I+ ii III IV V+ vi viiº VIII+
Bright minor #5#6 33153133 5|2 b4 2|5 #5#6 A B C Db E F Gb Hb i II III IV+ v viº VII+ VIII+
Middle major b3 31531333 4|3 b3 1|6 #4#5 A B Cb D E Fb Gb Hb I II III+ iv vº VI+ VII+ viii Has both 4/3 and 3/2
Dark major b2 15313333 3|4 b2 0|7 #3#4 A Bb C D Eb Fb Gb Hb I III+ iii ivº V+ VI+ vii VIII 10:12:15 on the tonic

Has both 4/3 and 3/2

Bright augmented #2#3 53313331 7|0 #2#3 A B# C# D E F G H I+ ii iiiº IV+ V+ vi VII VIII+
Middle minor b8 33133315 2|5 b8 A B Cb Db Eb Fb Gb Hbb i iiº III+ IV+ v VI VII+ VIII+ 8:9:10:11:12 on the tonic
Bright diminished 31333153 1|6 b7 A Bb Cb Db Eb Fb Gbb Hb iº II+ III+ iv V VI+ VII+ viii 8:9:10:11:12 on the tonic

MODMOS with 7th note in generator chain flattened or 2nd sharpened: #.'##'####.#

Functional name Step pattern UDP name #1 UDP name #2 Spelling Triad qualities (3-step triads) Other Notes
Bright major #8 33333151 7|0 b7 5|2 #8 A B C D E F Gb H I II+ III iv V vi VII+ viii Brightest major with all consonant 3-step triads

Major triads on 1/1, 6/5, 36/25 (with roots on 4/3, 8/5, 48/25)

Minor triads on 4/3, 8/5, 48/25 (with roots on 10/9, 4/3, 8/5)

Dark augmented b6 33331513 6|1 b6 4|3 #7 A B C D E Fb G Hb I+ II iii IV v VI+ vii VIII 10:12:15 on the tonic

Has both 4/3 and 3/2

Bright major b5, Dark major #6 33315133 5|2 b5 3|4 #6 A B C D Eb F Gb Hb I ii III iv V+ vi VII VIII+ Major triads on 1/1, 6/5, 5/3 (with roots on 4/3, 8/5, 10/9)

Minor triads on 10/9, 4/3, 8/5 (with roots on 9/5, 10/9, 4/3)

Bright minor #5 33151333 4|3 b4 2|5 #5 A B C Db E Fb Gb Hb i II iii IV+ v VI VII+ VIII Brightest minor with all consonant 3-step triads

Major triads on 10/9, 3/2, 9/5 (with roots on 36/25, 1/1, 6/5)

Minor triads on 1/1, 6/5, 36/25 (with roots on 5/3, 1/1, 6/5)

Dark major v3 31513333 3|4 b3 1|6 #4 A B Cb D Eb Fb Gb Hb I ii III+ iv V VI+ VII viii Major triads on 1/1, 25/18, 5/3 (with roots on 4/3, 9/5, 10/9)

Minor triads on 10/9, 4/3, 9/5 (with roots on 9/5, 10/9, 3/2)

Has both 4/3 and 3/2

Bright minor b2, Dark minor #3 15133333 2|5 b2 0|7 #3 A Bb C Db Eb Fb Gb Hb i II+ iii IV V+ VI vii VIII 8:10:11:12 and 10:12:15 on the tonic

Major triads on 5/4, 3/2, 9/5 (with roots on 5/3, 1/1, 6/5)

Minor triads on 1/1, 6/5, 5/3 (with roots on 5/3, 1/1, 25/18)

Bright augmented #2 51333331 7|0 #2 A B# C D E F G H I+ ii III IV+ V vi VII viii Brightest mode with all consonant 3-step triads
Dark minor b8 13333315 0|7 b8 A Bb Cb Db Eb Fb Gb Hbb i II III+ IV v VI vii VIII+ Darkest mode/minor with all consonant 3-step triads

8:9:10:11:12 on the tonic (8:9:10:11:12:14 in 15edo)

Major triads on 25/24, 5/4, 3/2 (with roots on 25/18, 5/3, 1/1)

Minor triads on 1/1, 25/18, 5/3 (with roots on 5/3, 9/8, 25/18)

MODMOS with 3rd note in generator chain sharpened: ##.'#'####..#

Functional name Step pattern UDP name #1 UDP name #2 Spelling Triad qualities (3-step triads) Other Notes
Bright augmented #3 35133331 7|0 #3 A B C# D E F G H I+ II+ iiiº IV V+ vi vii VIII
Dark augmented #2 51333313 6|1 #2 A B# C D E F G Hb I+ iiº III IV+ v vi VII VIII+
Dark diminished 13333135 0|7 b7b8 A Bb Cb Db Eb Fb Gbb Hbb iº II III+ iv v VI VII+ VIII+ 8:9:10:11:12 on the tonic

8:9:10:11:12:14 on the tonic in 15edo

Middle major #8 33331351 4|3 #8 7|0 b6b7 A B C D E Fb Gb H I II+ iii iv V VI+ VII+ viiiº 10:12:15 on the tonic

Has both 4/3 and 3/2

Dark augmented b5b6 33313513 3|4 #7 6|1 b5b6 A B C D Eb Fb G Hb I+ ii iii IV V+ VI+ viiº VIII 10:12:15 on the tonic

Has both 4/3 and 3/2

Bright minor #6 33135133 2|5 #6 5|2 b4b5 A B C Db Eb F Gb Hb i ii III IV+ V+ viº VII VIII+
Middle minor #5 31351333 1|6 #5 4|3 b3b4 A B Cb Db E Fb Gb Hb i II III+ IV+ vº VI VII+ viii 8:9:10:12 on the tonic
Dark major b2b3 13513333 0|7 #4 3|4 b2b3 A Bb Cb D Eb Fb Gb Hb I II+ III+ ivº V VI+ vii viii Has both 4/3 and 3/2

'MODMOS with 4th note in generator chain sharpened: ###.'####...#

Step pattern UDP name Spelling Other Notes
33513331 7|0 #4 A B C D# E F G H
35133331 6|1 #3 A B C# D E F G Hb
51333313 5|2 #2 A B# C D E F Gb Hb
13333135 0|7 b6b7b8 A Bb Cb Db Eb Fbb Gbb Hbb
33331351 3|4 #8 A B C D Eb Fb Gb H
33313513 2|5 #7 A B C Db Eb Fb G Hb
33135133 1|6 #6 A B Cb Db Eb F Gb Hb
31351333 0|7 #5 A Bb Cb Db E Fb Gb Hb

'MODMOS with 5th note in generator chain sharpened: ####.'###....#

Step pattern UDP name Spelling Other Notes
33351331 7|0 #5 A B C D E# F G H
33513331 6|1 #4 A B C D# E F G Hb
35133313 5|2 #3 A B C# D E F Gb Hb
51333133 4|3 #2 A B# C D E Fb Gb Hb
13331335 0|7 b5b6b7b8 A Bb Cb Db Ebb Fbb Gbb Hbb
33313351 2|5 #8 A B C Db Eb Fb Gb H
33133513 1|6 #7 A B Cb Db Eb Fb G Hb
31335133 0|7 #6 A Bb Cb Db Eb F Gb Hb

'MODMOS with 6th note in generator chain sharpened: #####.'##.....#

Step pattern UDP name Spelling Other Notes
33335131 7|0 #6 A B C D E F# G H
33351313 6|1 #5 A B C D E# F G Hb
33513133 5|2 #4 A B C D# E F Gb Hb
35131333 4|3 #3 A B C# D E Fb Gb Hb
51313333 3|4 #2 A B# C D Eb Fb Gb Hb
13133335 0|7 b4b5b6b7b8 A Bb Cb Dbb Ebb Fbb Gbb Hbb
31333351 1|6 #8 A B Cb Db Eb Fb Gb H
13333513 0|7 #7 A Bb Cb Db Eb Fb G Hb

'MODMOS with 7th note in generator chain sharpened: ######.'#......#

Step pattern UDP name Spelling Other Notes
33333511 7|0 #7 A B C D E F G# H
33335113 6|1 #6 A B C D E F# G Hb
33351133 5|2 #5 A B C D E# F Gb Hb
33511333 4|3 #4 A B C D# E Fb Gb Hb
35113333 3|4 #3 A B C# D Eb Fb Gb Hb
51133333 2|5 #2 A B# C Db Eb Fb Gb Hb
11333335 0|7 b3b4b5b6b7b8 A Bb Cbb Dbb Ebb Fbb Gbb Hbb
13333351 0|7 #8 A Bb Cb Db Eb Fb Gb H

Alterations by Porcupine[7] chroma

MODMOS with 2nd note in generator chain flattened

Step pattern UDP name Spelling Other notes
24333331 7|0 v2 A Bv C D E F G H
43333312 6|1 ^2^3^4^5^6^7^8 A B^ C^ D^ E^ F^ G^ Hb^
33333124 5|2 v8 A B C D E F Gb Hbv
33331243 4|3 v7 A B C D E Fb Gbv Hb
33312433 3|4 v6 A B C D Eb Fbv Gb Hb
33124333 2|5 v5 A B C Db Ebv Fb Gb Hb
31243333 1|6 v4 A B Cb Dbv Eb Fb Gb Hb
12433333 0|7 v3 A Bb Cbv Db Eb Fb Gb Hb

MODMOS with 3rd note in generator chain flattened

Step pattern UDP name Spelling Other notes
32433331 7|0 v3 A B Cv D E F G H
24333313 6|1 v2 A Bv C D E F G Hb
43333132 5|2 ^2^3^4^5^6^7^8 A B^ C^ D^ E^ F^ Gb^ Hb^
33331324 4|3 v8 A B C D E Fb Gb Hbv
33313243 3|4 v7 A B C D Eb Fb Gbv Hb
33132433 2|5 v6 A B C Db Eb Fbv Gb Hb
31324333 1|6 v5 A B Cb Db Ebv Fb Gb Hb
13243333 0|7 v4 A Bb Cb Dbv Eb Fb Gb Hb

MODMOS with 4th note in generator chain flattened

Step pattern UDP name Spelling Other notes
33243331 7|0 v4 A B C Dv E F G H
32433313 6|1 v3 A B Cv D E F G Hb
24333133 5|2 v2 A Bv C D E F Gb Hb
43331332 4|3 ^2^3^4^5^6^7^8 A B^ C^ D^ E^ Fb^ Gb^ Hb^
33313324 3|4 v8 A B C D Eb Fb Gb Hbv
33133243 2|5 v7 A B C Db Eb Fb Gbv Hb
31332433 1|6 v6 A B Cb Db Eb Fbv Gb Hb
13324333 0|7 v5 A Bb Cb Db Ebv Fb Gb Hb

MODMOS with 5th note in generator chain flattened

Step pattern UDP name Spelling Other notes
33324331 7|0 v5 A B C D Ev F G H
33243313 6|1 v4 A B C Dv E F G Hb
32433133 5|2 v3 A B Cv D E F Gb Hb
24331333 4|3 v2 A Bv C D E Fb Gb Hb
43313332 3|4 ^2^3^4^5^6^7^8 A B^ C^ D^ Eb^ Fb^ Gb^ Hb^
33133324 2|5 v8 A B C Db Eb Fb Gb Hbv
31333243 1|6 v7 A B Cb Db Eb Fb Gbv Hb
13332433 0|7 v6 A Bb Cb Db Eb Fbv Gb Hb

MODMOS with 6th note in generator chain flattened

Step pattern UDP name Spelling Other notes
33332431 7|0 v6 A B C D E Fv G H
33324313 6|1 v5 A B C D Ev F G Hb
33243133 5|2 v4 A B C Dv E F Gb Hb
32431333 4|3 v3 A B Cv D E Fb Gb Hb
24313333 3|4 v2 A Bv C D Eb Fb Gb Hb
43133332 2|5 ^2^3^4^5^6^7^8 A B^ C^ Db^ Eb^ Fb^ Gb^ Hb^
31333324 1|6 v8 A B Cb Db Eb Fb Gb Hbv
13333243 0|7 v7 A Bb Cb Db Eb Fb Gbv Hb

MODMOS with 7th note in generator chain flattened

Step pattern UDP name Spelling Other notes
33333241 7|0 v7 A B C D E F Gv H
33332413 6|1 v6 A B C D E Fv G Hb
33324133 5|2 v5 A B C D Ev F Gb Hb
33241333 4|3 v4 A B C Dv E Fb Gb Hb
32413333 3|4 v3 A B Cv D Eb Fb Gb Hb
24133333 2|5 v2 A Bv C Db Eb Fb Gb Hb
41333332 1|6 ^2^3^4^5^6^7^8 A B^ Cb^ Db^ Eb^ Fb^ Gb^ Hb^
13333324 0|7 v8 A Bb Cb Db Eb Fb Gb Hbv

MODMOS with 8th note in generator chain flattened

Step pattern UDP name Spelling Other notes
33333322 7|0 v8 A B C D E F G Hv
33333223 6|1 v7 A B C D E F Gv Hb
33332233 5|2 v6 A B C D E Fv Gb Hb
33322333 4|3 v5 A B C D Ev Fb Gb Hb
33223333 3|4 v4 A B C Dv Eb Fb Gb Hb
32233333 2|5 v3 A B Cv Db Eb Fb Gb Hb
22333333 1|6 v2 A Bv Cb Db Eb Fb Gb Hb
23333332 0|7 ^2^3^4^5^6^7^8 A Bb^ Cb^ Db^ Eb^ Fb^ Gb^ Hb^

MODMOS with 1st note in generator chain sharpened (in 22edo this gives same modes as flattening 8th note)

Step pattern UDP name Spelling Other notes
23333332 7|0 v2v3v4v5v6v7v8 A Bv Cv Dv Ev Fv Gv Hv
33333322 6|1 ^8 A B C D E F G Hb^
33333223 5|2 ^7 A B C D E F Gb^ Hb
33332233 4|3 ^6 A B C D E Fb^ Gb Hb
33322333 3|4 ^5 A B C D Eb^ Fb Gb Hb
33223333 2|5 ^4 A B C Db^ Eb Fb Gb Hb
32233333 1|6 ^3 A B Cb^ Db Eb Fb Gb Hb
22333333 0|7 ^2 A Bb^ Cb Db Eb Fb Gb Hb

MODMOS with 2nd note in generator chain sharpened

Step pattern UDP name Spelling Other notes
42333331 7|0 ^2 A B^ C D E F G H
23333314 6|1 v2v3v4v5v6v7v8 A Bv Cv Dv Ev Fv Gv Hbv
33333142 5|2 ^8 A B C D E F Gb Hb^
33331423 4|3 ^7 A B C D E Fb Gb^ Hb
33314233 3|4 ^6 A B C D Eb Fb^ Gb Hb
33142333 2|5 ^5 A B C Db Eb^ Fb Gb Hb
31423333 1|6 ^4 A B Cb Db^ Eb Fb Gb Hb
14233333 0|7 ^3 A Bb Cb^ Db Eb Fb Gb Hb

MODMOS with 3rd note in generator chain sharpened

Step pattern UDP name Spelling Other notes
34233331 7|0 ^3 A B C^ D E F G H
42333313 6|1^2 A B^ C D E F G Hb
23333134 5|2 v2v3v4v5v6v7v8 A Bv Cv Dv Ev Fv Gbv Hbv
33331342 4|3 ^8 A B C D E Fb Gb Hb^
33313423 3|4 ^7 A B C D Eb Fb Gb^ Hb
33134233 2|5 ^6 A B C Db Eb Fb^ Gb Hb
31342333 1|6 ^5 A B Cb Db Eb^ Fb Gb Hb
13423333 0|7 ^4 A Bb Cb Db^ Eb Fb Gb Hb

MODMOS with 4th note in generator chain sharpened

Step pattern UDP name Spelling Other notes
33423331 7|0 ^4 A B C D^ E F G H
34233313 6|1^3 A B C^ D E F G Hb
42333133 5|2 ^2 A B^ C D E F Gb Hb
23331334 4|3 v2v3v4v5v6v7v8 A Bv Cv Dv Ev Fbv Gbv Hbv
33313342 3|4 ^8 A B C D Eb Fb Gb Hb^
33133423 2|5 ^7 A B C Db Eb Fb Gb^ Hb
31334233 1|6 ^6 A B Cb Db Eb Fb^ Gb Hb
13342333 0|7 ^5 A Bb Cb Db Eb^ Fb Gb Hb

MODMOS with 5th note in generator chain sharpened

Step pattern UDP name Spelling Other notes
33342331 7|0 ^5 A B C D E^ F G H
33423313 6|1^4 A B C D^ E F G Hb
34233133 5|2 ^3 A B C^ D E F Gb Hb
42331333 4|3 ^2 A B^ C D E Fb Gb Hb
23313334 3|4 v2v3v4v5v6v7v8 A Bv Cv Dv Ebv Fbv Gbv Hbv
33133342 2|5 ^8 A B C Db Eb Fb Gb Hb^
31333423 1|6 ^7 A B Cb Db Eb Fb Gb^ Hb
13334233 0|7 ^6 A Bb Cb Db Eb Fb^ Gb Hb

MODMOS with 6th note in generator chain sharpened

Step pattern UDP name Spelling Other notes
33334231 7|0 ^6 A B C D E F^ G H
33342313 6|1 ^5 A B C D E^ F G Hb
33423133 5|2 ^4 A B C D^ E F Gb Hb
34231333 4|3 ^3 A B C^ D E Fb Gb Hb
42313333 3|4 ^2 A B^ C D Eb Fb Gb Hb
23133334 2|5 v2v3v4v5v6v7v8 A Bv Cv Dbv Ebv Fbv Gbv Hbv
31333342 1|6 ^8 A B Cb Db Eb Fb Gb Hb^
13333423 0|7 ^7 A Bb Cb Db Eb Fb Gb^ Hb

MODMOS with 7th note in generator chain sharpened

Step pattern UDP name Spelling Other notes
33333421 7|0 ^7 A B C D E F G^ H
33334213 6|1 ^6 A B C D E F^ G Hb
33342133 5|2 ^5 A B C D E^ F Gb Hb
33421333 4|3 ^4 A B C D^ E Fb Gb Hb
34213333 3|4 ^3 A B C^ D Eb Fb Gb Hb
42133333 2|5 ^2 A B^ C Db Eb Fb Gb Hb
21333334 1|6 v2v3v4v5v6v7v8 A Bv Cbv Dbv Ebv Fbv Gbv Hbv
13333342 0|7 ^8 A Bb Cb Db Eb Fb Gb Hb^
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