Porcupine Temperament Modal Harmony

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Intro To Porcupine

Porcupine temperament has a number of significant properties that make it somewhat unique in the universe of temperaments.

Porcupine is one of the few reasonably good 5-limit temperaments, alongside meantone (and perhaps mavila), 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. This is important, because if you want to use 15edo or 22edo in a somewhat "heptatonic" fashion, where 5/4 and 6/5 are types of "third", 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. Furthermore, *any* heptatonic scale in 15edo or 22edo can be viewed as a MODMOS of the porcupine-7 MOS.

Lastly, porcupine temperament is extremely notable as being, in a certain sense, the simplest 5-limit temperament that is not supported by 12-EDO (and is thus inherently xenharmonic), but is at least as good intonationally. To be precise, porcupine temperament has the following properties:

1. It is the simplest 5-limit temperament that is at least as precise as 12-EDO, and which is not supported by 12-EDO. 2. In a temperament search of 5-limit temperaments, using the standard search parameter of 5 cents of error, porcupine is the first temperament in the results that is not supported by 12.

Porcupine remains the "best" such temperament even if the maximum error is relaxed somewhat, until eventually being superceded by mavila temperament, which is simpler but much less accurate than porcupine temperament (using standard harmonic timbres).


Brief Intro to Modal Harmony and MODMOSes

Porcupine is a temperament completely capable of diverse harmony. Using it's MOS in conjunction with its 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 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.

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 the 7-note MOS. 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.

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.

Reasons Why Porcupine Will Make for The Best Modal Harmony Ever

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 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.

(To be continued...)

Porcupine[7] and its MODMOSs

The below mode names are given in 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, which are listed as "William's Name" below.

The scale's nominals can be named by the normal 7 tone alphabet starting G but some feel that with superpyth using the same nominals in an entirely opposite way, it may be beneficial to use an entirely different set of letters for porcupine which William Lynch created using 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"

The Porcupine[7] MOS

William's Name 22edo Step Pattern 15edo Step Pattern UDP Name Spelling Alt Spelling Triad Qualities Other Notes
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)
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)
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)
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)
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 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 Diminished
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 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: #..####.## Reptiles

Consists of unbroken chains of 4/3s

William's 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.

Symmetrical MODMOS with 2nd note in generator chain sharpened or 6th note flattened: #.#####.# Farm Animals

Consists of unbroken chains of 4/3s

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

William's 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

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

Consists of unbroken chains of 4/3s

William's 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: ###.###...#

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] chroma-positive 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.

The Porcupine[8] MOS

William's Name Step Pattern UDP Name Traditional 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

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: #..'##'###.##

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: #.'##'####.#

Step Pattern UDP Name Spelling Other Notes
33333151 7|0 b7 A B C D E F Gb H
33331513 6|1 b6 A B C D E Fb G Hb
33315133 5|2 b5 A B C D Eb F Gb Hb
33151333 4|3 b4 A B C Db E Fb Gb Hb
31513333 3|4 b3 A B Cb D Eb Fb Gb Hb
15133333 2|5 b2 A Bb C Db Eb Fb Gb Hb
51333331 7|0 #2 A B# C D E F G H
13333315 0|7 b8 A Bb Cb Db Eb Fb Gb Hbb

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

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: ###.'####...#

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^