Porcupine Temperament Modal Harmony
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Porcupine remains the "best" such temperament even if the maximum error is relaxed somewhat, until eventually being superceded by mavila temperament, which is simpler but much less accurate than porcupine temperament (using standard harmonic timbres).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.
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. 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.
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.
Porcupine[7] and its MODMOSs
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 Name | 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 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: #..'##'###.##
| 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^ |