Porcupine Temperament Modal Harmony
Intro To Porcupine[edit]
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 3/2 as a type of "fifth", thinking of those ETs in terms of porcupine temperament is the ideal conceptual approach. (To be continued...)
Brief Intro to Modal Harmony and MODMOSes[edit]
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 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 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.
Reasons Why Porcupine Will Make for The Best Modal Harmony Ever[edit]
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[edit]
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.
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[edit]
| Mode 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) | File:Porcupineotonalmajor22edo.mp3 |
| 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) | File:Porcupinesymmetricminor22edo.mp3 |
| 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[edit]
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
| 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.
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
| 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 |
MODMOS with 3rd note in generator chain sharpened: ##.####..# Big Cats
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: ###.###...#
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[edit]
| 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[edit]
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.
The Porcupine[8] MOS[edit]
| Mode 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[edit]
Alterations by porcupine[8] chroma[edit]
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[edit]
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^ |