User:Ganaram inukshuk/Tables
This page is for xen-related tables that I've made but don't have an exact place elsewhere on the wiki (yet).
Scale Table
I've had the idea of using a rectangular horogram to represent how mosses of a specific generator pair are related to one another, only to learn that I can copy-paste the entire tables from Excel into the wiki editor. I doubt I'd be the first person to do this, but this would be a nice way to list the mosses of an edo. The idea to include scale and step ratio information occurred mid-editing. Here's a few examples.
Temperament Agnostic Information Only
Notes:
- The generator pairs are ordered starting from ceil(n/2)\n and floor(n/2)\n and ending at (n-2)\n and 2\n. Including every possible pair from 1\n to (n-1)\n to (n-1)\n to 1\n would be redundant since the pair k\n and (n-k)\n would produce a table that's identical to (n-k)\n and k\n but reversed.
- (n-1)\n and 1\n is not included since it produces a sequence of "monolarge" scales where every scale in the table has the same size of small step.
- Information from the page for 19edo and its subpages (as of time of writing) is used as sample data.
- A few unnamed mosses are given tentative names based on names from their respective pages (EG, klesitonic) or based on existing names (EG, tetric).
| Step Pattern (19edo) | Mos | Step Ratio | TAMNAMS Name (if applicable) | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 10 | 9 | 1L 1s | 10:9 | Generator Pair | |||||||||||||||||
| 1 | 9 | 9 | 2L 1s | 9:1 | |||||||||||||||||
| 1 | 1 | 8 | 1 | 8 | 2L 3s | 8:1 | Pentic | ||||||||||||||
| 1 | 1 | 1 | 7 | 1 | 1 | 7 | 2L 5s | 7:1 | Antidiatonic | ||||||||||||
| 1 | 1 | 1 | 1 | 6 | 1 | 1 | 1 | 6 | 2L 7s | 6:1 | Joanatonic | ||||||||||
| 1 | 1 | 1 | 1 | 1 | 5 | 1 | 1 | 1 | 1 | 5 | 2L 9s | 5:1 | |||||||||
| 1 | 1 | 1 | 1 | 1 | 1 | 4 | 1 | 1 | 1 | 1 | 1 | 4 | 2L 11s | 4:1 | |||||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 2L 13s | 3:1 | |||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2L 15s | 2:1 | |||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |||
| Step Pattern (19edo) | Mos | Step Ratio | TAMNAMS Name (if applicable) | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 11 | 8 | 1L 1s | 11:8 | Generator Pair | |||||||||||||||||
| 3 | 8 | 8 | 2L 1s | 8:3 | |||||||||||||||||
| 3 | 3 | 5 | 3 | 5 | 2L 3s | 5:3 | Pentic | ||||||||||||||
| 3 | 3 | 3 | 2 | 3 | 3 | 2 | 5L 2s | 3:2 | Diatonic | ||||||||||||
| 1 | 2 | 1 | 2 | 1 | 2 | 2 | 1 | 2 | 1 | 2 | 2 | 7L 5s | 2:1 | M-chromatic | |||||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |||
| Step Pattern (19edo) | Mos | Step Ratio | TAMNAMS Name (if applicable) | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 12 | 7 | 1L 1s | 12:7 | Generator Pair | |||||||||||||||||
| 5 | 7 | 7 | 2L 1s | 7:5 | |||||||||||||||||
| 5 | 5 | 2 | 5 | 2 | 3L 2s | 5:2 | Antipentic | ||||||||||||||
| 3 | 2 | 3 | 2 | 2 | 3 | 2 | 2 | 3L 5s | 3:2 | Sensoid | |||||||||||
| 1 | 2 | 2 | 1 | 2 | 2 | 2 | 1 | 2 | 2 | 2 | 8L 3s | 2:1 | |||||||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |||
| Step Pattern (19edo) | Mos | Step Ratio | TAMNAMS Name (if applicable) | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 13 | 6 | 1L 1s | 13:6 | Generator Pair | |||||||||||||||||
| 7 | 6 | 6 | 1L 2s | 7:6 | |||||||||||||||||
| 1 | 6 | 6 | 6 | 3L 1s | 6:1 | Tetric (placeholder name for sake of completness) | |||||||||||||||
| 1 | 1 | 5 | 1 | 5 | 1 | 5 | 3L 4s | 5:1 | Mosh | ||||||||||||
| 1 | 1 | 1 | 4 | 1 | 1 | 4 | 1 | 1 | 4 | 3L 7s | 4:1 | Sephiroid | |||||||||
| 1 | 1 | 1 | 1 | 3 | 1 | 1 | 1 | 3 | 1 | 1 | 1 | 3 | 3L 10s | 3:1 | |||||||
| 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 2 | 3L 13s | 2:1 | ||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |||
| Step Pattern (19edo) | Mos | Step Ratio | TAMNAMS Name (if applicable) | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 14 | 5 | 1L 1s | 14:5 | Generator Pair | |||||||||||||||||
| 9 | 5 | 5 | 1L 2s | 9:5 | |||||||||||||||||
| 4 | 5 | 5 | 5 | 3L 1s | 5:4 | Tetric | |||||||||||||||
| 4 | 4 | 1 | 4 | 1 | 4 | 1 | 4L 3s | 4:1 | Smitonic | ||||||||||||
| 3 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | 4L 7s | 3:1 | Kleistonic (proposed name from 4L 7s page) | ||||||||
| 2 | 1 | 1 | 2 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 4L 11s | 2:1 | |||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |||
| Step Pattern (19edo) | Mos | Step Ratio | TAMNAMS Name (if applicable) | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 15 | 4 | 1L 1s | 15:4 | Generator Pair | |||||||||||||||||
| 11 | 4 | 4 | 1L 2s | 11:4 | |||||||||||||||||
| 7 | 4 | 4 | 4 | 1L 3s | 7:4 | ||||||||||||||||
| 3 | 4 | 4 | 4 | 4 | 4L 1s | 4:3 | Manic | ||||||||||||||
| 3 | 3 | 1 | 3 | 1 | 3 | 1 | 3 | 1 | 5L 4s | 3:1 | Semiquartal | ||||||||||
| 2 | 1 | 2 | 1 | 1 | 2 | 1 | 1 | 2 | 1 | 1 | 2 | 1 | 1 | 5L 9s | 2:1 | ||||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |||
| Step Pattern (19edo) | Mos | Step Ratio | TAMNAMS Name (if applicable) | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 16 | 3 | 1L 1s | 16:3 | Generator Pair | |||||||||||||||||
| 13 | 3 | 3 | 1L 2s | 13:3 | |||||||||||||||||
| 10 | 3 | 3 | 3 | 1L 3s | 10:3 | ||||||||||||||||
| 7 | 3 | 3 | 3 | 3 | 1L 4s | 7:3 | |||||||||||||||
| 4 | 3 | 3 | 3 | 3 | 3 | 1L 5s | 4:3 | ||||||||||||||
| 1 | 3 | 3 | 3 | 3 | 3 | 3 | 6L 1s | 3:1 | Archeotonic | ||||||||||||
| 1 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 6L 7s | 2:1 | |||||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |||
| Step Pattern (19edo) | Mos | Step Ratio | TAMNAMS Name (if applicable) | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 17 | 2 | 1L 1s | 17:2 | Generator Pair | |||||||||||||||||
| 15 | 2 | 2 | 1L 2s | 15:2 | |||||||||||||||||
| 13 | 2 | 2 | 2 | 1L 3s | 13:2 | ||||||||||||||||
| 11 | 2 | 2 | 2 | 2 | 1L 4s | 11:2 | |||||||||||||||
| 9 | 2 | 2 | 2 | 2 | 2 | 1L 5s | 9:2 | ||||||||||||||
| 7 | 2 | 2 | 2 | 2 | 2 | 2 | 1L 6s | 7:2 | |||||||||||||
| 5 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1L 7s | 5:2 | ||||||||||||
| 3 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1L 8s | 3:2 | |||||||||||
| 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 9L 1s | 2:1 | Sinatonic | |||||||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |||
General (Temperament-Agnostic) Information and Temperament Information
Notes:
- The generator pairs are ordered starting from ceil(n/2)\n and floor(n/2)\n and ending at (n-2)\n and 2\n. Including every possible pair from 1\n to (n-1)\n to (n-1)\n to 1\n would be redundant since the pair k\n and (n-k)\n would produce a table that's identical to (n-k)\n and k\n but reversed.
(n-1)\n and 1\n is not included since it produces a sequence of "monolarge" scales where every scale in the table has the same size of small step.- Information from the page for 19edo and its subpages (as of time of writing) is used as sample data.
- A few unnamed mosses are given tentative names based on names from their respective pages (EG, klesitonic) or based on existing names (EG, tetric).
- Scale codes are given for scales whose step sizes are single-digit numbers.
| Step Pattern | General Information | Temperament Information | |||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Generator pair of 10\19 and 9\19 | Scale Code | Mos | Step Ratio | TAMNAMS Name | Scales | ||||||||||||||||||
| 10 | 9 | 1L 1s | 10:9 | ||||||||||||||||||||
| 1 | 9 | 9 | 199 | 2L 1s | 9:1 | ||||||||||||||||||
| 1 | 1 | 8 | 1 | 8 | 11818 | 2L 3s | 8:1 | pentic | liese[5] | ||||||||||||||
| 1 | 1 | 1 | 7 | 1 | 1 | 7 | 1117117 | 2L 5s | 7:1 | antidiatonic | liese[7] | ||||||||||||
| 1 | 1 | 1 | 1 | 6 | 1 | 1 | 1 | 6 | 111161116 | 2L 7s | 6:1 | joanatonic | liese[9] | ||||||||||
| 1 | 1 | 1 | 1 | 1 | 5 | 1 | 1 | 1 | 1 | 5 | 11111511115 | 2L 9s | 5:1 | liese[11] | |||||||||
| 1 | 1 | 1 | 1 | 1 | 1 | 4 | 1 | 1 | 1 | 1 | 1 | 4 | 1111114111114 | 2L 11s | 4:1 | liese[13] | |||||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 1 | 1 | 1 | 1 | 1 | 1 | 3 | 111111131111113 | 2L 13s | 3:1 | liese[15] | |||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 11111111211111112 | 2L 15s | 2:1 | liese[17] | |||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |||||
| Generator pair of 11\19 and 8\19 | Scale Code | Mos | Step Ratio | TAMNAMS Name | Scales | ||||||||||||||||||
| 11 | 8 | 1L 1s | 11:8 | ||||||||||||||||||||
| 3 | 8 | 8 | 388 | 2L 1s | 8:3 | ||||||||||||||||||
| 3 | 3 | 5 | 3 | 5 | 33535 | 2L 3s | 5:3 | pentic | meantone[5] | ||||||||||||||
| 3 | 3 | 3 | 2 | 3 | 3 | 2 | 3332332 | 5L 2s | 3:2 | diatonic | meantone[7] | ||||||||||||
| 1 | 2 | 1 | 2 | 1 | 2 | 2 | 1 | 2 | 1 | 2 | 2 | 121212212122 | 7L 5s | 2:1 | m-chromatic | meantone[12] | |||||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |||||
| Generator pair of 12\19 and 7\19 | Scale Code | Mos | Step Ratio | TAMNAMS Name | Scales | ||||||||||||||||||
| 12 | 7 | 1L 1s | 12:7 | ||||||||||||||||||||
| 5 | 7 | 7 | 577 | 2L 1s | 7:5 | ||||||||||||||||||
| 5 | 5 | 2 | 5 | 2 | 55252 | 3L 2s | 5:2 | antipentic | sensi[5] | ||||||||||||||
| 3 | 2 | 3 | 2 | 2 | 3 | 2 | 2 | 32322322 | 3L 5s | 3:2 | sensoid | sensi[8] | |||||||||||
| 1 | 2 | 2 | 1 | 2 | 2 | 2 | 1 | 2 | 2 | 2 | 12212221222 | 8L 3s | 2:1 | sensi[11] | |||||||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |||||
| Generator pair of 13\19 and 6\19 | Scale Code | Mos | Step Ratio | TAMNAMS Name | Scales | ||||||||||||||||||
| 13 | 6 | 1L 1s | 13:6 | ||||||||||||||||||||
| 7 | 6 | 6 | 766 | 1L 2s | 7:6 | ||||||||||||||||||
| 1 | 6 | 6 | 6 | 1666 | 3L 1s | 6:1 | tetric | ||||||||||||||||
| 1 | 1 | 5 | 1 | 5 | 1 | 5 | 1151515 | 3L 4s | 5:1 | mosh | magic[7] | ||||||||||||
| 1 | 1 | 1 | 4 | 1 | 1 | 4 | 1 | 1 | 4 | 1114114114 | 3L 7s | 4:1 | sephiroid | magic[10] | |||||||||
| 1 | 1 | 1 | 1 | 3 | 1 | 1 | 1 | 3 | 1 | 1 | 1 | 3 | 1111311131113 | 3L 10s | 3:1 | magic[13] | |||||||
| 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 2 | 1111121111211112 | 3L 13s | 2:1 | magic[16] | ||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |||||
| Generator pair of 14\19 and 5\19 | Scale Code | Mos | Step Ratio | TAMNAMS Name | Scales | ||||||||||||||||||
| 14 | 5 | 1L 1s | 14:5 | ||||||||||||||||||||
| 9 | 5 | 5 | 955 | 1L 2s | 9:5 | ||||||||||||||||||
| 4 | 5 | 5 | 5 | 4555 | 3L 1s | 5:4 | tetric | ||||||||||||||||
| 4 | 4 | 1 | 4 | 1 | 4 | 1 | 4414141 | 4L 3s | 4:1 | smitonic | kleismic[7] | ||||||||||||
| 3 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | 3 | 1 | 1 | 31311311311 | 4L 7s | 3:1 | kleistonic | kleismic[11] | ||||||||
| 2 | 1 | 1 | 2 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 211211121112111 | 4L 11s | 2:1 | kleismic[15] | |||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |||||
| Generator pair of 15\19 and 4\19 | Scale Code | Mos | Step Ratio | TAMNAMS Name | Scales | ||||||||||||||||||
| 15 | 4 | 1L 1s | 15:4 | ||||||||||||||||||||
| 11 | 4 | 4 | 1L 2s | 11:4 | |||||||||||||||||||
| 7 | 4 | 4 | 4 | 7444 | 1L 3s | 7:4 | |||||||||||||||||
| 3 | 4 | 4 | 4 | 4 | 34444 | 4L 1s | 4:3 | manic | godzilla[5] | ||||||||||||||
| 3 | 3 | 1 | 3 | 1 | 3 | 1 | 3 | 1 | 331313131 | 5L 4s | 3:1 | semiquartal | godzilla[9] | ||||||||||
| 2 | 1 | 2 | 1 | 1 | 2 | 1 | 1 | 2 | 1 | 1 | 2 | 1 | 1 | 21211211211211 | 5L 9s | 2:1 | godzilla[14] | ||||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |||||
| Generator pair of 16\19 and 3\19 | Scale Code | Mos | Step Ratio | TAMNAMS Name | Scales | ||||||||||||||||||
| 16 | 3 | 1L 1s | 16:3 | ||||||||||||||||||||
| 13 | 3 | 3 | 1L 2s | 13:3 | |||||||||||||||||||
| 10 | 3 | 3 | 3 | 1L 3s | 10:3 | ||||||||||||||||||
| 7 | 3 | 3 | 3 | 3 | 73333 | 1L 4s | 7:3 | ||||||||||||||||
| 4 | 3 | 3 | 3 | 3 | 3 | 433333 | 1L 5s | 4:3 | deutone[6] | ||||||||||||||
| 1 | 3 | 3 | 3 | 3 | 3 | 3 | 1333333 | 6L 1s | 3:1 | archeotonic | deutone[7] | ||||||||||||
| 1 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | 1121212121212 | 6L 7s | 2:1 | deutone[13] | |||||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |||||
| Generator pair of 17\19 and 2\19 | Scale Code | Mos | Step Ratio | TAMNAMS Name | Scales | ||||||||||||||||||
| 17 | 2 | 1L 1s | 17:2 | ||||||||||||||||||||
| 15 | 2 | 2 | 1L 2s | 15:2 | |||||||||||||||||||
| 13 | 2 | 2 | 2 | 1L 3s | 13:2 | ||||||||||||||||||
| 11 | 2 | 2 | 2 | 2 | 1L 4s | 11:2 | |||||||||||||||||
| 9 | 2 | 2 | 2 | 2 | 2 | 922222 | 1L 5s | 9:2 | |||||||||||||||
| 7 | 2 | 2 | 2 | 2 | 2 | 2 | 7222222 | 1L 6s | 7:2 | ||||||||||||||
| 5 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 52222222 | 1L 7s | 5:2 | |||||||||||||
| 3 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 322222222 | 1L 8s | 3:2 | negri[9] | |||||||||||
| 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 1222222222 | 9L 1s | 2:1 | sinatonic | negri[10] | |||||||||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |||||
| Generator pair of 18\19 and 1\19 | Scale Code | Mos | Step Ratio | TAMNAMS Name | Scales | ||||||||||||||||||
| 18 | 1 | 1L 1s | 18:1 | ||||||||||||||||||||
| 17 | 1 | 1 | 1L 2s | 17:1 | |||||||||||||||||||
| 16 | 1 | 1 | 1 | 1L 3s | 16:1 | ||||||||||||||||||
| 15 | 1 | 1 | 1 | 1 | 1L 4s | 15:1 | |||||||||||||||||
| 14 | 1 | 1 | 1 | 1 | 1 | 1L 5s | 14:1 | ||||||||||||||||
| 13 | 1 | 1 | 1 | 1 | 1 | 1 | 1L 6s | 13:1 | |||||||||||||||
| 12 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1L 7s | 12:1 | ||||||||||||||
| 11 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1L 8s | 11:1 | |||||||||||||
| 10 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1L 9s | 10:1 | ||||||||||||
| 9 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 91111111111 | 1L 10s | 9:1 | ||||||||||
| 8 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 811111111111 | 1L 11s | 8:1 | |||||||||
| 7 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 7111111111111 | 1L 12s | 7:1 | ||||||||
| 6 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 61111111111111 | 1L 13s | 6:1 | |||||||
| 5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 511111111111111 | 1L 14s | 5:1 | ||||||
| 4 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 4111111111111111 | 1L 15s | 4:1 | |||||
| 3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 31111111111111111 | 1L 16s | 3:1 | ||||
| 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 211111111111111111 | 1L 17s | 2:1 | |||
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |||||
Mode and Interval Table
Based on the scale table, there is also the idea of a mode table. Since the modes of a scale affect its scale degrees, this also serves as an interval table.
Notes:
- The names of mosses and intervals are based on TAMNAMS naming conventions.
- As this is an interval table, intervals are based on the root of the scale and whichever scale degree is k steps up from the root. For intervals that have two sizes (major and minor, augmented and perfect, or perfect and diminished), bold text denotes the larger of the two intervals. (This is far more striking with color coding.)
| Mos | Scale Code | UDP | Mode Name | 0-step
(unison) |
1-step | 2-step | 3-step | 4-step | 5-step | 6-step | 7-step
(octave) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Diatonic (5L 2s) | LLLsLLs | 6|0 | Lydian | Perfect | Maj | Maj | Aug | Perfect | Maj | Maj | Perfect |
| LLsLLLs | 5|1 | Ionian | Perfect | Maj | Maj | Perfect | Perfect | Maj | Maj | Perfect | |
| LLsLLsL | 4|2 | Mixolydian | Perfect | Maj | Maj | Perfect | Perfect | Maj | min | Perfect | |
| LsLLLsL | 3|3 | Dorian | Perfect | Maj | min | Perfect | Perfect | Maj | min | Perfect | |
| LsLLsLL | 2|4 | Aeolian | Perfect | Maj | min | Perfect | Perfect | min | min | Perfect | |
| sLLLsLL | 1|5 | Phrygian | Perfect | min | min | Perfect | Perfect | min | min | Perfect | |
| sLLsLLL | 0|6 | Locrian | Perfect | min | min | Perfect | dim | min | min | Perfect |
| Mos | Scale Code | UDP | Mode Name | 0-step
(unison) |
1-step | 2-step | 3-step | 4-step | 5-step | 6-step | 7-step
(octave) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Mosh (3L 4s) | LsLsLss | 6|0 | Dril | Perfect | Maj | Perfect | Maj | Maj | Aug | Maj | Perfect |
| LsLssLs | 5|1 | Gil | Perfect | Maj | Perfect | Maj | Maj | Perfect | Maj | Perfect | |
| LssLsLs | 4|2 | Kleeth | Perfect | Maj | Perfect | min | Maj | Perfect | Maj | Perfect | |
| sLsLsLs | 3|3 | Bish | Perfect | min | Perfect | min | Maj | Perfect | Maj | Perfect | |
| sLsLssL | 2|4 | Fish | Perfect | min | Perfect | min | Maj | Perfect | min | Perfect | |
| sLssLsL | 1|5 | Jwl | Perfect | min | Perfect | min | min | Perfect | min | Perfect | |
| ssLsLsL | 0|6 | Led | Perfect | min | dim | min | min | Perfect | min | Perfect |
Mos Family Tree as a Table
The following is the mos family tree, formatted as a table. The table consists of 6 generations, or up to 5th-order child mosses.
| Mos Family Tree (single-period only) | |||||
|---|---|---|---|---|---|
| Parent Scale | 1st-order child mosses | 2nd-order child mosses | 3rd-order child mosses | 4th-order child mosses | 5th-order child mosses |
| 1L 1s | 1L 2s | 1L 3s | 1L 4s | 1L 5s | 1L 6s |
| 6L 1s | |||||
| 5L 1s | 5L 6s | ||||
| 6L 5s | |||||
| 4L 1s | 4L 5s | 4L 9s | |||
| 9L 4s | |||||
| 5L 4s | 5L 9s | ||||
| 9L 5s | |||||
| 3L 1s | 3L 4s | 3L 7s | 3L 10s | ||
| 10L 3s | |||||
| 7L 3s | 7L 10s | ||||
| 10L 7s | |||||
| 4L 3s | 4L 7s | 4L 11s | |||
| 11L 4s | |||||
| 7L 4s | 7L 11s | ||||
| 11L 7s | |||||
| 2L 1s | 2L 3s | 2L 5s | 2L 7s | 2L 9s | |
| 9L 2s | |||||
| 7L 2s | 7L 9s | ||||
| 9L 7s | |||||
| 5L 2s | 5L 7s | 5L 12s | |||
| 12L 5s | |||||
| 7L 5s | 7L 12s | ||||
| 12L 7s | |||||
| 3L 2s | 3L 5s | 3L 8s | 3L 11s | ||
| 11L 3s | |||||
| 8L 3s | 8L 11s | ||||
| 11L 8s | |||||
| 5L 3s | 5L 8s | 5L 13s | |||
| 13L 5s | |||||
| 8L 5s | 8L 13s | ||||
| 13L 8 | |||||
Alternate ways of organizing mosses named under TAMNAMS
Using the MOS family tree (with outdated names)
| Mos Family Tree (single-period only), with TAMNAMS Names
italics denote 1L ns scales (named for completeness); asterisks denote non-official names (from my own notes) | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Progenitor scale | 1st-order child mosses | 2nd-order child mosses | 3rd-order child mosses | 4th-order child mosses | 5th-order child mosses | ||||||
| Steps | Scale name | Steps | Scale name | Steps | Scale name | Steps | Scale name | Steps | Scale name | Steps | Scale name |
| 1L 1s | prototonic* | 1L 2s |
|
1L 3s | antitetric* | 1L 4s | antimanic | 1L 5s | antimachinoid | 1L 6s | anti-archeotonic |
| 6L 1s | archeotonic | ||||||||||
| 5L 1s | machinoid | 5L 6s | |||||||||
| 6L 5s | |||||||||||
| 4L 1s | manic | 4L 5s | orwelloid | 4L 9s | |||||||
| 9L 4s | |||||||||||
| 5L 4s | semiquartal | 5L 9s | |||||||||
| 9L 5s | |||||||||||
| 3L 1s | tetric* | 3L 4s | mosh | 3L 7s | sephiroid | 3L 10s | |||||
| 10L 3s | |||||||||||
| 7L 3s | dicotonic | 7L 10s | |||||||||
| 10L 7s | |||||||||||
| 4L 3s | smitonic | 4L 7s | kleistonic | 4L 11s | |||||||
| 11L 4s | |||||||||||
| 7L 4s | suprasmitonic | 7L 11s | |||||||||
| 11L 7s | |||||||||||
| 2L 1s | deuteric* | 2L 3s | pentic | 2L 5s | antidiatonic | 2L 7s | joanatonic | 2L 9s | |||
| 9L 2s | |||||||||||
| 7L 2s | superdiatonic | 7L 9s | |||||||||
| 9L 7s | |||||||||||
| 5L 2s | diatonic | 5L 7s | p-chromatic | 5L 12s | p-superchromatic* | ||||||
| 12L 5s | |||||||||||
| 7L 5s | m-chromatic | 7L 12s | |||||||||
| 12L 7s | m-superchromatic* | ||||||||||
| 3L 2s | antipentic | 3L 5s | sensoid | 3L 8s | 3L 11s | ||||||
| 11L 3s | |||||||||||
| 8L 3s | 8L 11s | ||||||||||
| 11L 8s | |||||||||||
| 5L 3s | oneirotonic | 5L 8s | 5L 13s | ||||||||
| 13L 5s | |||||||||||
| 8L 5s | 8L 13s | ||||||||||
| 13L 8 | |||||||||||
Family tree limited to 10 notes and with up to 5 periods
| Family tree of single-period mosses, limited to 10-note scales | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Root | 1st-order child scales | 2nd-order child scales | 3rd-order child scales | 4th-order child scales | 5th-order child scales | 6th-order child scales | 7th-order child scales | 8th-order child scales | |||||||||
| Mos | Name | Mos | Name | Mos | Name | Mos | Name | Mos | Name | Mos | Name | Mos | Name | Mos | Name | Mos | Name |
| 1L 1s | trivial | 1L 2s | antrial | 1L 3s | antetric | 1L 4s | pedal | 1L 5s | antimachinoid | 1L 6s | onyx | 1L 7s | antipine | 1L 8s | antisubneutralic | 1L 9s | antisinatonic |
| 9L 1s | sinatonic | ||||||||||||||||
| 8L 1s | subneutralic | ||||||||||||||||
| 7L 1s | pine | ||||||||||||||||
| 6L 1s | archeotonic | ||||||||||||||||
| 5L 1s | machinoid | ||||||||||||||||
| 4L 1s | manual | 5L 4s | semiquartal | ||||||||||||||
| 4L 5s | gramitonic | ||||||||||||||||
| 3L 1s | tetric | 4L 3s | smitonic | ||||||||||||||
| 3L 4s | mosh | 7L 3s | dicoid | ||||||||||||||
| 3L 7s | sephiroid | ||||||||||||||||
| 2L 1s | trial | 3L 2s | antipentic | 3L 5s | checkertonic | ||||||||||||
| 5L 3s | oneirotonic | ||||||||||||||||
| 2L 3s | pentic | 5L 2s | diatonic | ||||||||||||||
| 2L 5s | antidiatonic | 7L 2s | superdiatonic | ||||||||||||||
| 2L 7s | balzano | ||||||||||||||||
| Family tree of 2-period mosses, limited to 10-note scales | |||||||||||||||||
| Root | 1st-order child scales | 2nd-order child scales | 3rd-order child scales | ||||||||||||||
| Mos | Name | Mos | Name | Mos | Name | Mos | Name | ||||||||||
| 2L 2s | biwood | 2L 4s | malic | 2L 6s | subaric | 2L 8s | jaric | ||||||||||
| 8L 2s | taric | ||||||||||||||||
| 6L 2s | ekic | ||||||||||||||||
| 4L 2s | citric | 6L 4s | lemon | ||||||||||||||
| 4L 6s | lime | ||||||||||||||||
| Family tree of 3-period mosses, limited to 10-note scales | |||||||||||||||||
| Root | 1st-order child scales | ||||||||||||||||
| Mos | Name | Mos | Name | ||||||||||||||
| 3L 3s | triwood | 3L 6s | tcherepnin | ||||||||||||||
| 6L 3s | hyrulic | ||||||||||||||||
| Family tree of 4-period mosses, limited to 10-note scales | |||||||||||||||||
| Root | |||||||||||||||||
| Mos | Name | ||||||||||||||||
| 4L 4s | tetrawood, diminished | ||||||||||||||||
| Family tree of 5-period mosses, limited to 10-note scales | |||||||||||||||||
| Root | |||||||||||||||||
| Mos | Name | ||||||||||||||||
| 5L 5s | pentawood | ||||||||||||||||
Mos Family Tree for an Edo
The basis of this diagram is simple: take the infinite mos family tree and only show the scales that are available for a specific edo.
19edo Example
The table shown below is the mos family tree for 19edo.
| Mos Family Tree for 19edo | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Generator Pair | 18\19 - 1\19 | 17\19 - 2\19 | 16\19 - 3\19 | 15\19 - 4\19 | 14\19 - 5\19 | 13\19 - 6\19 | 12\19 - 7\19 | 11\19 - 8\19 | 10\19 - 9\19 |
| Gen. 1 | 1L 1s | ||||||||
| Gen. 2 | 1L 2s | 2L 1s | |||||||
| Gen. 3 | 1L 3s | 3L 1s | 3L 2s | 2L 3s | |||||
| Gen. 4 | 1L 4s | 4L 1s | 4L 3s | 3L 4s | 3L 5s | 5L 2s | 2L 5s | ||
| Gen. 5 | 1L 5s | 5L 4s | 4L 7s | 3L 7s | 8L 3s | 7L 5s | 2L 7s | ||
| Gen. 6 | 1L 6s | 6L 1s | 5L 9s | 4L 11s | 3L 10s | 2L 9s | |||
| Gen. 7 | 1L 7s | 6L 7s | 3L 13s | 2L 11s | |||||
| Gen. 8 | 1L 8s | 2L 13s | |||||||
| Gen. 9 | 1L 9s | 2L 15s | |||||||
| Gen. 10 | 1L 10s | ||||||||
| Gen. 11 | 1L 11s | ||||||||
| Gen. 12 | 1L 12s | ||||||||
| Gen. 13 | 1L 13s | ||||||||
| Gen. 14 | 1L 14s | ||||||||
| Gen. 15 | 1L 15s | ||||||||
| Gen. 16 | 1L 16s | ||||||||
| Gen. 17 | 1L 17s | ||||||||
This tree can be thought of as a pruned mos family tree, where every leaf node corresponds to a mos available to 19edo with a step ratio of 2:1. To conceptualize this tree better, consider the leaf node 7L 5s. Since the entire structure is a binary tree (that is, there are no loopy paths), there is one and only one unique path that starts from 1L 1s and ends at 7L 5s. Likewise, all other leaf nodes have a unique path that, when traversed backwards, merges back with 1L 1s.
Note that all of these paths inevitably overlap. It's important to note that these overlaps are due to each path having multiple mosses in common with one another; for a node with two child nodes, the two child scales don't share the same generator pair, only a common mos from the parent node. Pruning a mos tree by generator pair isolates a single linear path between 1L 1s and the leaf node with the step ratio of 2:1; put another way, the tree would be pruned down to a single, finite branch.
Note the curious case of 1L 7s in this example. It should be the leaf node for the generator pair 17\19 and 2\19, but since that scale is also available to the generator pair of 18\19 and 1\19, it's not and that branch continues to 1L 17s. Technically speaking, the branches for the generator pairs of 18\19-1\19 and 17\19-2\19 coincide.
31edo Example
This table does away with generation numbers and includes the "terminating edo" (the edo resulted when the mos xL ys with a step ratio of L:s = 2:1 produces a pair of indistinguishable child scales xL (x+y)s and (x+y)L xs whose step ratios are both 1:1, or k:k if L and s share a common factor k). Also, no merged cells; hopefully, that illustrates things a bit better.
| Mos Family Tree for 31edo | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 30\31 - 1\31 | 29\31 - 2\31 | 28\31 - 3\31 | 27\31 - 4\31 | 26\31 - 5\31 | 25\31 - 6\31 | 24\31 - 7\31 | 23\31 - 8\31 | 22\31 - 9\31 | 21\31 - 10\31 | 20\31 - 11\31 | 19\31 - 12\31 | 18\31 - 13\31 | 17\31 - 14\31 | 16\31 - 15\31 |
| 1L 1s | 1L 1s | 1L 1s | 1L 1s | 1L 1s | 1L 1s | 1L 1s | 1L 1s | 1L 1s | 1L 1s | 1L 1s | 1L 1s | 1L 1s | 1L 1s | 1L 1s |
| 1L 2s | 1L 2s | 1L 2s | 1L 2s | 1L 2s | 1L 2s | 1L 2s | 1L 2s | 1L 2s | 1L 2s | 2L 1s | 2L 1s | 2L 1s | 2L 1s | 2L 1s |
| 1L 3s | 1L 3s | 1L 3s | 1L 3s | 1L 3s | 1L 3s | 1L 3s | 3L 1s | 3L 1s | 3L 1s | 3L 2s | 3L 2s | 2L 3s | 2L 3s | 2L 3s |
| 1L 4s | 1L 4s | 1L 4s | 1L 4s | 1L 4s | 1L 4s | 4L 1s | 4L 3s | 3L 4s | 3L 4s | 3L 5s | 5L 3s | 5L 2s | 2L 5s | 2L 5s |
| 1L 5s | 1L 5s | 1L 5s | 1L 5s | 1L 5s | 5L 1s | 4L 5s | 4L 7s | 7L 3s | 3L 7s | 3L 8s | 5L 8s | 7L 5s | 2L 7s | 2L 7s |
| 1L 6s | 1L 6s | 1L 6s | 1L 6s | 6L 1s | 5L 6s | 9L 4s | 4L 11s | 7L 10s | 3L 10s | 3L 11s | 13L 5s | 12L 7s | 9L 2s | 2L 9s |
| 1L 7s | 1L 7s | 1L 7s | 7L 1s | 6L 7s | 5L 11s | 9L 13s | 4L 15s | 7L 17s | 3L 13s | 14L 3s | 31edo | 31edo | 11L 9s | 2L 11s |
| 1L 8s | 1L 8s | 1L 8s | 8L 7s | 6L 13s | 5L 16s | 31edo | 4L 19s | 31edo | 3L 16s | 31edo | 31edo | 2L 13s | ||
| 1L 9s | 1L 9s | 1L 9s | 8L 15s | 6L 19s | 5L 21s | 4L 23s | 3L 19s | 2L 15s | ||||||
| 1L 10s | 1L 10s | 10L 1s | 31edo | 31edo | 31edo | 31edo | 3L 22s | 2L 17s | ||||||
| 1L 11s | 1L 11s | 10L 11s | 3L 25s | 2L 19s | ||||||||||
| 1L 12s | 1L 12s | 31edo | 31edo | 2L 21s | ||||||||||
| 1L 13s | 1L 13s | 2L 23s | ||||||||||||
| 1L 14s | 1L 14s | 2L 25s | ||||||||||||
| 1L 15s | 15L 1s | 2L 27s | ||||||||||||
| 1L 16s | 31edo | 31edo | ||||||||||||
| 1L 17s | ||||||||||||||
| 1L 18s | ||||||||||||||
| 1L 19s | ||||||||||||||
| 1L 20s | ||||||||||||||
| 1L 21s | ||||||||||||||
| 1L 22s | ||||||||||||||
| 1L 23s | ||||||||||||||
| 1L 24s | ||||||||||||||
| 1L 25s | ||||||||||||||
| 1L 26s | ||||||||||||||
| 1L 27s | ||||||||||||||
| 1L 28s | ||||||||||||||
| 1L 29s | ||||||||||||||
| 31edo | ||||||||||||||