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User:Ganaram inukshuk/Tables

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Revision as of 05:03, 22 March 2022 by Ganaram inukshuk (talk | contribs) (→Temperament-Agnostic and Temperament Information: Merged all the individual tables into one giant table for combined temperament-agnostic and temperament-based information. (Now I wish this was its own template...))

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
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