User:Ganaram inukshuk/Tables

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Revision as of 09:10, 21 March 2022 by Ganaram inukshuk (talk | contribs) (Reorganized the page to state that the tables use 19edo as sample data. Testing out tables that include both temperament info and temperament-agnostic info.)
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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.

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.

Temperament Agnostic Information Only

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

Temperament-Agnostic and Temperament Information

Step Pattern Temperament-Agnostic Information Temperament
Scale Code Mos Step Ratio TAMNAMS Name
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
Step Pattern Temperament-Agnostic Information Temperament
Scale Code Mos Step Ratio TAMNAMS Name
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 19ed
Step Pattern Temperament-Agnostic Information Temperament
Scale Code Mos Step Ratio TAMNAMS Name
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
Step Pattern Temperament-Agnostic Information Temperament
Scale Code Mos Step Ratio TAMNAMS Name
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
Step Pattern Temperament-Agnostic Information Temperament
Scale Code Mos Step Ratio TAMNAMS Name
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
Step Pattern Temperament-Agnostic Information Temperament
Scale Code Mos Step Ratio TAMNAMS Name
15 4 1L 1s 15:4
11 4 4 1144 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
Step Pattern Temperament-Agnostic Information Temperament
Scale Code Mos Step Ratio TAMNAMS Name
16 3 1L 1s 16:3
13 3 3 1333 1L 2s 13:3
10 3 3 3 10333 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
Step Pattern Temperament-Agnostic Information Temperament
Scale Code Mos Step Ratio TAMNAMS Name
17 2 1L 1s 17:2
15 2 2 1522 1L 2s 15:2
13 2 2 2 13222 1L 3s 13:2
11 2 2 2 2 112222 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


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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