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User:Ganaram inukshuk/Tables

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Revision as of 21:16, 19 March 2022 by Ganaram inukshuk (talk | contribs) (→Interval Table: Added interval/mode 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.

19edo Moment-of-Symmetry Scales

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.
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

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 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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