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User:Ganaram inukshuk/Sandbox

< User:Ganaram inukshuk
Revision as of 01:42, 28 January 2024 by Ganaram inukshuk (talk | contribs)

This is a sandbox page for me (Ganaram) to test out a few things before deploying things. (Expect some mess.)

Template test area

Intervals of 12edo (as a 2.3.5.7.17.19 subgroup temperament)
Degree Cents Approximated JI intervals
2-limit 3-limit 5-limit 7-limit 17-limit 19-limit
0 0.000 1/1
1 100.000 16/15
25/24 		15/14
21/20 		17/16
18/17 		19/18
20/19
2 200.000 9/8 10/9 28/25 17/15
96/85 		64/57
3 300.000 32/27 6/5 20/17 19/16
4 400.000 5/4
32/25 		51/40
64/51 		24/19
5 500.000 4/3 27/20 21/16 19/14
6 600.000 45/32
64/45 		7/5
10/7 		17/12
24/17
7 700.000 3/2 40/27 32/21 28/19
8 800.000 8/5
25/16 		51/32
80/51 		19/12
9 900.000 27/16 5/3 17/10 32/19
10 1000.000 16/9 9/5 25/14 30/17
85/48 		57/32
11 1100.000 15/8
48/25 		28/15
40/21 		17/9
32/17 		19/10
36/19
12 1200.000 2/1


Intervals of 72edo (as a 2.3.5.7.11.19 subgroup temperament)
Degree Cents Approximated JI intervals
2-limit 3-limit 5-limit 7-limit 11-limit 19-limit
0 0.000 1/1
1 16.667 81/80 96/95
2 33.333 49/48 56/55 57/56
3 50.000 36/35 33/32
4 66.667 25/24 28/27 80/77
5 83.333 21/20 22/21
6 100.000 128/121
7 116.667 16/15 15/14 77/72
8 133.333 27/25
9 150.000 160/147 12/11
10 166.667 11/10
11 183.333 10/9 49/44
12 200.000 9/8 28/25 64/57
13 216.667 25/22
112/99
14 233.333 8/7 55/48
15 250.000 22/19
16 266.667 7/6 64/55
17 283.333 33/28 112/95
18 300.000 25/21 19/16
19 316.667 6/5 77/64 160/133
20 333.333 40/33
21 350.000 49/40
60/49 		11/9
27/22
22 366.667 99/80
23 383.333 5/4 56/45 96/77
24 400.000 44/35 24/19
25 416.667 80/63 14/11
26 433.333 9/7
27 450.000 35/27 57/44
28 466.667 21/16
64/49 		72/55
29 483.333 33/25
160/121 		95/72
30 500.000 4/3
31 516.667 27/20 128/95
32 533.333 49/36 15/11 19/14
33 550.000 48/35 11/8
34 566.667 25/18
35 583.333 7/5 88/63 80/57
36 600.000
37 616.667 10/7 63/44 57/40
38 633.333 36/25
39 650.000 35/24 16/11
40 666.667 72/49 22/15 28/19
41 683.333 40/27 95/64
42 700.000 3/2
43 716.667 50/33
121/80 		144/95
44 733.333 32/21
49/32 		55/36
45 750.000 54/35 88/57
46 766.667 14/9
47 783.333 63/40 11/7
48 800.000 35/22 19/12
49 816.667 8/5 45/28 77/48
50 833.333 160/99
51 850.000 49/30
80/49 		18/11
44/27
52 866.667 33/20
53 883.333 5/3 128/77 133/80
54 900.000 42/25 32/19
55 916.667 56/33 95/56
56 933.333 12/7 55/32
57 950.000 19/11
58 966.667 7/4 96/55
59 983.333 44/25
99/56
60 1000.000 16/9 25/14 57/32
61 1016.667 9/5 88/49
62 1033.333 20/11
63 1050.000 147/80 11/6
64 1066.667 50/27
65 1083.333 15/8 28/15 144/77
66 1100.000 121/64
67 1116.667 40/21 21/11
68 1133.333 48/25 27/14 77/40
69 1150.000 35/18 64/33
70 1166.667 96/49 55/28 112/57
71 1183.333 160/81 95/48
72 1200.000 2/1


Intervals of 5edo (as a 5-limit temperament)
Degree Cents Approximated JI intervals
2-limit 3-limit 5-limit
0 0.000 1/1
1 240.000 9/8
32/27 		10/9
2 480.000 4/3 27/20
32/25
3 720.000 3/2 25/16
40/27
4 960.000 16/9
27/16 		9/5
5 1200.000 2/1


Intervals of 13edt (as a 3.5.7 subgroup temperament)
Degree Cents Approximated JI intervals
3-limit 5-limit 7-limit
0 0.000 1/1
1 146.304 27/25
2 292.608 25/21
3 438.913 9/7
35/27
4 585.217 7/5
5 731.521 75/49
6 877.825 5/3 81/49
7 1024.130 9/5 49/27
8 1170.434 49/25
9 1316.738 15/7
10 1463.042 7/3
81/35
11 1609.347 63/25
12 1755.651 25/9
13 1901.955 3/1


Intervals of 7edf (as a 5-limit temperament)
Degree Cents Approximated JI intervals
2-limit 3-limit 5-limit
0 0.000 1/1
1 100.279 16/15
25/24
2 200.559 9/8 10/9
3 300.838 32/27 6/5
75/64
4 401.117 81/64 5/4
32/25
5 501.396 4/3 27/20
6 601.676 36/25
45/32
7 701.955 3/2


Generalized ET/ED intro

For nonoctave equaves: k equal divisions of p/q (abbreviated kedp/q) is a non-octave tuning system based on dividing p/q into k equal pieces of exactly/about s¢ each. Each step of kedp/q represents the frequency ratio of (p/q)1/k or the kth root of p/q.

For edos: k equal divisions of the octave (abbreviated kedo), also called k-tone equal temperament (ktet) or k equal temperament (ket) when viewed under a regular temperament perspective, is the tuning system that divides the octave into k equal parts of exactly/about r¢ each. Each step of kedo represents a frequency ratio of 21/k, or the kth root of 2.

For edts: k equal divisions of the tritave or twelfth (abbreviated kedt or ked3) is a non-octave tuning system that divides the 3rd harmonic, or 3/1, into k equal parts of exactly/about r¢ each. Each step of kedo represents a frequency ratio of 31/k, or the kth root of 3.

For edfs: k equal divisions of the fifth (abbreviated kedf or ked3/2) is a non-octave tuning system that divides the perfect fifth, or 3/2, into k equal parts of exactly/about r¢ each. Each step of kedo represents a frequency ratio of (3/2)1/k, or the kth root of 3/2.

For nonoctave equaves: k equal divisions of p/q (abbreviated kedp/q) is a non-octave tuning system that divides p/q into k equal pieces of exactly/about s¢ each. Each step of kedp/q represents the frequency ratio of (p/q)1/k or the kth root of p/q.

JI ratio intro

For general ratios: m/n, also called interval-name, is a p-limit just intonation ratio of exactly/about r¢.

For harmonics: m/1, also called interval-name, is a just intonation ration that represents the mth harmonic of exactly/about r¢.

MOS step sizes

3L 4s step sizes
Interval Basic 3L 4s

(10edo, L:s = 2:1)

Hard 3L 4s

(13edo, L:s = 3:1)

Soft 3L 4s

(17edo, L:s = 3:2)

Approx. JI ratios
Steps Cents Steps Cents Steps Cents
Large step 2 240¢ 3 276.9¢ 3 211.8¢ Hide column if no ratios given
Small step 1 120¢ 1 92.3¢ 2 141.2¢
Bright generator 3 360¢ 4 369.2¢ 5 355.6¢

Notes:

  • Allow option to show the bright generator, dark generator, or no generator.
  • JI ratios column only shows if there are any ratios to show

Expanded MOS intro

The following pieces of information may be worth adding:

  • Distinguishing between TAMNAMS names from other, noteworthy non-TAMNAMS names. Equave-agnostic names can be treated as TAMNAMS name for appropriate mosses (EG, 4L 1s).
  • The specific step pattern for the true mos. (The template will have a link to the page for rotations.)
  • Simple edos (or ed<p/q>) that support the mos.
  • Support for TAMEX names, or how the mos relates to another, ancestral TAMNAMS-named mos. Extensions include chromatic, enharmonic, subchromatic, and descendant. This requires standardizing the naming scheme for descendant mosses before it can be added.
    • TAMEX is short for temperament-agnostic moment-of-symmetry scale extension naming system.
  • Whether the mos exhibits Rothenberg propriety.

Base wording

xL ys<p/q>, named mosname (also called alt-mosname), is a(n) equave-equivalent moment-of-symmetry scale containing x large steps(s) and y small step(s), repeating every equave. Modes of this scale are based on the step pattern of step-pattern. Equal divisions of the equave that support this scale include basic-ed, hard-ed, and soft-ed. Generators that produce this scale range from g1¢ to g2¢, or from d1¢ or d2¢.

nxL nys<p/q>, named mosname (also called alt-mosname), is a(n) equave-equivalent moment-of-symmetry scale, containing nx large steps(s) and ny small step(s), with a period of x large step(s) and y small steps(s) that repeats every equave-fraction, or n times every equave. Modes of this scale are based on the step pattern of step-pattern. Equal divisions of the equave that support this scale include basic-ed, hard-ed, and soft-ed. Generators that produce this scale range from g1¢ to g2¢, or from d1¢ or d2¢.

Supplemental info

For monosmall and monosmall-per-period mosses: Scales of this form always exhibit Rothenberg propriety because there is only one small step per period.

For mosses that descend from a TAMNAMS-named mos: xL ys<p/q> is a kth-order descendant scale of zL ws<p/q>, an extension of zL ws<p/q> scales with a step-ratio-range step ratio.

Examples

5L 7s, also called p-chromatic, is an octave-equivalent moment of symmetry scale containing 5 large steps and 7 small steps, repeating every octave. 5L 7s is a chromatic scale of 5L 2s, an extension of 5L 2s scales with a hard-of-basic step ratio. Equal divisions of the octave that support this scale's step pattern include 17edo, 22edo, and 29edo. Generators that produce this scale range from 700¢ to 720¢, or from 480¢ to 500¢.

Mbox template test

These would be their own templates.

Mos ancestors and descendants

2nd ancestor 1st ancestor Mos 1st descendants 2nd descendants
uL vs zL ws xL ys xL (x+y)s xL (2x+y)s
(2x+y)L xs
(x+y)L xs (2x+y)L (x+y)s
(x+y)L (2x+y)s
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