User:Ganaram inukshuk/Sandbox: Difference between revisions
Cleanup sandbox; added JI ratio intros and ED intros |
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===Generalized ET/ED intro=== | ===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)<sup>1/k</sup> or the kth root of p/q. | 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)<sup>1/k</sup> 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 3<sup>1/k</sup>, 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)<sup>1/k</sup>, 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)<sup>1/k</sup> 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=== | ===MOS step sizes=== | ||
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===Mbox template test=== | ===Mbox template test=== | ||
These would be their own templates. | These would be their own templates. | ||
===Mos ancestors and descendants=== | ===Mos ancestors and descendants=== |
Revision as of 01:40, 28 January 2024
This is a sandbox page for me (Ganaram) to test out a few things before deploying things. (Expect some mess.)
Template test area
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 |
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 |
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 |
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 |
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
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 |