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Templat testing
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== Template test area==
== Template test area==
{{JI ratios in ED|ED=12|Prime Limit=7}}
{{JI ratios in ED|ED=72|Prime Limit=23}}


{{JI ratios in ED|ED=5|Prime Limit=5}}
{{JI ratios in ED|ED=5|Prime Limit=5}}

Revision as of 00:13, 26 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

Intervals of 72edo (as a 23-limit temperament)
Degree Cents Approximated JI intervals
2-limit 3-limit 5-limit 7-limit 11-limit 13-limit 17-limit 19-limit 23-limit
0 0.000 1/1
1 16.667 96/95
2 33.333 49/48 56/55 52/51
3 50.000 36/35 33/32 34/33
35/34
4 66.667 25/24 28/27 80/77 26/25
27/26
5 83.333 21/20 22/21
6 100.000 52/49 17/16
18/17
7 116.667 16/15 15/14
8 133.333 27/25
9 150.000 12/11
10 166.667 11/10 56/51
11 183.333 10/9 49/44
12 200.000 9/8 28/25 64/57
13 216.667 25/22 17/15 26/23
14 233.333 8/7 55/48 39/34
15 250.000 15/13
52/45 		22/19
16 266.667 7/6 64/55
17 283.333 33/28 20/17 46/39
18 300.000 25/21 19/16
19 316.667 6/5
20 333.333 40/33 17/14 23/19
21 350.000 49/40
60/49 		11/9
27/22
22 366.667 26/21 21/17
68/55
23 383.333 5/4 56/45 96/77
24 400.000 44/35 34/27 24/19
25 416.667 80/63 14/11 33/26 51/40 88/69
26 433.333 9/7 50/39
27 450.000 35/27 13/10 22/17 57/44
28 466.667 21/16
64/49 		72/55 17/13
29 483.333 33/25 45/34
30 500.000 4/3
31 516.667 27/20 35/26
32 533.333 49/36 15/11 34/25 19/14
33 550.000 48/35 11/8
34 566.667 25/18 18/13 68/49
35 583.333 7/5 88/63 80/57
36 600.000 17/12
24/17
37 616.667 10/7 63/44 57/40
38 633.333 36/25 13/9 49/34
39 650.000 35/24 16/11
40 666.667 72/49 22/15 25/17 28/19
41 683.333 40/27 52/35
42 700.000 3/2
43 716.667 50/33 68/45
44 733.333 32/21
49/32 		55/36 26/17
45 750.000 54/35 20/13 17/11 88/57
46 766.667 14/9 39/25
47 783.333 63/40 11/7 52/33 80/51 69/44
48 800.000 35/22 27/17 19/12
49 816.667 8/5 45/28 77/48
50 833.333 21/13 34/21
55/34
51 850.000 49/30
80/49 		18/11
44/27
52 866.667 33/20 28/17 38/23
53 883.333 5/3
54 900.000 42/25 32/19
55 916.667 56/33 17/10 39/23
56 933.333 12/7 55/32
57 950.000 26/15
45/26 		19/11
58 966.667 7/4 96/55 68/39
59 983.333 44/25 30/17 23/13
60 1000.000 16/9 25/14 57/32
61 1016.667 9/5 88/49
62 1033.333 20/11 51/28
63 1050.000 11/6
64 1066.667 50/27
65 1083.333 15/8 28/15
66 1100.000 49/26 17/9
32/17
67 1116.667 40/21 21/11
68 1133.333 48/25 27/14 77/40 25/13
52/27
69 1150.000 35/18 64/33 33/17
68/35
70 1166.667 96/49 55/28 51/26
71 1183.333 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 1ed9/8 (as a 3.5.7 subgroup temperament)
Degree Cents Approximated JI intervals
3-limit 5-limit 7-limit
0 0.000 1/1
1 203.910 9/8


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.

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.

Stub page:

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Reason: page contains advanced concepts. You can edit this page to improve it.

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Math symbols test

Isolated symbols

[math]\displaystyle{ T := [ t_1, t_2, ..., t_m ] }[/math] [math]\displaystyle{ S := [ s_1, s_2, ..., s_m ] }[/math] [math]\displaystyle{ P := [ p_1, p_2, ..., p_n ] }[/math]

Sample text

Pulled from muddle page.

Let the target scale T be a sequence of steps [ t1, t2, t3, ... , tm ], the parent scale P be a sequence of steps [ p1, p2, p3, ... , pn ], and the resulting muddle scale S be a sequence of steps [ s1, s2, s3, ... , sm ]. Note that the number of steps in P must be equal to the sum of all ti from T. Also note that both ti and pi are both numeric values, as with si.

The first step s1 of the muddle scale is the sum of the first t1 steps from P, the next step s2 is the sum of the next t2 steps after that (after the previous t1 steps), the next step s3 is the sum of the next t3 steps after that (after the previous t1+t2 steps), and so on, where the last step sm is the sum of the last tm steps from P. For example, if s1 is made from the first 3 steps of P (p1, p2, and p3), then the next step p2 is the sum of the next t2 steps after p3, meaning the sum starts at (and includes) p4.

Interval and degree tables

The following two tables were made using a custom program (dubbed Moscalc and Modecalc) whose output is formatted for use with MediaWiki.

Intervals of 2L 5s for each mode
Mode UDP Rotational order mosunison 1-mosstep 2-mosstep 3-mosstep 4-mosstep 5-mosstep 6-mosstep mosoctave
LssLsss 6|0 0 0 L L+s L+2s 2L+2s 2L+3s 2L+4s 2L+5s
LsssLss 5|1 3 0 L L+s L+2s L+3s 2L+3s 2L+4s 2L+5s
sLssLss 4|2 6 0 s L+s L+2s L+3s 2L+3s 2L+4s 2L+5s
sLsssLs 3|3 2 0 s L+s L+2s L+3s L+4s 2L+4s 2L+5s
ssLssLs 2|4 5 0 s 2s L+2s L+3s L+4s 2L+4s 2L+5s
ssLsssL 1|5 1 0 s 2s L+2s L+3s L+4s L+5s 2L+5s
sssLssL 0|6 4 0 s 2s 3s L+3s L+4s L+5s 2L+5s


Degrees of 2L 5s for each mode
Mode UDP Rotational order 0-mosdegree 1-mosdegree 2-mosdegree 3-mosdegree 4-mosdegree 5-mosdegree 6-mosdegree 7-mosdegree
LssLsss 6|0 0 perfect major major perfect augmented major major perfect
LsssLss 5|1 3 perfect major major perfect perfect major major perfect
sLssLss 4|2 6 perfect minor major perfect perfect major major perfect
sLsssLs 3|3 2 perfect minor major perfect perfect minor major perfect
ssLssLs 2|4 5 perfect minor minor perfect perfect minor major perfect
ssLsssL 1|5 1 perfect minor minor perfect perfect minor minor perfect
sssLssL 0|6 4 perfect minor minor diminished perfect minor minor perfect

Note: don't merge cells on a table with sorting.

Intervals of 2L 5s for each mode (with mode names)
Mode Mode name UDP Rotational order mosunison 1-mosstep 2-mosstep 3-mosstep 4-mosstep 5-mosstep 6-mosstep mosoctave
LssLsss antilocrian 6|0 0 0 L L+s L+2s 2L+2s 2L+3s 2L+4s 2L+5s
LsssLss antiphrygian 5|1 3 0 L L+s L+2s L+3s 2L+3s 2L+4s 2L+5s
sLssLss anti-aeolian 4|2 6 0 s L+s L+2s L+3s 2L+3s 2L+4s 2L+5s
sLsssLs antidorian 3|3 2 0 s L+s L+2s L+3s L+4s 2L+4s 2L+5s
ssLssLs antimixolydian 2|4 5 0 s 2s L+2s L+3s L+4s 2L+4s 2L+5s
ssLsssL anti-ionian 1|5 1 0 s 2s L+2s L+3s L+4s L+5s 2L+5s
sssLssL antilydian 0|6 4 0 s 2s 3s L+3s L+4s L+5s 2L+5s
Degrees of 2L 5s for each mode (with mode names)
Mode Mode name UDP Rotational order 0-mosdegree 1-mosdegree 2-mosdegree 3-mosdegree 4-mosdegree 5-mosdegree 6-mosdegree 7-mosdegree
LssLsss antilocrian 6|0 0 perfect major major perfect augmented major major perfect
LsssLss antiphrygian 5|1 3 perfect major major perfect perfect major major perfect
sLssLss anti-aeolian 4|2 6 perfect minor major perfect perfect major major perfect
sLsssLs antidorian 3|3 2 perfect minor major perfect perfect minor major perfect
ssLssLs antimixolydian 2|4 5 perfect minor minor perfect perfect minor major perfect
ssLsssL anti-ionian 1|5 1 perfect minor minor perfect perfect minor minor perfect
sssLssL antilydian 0|6 4 perfect minor minor diminished perfect minor minor perfect

Alternate mos tables

Pattern Number of notes Number of periods Name Prefix
1L 1s 2 1 trivial triv-
1L 1s 2 1 monowood monowd-
1L 2s 3 1 antrial atri-
2L 1s 3 1 trial tri-
1L 3s 4 1 antetric atetra-
2L 2s 4 2 biwood biwd-
3L 1s 4 1 tetric tetra-
1L 4s 5 1 pedal ped-
2L 3s 5 1 pentic pent-
3L 2s 5 1 antipentic apent-
4L 1s 5 1 manual manu-
1L 5s 6 1 antimachinoid amech-
2L 4s 6 2 anticitric acitro-
3L 3s 6 3 triwood triwd-
4L 2s 6 2 citric citro-
5L 1s 6 1 machinoid mech-
1L 6s 7 1 onyx on-
2L 5s 7 1 antidiatonic pel-
3L 4s 7 1 mosh mosh-
4L 3s 7 1 smitonic smi-
5L 2s 7 1 diatonic none
6L 1s 7 1 arch(a)eotonic arch-
1L 7s 8 1 antipine apine-
2L 6s 8 2 antiekic anek-
3L 5s 8 1 checkertonic check-
4L 4s 8 4 tetrawood; diminished tetwd-
5L 3s 8 1 oneirotonic neiro-
6L 2s 8 2 ekic ek-
7L 1s 8 1 pine pine-
1L 8s 9 1 antisubneutralic ablu-
2L 7s 9 1 balzano bal- /bæl/
3L 6s 9 3 tcherepnin cher-
4L 5s 9 1 gramitonic gram-
5L 4s 9 1 semiquartal cthon-
6L 3s 9 3 hyrulic hyru-
7L 2s 9 1 superdiatonic arm-
8L 1s 9 1 subneutralic blu-
1L 9s 10 1 antisinatonic asina-
2L 8s 10 2 jaric jara-
3L 7s 10 1 sephiroid seph-
4L 6s 10 2 lime lime-
5L 5s 10 5 pentawood penwd-
6L 4s 10 2 lemon lem-
7L 3s 10 1 dicoid /'daɪkɔɪd/ dico-
8L 2s 10 2 taric tara-
9L 1s 10 1 sinatonic sina-

Scale trees of 1L 1s, 1L 2s, and 2L 1s (sandbox)

Generator Bright gen. Dark gen. L s L/s Ranges of mosses
1\2 600.000 600.000 1 1 1.000
6\11 654.545 545.455 6 5 1.200 2L 5s range (includes 2L 7s and 7L 2s)
5\9 666.667 533.333 5 4 1.250
9\16 675.000 525.000 9 7 1.286
4\7 685.714 514.286 4 3 1.333 Basic 2L 3s
11\19 694.737 505.263 11 8 1.375 5L 2s range (includes 7L 5s and 5L 7s)
7\12 700.000 500.000 7 5 1.400
10\17 705.882 494.118 10 7 1.429
3\5 720.000 480.000 3 2 1.500 Basic 2L 1s
11\18 733.333 466.667 11 7 1.571 5L 3s range
8\13 738.462 461.538 8 5 1.600
13\21 742.857 457.143 13 8 1.625
5\8 750.000 450.000 5 3 1.667 Basic 3L 2s
12\19 757.895 442.105 12 7 1.714 3L 5s range
7\11 763.636 436.364 7 4 1.750
9\14 771.429 428.571 9 5 1.800
2\3 800.000 400.000 2 1 2.000 Basic 1L 1s (dividing line between 2L 1s and 1L 2s)
9\13 830.769 369.231 9 4 2.250 3L 4s range (includes 3L 7s and 7L 3s)
7\10 840.000 360.000 7 3 2.333
12\17 847.059 352.941 12 5 2.400
5\7 857.143 342.857 5 2 2.500 Basic 3L 1s
13\18 866.667 333.333 13 5 2.600 4L 3s range
8\11 872.727 327.273 8 3 2.667
11\15 880.000 320.000 11 4 2.750
3\4 900.000 300.000 3 1 3.000 Basic 1L 2s
10\13 923.077 276.923 10 3 3.333 Range of 1L 4s (includes 4L 5s and 5L 4s)
7\9 933.333 266.667 7 2 3.500
11\14 942.857 257.143 11 3 3.667
4\5 960.000 240.000 4 1 4.000 Basic 1L 4s
9\11 981.818 218.182 9 2 4.500 Range of 4L 1s (includes 5L 1s and 1L 5s)
5\6 1000.000 200.000 5 1 5.000
6\7 1028.571 171.429 6 1 6.000
1\1 1200.000 0.000 1 0 → inf

Module and template sandbox

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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