User:Ganaram inukshuk/Sandbox: Difference between revisions

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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.
Stub page:
{{Mbox|type=notice|text=This page is a '''stub'''. You can help the Xenharmonic Wiki by expanding it.}}
Page needs cleanup (with example reason):
{{Mbox|type=notice|text=This article may require '''cleanup'''.
Reason: ''page contains advanced concepts.''
You can edit this page to improve it.}}
Page under construction:
{{Mbox|type=notice|text=This article is '''being created or in the process of being rewritten''', and is '''not yet ready for use'''. You are welcome to help with editing this page.}}
==Math symbols test==
===Isolated symbols===
<math>T := [ t_1, t_2, ..., t_m ]</math>
<math>S := [ s_1, s_2, ..., s_m ]</math>
<math>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.
{| class="wikitable sortable" style="text-align: left;"
|+<!-- caption -->Intervals of 2L 5s for each mode
|-
!Mode!!UDP!! align="right" |Rotational order!! align="right" |mosunison!!1-mosstep!!2-mosstep!!3-mosstep!!4-mosstep!!5-mosstep!!6-mosstep!!mosoctave
|-
|LssLsss||6<nowiki>|</nowiki>0|| align="right" |0|| align="right" |0||L||L+s||L+2s||2L+2s||2L+3s||2L+4s||2L+5s
|-
|LsssLss||5<nowiki>|</nowiki>1|| align="right" |3|| align="right" |0||L||L+s||L+2s||L+3s||2L+3s||2L+4s||2L+5s
|-
|sLssLss||4<nowiki>|</nowiki>2|| align="right" |6|| align="right" |0||s||L+s||L+2s||L+3s||2L+3s||2L+4s||2L+5s
|-
|sLsssLs||3<nowiki>|</nowiki>3|| align="right" |2|| align="right" |0||s||L+s||L+2s||L+3s||L+4s||2L+4s||2L+5s
|-
|ssLssLs||2<nowiki>|</nowiki>4|| align="right" |5|| align="right" |0||s||2s||L+2s||L+3s||L+4s||2L+4s||2L+5s
|-
|ssLsssL||1<nowiki>|</nowiki>5|| align="right" |1|| align="right" |0||s||2s||L+2s||L+3s||L+4s||L+5s||2L+5s
|-
|sssLssL||0<nowiki>|</nowiki>6|| align="right" |4|| align="right" |0||s||2s||3s||L+3s||L+4s||L+5s||2L+5s
|}
{| class="wikitable sortable" style="text-align: left;"
|+Degrees of 2L 5s for each mode
|-
!Mode!!UDP!! align="right" |Rotational order!!0-mosdegree!!1-mosdegree!!2-mosdegree!!3-mosdegree!!4-mosdegree!!5-mosdegree!!6-mosdegree!!7-mosdegree
|-
|LssLsss||6<nowiki>|</nowiki>0|| align="right" |0||perfect||major||major||perfect||augmented||major||major||perfect
|-
|LsssLss||5<nowiki>|</nowiki>1|| align="right" |3||perfect||major||major||perfect||perfect||major||major||perfect
|-
|sLssLss||4<nowiki>|</nowiki>2|| align="right" |6||perfect||minor||major||perfect||perfect||major||major||perfect
|-
|sLsssLs||3<nowiki>|</nowiki>3|| align="right" |2||perfect||minor||major||perfect||perfect||minor||major||perfect
|-
|ssLssLs||2<nowiki>|</nowiki>4|| align="right" |5||perfect||minor||minor||perfect||perfect||minor||major||perfect
|-
|ssLsssL||1<nowiki>|</nowiki>5|| align="right" |1||perfect||minor||minor||perfect||perfect||minor||minor||perfect
|-
|sssLssL||0<nowiki>|</nowiki>6|| align="right" |4||perfect||minor||minor||diminished||perfect||minor||minor||perfect
|}
Note: don't merge cells on a table with sorting.
{| class="wikitable sortable" style="text-align: left;"
|+Intervals of 2L 5s for each mode (with mode names)
|-
!Mode
!Mode name!!UDP!! align="right" |Rotational order!! align="right" |mosunison!!1-mosstep!!2-mosstep!!3-mosstep!!4-mosstep!!5-mosstep!!6-mosstep!!mosoctave
|-
|LssLsss
|antilocrian||6<nowiki>|</nowiki>0|| align="right" |0|| align="right" |0||L||L+s||L+2s||2L+2s||2L+3s||2L+4s||2L+5s
|-
|LsssLss
|antiphrygian||5<nowiki>|</nowiki>1|| align="right" |3|| align="right" |0||L||L+s||L+2s||L+3s||2L+3s||2L+4s||2L+5s
|-
|sLssLss
|anti-aeolian||4<nowiki>|</nowiki>2|| align="right" |6|| align="right" |0||s||L+s||L+2s||L+3s||2L+3s||2L+4s||2L+5s
|-
|sLsssLs
|antidorian||3<nowiki>|</nowiki>3|| align="right" |2|| align="right" |0||s||L+s||L+2s||L+3s||L+4s||2L+4s||2L+5s
|-
|ssLssLs
|antimixolydian||2<nowiki>|</nowiki>4|| align="right" |5|| align="right" |0||s||2s||L+2s||L+3s||L+4s||2L+4s||2L+5s
|-
|ssLsssL
|anti-ionian||1<nowiki>|</nowiki>5|| align="right" |1|| align="right" |0||s||2s||L+2s||L+3s||L+4s||L+5s||2L+5s
|-
|sssLssL
|antilydian||0<nowiki>|</nowiki>6|| align="right" |4|| align="right" |0||s||2s||3s||L+3s||L+4s||L+5s||2L+5s
|}
{| class="wikitable sortable" style="text-align: left;"
|+Degrees of 2L 5s for each mode (with mode names)
|-
!Mode
!Mode name!!UDP!! align="right" |Rotational order!!0-mosdegree!!1-mosdegree!!2-mosdegree!!3-mosdegree!!4-mosdegree!!5-mosdegree!!6-mosdegree!!7-mosdegree
|-
|LssLsss
|antilocrian||6<nowiki>|</nowiki>0|| align="right" |0||perfect||major||major||perfect||augmented||major||major||perfect
|-
|LsssLss
|antiphrygian||5<nowiki>|</nowiki>1|| align="right" |3
|perfect
|major
|major
|perfect||perfect
|major
|major||perfect
|-
|sLssLss
|anti-aeolian||4<nowiki>|</nowiki>2|| align="right" |6
|perfect||minor
|major
|perfect
|perfect
|major
|major||perfect
|-
|sLsssLs
|antidorian||3<nowiki>|</nowiki>3|| align="right" |2
|perfect
|minor
|major
|perfect
|perfect||minor
|major||perfect
|-
|ssLssLs
|antimixolydian||2<nowiki>|</nowiki>4|| align="right" |5
|perfect
|minor||minor
|perfect
|perfect
|minor
|major||perfect
|-
|ssLsssL
|anti-ionian||1<nowiki>|</nowiki>5|| align="right" |1
|perfect
|minor
|minor
|perfect
|perfect
|minor||minor||perfect
|-
|sssLssL
|antilydian||0<nowiki>|</nowiki>6|| align="right" |4
|perfect
|minor
|minor||diminished
|perfect
|minor
|minor||perfect
|}
==Alternate mos tables==
{| class="wikitable sortable"
!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)==
{| class="wikitable"
! colspan="6" |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
| rowspan="3" |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
| rowspan="3" |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
| rowspan="3" |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
| rowspan="3" |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
| rowspan="3" |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
| rowspan="3" |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
| rowspan="3" |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
| rowspan="3" |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===
===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

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