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Cleanup sandbox; added JI ratio intros and ED intros
Line 14: Line 14:
===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===
Retrieved from "https://en.xen.wiki/w/User:Ganaram_inukshuk/Sandbox"