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This page is for xen-related tables that I've made but don't have an exact place elsewhere on the wiki (yet).
This page is for xen-related tables that I've made but don't have an exact place elsewhere on the wiki (yet).


== Scale Table ==
== Golden ratio tunings of mosses ==
I've had the idea of using a [[User:Ganaram inukshuk/Diagrams#MOS Diagrams for a Specific EDO|rectangular horogram]] to represent how mosses of a specific generator pair are related to one another, only to learn that I can copy-paste the entire tables from Excel into the wiki editor. I doubt I'd be the first person to do this, but this would be a nice way to list the mosses of an edo. The idea to include scale and step ratio information occurred mid-editing. Here's a few examples.
 
=== Temperament Agnostic Information Only ===
Notes:
* The generator pairs are ordered starting from ceil(n/2)\n and floor(n/2)\n and ending at (n-2)\n and 2\n. Including every possible pair from 1\n to (n-1)\n to (n-1)\n to 1\n would be redundant since the pair k\n and (n-k)\n would produce a table that's identical to (n-k)\n and k\n but reversed.
* (n-1)\n and 1\n is not included since it produces a sequence of "monolarge" scales where every scale in the table has the same size of small step.
* Information from the page for [[19edo]] and its subpages (as of time of writing) is used as sample data.
* A few unnamed mosses are given tentative names based on names from their respective pages (EG, klesitonic) or based on existing names (EG, tetric).
{| class="wikitable"
{| class="wikitable"
! colspan="19" |'''Step Pattern (19edo)'''
!Parent scale
!'''Mos'''
!Child scale
!'''[[TAMNAMS#Step ratio spectrum|Step Ratio]]'''
!Grandchild scale
!'''[[TAMNAMS#Mos pattern names|TAMNAMS Name]] (if applicable)'''
!Great-grandchild scale
!4th-order descendant
!5th-order descendant
!6-order descendant
|-
|-
| colspan="10" |10
!xL ys
| colspan="9" |9
!(x+y)L xs
|1L 1s
!(2x+y)L (x+y)s
|10:9
!(3x+2y)L (2x+y)s
|Generator Pair
!(5x+3y)L (3x+2y)s
!(8x+5y)L (5x+3y)s
!(13x+8y)L (8x+5y)s
|-
|-
|1
! colspan="7" |
| colspan="9" |9
| colspan="9" |9
|2L 1s
|9:1
|
|-
|-
|1
|1L 5s
|1
|6L 1s
| colspan="8" |8
|7L 6s
|1
|13L 7s
| colspan="8" |8
|20L 13s
|[[2L 3s]]
|33L 20s
|8:1
|53L 33s
|Pentic
|-
|-
|1
|2L 4s
|1
|6L 2s
|1
|8L 6s
| colspan="7" |7
|14L 8s
|1
|22L 14s
|1
|36L 22s
| colspan="7" |7
|58L 36s
|[[2L 5s]]
|7:1
|Antidiatonic
|-
|-
|1
|3L 3s
|1
|6L 3s
|1
|9L 6s
|1
|15L 9s
| colspan="6" |6
|24L 15s
|1
|39L 24s
|1
|63L 39s
|1
| colspan="6" |6
|[[2L 7s]]
|6:1
|Joanatonic
|-
|-
|1
|4L 3s
|1
|7L 4s
|1
|11L 7s
|1
|18L 11s
|1
|29L 18s
| colspan="5" |5
|47L 29s
|1
|76L 47s
|1
|1
|1
| colspan="5" |5
|[[2L 9s]]
|5:1
|
|-
|-
|1
|5L 1s
|1
|6L 5s
|1
|11L 6s
|1
|17L 11s
|1
|28L 17s
|1
|45L 28s
| colspan="4" |4
|73L 45s
|1
|1
|1
|1
|1
| colspan="4" |4
|[[2L 11s]]
|4:1
|
|-
|-
|1
! colspan="7" |
|1
|1
|1
|1
|1
|1
| colspan="3" |3
|1
|1
|1
|1
|1
|1
| colspan="3" |3
|[[2L 13s]]
|3:1
|
|-
|-
|1
|1L 6s
|1
|7L 1s
|1
|8L 7s
|1
|15L 8s
|1
|23L 15s
|1
|38L 23s
|1
|61L 38s
|1
| colspan="2" |2
|1
|1
|1
|1
|1
|1
|1
| colspan="2" |2
|[[2L 15s]]
|2:1
|
|-
|-
|1
|2L 5s
|1
|7L 2s
|1
|9L 7s
|1
|16L 9s
|1
|25L 16s
|1
|41L 25s
|1
|66L 41s
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="3" |
|}
{| class="wikitable"
! colspan="19" |'''Step Pattern (19edo)'''
!'''Mos'''
!'''Step Ratio'''
!'''TAMNAMS Name (if applicable)'''
|-
|-
| colspan="11" |11
|3L 4s
| colspan="8" |8
|7L 3s
|1L 1s
|10L 7s
|11:8
|17L 10s
|Generator Pair
|27L 17s
|44L 27s
|71L 44s
|-
|-
| colspan="3" |3
|4L 3s
| colspan="8" |8
|7L 4s
| colspan="8" |8
|11L 7s
|2L 1s
|18L 11s
|8:3
|29L 18s
|
|47L 29s
|76L 47s
|-
|-
| colspan="3" |3
|5L 2s
| colspan="3" |3
|7L 5s
| colspan="5" |5
|12L 7s
| colspan="3" |3
|19L 12s
| colspan="5" |5
|31L 19s
|[[2L 3s]]
|50L 31s
|5:3
|81L 50s
|Pentic
|-
|-
| colspan="3" |3
|6L 1s
| colspan="3" |3
|7L 6s
| colspan="3" |3
|13L 7s
| colspan="2" |2
|20L 13s
| colspan="3" |3
|33L 20s
| colspan="3" |3
|53L 33s
| colspan="2" |2
|86L 53s
|[[5L 2s]]
|3:2
|Diatonic
|-
|-
|1
! colspan="7" |
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|[[7L 5s]]
|2:1
|M-chromatic
|-
|-
|1
|1L 7s
|1
|8L 1s
|1
|9L 8s
|1
|17L 9s
|1
|26L 17s
|1
|43L 26s
|1
|69L 43s
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="3" |
|}
{| class="wikitable"
! colspan="19" |'''Step Pattern (19edo)'''
!'''Mos'''
!'''Step Ratio'''
!'''TAMNAMS Name (if applicable)'''
|-
|-
| colspan="12" |12
|2L 6s
| colspan="7" |7
|8L 2s
|1L 1s
|10L 8s
|12:7
|18L 10s
|Generator Pair
|28L 18s
|46L 28s
|74L 46s
|-
|-
| colspan="5" |5
|3L 5s
| colspan="7" |7
|8L 3s
| colspan="7" |7
|11L 8s
|2L 1s
|19L 11s
|7:5
|30L 19s
|
|49L 30s
|79L 49s
|-
|-
| colspan="5" |5
|4L 4s
| colspan="5" |5
|8L 4s
| colspan="2" |2
|12L 8s
| colspan="5" |5
|20L 12s
| colspan="2" |2
|32L 20s
|[[3L 2s]]
|52L 32s
|5:2
|84L 52s
|Antipentic
|-
|-
| colspan="3" |3
|5L 3s
| colspan="2" |2
|8L 5s
| colspan="3" |3
|13L 8s
| colspan="2" |2
|21L 13s
| colspan="2" |2
|34L 21s
| colspan="3" |3
|55L 34s
| colspan="2" |2
|89L 55s
| colspan="2" |2
|[[3L 5s]]
|3:2
|Sensoid
|-
|-
|1
|6L 2s
| colspan="2" |2
|8L 6s
| colspan="2" |2
|14L 8s
|1
|22L 14s
| colspan="2" |2
|36L 22s
| colspan="2" |2
|58L 36s
| colspan="2" |2
|94L 58s
|1
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[8L 3s]]
|2:1
|
|-
|-
|1
|7L 1s
|1
|8L 7s
|1
|15L 8s
|1
|23L 15s
|1
|38L 23s
|1
|61L 38s
|1
|99L 61s
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="3" |
|}
{| class="wikitable"
! colspan="19" |'''Step Pattern (19edo)'''
!'''Mos'''
!'''Step Ratio'''
!'''TAMNAMS Name (if applicable)'''
|-
|-
| colspan="13" |13
! colspan="7" |
| colspan="6" |6
|1L 1s
|13:6
|Generator Pair
|-
|-
| colspan="7" |7
|1L 8s
| colspan="6" |6
|9L 1s
| colspan="6" |6
|10L 9s
|1L 2s
|19L 10s
|7:6
|29L 19s
|
|48L 29s
|77L 48s
|-
|-
|1
|2L 7s
| colspan="6" |6
|9L 2s
| colspan="6" |6
|11L 9s
| colspan="6" |6
|20L 11s
|[[3L 1s]]
|31L 20s
|6:1
|51L 31s
|Tetric (placeholder name for sake of completness)
|82L 51s
|-
|-
|1
|3L 6s
|1
|9L 3s
| colspan="5" |5
|12L 9s
|1
|21L 12s
| colspan="5" |5
|33L 21s
|1
|54L 33s
| colspan="5" |5
|87L 54s
|[[3L 4s]]
|5:1
|Mosh
|-
|-
|1
|4L 5s
|1
|9L 4s
|1
|13L 9s
| colspan="4" |4
|22L 13s
|1
|35L 22s
|1
|57L 35s
| colspan="4" |4
|92L 57s
|1
|1
| colspan="4" |4
|[[3L 7s]]
|4:1
|Sephiroid
|-
|-
|1
|5L 4s
|1
|9L 5s
|1
|14L 9s
|1
|23L 14s
| colspan="3" |3
|37L 23s
|1
|60L 37s
|1
|97L 60s
|1
| colspan="3" |3
|1
|1
|1
| colspan="3" |3
|[[3L 10s]]
|3:1
|
|-
|-
|1
|6L 3s
|1
|9L 6s
|1
|15L 9s
|1
|24L 15s
|1
|39L 24s
| colspan="2" |2
|63L 39s
|1
|102L 63s
|1
|1
|1
| colspan="2" |2
|1
|1
|1
|1
| colspan="2" |2
|[[3L 13s]]
|2:1
|
|-
|-
|1
|7L 2s
|1
|9L 7s
|1
|16L 9s
|1
|25L 16s
|1
|41L 25s
|1
|66L 41s
|1
|107L 66s
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="3" |
|}
{| class="wikitable"
! colspan="19" |'''Step Pattern (19edo)'''
!'''Mos'''
!'''Step Ratio'''
!'''TAMNAMS Name (if applicable)'''
|-
|-
| colspan="14" |14
|8L 1s
| colspan="5" |5
|9L 8s
|1L 1s
|17L 9s
|14:5
|26L 17s
|Generator Pair
|43L 26s
|69L 43s
|112L 69s
|-
|-
| colspan="9" |9
! colspan="7" |
| colspan="5" |5
| colspan="5" |5
|1L 2s
|9:5
|
|-
|-
| colspan="4" |4
|1L 9s
| colspan="5" |5
|10L 1s
| colspan="5" |5
|11L 10s
| colspan="5" |5
|21L 11s
|[[3L 1s]]
|32L 21s
|5:4
|53L 32s
|Tetric
|85L 53s
|-
|-
| colspan="4" |4
|2L 8s
| colspan="4" |4
|10L 2s
|1
|12L 10s
| colspan="4" |4
|22L 12s
|1
|34L 22s
| colspan="4" |4
|56L 34s
|1
|90L 56s
|[[4L 3s]]
|4:1
|Smitonic
|-
|-
| colspan="3" |3
|3L 7s
|1
|10L 3s
| colspan="3" |3
|13L 10s
|1
|23L 13s
|1
|36L 23s
| colspan="3" |3
|59L 36s
|1
|95L 59s
|1
| colspan="3" |3
|1
|1
|[[4L 7s]]
|3:1
|Kleistonic (proposed name from 4L 7s page)
|-
|-
| colspan="2" |2
|4L 6s
|1
|10L 4s
|1
|14L 10s
| colspan="2" |2
|24L 14s
|1
|38L 24s
|1
|62L 38s
|1
|100L 62s
| colspan="2" |2
|1
|1
|1
| colspan="2" |2
|1
|1
|1
|[[4L 11s]]
|2:1
|
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="3" |
|}
{| class="wikitable"
! colspan="19" |'''Step Pattern (19edo)'''
!'''Mos'''
!'''Step Ratio'''
!'''TAMNAMS Name (if applicable)'''
|-
|-
| colspan="15" |15
|5L 5s
| colspan="4" |4
|10L 5s
|1L 1s
|15L 10s
|15:4
|25L 15s
|Generator Pair
|40L 25s
|65L 40s
|105L 65s
|-
|-
| colspan="11" |11
|6L 4s
| colspan="4" |4
|10L 6s
| colspan="4" |4
|16L 10s
|1L 2s
|26L 16s
|11:4
|42L 26s
|
|68L 42s
|110L 68s
|-
|-
| colspan="7" |7
|7L 3s
| colspan="4" |4
|10L 7s
| colspan="4" |4
|17L 10s
| colspan="4" |4
|27L 17s
|[[1L 3s]]
|44L 27s
|7:4
|71L 44s
|
|115L 71s
|-
|-
| colspan="3" |3
|8L 2s
| colspan="4" |4
|10L 8s
| colspan="4" |4
|18L 10s
| colspan="4" |4
|28L 18s
| colspan="4" |4
|46L 28s
|[[4L 1s]]
|74L 46s
|4:3
|120L 74s
|Manic
|-
|-
| colspan="3" |3
|9L 1s
| colspan="3" |3
|10L 9s
|1
|19L 10s
| colspan="3" |3
|29L 19s
|1
|48L 29s
| colspan="3" |3
|77L 48s
|1
|125L 77s
| colspan="3" |3
|}
|1
 
|[[5L 4s]]
== Scale Table ==
|3:1
I've had the idea of using a [[User:Ganaram inukshuk/Diagrams#MOS Diagrams for a Specific EDO|rectangular horogram]] to represent how mosses of a specific generator pair are related to one another, only to learn that I can copy-paste the entire tables from Excel into the wiki editor. I doubt I'd be the first person to do this, but this would be a nice way to list the mosses of an edo. The idea to include scale and step ratio information occurred mid-editing.
|Semiquartal
 
Deployed examples can be found under [[MOS scales of 17edo|17edo mos scales]] and [[31edo MOS scales|31edo mos scales]].
{| class="wikitable mw-collapsible"
! colspan="12" |Mos Family Tree (single-period only), with TAMNAMS Names
italics denote 1L ns scales (named for completeness); asterisks denote non-official names (from my own notes)
|-
|-
| colspan="2" |2
! colspan="2" |Progenitor scale
|1
! colspan="2" |1st-order child mosses
| colspan="2" |2
! colspan="2" |2nd-order child mosses
|1
! colspan="2" |3rd-order child mosses
|1
! colspan="2" |4th-order child mosses
| colspan="2" |2
! colspan="2" |5th-order child mosses
|1
|1
| colspan="2" |2
|1
|1
| colspan="2" |2
|1
|1
|[[5L 9s]]
|2:1
|
|-
|-
|1
!Steps
|1
!Scale name
|1
!Steps
|1
!Scale name
|1
!Steps
|1
!Scale name
|1
!Steps
|1
!Scale name
|1
!Steps
|1
!Scale name
|1
!Steps
|1
!Scale name
|1
|1
|1
|1
|1
|1
|1
| colspan="3" |
|}
{| class="wikitable"
! colspan="19" |'''Step Pattern (19edo)'''
!'''Mos'''
!'''Step Ratio'''
!'''TAMNAMS Name (if applicable)'''
|-
|-
| colspan="16" |16
| rowspan="63" |1L 1s
| colspan="3" |3
| rowspan="63" |prototonic*
|1L 1s
| rowspan="31" |1L 2s
|16:3
| rowspan="31" |<blockquote>''antideuteric*''</blockquote>
|Generator Pair
| rowspan="15" |1L 3s
| rowspan="15" |''antitetric*''
| rowspan="7" |1L 4s
| rowspan="7" |''antimanic''
| rowspan="3" |1L 5s
| rowspan="3" |''antimachinoid''
|1L 6s
|''anti-archeotonic''
|-
|-
| colspan="13" |13
| colspan="3" |3
| colspan="3" |3
|1L 2s
|13:3
|
|
|-
| colspan="10" |10
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
|[[1L 3s]]
|10:3
|
|
|-
|-
| colspan="7" |7
|6L 1s
| colspan="3" |3
|archeotonic
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
|[[1L 4s]]
|7:3
|
|-
|-
| colspan="4" |4
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
|[[1L 5s]]
|4:3
|
|
|-
|1
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
|[[6L 1s]]
|3:1
|Archeotonic
|-
|1
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|[[6L 7s]]
|2:1
|
|
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="3" |
|}
{| class="wikitable"
! colspan="19" |'''Step Pattern (19edo)'''
!'''Mos'''
!'''Step Ratio'''
!'''TAMNAMS Name (if applicable)'''
|-
| colspan="17" |17
| colspan="2" |2
|1L 1s
|17:2
|Generator Pair
|-
| colspan="15" |15
| colspan="2" |2
| colspan="2" |2
|1L 2s
|15:2
|
|
|-
| colspan="13" |13
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[1L 3s]]
|13:2
|
|
|-
|-
| colspan="11" |11
| rowspan="3" |5L 1s
| colspan="2" |2
| rowspan="3" |machinoid
| colspan="2" |2
|5L 6s
| colspan="2" |2
| colspan="2" |2
|[[1L 4s]]
|11:2
|
|
|-
|-
| colspan="9" |9
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[1L 5s]]
|9:2
|
|
|-
| colspan="7" |7
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[1L 6s]]
|7:2
|
|
|-
|-
| colspan="5" |5
|6L 5s
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[1L 7s]]
|5:2
|
|
|-
|-
| colspan="3" |3
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[1L 8s]]
|3:2
|
|
|-
|1
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[9L 1s]]
|2:1
|Sinatonic
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="3" |
|}
=== General (Temperament-Agnostic) Information and Temperament Information ===
Notes:
* The generator pairs are ordered starting from ceil(n/2)\n and floor(n/2)\n and ending at (n-2)\n and 2\n. Including every possible pair from 1\n to (n-1)\n to (n-1)\n to 1\n would be redundant since the pair k\n and (n-k)\n would produce a table that's identical to (n-k)\n and k\n but reversed.
* <s>(n-1)\n and 1\n is not included since it produces a sequence of "monolarge" scales where every scale in the table has the same size of small step.</s>
* Information from the page for [[19edo]] and its subpages (as of time of writing) is used as sample data.
* A few unnamed mosses are given tentative names based on names from their respective pages (EG, klesitonic) or based on existing names (EG, tetric).
* Scale codes are given for scales whose step sizes are single-digit numbers.
{| class="wikitable"
! colspan="19" |Step Pattern
! colspan="4" |General Information
!Temperament Information
|-
! colspan="19" |Generator pair of 10\19 and 9\19
!Scale Code
!Mos
![[TAMNAMS#Step%20ratio%20spectrum|Step Ratio]]
![[TAMNAMS#Mos%20pattern%20names|TAMNAMS Name]]
!Scales
|-
| colspan="10" |10
| colspan="9" |9
|
|
|1L 1s
|10:9
|
|
|
|
|-
|1
| colspan="9" |9
| colspan="9" |9
|199
|2L 1s
|9:1
|
|
|
|
|-
|-
|1
| rowspan="7" |4L 1s
|1
| rowspan="7" |manic
| colspan="8" |8
| rowspan="3" |4L 5s
|1
| rowspan="3" |orwelloid
| colspan="8" |8
|4L 9s
|11818
|
|[[2L 3s]]
|8:1
|pentic
|[[liese]][5]
|-
|-
|1
|1
|1
| colspan="7" |7
|1
|1
| colspan="7" |7
|1117117
|[[2L 5s]]
|7:1
|antidiatonic
|liese[7]
|-
|1
|1
|1
|1
| colspan="6" |6
|1
|1
|1
| colspan="6" |6
|111161116
|[[2L 7s]]
|6:1
|joanatonic
|liese[9]
|-
|1
|1
|1
|1
|1
| colspan="5" |5
|1
|1
|1
|1
| colspan="5" |5
|11111511115
|[[2L 9s]]
|5:1
|
|
|liese[11]
|
|-
|-
|1
|9L 4s
|1
|1
|1
|1
|1
| colspan="4" |4
|1
|1
|1
|1
|1
| colspan="4" |4
|1111114111114
|[[2L 11s]]
|4:1
|
|
|liese[13]
|-
|-
|1
|1
|1
|1
|1
|1
|1
| colspan="3" |3
|1
|1
|1
|1
|1
|1
| colspan="3" |3
|111111131111113
|[[2L 13s]]
|3:1
|
|
|liese[15]
|-
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="2" |2
|1
|1
|1
|1
|1
|1
|1
| colspan="2" |2
|11111111211111112
|[[2L 15s]]
|2:1
|
|
|liese[17]
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="5" |
|-
! colspan="19" |Generator pair of 11\19 and 8\19
!Scale Code
!Mos
!Step Ratio
!TAMNAMS Name
!Scales
|-
| colspan="11" |11
| colspan="8" |8
|
|
|1L 1s
|11:8
|
|
|-
| rowspan="3" |5L 4s
| rowspan="3" |semiquartal
|5L 9s
|
|
|-
|-
| colspan="3" |3
| colspan="8" |8
| colspan="8" |8
|388
|2L 1s
|8:3
|
|
|
|
|-
|-
| colspan="3" |3
|9L 5s
| colspan="3" |3
|
| colspan="5" |5
| colspan="3" |3
| colspan="5" |5
|33535
|[[2L 3s]]
|5:3
|pentic
|[[meantone]][5]
|-
|-
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
|3332332
|[[5L 2s]]
|3:2
|diatonic
|meantone[7]
|-
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|121212212122
|[[7L 5s]]
|2:1
|m-chromatic
|meantone[12]
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="5" |
|-
! colspan="19" |Generator pair of 12\19 and 7\19
!Scale Code
!Mos
!Step Ratio
!TAMNAMS Name
!Scales
|-
| colspan="12" |12
| colspan="7" |7
|
|
|1L 1s
|12:7
|
|
|
|
|-
| colspan="5" |5
| colspan="7" |7
| colspan="7" |7
|577
|2L 1s
|7:5
|
|
|
|
|-
| colspan="5" |5
| colspan="5" |5
| colspan="2" |2
| colspan="5" |5
| colspan="2" |2
|55252
|[[3L 2s]]
|5:2
|antipentic
|[[sensi]][5]
|-
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="2" |2
|32322322
|[[3L 5s]]
|3:2
|sensoid
|sensi[8]
|-
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|12212221222
|[[8L 3s]]
|2:1
|
|
|sensi[11]
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="5" |
|-
! colspan="19" |Generator pair of 13\19 and 6\19
!Scale Code
!Mos
!Step Ratio
!TAMNAMS Name
!Scales
|-
| colspan="13" |13
| colspan="6" |6
|
|
|1L 1s
|13:6
|
|
|-
| rowspan="15" |3L 1s
| rowspan="15" |tetric*
| rowspan="7" |3L 4s
| rowspan="7" |mosh
| rowspan="3" |3L 7s
| rowspan="3" |sephiroid
|3L 10s
|
|
|-
|-
| colspan="7" |7
| colspan="6" |6
| colspan="6" |6
|766
|1L 2s
|7:6
|
|
|
|
|-
|-
|1
|10L 3s
| colspan="6" |6
| colspan="6" |6
| colspan="6" |6
|1666
|[[3L 1s]]
|6:1
|tetric
|
|
|-
|-
|1
|1
| colspan="5" |5
|1
| colspan="5" |5
|1
| colspan="5" |5
|1151515
|[[3L 4s]]
|5:1
|mosh
|[[magic]][7]
|-
|1
|1
|1
| colspan="4" |4
|1
|1
| colspan="4" |4
|1
|1
| colspan="4" |4
|1114114114
|[[3L 7s]]
|4:1
|sephiroid
|magic[10]
|-
|1
|1
|1
|1
| colspan="3" |3
|1
|1
|1
| colspan="3" |3
|1
|1
|1
| colspan="3" |3
|1111311131113
|[[3L 10s]]
|3:1
|
|
|magic[13]
|-
|1
|1
|1
|1
|1
| colspan="2" |2
|1
|1
|1
|1
| colspan="2" |2
|1
|1
|1
|1
| colspan="2" |2
|1111121111211112
|[[3L 13s]]
|2:1
|
|
|magic[16]
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="5" |
|-
! colspan="19" |Generator pair of 14\19 and 5\19
!Scale Code
!Mos
!Step Ratio
!TAMNAMS Name
!Scales
|-
| colspan="14" |14
| colspan="5" |5
|
|
|1L 1s
|14:5
|
|
|-
| rowspan="3" |7L 3s
| rowspan="3" |dicotonic
|7L 10s
|
|
|-
|-
| colspan="9" |9
| colspan="5" |5
| colspan="5" |5
|955
|1L 2s
|9:5
|
|
|
|
|-
|-
| colspan="4" |4
|10L 7s
| colspan="5" |5
| colspan="5" |5
| colspan="5" |5
|4555
|[[3L 1s]]
|5:4
|tetric
|
|
|-
|-
| colspan="4" |4
| colspan="4" |4
|1
| colspan="4" |4
|1
| colspan="4" |4
|1
|4414141
|[[4L 3s]]
|4:1
|smitonic
|[[kleismic]][7]
|-
| colspan="3" |3
|1
| colspan="3" |3
|1
|1
| colspan="3" |3
|1
|1
| colspan="3" |3
|1
|1
|31311311311
|[[4L 7s]]
|3:1
|kleistonic
|kleismic[11]
|-
| colspan="2" |2
|1
|1
| colspan="2" |2
|1
|1
|1
| colspan="2" |2
|1
|1
|1
| colspan="2" |2
|1
|1
|1
|211211121112111
|[[4L 11s]]
|2:1
|
|
|kleismic[15]
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="5" |
|-
! colspan="19" |Generator pair of 15\19 and 4\19
!Scale Code
!Mos
!Step Ratio
!TAMNAMS Name
!Scales
|-
| colspan="15" |15
| colspan="4" |4
|
|
|1L 1s
|15:4
|
|
|
|
|-
| colspan="11" |11
| colspan="4" |4
| colspan="4" |4
|
|
|1L 2s
|11:4
|
|
|-
| rowspan="7" |4L 3s
| rowspan="7" |smitonic
| rowspan="3" |4L 7s
| rowspan="3" |kleistonic
|4L 11s
|
|
|-
|-
| colspan="7" |7
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
|7444
|[[1L 3s]]
|7:4
|
|
|
|
|-
|-
| colspan="3" |3
|11L 4s
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
|34444
|[[4L 1s]]
|4:3
|manic
|[[Semaphore and Godzilla|godzilla]][5]
|-
| colspan="3" |3
| colspan="3" |3
|1
| colspan="3" |3
|1
| colspan="3" |3
|1
| colspan="3" |3
|1
|331313131
|[[5L 4s]]
|3:1
|semiquartal
|godzilla[9]
|-
| colspan="2" |2
|1
| colspan="2" |2
|1
|1
| colspan="2" |2
|1
|1
| colspan="2" |2
|1
|1
| colspan="2" |2
|1
|1
|21211211211211
|[[5L 9s]]
|2:1
|
|
|godzilla[14]
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="5" |
|-
! colspan="19" |Generator pair of 16\19 and 3\19
!Scale Code
!Mos
!Step Ratio
!TAMNAMS Name
!Scales
|-
|-
| colspan="16" |16
| colspan="3" |3
|
|1L 1s
|16:3
|
|
|
|-
| colspan="13" |13
| colspan="3" |3
| colspan="3" |3
|
|
|1L 2s
|13:3
|
|
|
|
|-
|-
| colspan="10" |10
| rowspan="3" |7L 4s
| colspan="3" |3
| rowspan="3" |suprasmitonic
| colspan="3" |3
|7L 11s
| colspan="3" |3
|
|[[1L 3s]]
|10:3
|
|
|
|-
|-
| colspan="7" |7
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
|73333
|[[1L 4s]]
|7:3
|
|
|
|
|-
|-
| colspan="4" |4
|11L 7s
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
|433333
|[[1L 5s]]
|4:3
|
|
|[[deutone]][6]
|-
|1
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
|1333333
|[[6L 1s]]
|3:1
|archeotonic
|deutone[7]
|-
|-
|1
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|1121212121212
|[[6L 7s]]
|2:1
|
|
|deutone[13]
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="5" |
|-
! colspan="19" |Generator pair of 17\19 and 2\19
!Scale Code
!Mos
!Step Ratio
!TAMNAMS Name
!Scales
|-
| colspan="17" |17
| colspan="2" |2
|
|
|1L 1s
|17:2
|
|
|
|
|-
| colspan="15" |15
| colspan="2" |2
| colspan="2" |2
|
|
|1L 2s
|15:2
|
|
|
|
|-
| colspan="13" |13
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|
|
|[[1L 3s]]
|13:2
|
|
|
|
|-
|-
| colspan="11" |11
| rowspan="31" |2L 1s
| colspan="2" |2
| rowspan="31" |deuteric*
| colspan="2" |2
| rowspan="15" |2L 3s
| colspan="2" |2
| rowspan="15" |pentic
| colspan="2" |2
| rowspan="7" |2L 5s
| rowspan="7" |antidiatonic
| rowspan="3" |2L 7s
| rowspan="3" |joanatonic
|2L 9s
|
|
|[[1L 4s]]
|-
|11:2
|
|
|
|
|-
|-
| colspan="9" |9
|9L 2s
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|922222
|[[1L 5s]]
|9:2
|
|
|
|-
|-
| colspan="7" |7
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|7222222
|[[1L 6s]]
|7:2
|
|
|
|
|-
| colspan="5" |5
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|52222222
|[[1L 7s]]
|5:2
|
|
|
|
|-
|-
| colspan="3" |3
| rowspan="3" |7L 2s
| colspan="2" |2
| rowspan="3" |superdiatonic
| colspan="2" |2
|7L 9s
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|322222222
|[[1L 8s]]
|3:2
|
|
|[[negri]][9]
|-
|1
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|1222222222
|[[9L 1s]]
|2:1
|sinatonic
|negri[10]
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="5" |
|-
! colspan="19" |Generator pair of 18\19 and 1\19
!Scale Code
!Mos
!Step Ratio
!TAMNAMS Name
!Scales
|-
|-
| colspan="18" |18
|1
|
|
|1L 1s
|18:1
|
|
|-
|9L 7s
|
|
|-
|-
| colspan="17" |17
|1
|1
|
|
|1L 2s
|17:1
|
|
|
|
|-
| colspan="16" |16
|1
|1
|1
|
|
|[[1L 3s]]
|16:1
|
|
|
|
|-
|-
| colspan="15" |15
| rowspan="7" |5L 2s
|1
| rowspan="7" |diatonic
|1
| rowspan="3" |5L 7s
|1
| rowspan="3" |p-chromatic
|1
|5L 12s
|p-superchromatic*
|-
|
|
|[[1L 4s]]
|15:1
|
|
|-
|12L 5s
|
|
|-
|-
| colspan="14" |14
|1
|1
|1
|1
|1
|
|
|[[1L 5s]]
|
|14:1
|
|
|
|
|-
|-
| colspan="13" |13
| rowspan="3" |7L 5s
|1
| rowspan="3" |m-chromatic
|1
|7L 12s
|1
|1
|1
|1
|
|
|[[1L 6s]]
|-
|13:1
|
|
|
|
|-
|-
| colspan="12" |12
|12L 7s
|1
|m-superchromatic*
|1
|1
|1
|1
|1
|1
|
|[[1L 7s]]
|12:1
|
|
|-
|-
| colspan="11" |11
|1
|1
|1
|1
|1
|1
|1
|1
|
|
|[[1L 8s]]
|11:1
|
|
|
|
|-
| colspan="10" |10
|1
|1
|1
|1
|1
|1
|1
|1
|1
|
|
|[[1L 9s]]
|10:1
|
|
|
|
|-
| colspan="9" |9
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|91111111111
|[[1L 10s]]
|9:1
|
|
|
|
|-
|-
| colspan="8" |8
| rowspan="15" |3L 2s
|1
| rowspan="15" |antipentic
|1
| rowspan="7" |3L 5s
|1
| rowspan="7" |sensoid
|1
| rowspan="3" |3L 8s
|1
| rowspan="3" |
|1
|3L 11s
|1
|1
|1
|1
|1
|811111111111
|[[1L 11s]]
|8:1
|
|
|
|-
|-
| colspan="7" |7
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|7111111111111
|[[1L 12s]]
|7:1
|
|
|
|
|-
|-
| colspan="6" |6
|11L 3s
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|61111111111111
|[[1L 13s]]
|6:1
|
|
|
|-
|-
| colspan="5" |5
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|511111111111111
|[[1L 14s]]
|5:1
|
|
|
|
|-
| colspan="4" |4
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|4111111111111111
|[[1L 15s]]
|4:1
|
|
|
|
|-
|-
| colspan="3" |3
| rowspan="3" |8L 3s
|1
| rowspan="3" |
|1
|8L 11s
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|31111111111111111
|[[1L 16s]]
|3:1
|
|
|
|-
|-
| colspan="2" |2
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|211111111111111111
|[[1L 17s]]
|2:1
|
|
|
|
|-
|-
|1
|11L 8s
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="5" |
|}
 
== Mode and Interval Table ==
Based on the scale table, there is also the idea of a mode table. Since the modes of a scale affect its scale degrees, this also serves as an interval table.
 
Notes:
 
* The names of mosses and intervals are based on [[TAMNAMS]] naming conventions.
* As this is an interval table, intervals are based on the root of the scale and whichever scale degree is k steps up from the root. For intervals that have two sizes (major and minor, augmented and perfect, or perfect and diminished), '''bold''' text denotes the larger of the two intervals. (This is far more striking with color coding.)
 
{| class="wikitable"
!'''Mos'''
!'''Scale Code'''
!'''UDP'''
!'''Mode Name'''
!0-step
(unison)
!1-step
!2-step
!3-step
!4-step
!5-step
!6-step
!7-step
(octave)
|-
| rowspan="7" |Diatonic (5L 2s)
|LLLsLLs
|<nowiki>6|0</nowiki>
|Lydian
|Perfect
|'''Maj'''
|'''Maj'''
|'''Aug'''
|'''Perfect'''
|'''Maj'''
|'''Maj'''
|Perfect
|-
|LLsLLLs
|<nowiki>5|1</nowiki>
|Ionian
|Perfect
|'''Maj'''
|'''Maj'''
|Perfect
|'''Perfect'''
|'''Maj'''
|'''Maj'''
|Perfect
|-
|LLsLLsL
|<nowiki>4|2</nowiki>
|Mixolydian
|Perfect
|'''Maj'''
|'''Maj'''
|Perfect
|'''Perfect'''
|'''Maj'''
|min
|Perfect
|-
|LsLLLsL
|<nowiki>3|3</nowiki>
|Dorian
|Perfect
|'''Maj'''
|min
|Perfect
|'''Perfect'''
|'''Maj'''
|min
|Perfect
|-
|LsLLsLL
|<nowiki>2|4</nowiki>
|Aeolian
|Perfect
|'''Maj'''
|min
|Perfect
|'''Perfect'''
|min
|min
|Perfect
|-
|sLLLsLL
|<nowiki>1|5</nowiki>
|Phrygian
|Perfect
|min
|min
|Perfect
|'''Perfect'''
|min
|min
|Perfect
|-
|sLLsLLL
|<nowiki>0|6</nowiki>
|Locrian
|Perfect
|min
|min
|Perfect
|dim
|min
|min
|Perfect
|}
{| class="wikitable"
!'''Mos'''
!'''Scale Code'''
!'''UDP'''
!'''Mode Name'''
!0-step
(unison)
!1-step
!2-step
!3-step
!4-step
!5-step
!6-step
!7-step
(octave)
|-
| rowspan="7" |Mosh (3L 4s)
|LsLsLss
|<nowiki>6|0</nowiki>
|Dril
|Perfect
|'''Maj'''
|'''Perfect'''
|'''Maj'''
|'''Maj'''
|'''Aug'''
|'''Maj'''
|Perfect
|-
|LsLssLs
|<nowiki>5|1</nowiki>
|Gil
|Perfect
|'''Maj'''
|'''Perfect'''
|'''Maj'''
|'''Maj'''
|Perfect
|'''Maj'''
|Perfect
|-
|LssLsLs
|<nowiki>4|2</nowiki>
|Kleeth
|Perfect
|'''Maj'''
|'''Perfect'''
|min
|'''Maj'''
|Perfect
|'''Maj'''
|Perfect
|-
|sLsLsLs
|<nowiki>3|3</nowiki>
|Bish
|Perfect
|min
|'''Perfect'''
|min
|'''Maj'''
|Perfect
|'''Maj'''
|Perfect
|-
|sLsLssL
|<nowiki>2|4</nowiki>
|Fish
|Perfect
|min
|'''Perfect'''
|min
|'''Maj'''
|Perfect
|min
|Perfect
|-
|sLssLsL
|<nowiki>1|5</nowiki>
|Jwl
|Perfect
|min
|'''Perfect'''
|min
|min
|Perfect
|min
|Perfect
|-
|ssLsLsL
|<nowiki>0|6</nowiki>
|Led
|Perfect
|min
|dim
|min
|min
|Perfect
|min
|Perfect
|}
 
== Mos Family Tree as a Table ==
The following is the mos family tree, formatted as a table. The table consists of 6 generations.
{| class="wikitable mw-collapsible"
! colspan="6" |Mos Family Tree (single-period only)
|-
!Gen. 1
!Gen. 2
!Gen. 3
!Gen. 4
!Gen. 5
!Gen. 6
|-
| rowspan="63" |1L 1s
| rowspan="31" |1L 2s
| rowspan="15" |1L 3s
| rowspan="7" |1L 4s
| rowspan="3" |1L 5s
|1L 6s
|-
|
|
|-
|6L 1s
|-
|-
|
|
|
|
|-
| rowspan="3" |5L 1s
|5L 6s
|-
|
|
|-
|6L 5s
|-
|
|
|
|
|
|
|-
|-
| rowspan="7" |4L 1s
| rowspan="7" |5L 3s
| rowspan="3" |4L 5s
| rowspan="7" |oneirotonic
|4L 9s
| rowspan="3" |5L 8s
|-
| rowspan="3" |
|5L 13s
|
|
|-
|9L 4s
|-
|-
|
|
|
|
|-
|-
| rowspan="3" |5L 4s
|13L 5s
|5L 9s
|-
|
|
|-
|9L 5s
|-
|-
|
|
Line 2,311: Line 630:
|
|
|-
|-
| rowspan="15" |3L 1s
| rowspan="3" |8L 5s
| rowspan="7" |3L 4s
| rowspan="3" |
| rowspan="3" |3L 7s
|8L 13s
|3L 10s
|-
|
|
|-
|10L 3s
|-
|-
|
|
|
|
|-
|-
| rowspan="3" |7L 3s
|13L 8
|7L 10s
|-
|
|
|}
=== Family tree limited to 10 notes and with up to 5 periods ===
Mosses whose children exceed 10 notes are shown in bold. (Stars indicate mosses whose descendants now bear at least a mos intro and infobox mos template. Double stars indicate mosses whose descendants already had those templates. Triple stars indicate that the mos's descendants lack a page.)
{| class="wikitable"
! colspan="18" |Family tree of single-period mosses, limited to 10-note scales
|-
|-
|10L 7s
! colspan="2" |Root
! colspan="2" |1st-order child scales
! colspan="2" |2nd-order child scales
! colspan="2" |3rd-order child scales
! colspan="2" |4th-order child scales
! colspan="2" |5th-order child scales
! colspan="2" |6th-order child scales
! colspan="2" |7th-order child scales
! colspan="2" |8th-order child scales
|-
|-
|
!Mos
|
!Name
|
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Mos
!Name
|-
|-
| rowspan="7" |4L 3s
| rowspan="16" |1L 1s
| rowspan="3" |4L 7s
| rowspan="16" |trivial
|4L 11s
| rowspan="11" |1L 2s
| rowspan="11" |antrial
| rowspan="8" |1L 3s
| rowspan="8" |antetric
| rowspan="6" |1L 4s
| rowspan="6" |pedal
| rowspan="5" |1L 5s
| rowspan="5" |antimachinoid
| rowspan="4" |1L 6s
| rowspan="4" |onyx
| rowspan="3" |1L 7s
| rowspan="3" |antipine
| rowspan="2" |1L 8s
| rowspan="2" |antisubneutralic
|[[1L 9s]]
|'''antisinatonic *'''
|-
|-
|
|[[9L 1s]]
|'''sinatonic *'''
|-
|-
|11L 4s
|[[8L 1s]]
|'''subneutralic **'''
| colspan="2" rowspan="14" |
|-
|-
|
|[[7L 1s]]
|
|'''pine *'''
| colspan="2" rowspan="13" |
|-
|-
| rowspan="3" |7L 4s
|[[6L 1s]]
|7L 11s
|'''archaeotonic **'''
| colspan="2" rowspan="12" |
|-
|-
|
|[[5L 1s]]
|'''machinoid *'''
| colspan="2" rowspan="11" |
|-
|-
|11L 7s
| rowspan="2" |4L 1s
| rowspan="2" |manual
|[[5L 4s]]
|'''semiquartal *'''
|-
|-
|
|[[4L 5s]]
|
|'''gramitonic *'''
|
|
|
|-
|-
| rowspan="31" |2L 1s
| rowspan="3" |3L 1s
| rowspan="15" |2L 3s
| rowspan="3" |tetric
| rowspan="7" |2L 5s
|[[4L 3s]]
| rowspan="3" |2L 7s
|'''smitonic *'''
|2L 9s
| colspan="2" |
|-
|-
|
| rowspan="2" |3L 4s
| rowspan="2" |mosh
|[[7L 3s]]
|'''dicoid *'''
|-
|-
|9L 2s
|[[3L 7s]]
|'''sephiroid *'''
|-
|-
|
| rowspan="5" |2L 1s
|
| rowspan="5" |trial
| rowspan="2" |3L 2s
| rowspan="2" |antipentic
|[[3L 5s]]
|'''checkertonic *'''
| colspan="2" rowspan="3" |
|-
|-
| rowspan="3" |7L 2s
|[[5L 3s]]
|7L 9s
|'''oneirotonic **'''
|-
|-
|
| rowspan="3" |2L 3s
| rowspan="3" |pentic
|[[5L 2s]]
|'''diatonic *'''
|-
|-
|9L 7s
| rowspan="2" |2L 5s
| rowspan="2" |antidiatonic
|[[7L 2s]]
|'''armotonic **'''
|-
|-
|
|[[2L 7s]]
|
|'''balzano *'''
|
|-
|-
| rowspan="7" |5L 2s
! colspan="18" |Family tree of 2-period mosses, limited to 10-note scales
| rowspan="3" |5L 7s
|5L 12s
|-
|-
|
! colspan="2" |Root
! colspan="2" |1st-order child scales
! colspan="2" |2nd-order child scales
! colspan="2" |3rd-order child scales
! colspan="10" rowspan="2" |
|-
|-
|12L 5s
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Mos
!Name
|-
|-
|
| rowspan="5" |2L 2s
|
| rowspan="5" |biwood
| rowspan="3" |2L 4s
| rowspan="3" |malic
| rowspan="2" |2L 6s
| rowspan="2" |subaric
|[[2L 8s]]
|'''jaric *'''
| colspan="10" rowspan="5" |
|-
|-
| rowspan="3" |7L 5s
|[[8L 2s]]
|7L 12s
|'''taric ***'''
|-
|-
|
|[[6L 2s]]
|'''ekic **'''
| colspan="2" rowspan="3" |
|-
|-
|12L 7s
| rowspan="2" |4L 2s
| rowspan="2" |citric
|[[6L 4s]]
|'''lemon *'''
|-
|-
|
|[[4L 6s]]
|
|'''lime *'''
|
|
|-
|-
| rowspan="15" |3L 2s
! colspan="18" |Family tree of 3-period mosses, limited to 10-note scales
| rowspan="7" |3L 5s
| rowspan="3" |3L 8s
|3L 11s
|-
|-
|
! colspan="2" |Root
! colspan="2" |1st-order child scales
! colspan="14" rowspan="2" |
|-
|-
|11L 3s
!Mos
!Name
!Mos
!Name
|-
|-
|
| rowspan="2" |3L 3s
|
| rowspan="2" |triwood
|[[3L 6s]]
|'''tcherepnin *'''
| colspan="14" rowspan="2" |
|-
|-
| rowspan="3" |8L 3s
|[[6L 3s]]
|8L 11s
|'''hyrulic *'''
|-
|-
|
! colspan="18" |Family tree of 4-period mosses, limited to 10-note scales
|-
|-
|11L 8s
! colspan="2" |Root
! colspan="16" rowspan="2" |
|-
|-
|
!Mos
|
!Name
|
|-
|-
| rowspan="7" |5L 3s
|[[4L 4s]]
| rowspan="3" |5L 8s
|'''tetrawood **'''
|5L 13s
| colspan="16" |
|-
|-
|
! colspan="18" |Family tree of 5-period mosses, limited to 10-note scales
|-
|-
|13L 5s
! colspan="2" |Root
! colspan="16" rowspan="2" |
|-
|-
|
!Mos
|
!Name
|-
| rowspan="3" |8L 5s
|8L 13s
|-
|-
|
|[[5L 5s]]
|-
|'''pentawood *'''
|13L 8
| colspan="16" |
|}
|}


Line 2,633: Line 1,033:
Note the curious case of 1L 7s in this example. It should be the leaf node for the generator pair 17\19 and 2\19, but since that scale is also available to the generator pair of 18\19 and 1\19, it's not and that branch continues to 1L 17s. Technically speaking, the branches for the generator pairs of 18\19-1\19 and 17\19-2\19 coincide.
Note the curious case of 1L 7s in this example. It should be the leaf node for the generator pair 17\19 and 2\19, but since that scale is also available to the generator pair of 18\19 and 1\19, it's not and that branch continues to 1L 17s. Technically speaking, the branches for the generator pairs of 18\19-1\19 and 17\19-2\19 coincide.


=== 31edo Example ===
== Mos-edo table ==
This table does away with generation numbers and includes the "terminating edo" (the edo resulted when the mos xL ys with a step ratio of L:s = 2:1 produces a pair of indistinguishable child scales xL (x+y)s and (x+y)L xs whose step ratios are both 1:1, or k:k if L and s share a common factor k). Also, no merged cells; hopefully, that illustrates things a bit better.
This table shows what edos are possible for a given mos; in other words, given a mos xL ys (where x and y are fixed), L and s can vary to produce different edos (where L > s). The example below is for 12edo. Degenerate cases lie along the edges of the triangle, with the diagonal (in '''bold''') are for edos where L:s = 1:1.
{| class="wikitable"
{| class="wikitable"
! colspan="15" |Mos Family Tree for 31edo
! colspan="2" rowspan="2" |Edos of 5L 2s
|-
! colspan="11" |Small step size (s)
!30\31 - 1\31
!29\31 - 2\31
!28\31 - 3\31
!27\31 - 4\31
!26\31 - 5\31
!25\31 - 6\31
!24\31 - 7\31
!23\31 - 8\31
!22\31 - 9\31
!21\31 - 10\31
!20\31 - 11\31
!19\31 - 12\31
!18\31 - 13\31
!17\31 - 14\31
!16\31 - 15\31
|-
|1L 1s
|1L 1s
|1L 1s
|1L 1s
|1L 1s
|1L 1s
|1L 1s
|1L 1s
|1L 1s
|1L 1s
|1L 1s
|1L 1s
|1L 1s
|1L 1s
|1L 1s
|-
|1L 2s
|1L 2s
|1L 2s
|1L 2s
|1L 2s
|1L 2s
|1L 2s
|1L 2s
|1L 2s
|1L 2s
|2L 1s
|2L 1s
|2L 1s
|2L 1s
|2L 1s
|-
|1L 3s
|1L 3s
|1L 3s
|1L 3s
|1L 3s
|1L 3s
|1L 3s
|3L 1s
|3L 1s
|3L 1s
|3L 2s
|3L 2s
|2L 3s
|2L 3s
|2L 3s
|-
|1L 4s
|1L 4s
|1L 4s
|1L 4s
|1L 4s
|1L 4s
|4L 1s
|4L 3s
|3L 4s
|3L 4s
|3L 5s
|5L 3s
|5L 2s
|2L 5s
|2L 5s
|-
|1L 5s
|1L 5s
|1L 5s
|1L 5s
|1L 5s
|5L 1s
|4L 5s
|4L 7s
|7L 3s
|3L 7s
|3L 8s
|5L 8s
|7L 5s
|2L 7s
|2L 7s
|-
|-
|1L 6s
!0
|1L 6s
!1
|1L 6s
!2
|1L 6s
!3
|6L 1s
!4
|5L 6s
!5
|9L 4s
!6
|4L 11s
!7
|7L 10s
!8
|3L 10s
!9
|3L 11s
!10
|13L 5s
|12L 7s
|9L 2s
|2L 9s
|-
|-
|1L 7s
! rowspan="11" |Large step size (L)
|1L 7s
!0
|1L 7s
|'''0'''
|7L 1s
|6L 7s
|5L 11s
|9L 13s
|4L 15s
|7L 17s
|3L 13s
|14L 3s
|31edo
|31edo
|11L 9s
|2L 11s
|-
|1L 8s
|1L 8s
|1L 8s
|8L 7s
|6L 13s
|5L 16s
|31edo
|4L 19s
|31edo
|3L 16s
|31edo
|
|
|
|
|31edo
|2L 13s
|-
|1L 9s
|1L 9s
|1L 9s
|8L 15s
|6L 19s
|5L 21s
|
|
|4L 23s
|
|
|3L 19s
|
|
|
|
|
|
|
|
|2L 15s
|-
|1L 10s
|1L 10s
|10L 1s
|31edo
|31edo
|31edo
|
|
|31edo
|
|
|3L 22s
|
|
|
|
|2L 17s
|-
|-
|1L 11s
!1
|1L 11s
|''5''
|10L 11s
|'''7'''
|
|
|
|
Line 2,823: Line 1,074:
|
|
|
|
|3L 25s
|
|
|
|
|
|
|
|2L 19s
|-
|-
|1L 12s
!2
|1L 12s
|''10''
|31edo
|12
|
|'''14'''
|
|
|
|
Line 2,839: Line 1,087:
|
|
|
|
|31edo
|
|
|
|
|
|
|
|2L 21s
|-
|-
|1L 13s
!3
|1L 13s
|''15''
|
|17
|
|19
|
|'''21'''
|
|
|
|
Line 2,858: Line 1,103:
|
|
|
|
|
|
|2L 23s
|-
|-
|1L 14s
!4
|1L 14s
|''20''
|
|22
|24
|26
|'''28'''
|
|
|
|
Line 2,871: Line 1,116:
|
|
|
|
|-
!5
|''25''
|27
|29
|31
|33
|'''35'''
|
|
|
|
Line 2,876: Line 1,129:
|
|
|
|
|2L 25s
|-
|-
|1L 15s
!6
|15L 1s
|''30''
|
|32
|
|34
|
|36
|
|38
|
|40
|'''42'''
|
|
|
|
|
|
|
|
|-
!7
|''35''
|37
|39
|41
|43
|45
|47
|'''49'''
|
|
|
|
|
|
|2L 27s
|-
|-
|1L 16s
!8
|31edo
|''40''
|
|42
|
|44
|
|46
|
|48
|
|50
|
|52
|
|54
|
|'''56'''
|
|
|
|
|
|
|31edo
|-
|-
|1L 17s
!9
|
|''45''
|
|47
|
|49
|
|51
|
|53
|
|55
|
|57
|
|59
|
|61
|
|'''63'''
|
|
|
|
|
|-
|-
|1L 18s
!10
|
|''50''
|
|52
|
|54
|
|56
|
|58
|
|60
|
|62
|
|64
|
|66
|
|68
|
|'''70'''
|
|}
|
An alternate table shows mosses where L:s = 2:1 is on the diagonal, dividing the table into a soft half and a hard half. Here, two additional diagonals are shown in '''bold''', one each for L:s = 3:1 and L:s = 3:2. Rows represent chroma size rather than large step size.
|
{| class="wikitable"
! colspan="2" rowspan="2" |Edos of 5L 2s
! colspan="11" |Small step size (s)
|-
|-
|1L 19s
!0
|
!1
|
!2
|
!3
|
!4
|
!5
|
!6
|
!7
|
!8
|
!9
|
!10
|
|
|
|
|-
|-
|1L 20s
! rowspan="11" |Chroma size
|
<nowiki>|L-s|</nowiki>
|
!0
|
|'''0'''
|
|''7''
|
|''14''
|
|''21''
|
|''28''
|
|''35''
|
|''42''
|
|''49''
|
|''56''
|
|''63''
|
|''70''
|
|-
|-
|1L 21s
!1
|
|''5''
|
|'''12'''
|
|'''19'''
|
|26
|
|33
|
|40
|
|47
|
|54
|
|61
|
|68
|
|75
|
|
|
|-
|-
|1L 22s
!2
|
|''10''
|
|'''17'''
|
|'''24'''
|
|31
|
|'''38'''
|
|45
|
|52
|
|59
|
|66
|
|73
|
|80
|
|
|
|-
|-
|1L 23s
!3
|
|''15''
|
|22
|
|29
|
|'''36'''
|
|43
|
|50
|
|'''57'''
|
|64
|
|71
|
|78
|
|85
|
|
|
|-
|-
|1L 24s
!4
|
|''20''
|
|27
|
|'''34'''
|
|41
|
|'''48'''
|
|55
|
|62
|
|69
|
|'''76'''
|
|83
|
|90
|
|
|
|-
|-
|1L 25s
!5
|
|''25''
|
|32
|
|39
|
|46
|
|53
|
|'''60'''
|
|67
|
|74
|
|81
|
|88
|
|'''95'''
|
|
|
|-
|-
|1L 26s
!6
|
|''30''
|
|37
|
|44
|
|'''51'''
|
|58
|
|65
|
|'''72'''
|
|79
|
|86
|
|93
|
|100
|
|
|
|-
|-
|1L 27s
!7
|
|''35''
|
|42
|
|49
|
|56
|
|63
|
|70
|
|77
|
|'''84'''
|
|91
|
|98
|
|105
|
|
|
|-
|-
|1L 28s
!8
|
|''40''
|
|47
|
|54
|
|61
|
|'''68'''
|
|75
|
|82
|
|89
|
|'''96'''
|
|103
|
|110
|
|
|
|-
|-
|1L 29s
!9
|
|''45''
|
|52
|
|59
|
|66
|
|73
|
|80
|
|87
|
|94
|
|101
|
|'''108'''
|
|115
|
|
|
|-
|-
|31edo
!10
|
|''50''
|
|57
|
|64
|
|71
|
|78
|
|'''85'''
|
|92
|
|99
|
|106
|
|113
|
|'''120'''
|
|
|
|}
|}
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