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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
|1
| colspan="8" |8
|1
| colspan="8" |8
|[[2L 3s]]
|8:1
|Pentic
|-
|1
|1
|1
| colspan="7" |7
|1
|1
| colspan="7" |7
|[[2L 5s]]
|7:1
|Antidiatonic
|-
|1
|1
|1
|1
| colspan="6" |6
|1
|1
|1
| colspan="6" |6
|[[2L 7s]]
|6:1
|Joanatonic
|-
|1
|1
|1
|1
|1
| colspan="5" |5
|1
|1
|1
|1
| colspan="5" |5
|[[2L 9s]]
|5:1
|
|-
|1
|1
|1
|1
|1
|1
| colspan="4" |4
|1
|1
|1
|1
|1
| colspan="4" |4
|[[2L 11s]]
|4:1
|
|-
|1
|1
|1
|1
|1
|1
|1
| colspan="3" |3
|1
|1
|1
|1
|1
|1
| colspan="3" |3
|[[2L 13s]]
|3:1
|
|-
|1
|1
|1
|1
|1
|1
|1
|1
| colspan="2" |2
|1
|1
|1
|1
|1
|1
|1
| colspan="2" |2
|[[2L 15s]]
|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="11" |11
| colspan="8" |8
|1L 1s
|11:8
|Generator Pair
|-
| colspan="3" |3
| colspan="8" |8
| colspan="8" |8
|2L 1s
|8:3
|
|-
| colspan="3" |3
| colspan="3" |3
| colspan="5" |5
| colspan="3" |3
| colspan="5" |5
|[[2L 3s]]
|5:3
|Pentic
|-
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="2" |2
|[[5L 2s]]
|3:2
|Diatonic
|-
|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
|[[7L 5s]]
|2:1
|M-chromatic
|-
|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="12" |12
| colspan="7" |7
|1L 1s
|12:7
|Generator Pair
|-
| colspan="5" |5
| colspan="7" |7
| colspan="7" |7
|2L 1s
|7:5
|
|-
| colspan="5" |5
| colspan="5" |5
| colspan="2" |2
| colspan="5" |5
| colspan="2" |2
|[[3L 2s]]
|5:2
|Antipentic
|-
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="2" |2
|[[3L 5s]]
|3:2
|Sensoid
|-
|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
|[[8L 3s]]
|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="13" |13
| colspan="6" |6
|1L 1s
|13:6
|Generator Pair
|-
| colspan="7" |7
| colspan="6" |6
| colspan="6" |6
|1L 2s
|7:6
|
|-
|1
| colspan="6" |6
| colspan="6" |6
| colspan="6" |6
|[[3L 1s]]
|6:1
|Tetric (placeholder name for sake of completness)
|-
|1
|1
| colspan="5" |5
|1
| colspan="5" |5
|1
| colspan="5" |5
|[[3L 4s]]
|5:1
|Mosh
|-
|1
|1
|1
| colspan="4" |4
|1
|1
| colspan="4" |4
|1
|1
| colspan="4" |4
|[[3L 7s]]
|4:1
|Sephiroid
|-
|1
|1
|1
|1
| colspan="3" |3
|1
|1
|1
| colspan="3" |3
|1
|1
|1
| colspan="3" |3
|[[3L 10s]]
|3:1
|
|-
|1
|1
|1
|1
|1
| colspan="2" |2
|1
|1
|1
|1
| colspan="2" |2
|1
|1
|1
|1
| colspan="2" |2
|[[3L 13s]]
|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="14" |14
| colspan="5" |5
|1L 1s
|14:5
|Generator Pair
|-
| colspan="9" |9
| colspan="5" |5
| colspan="5" |5
|1L 2s
|9:5
|
|-
| colspan="4" |4
| colspan="5" |5
| colspan="5" |5
| colspan="5" |5
|[[3L 1s]]
|5:4
|Tetric
|-
| colspan="4" |4
| colspan="4" |4
|1
| colspan="4" |4
|1
| colspan="4" |4
|1
|[[4L 3s]]
|4:1
|Smitonic
|-
| colspan="3" |3
|1
| colspan="3" |3
|1
|1
| colspan="3" |3
|1
|1
| colspan="3" |3
|1
|1
|[[4L 7s]]
|3:1
|Kleistonic (proposed name from 4L 7s page)
|-
| colspan="2" |2
|1
|1
| colspan="2" |2
|1
|1
|1
| 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
| colspan="4" |4
|1L 1s
|15:4
|Generator Pair
|-
| colspan="11" |11
| colspan="4" |4
| colspan="4" |4
|1L 2s
|11:4
|
|-
| colspan="7" |7
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
|[[1L 3s]]
|7:4
|
|-
| colspan="3" |3
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
|[[4L 1s]]
|4:3
|Manic
|-
| colspan="3" |3
| colspan="3" |3
|1
| colspan="3" |3
|1
| colspan="3" |3
|1
| colspan="3" |3
|1
|[[5L 4s]]
|3:1
|Semiquartal
|-
| colspan="2" |2
|1
| colspan="2" |2
|1
|1
| colspan="2" |2
|1
|1
| colspan="2" |2
|1
|1
| colspan="2" |2
|1
|1
|[[5L 9s]]
|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="16" |16
| colspan="3" |3
|1L 1s
|16:3
|Generator Pair
|-
| 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
| colspan="3" |3
| 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
| colspan="2" |2
| colspan="2" |2
| 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
| 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
|1
| colspan="8" |8
|1
| colspan="8" |8
|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
|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
|
|
|-
| colspan="3" |3
| colspan="8" |8
| colspan="8" |8
|388
|2L 1s
|8:3
|
|
|-
| colspan="3" |3
| 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
|
|
|-
| colspan="7" |7
| colspan="6" |6
| colspan="6" |6
|766
|1L 2s
|7:6
|
|
|-
|1
| 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
|
|
|-
| colspan="9" |9
| colspan="5" |5
| colspan="5" |5
|955
|1L 2s
|9:5
|
|
|-
| colspan="4" |4
| 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
|
|
|-
| colspan="7" |7
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
|7444
|[[1L 3s]]
|7:4
|
|
|-
| colspan="3" |3
| 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
| colspan="3" |3
| colspan="3" |3
| 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
| 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
| colspan="2" |2
| colspan="2" |2
| 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
|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
| colspan="2" |2
| colspan="2" |2
| 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
|
|
|-
| colspan="17" |17
|1
|1
|
|1L 2s
|17:1
|
|
|-
| colspan="16" |16
|1
|1
|1
|
|[[1L 3s]]
|16:1
|
|
|-
| colspan="15" |15
|1
|1
|1
|1
|
|[[1L 4s]]
|15:1
|
|
|-
| colspan="14" |14
|1
|1
|1
|1
|1
|
|[[1L 5s]]
|14:1
|
|
|-
| colspan="13" |13
|1
|1
|1
|1
|1
|1
|
|[[1L 6s]]
|13:1
|
|
|-
| colspan="12" |12
|1
|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
|1
|1
|1
|1
|1
|1
|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
|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
|1
|1
|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
|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, or up to 5th-order child mosses.
{| class="wikitable mw-collapsible"
! colspan="6" |Mos Family Tree (single-period only)
|-
!Parent Scale
!1st-order child mosses
!2nd-order child mosses
!3rd-order child mosses
!4th-order child mosses
!5th-order child mosses
|-
| rowspan="63" |1L 1s
| rowspan="31" |1L 2s
| rowspan="15" |1L 3s
| rowspan="7" |1L 4s
| rowspan="3" |1L 5s
|1L 6s
|-
|
|-
|-
|1L 5s
|6L 1s
|6L 1s
|7L 6s
|13L 7s
|20L 13s
|33L 20s
|53L 33s
|-
|-
|
|2L 4s
|
|6L 2s
|8L 6s
|14L 8s
|22L 14s
|36L 22s
|58L 36s
|-
|-
| rowspan="3" |5L 1s
|3L 3s
|5L 6s
|6L 3s
|9L 6s
|15L 9s
|24L 15s
|39L 24s
|63L 39s
|-
|-
|
|4L 3s
|7L 4s
|11L 7s
|18L 11s
|29L 18s
|47L 29s
|76L 47s
|-
|-
|5L 1s
|6L 5s
|6L 5s
|11L 6s
|17L 11s
|28L 17s
|45L 28s
|73L 45s
|-
|-
|
! colspan="7" |
|
|
|-
|-
| rowspan="7" |4L 1s
|1L 6s
| rowspan="3" |4L 5s
|7L 1s
|4L 9s
|8L 7s
|15L 8s
|23L 15s
|38L 23s
|61L 38s
|-
|-
|
|2L 5s
|-
|7L 2s
|9L 4s
|9L 7s
|-
|16L 9s
|
|25L 16s
|
|41L 25s
|-
|66L 41s
| rowspan="3" |5L 4s
|5L 9s
|-
|
|-
|9L 5s
|-
|
|
|
|
|-
| rowspan="15" |3L 1s
| rowspan="7" |3L 4s
| rowspan="3" |3L 7s
|3L 10s
|-
|
|-
|10L 3s
|-
|
|
|-
| rowspan="3" |7L 3s
|7L 10s
|-
|
|-
|-
|3L 4s
|7L 3s
|10L 7s
|10L 7s
|17L 10s
|27L 17s
|44L 27s
|71L 44s
|-
|-
|
|4L 3s
|
|7L 4s
|
|-
| rowspan="7" |4L 3s
| rowspan="3" |4L 7s
|4L 11s
|-
|
|-
|11L 4s
|-
|
|
|-
| rowspan="3" |7L 4s
|7L 11s
|-
|
|-
|11L 7s
|11L 7s
|18L 11s
|29L 18s
|47L 29s
|76L 47s
|-
|-
|
|5L 2s
|
|7L 5s
|
|12L 7s
|
|19L 12s
|
|31L 19s
|50L 31s
|81L 50s
|-
|-
| rowspan="31" |2L 1s
|6L 1s
| rowspan="15" |2L 3s
|7L 6s
| rowspan="7" |2L 5s
|13L 7s
| rowspan="3" |2L 7s
|20L 13s
|2L 9s
|33L 20s
|53L 33s
|86L 53s
|-
|-
|
! colspan="7" |
|-
|-
|9L 2s
|1L 7s
|8L 1s
|9L 8s
|17L 9s
|26L 17s
|43L 26s
|69L 43s
|-
|-
|
|2L 6s
|
|8L 2s
|10L 8s
|18L 10s
|28L 18s
|46L 28s
|74L 46s
|-
|-
| rowspan="3" |7L 2s
|3L 5s
|7L 9s
|8L 3s
|11L 8s
|19L 11s
|30L 19s
|49L 30s
|79L 49s
|-
|-
|
|4L 4s
|8L 4s
|12L 8s
|20L 12s
|32L 20s
|52L 32s
|84L 52s
|-
|-
|9L 7s
|5L 3s
|8L 5s
|13L 8s
|21L 13s
|34L 21s
|55L 34s
|89L 55s
|-
|-
|
|6L 2s
|
|8L 6s
|
|14L 8s
|22L 14s
|36L 22s
|58L 36s
|94L 58s
|-
|-
| rowspan="7" |5L 2s
|7L 1s
| rowspan="3" |5L 7s
|8L 7s
|5L 12s
|15L 8s
|23L 15s
|38L 23s
|61L 38s
|99L 61s
|-
|-
|
! colspan="7" |
|-
|-
|12L 5s
|1L 8s
|9L 1s
|10L 9s
|19L 10s
|29L 19s
|48L 29s
|77L 48s
|-
|-
|
|2L 7s
|
|9L 2s
|11L 9s
|20L 11s
|31L 20s
|51L 31s
|82L 51s
|-
|-
| rowspan="3" |7L 5s
|3L 6s
|7L 12s
|9L 3s
|12L 9s
|21L 12s
|33L 21s
|54L 33s
|87L 54s
|-
|-
|
|4L 5s
|9L 4s
|13L 9s
|22L 13s
|35L 22s
|57L 35s
|92L 57s
|-
|-
|12L 7s
|5L 4s
|9L 5s
|14L 9s
|23L 14s
|37L 23s
|60L 37s
|97L 60s
|-
|-
|
|6L 3s
|
|9L 6s
|
|15L 9s
|
|24L 15s
|39L 24s
|63L 39s
|102L 63s
|-
|-
| rowspan="15" |3L 2s
|7L 2s
| rowspan="7" |3L 5s
|9L 7s
| rowspan="3" |3L 8s
|16L 9s
|3L 11s
|25L 16s
|41L 25s
|66L 41s
|107L 66s
|-
|-
|
|8L 1s
|9L 8s
|17L 9s
|26L 17s
|43L 26s
|69L 43s
|112L 69s
|-
|-
|11L 3s
! colspan="7" |
|-
|-
|
|1L 9s
|
|10L 1s
|11L 10s
|21L 11s
|32L 21s
|53L 32s
|85L 53s
|-
|-
| rowspan="3" |8L 3s
|2L 8s
|8L 11s
|10L 2s
|12L 10s
|22L 12s
|34L 22s
|56L 34s
|90L 56s
|-
|-
|
|3L 7s
|10L 3s
|13L 10s
|23L 13s
|36L 23s
|59L 36s
|95L 59s
|-
|-
|11L 8s
|4L 6s
|10L 4s
|14L 10s
|24L 14s
|38L 24s
|62L 38s
|100L 62s
|-
|-
|
|5L 5s
|
|10L 5s
|
|15L 10s
|25L 15s
|40L 25s
|65L 40s
|105L 65s
|-
|-
| rowspan="7" |5L 3s
|6L 4s
| rowspan="3" |5L 8s
|10L 6s
|5L 13s
|16L 10s
|26L 16s
|42L 26s
|68L 42s
|110L 68s
|-
|-
|
|7L 3s
|10L 7s
|17L 10s
|27L 17s
|44L 27s
|71L 44s
|115L 71s
|-
|-
|13L 5s
|8L 2s
|-
|10L 8s
|
|18L 10s
|
|28L 18s
|-
|46L 28s
| rowspan="3" |8L 5s
|74L 46s
|8L 13s
|120L 74s
|-
|
|-
|-
|13L 8
|9L 1s
|10L 9s
|19L 10s
|29L 19s
|48L 29s
|77L 48s
|125L 77s
|}
|}
== Scale Table ==
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.
Deployed examples can be found under [[MOS scales of 17edo|17edo mos scales]] and [[31edo MOS scales|31edo mos scales]].
{| class="wikitable mw-collapsible"
{| class="wikitable mw-collapsible"
! colspan="12" |Mos Family Tree (single-period only), with TAMNAMS Names
! colspan="12" |Mos Family Tree (single-period only), with TAMNAMS Names
italics denote 1L ns scales; asterisks denote non-official names (from my own notes)
italics denote 1L ns scales (named for completeness); asterisks denote non-official names (from my own notes)
|-
! colspan="2" |Progenitor scale
! colspan="2" |1st-order child mosses
! colspan="2" |2nd-order child mosses
! colspan="2" |3rd-order child mosses
! colspan="2" |4th-order child mosses
! colspan="2" |5th-order child mosses
|-
|-
!Parent Scale
!Steps
!Mos name
!Scale name
!1st-order child mosses
!Steps
!Mos name
!Scale name
!2nd-order child mosses
!Steps
!Mos name
!Scale name
!3rd-order child mosses
!Steps
!Mos name
!Scale name
!4th-order child mosses
!Steps
!Mos name
!Scale name
!5th-order child mosses
!Steps
!Mos name
!Scale name
|-
|-
| rowspan="63" |1L 1s
| rowspan="63" |1L 1s
Line 2,636: Line 511:
|-
|-
|9L 2s
|9L 2s
|ultradiatonic*
|
|-
|-
|
|
Line 2,666: Line 541:
| rowspan="3" |p-chromatic
| rowspan="3" |p-chromatic
|5L 12s
|5L 12s
|p²-chromatic*
|p-superchromatic*
|-
|-
|
|
Line 2,688: Line 563:
|-
|-
|12L 7s
|12L 7s
|m²-chromatic*
|m-superchromatic*
|-
|-
|
|
Line 2,765: Line 640:
|13L 8
|13L 8
|
|
|}
=== 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
|-
! 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="16" |1L 1s
| rowspan="16" |trivial
| 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 *'''
|-
|[[8L 1s]]
|'''subneutralic **'''
| colspan="2" rowspan="14" |
|-
|[[7L 1s]]
|'''pine *'''
| colspan="2" rowspan="13" |
|-
|[[6L 1s]]
|'''archaeotonic **'''
| colspan="2" rowspan="12" |
|-
|[[5L 1s]]
|'''machinoid *'''
| colspan="2" rowspan="11" |
|-
| rowspan="2" |4L 1s
| rowspan="2" |manual
|[[5L 4s]]
|'''semiquartal *'''
|-
|[[4L 5s]]
|'''gramitonic *'''
|-
| rowspan="3" |3L 1s
| rowspan="3" |tetric
|[[4L 3s]]
|'''smitonic *'''
| colspan="2" |
|-
| rowspan="2" |3L 4s
| rowspan="2" |mosh
|[[7L 3s]]
|'''dicoid *'''
|-
|[[3L 7s]]
|'''sephiroid *'''
|-
| rowspan="5" |2L 1s
| rowspan="5" |trial
| rowspan="2" |3L 2s
| rowspan="2" |antipentic
|[[3L 5s]]
|'''checkertonic *'''
| colspan="2" rowspan="3" |
|-
|[[5L 3s]]
|'''oneirotonic **'''
|-
| rowspan="3" |2L 3s
| rowspan="3" |pentic
|[[5L 2s]]
|'''diatonic *'''
|-
| rowspan="2" |2L 5s
| rowspan="2" |antidiatonic
|[[7L 2s]]
|'''armotonic **'''
|-
|[[2L 7s]]
|'''balzano *'''
|-
! colspan="18" |Family tree of 2-period mosses, limited to 10-note scales
|-
! 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" |
|-
!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" |
|-
|[[8L 2s]]
|'''taric ***'''
|-
|[[6L 2s]]
|'''ekic **'''
| colspan="2" rowspan="3" |
|-
| rowspan="2" |4L 2s
| rowspan="2" |citric
|[[6L 4s]]
|'''lemon *'''
|-
|[[4L 6s]]
|'''lime *'''
|-
! colspan="18" |Family tree of 3-period mosses, limited to 10-note scales
|-
! colspan="2" |Root
! colspan="2" |1st-order child scales
! colspan="14" rowspan="2" |
|-
!Mos
!Name
!Mos
!Name
|-
| rowspan="2" |3L 3s
| rowspan="2" |triwood
|[[3L 6s]]
|'''tcherepnin *'''
| colspan="14" rowspan="2" |
|-
|[[6L 3s]]
|'''hyrulic *'''
|-
! colspan="18" |Family tree of 4-period mosses, limited to 10-note scales
|-
! colspan="2" |Root
! colspan="16" rowspan="2" |
|-
!Mos
!Name
|-
|[[4L 4s]]
|'''tetrawood **'''
| colspan="16" |
|-
! colspan="18" |Family tree of 5-period mosses, limited to 10-note scales
|-
! colspan="2" |Root
! colspan="16" rowspan="2" |
|-
!Mos
!Name
|-
|[[5L 5s]]
|'''pentawood *'''
| colspan="16" |
|}
|}


Line 2,953: 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
!0
!29\31 - 2\31
!1
!28\31 - 3\31
!2
!27\31 - 4\31
!3
!26\31 - 5\31
!4
!25\31 - 6\31
!5
!24\31 - 7\31
!6
!23\31 - 8\31
!7
!22\31 - 9\31
!8
!21\31 - 10\31
!9
!20\31 - 11\31
!10
!19\31 - 12\31
!18\31 - 13\31
!17\31 - 14\31
!16\31 - 15\31
|-
|-
|1L 1s
! rowspan="11" |Large step size (L)
|1L 1s
!0
|1L 1s
|'''0'''
|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
|1L 6s
|1L 6s
|1L 6s
|6L 1s
|5L 6s
|9L 4s
|4L 11s
|7L 10s
|3L 10s
|3L 11s
|13L 5s
|12L 7s
|9L 2s
|2L 9s
|-
|1L 7s
|1L 7s
|1L 7s
|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 3,143: Line 1,073:
|
|
|
|
|3L 25s
|
|
|
|
|
|
|
|
|2L 19s
|-
|-
|1L 12s
!2
|1L 12s
|''10''
|31edo
|12
|
|'''14'''
|
|
|
|
|
|
|
|
|
|31edo
|
|
|
|
|
|
|
|
|2L 21s
|-
|-
|1L 13s
!3
|1L 13s
|''15''
|
|17
|19
|'''21'''
|
|
|
|
Line 3,176: Line 1,103:
|
|
|
|
|
|
|
|
|2L 23s
|-
|-
|1L 14s
!4
|1L 14s
|''20''
|22
|24
|26
|'''28'''
|
|
|
|
Line 3,190: Line 1,116:
|
|
|
|
|-
!5
|''25''
|27
|29
|31
|33
|'''35'''
|
|
|
|
Line 3,195: 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'''
|
|
|
|}
|}

Latest revision as of 06:30, 19 March 2025

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

Golden ratio tunings of mosses

Parent scale Child scale Grandchild scale Great-grandchild scale 4th-order descendant 5th-order descendant 6-order descendant
xL ys (x+y)L xs (2x+y)L (x+y)s (3x+2y)L (2x+y)s (5x+3y)L (3x+2y)s (8x+5y)L (5x+3y)s (13x+8y)L (8x+5y)s
1L 5s 6L 1s 7L 6s 13L 7s 20L 13s 33L 20s 53L 33s
2L 4s 6L 2s 8L 6s 14L 8s 22L 14s 36L 22s 58L 36s
3L 3s 6L 3s 9L 6s 15L 9s 24L 15s 39L 24s 63L 39s
4L 3s 7L 4s 11L 7s 18L 11s 29L 18s 47L 29s 76L 47s
5L 1s 6L 5s 11L 6s 17L 11s 28L 17s 45L 28s 73L 45s
1L 6s 7L 1s 8L 7s 15L 8s 23L 15s 38L 23s 61L 38s
2L 5s 7L 2s 9L 7s 16L 9s 25L 16s 41L 25s 66L 41s
3L 4s 7L 3s 10L 7s 17L 10s 27L 17s 44L 27s 71L 44s
4L 3s 7L 4s 11L 7s 18L 11s 29L 18s 47L 29s 76L 47s
5L 2s 7L 5s 12L 7s 19L 12s 31L 19s 50L 31s 81L 50s
6L 1s 7L 6s 13L 7s 20L 13s 33L 20s 53L 33s 86L 53s
1L 7s 8L 1s 9L 8s 17L 9s 26L 17s 43L 26s 69L 43s
2L 6s 8L 2s 10L 8s 18L 10s 28L 18s 46L 28s 74L 46s
3L 5s 8L 3s 11L 8s 19L 11s 30L 19s 49L 30s 79L 49s
4L 4s 8L 4s 12L 8s 20L 12s 32L 20s 52L 32s 84L 52s
5L 3s 8L 5s 13L 8s 21L 13s 34L 21s 55L 34s 89L 55s
6L 2s 8L 6s 14L 8s 22L 14s 36L 22s 58L 36s 94L 58s
7L 1s 8L 7s 15L 8s 23L 15s 38L 23s 61L 38s 99L 61s
1L 8s 9L 1s 10L 9s 19L 10s 29L 19s 48L 29s 77L 48s
2L 7s 9L 2s 11L 9s 20L 11s 31L 20s 51L 31s 82L 51s
3L 6s 9L 3s 12L 9s 21L 12s 33L 21s 54L 33s 87L 54s
4L 5s 9L 4s 13L 9s 22L 13s 35L 22s 57L 35s 92L 57s
5L 4s 9L 5s 14L 9s 23L 14s 37L 23s 60L 37s 97L 60s
6L 3s 9L 6s 15L 9s 24L 15s 39L 24s 63L 39s 102L 63s
7L 2s 9L 7s 16L 9s 25L 16s 41L 25s 66L 41s 107L 66s
8L 1s 9L 8s 17L 9s 26L 17s 43L 26s 69L 43s 112L 69s
1L 9s 10L 1s 11L 10s 21L 11s 32L 21s 53L 32s 85L 53s
2L 8s 10L 2s 12L 10s 22L 12s 34L 22s 56L 34s 90L 56s
3L 7s 10L 3s 13L 10s 23L 13s 36L 23s 59L 36s 95L 59s
4L 6s 10L 4s 14L 10s 24L 14s 38L 24s 62L 38s 100L 62s
5L 5s 10L 5s 15L 10s 25L 15s 40L 25s 65L 40s 105L 65s
6L 4s 10L 6s 16L 10s 26L 16s 42L 26s 68L 42s 110L 68s
7L 3s 10L 7s 17L 10s 27L 17s 44L 27s 71L 44s 115L 71s
8L 2s 10L 8s 18L 10s 28L 18s 46L 28s 74L 46s 120L 74s
9L 1s 10L 9s 19L 10s 29L 19s 48L 29s 77L 48s 125L 77s

Scale Table

I've had the idea of using a 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.

Deployed examples can be found under 17edo mos scales and 31edo mos scales.

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)

Progenitor scale 1st-order child mosses 2nd-order child mosses 3rd-order child mosses 4th-order child mosses 5th-order child mosses
Steps Scale name Steps Scale name Steps Scale name Steps Scale name Steps Scale name Steps Scale name
1L 1s prototonic* 1L 2s

antideuteric*

 1L 3s antitetric* 1L 4s antimanic 1L 5s antimachinoid 1L 6s anti-archeotonic
6L 1s archeotonic
5L 1s machinoid 5L 6s
6L 5s
4L 1s manic 4L 5s orwelloid 4L 9s
9L 4s
5L 4s semiquartal 5L 9s
9L 5s
3L 1s tetric* 3L 4s mosh 3L 7s sephiroid 3L 10s
10L 3s
7L 3s dicotonic 7L 10s
10L 7s
4L 3s smitonic 4L 7s kleistonic 4L 11s
11L 4s
7L 4s suprasmitonic 7L 11s
11L 7s
2L 1s deuteric* 2L 3s pentic 2L 5s antidiatonic 2L 7s joanatonic 2L 9s
9L 2s
7L 2s superdiatonic 7L 9s
9L 7s
5L 2s diatonic 5L 7s p-chromatic 5L 12s p-superchromatic*
12L 5s
7L 5s m-chromatic 7L 12s
12L 7s m-superchromatic*
3L 2s antipentic 3L 5s sensoid 3L 8s 3L 11s
11L 3s
8L 3s 8L 11s
11L 8s
5L 3s oneirotonic 5L 8s 5L 13s
13L 5s
8L 5s 8L 13s
13L 8

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.)

Family tree of single-period mosses, limited to 10-note scales
Root 1st-order child scales 2nd-order child scales 3rd-order child scales 4th-order child scales 5th-order child scales 6th-order child scales 7th-order child scales 8th-order child scales
Mos Name Mos Name Mos Name Mos Name Mos Name Mos Name Mos Name Mos Name Mos Name
1L 1s trivial 1L 2s antrial 1L 3s antetric 1L 4s pedal 1L 5s antimachinoid 1L 6s onyx 1L 7s antipine 1L 8s antisubneutralic 1L 9s antisinatonic *
9L 1s sinatonic *
8L 1s subneutralic **
7L 1s pine *
6L 1s archaeotonic **
5L 1s machinoid *
4L 1s manual 5L 4s semiquartal *
4L 5s gramitonic *
3L 1s tetric 4L 3s smitonic *
3L 4s mosh 7L 3s dicoid *
3L 7s sephiroid *
2L 1s trial 3L 2s antipentic 3L 5s checkertonic *
5L 3s oneirotonic **
2L 3s pentic 5L 2s diatonic *
2L 5s antidiatonic 7L 2s armotonic **
2L 7s balzano *
Family tree of 2-period mosses, limited to 10-note scales
Root 1st-order child scales 2nd-order child scales 3rd-order child scales
Mos Name Mos Name Mos Name Mos Name
2L 2s biwood 2L 4s malic 2L 6s subaric 2L 8s jaric *
8L 2s taric ***
6L 2s ekic **
4L 2s citric 6L 4s lemon *
4L 6s lime *
Family tree of 3-period mosses, limited to 10-note scales
Root 1st-order child scales
Mos Name Mos Name
3L 3s triwood 3L 6s tcherepnin *
6L 3s hyrulic *
Family tree of 4-period mosses, limited to 10-note scales
Root
Mos Name
4L 4s tetrawood **
Family tree of 5-period mosses, limited to 10-note scales
Root
Mos Name
5L 5s pentawood *

Mos Family Tree for an Edo

The basis of this diagram is simple: take the infinite mos family tree and only show the scales that are available for a specific edo.

19edo Example

The table shown below is the mos family tree for 19edo.

Mos Family Tree for 19edo
Generator Pair 18\19 - 1\19 17\19 - 2\19 16\19 - 3\19 15\19 - 4\19 14\19 - 5\19 13\19 - 6\19 12\19 - 7\19 11\19 - 8\19 10\19 - 9\19
Gen. 1 1L 1s
Gen. 2 1L 2s 2L 1s
Gen. 3 1L 3s 3L 1s 3L 2s 2L 3s
Gen. 4 1L 4s 4L 1s 4L 3s 3L 4s 3L 5s 5L 2s 2L 5s
Gen. 5 1L 5s 5L 4s 4L 7s 3L 7s 8L 3s 7L 5s 2L 7s
Gen. 6 1L 6s 6L 1s 5L 9s 4L 11s 3L 10s 2L 9s
Gen. 7 1L 7s 6L 7s 3L 13s 2L 11s
Gen. 8 1L 8s 2L 13s
Gen. 9 1L 9s 2L 15s
Gen. 10 1L 10s
Gen. 11 1L 11s
Gen. 12 1L 12s
Gen. 13 1L 13s
Gen. 14 1L 14s
Gen. 15 1L 15s
Gen. 16 1L 16s
Gen. 17 1L 17s

This tree can be thought of as a pruned mos family tree, where every leaf node corresponds to a mos available to 19edo with a step ratio of 2:1. To conceptualize this tree better, consider the leaf node 7L 5s. Since the entire structure is a binary tree (that is, there are no loopy paths), there is one and only one unique path that starts from 1L 1s and ends at 7L 5s. Likewise, all other leaf nodes have a unique path that, when traversed backwards, merges back with 1L 1s.

Note that all of these paths inevitably overlap. It's important to note that these overlaps are due to each path having multiple mosses in common with one another; for a node with two child nodes, the two child scales don't share the same generator pair, only a common mos from the parent node. Pruning a mos tree by generator pair isolates a single linear path between 1L 1s and the leaf node with the step ratio of 2:1; put another way, the tree would be pruned down to a single, finite branch.

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.

Mos-edo table

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.

Edos of 5L 2s Small step size (s)
0 1 2 3 4 5 6 7 8 9 10
Large step size (L) 0 0
1 5 7
2 10 12 14
3 15 17 19 21
4 20 22 24 26 28
5 25 27 29 31 33 35
6 30 32 34 36 38 40 42
7 35 37 39 41 43 45 47 49
8 40 42 44 46 48 50 52 54 56
9 45 47 49 51 53 55 57 59 61 63
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.

Edos of 5L 2s Small step size (s)
0 1 2 3 4 5 6 7 8 9 10
Chroma size

|L-s|

0 0 7 14 21 28 35 42 49 56 63 70
1 5 12 19 26 33 40 47 54 61 68 75
2 10 17 24 31 38 45 52 59 66 73 80
3 15 22 29 36 43 50 57 64 71 78 85
4 20 27 34 41 48 55 62 69 76 83 90
5 25 32 39 46 53 60 67 74 81 88 95
6 30 37 44 51 58 65 72 79 86 93 100
7 35 42 49 56 63 70 77 84 91 98 105
8 40 47 54 61 68 75 82 89 96 103 110
9 45 52 59 66 73 80 87 94 101 108 115
10 50 57 64 71 78 85 92 99 106 113 120
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