User:Ganaram inukshuk/Tables: Difference between revisions

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→Mos-temperament table: Table broke, was also similar to the scale table in a way
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→Alternate ways of organizing mosses named under TAMNAMS: Removed most of the mos-organizing trees since they represented one of two main trees; added "mos-edo" table (edmos/mosedo table?)
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== Scale Table ==
== 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. Here's a few examples.
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.


=== Temperament Agnostic Information Only ===
Deployed examples can be found under [[MOS scales of 17edo|17edo mos scales]] and [[31edo MOS scales|31edo mos scales]].
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"
! colspan="19" |'''Step Pattern (19edo)'''
!'''Mos'''
!'''[[TAMNAMS#Step ratio spectrum|Step Ratio]]'''
!'''[[TAMNAMS#Mos pattern names|TAMNAMS Name]] (if applicable)'''
|-
| colspan="10" |10
| colspan="9" |9
|1L 1s
|10:9
|Generator Pair
|-
|1
| 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
|-
|
|-
|6L 1s
|-
|
|
|-
| rowspan="3" |5L 1s
|5L 6s
|-
|
|-
|6L 5s
|-
|
|
|
|-
| rowspan="7" |4L 1s
| rowspan="3" |4L 5s
|4L 9s
|-
|
|-
|9L 4s
|-
|
|
|-
| 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
|-
|
|-
|10L 7s
|-
|
|
|
|-
| rowspan="7" |4L 3s
| rowspan="3" |4L 7s
|4L 11s
|-
|
|-
|11L 4s
|-
|
|
|-
| rowspan="3" |7L 4s
|7L 11s
|-
|
|-
|11L 7s
|-
|
|
|
|
|
|-
| rowspan="31" |2L 1s
| rowspan="15" |2L 3s
| rowspan="7" |2L 5s
| rowspan="3" |2L 7s
|2L 9s
|-
|
|-
|9L 2s
|-
|
|
|-
| rowspan="3" |7L 2s
|7L 9s
|-
|
|-
|9L 7s
|-
|
|
|
|-
| rowspan="7" |5L 2s
| rowspan="3" |5L 7s
|5L 12s
|-
|
|-
|12L 5s
|-
|
|
|-
| rowspan="3" |7L 5s
|7L 12s
|-
|
|-
|12L 7s
|-
|
|
|
|
|-
| rowspan="15" |3L 2s
| rowspan="7" |3L 5s
| rowspan="3" |3L 8s
|3L 11s
|-
|
|-
|11L 3s
|-
|
|
|-
| rowspan="3" |8L 3s
|8L 11s
|-
|
|-
|11L 8s
|-
|
|
|
|-
| rowspan="7" |5L 3s
| rowspan="3" |5L 8s
|5L 13s
|-
|
|-
|13L 5s
|-
|
|
|-
| rowspan="3" |8L 5s
|8L 13s
|-
|
|-
|13L 8
|}
 
== Alternate ways of organizing mosses named under TAMNAMS ==
 
=== Using the MOS family tree (with outdated names) ===
{| 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
Line 3,168: Line 723:
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" |Large step size
!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" |Small step size
|1L 7s
!0
|1L 7s
|''0''
|7L 1s
|''5''
|6L 7s
|''10''
|5L 11s
|''15''
|9L 13s
|''20''
|4L 15s
|''25''
|7L 17s
|''30''
|3L 13s
|''35''
|14L 3s
|''40''
|31edo
|''45''
|31edo
|''50''
|11L 9s
|2L 11s
|-
|-
|1L 8s
!1
|1L 8s
|1L 8s
|8L 7s
|6L 13s
|5L 16s
|31edo
|4L 19s
|31edo
|3L 16s
|31edo
|
|
|
|'''7'''
|31edo
|12
|2L 13s
|17
|22
|27
|32
|37
|42
|47
|52
|-
|-
|1L 9s
!2
|1L 9s
|1L 9s
|8L 15s
|6L 19s
|5L 21s
|
|4L 23s
|
|3L 19s
|
|
|
|
|
|
|'''14'''
|2L 15s
|19
|24
|29
|34
|39
|44
|49
|54
|-
|-
|1L 10s
!3
|1L 10s
|10L 1s
|31edo
|31edo
|31edo
|
|31edo
|
|
|3L 22s
|
|
|
|
|
|'''21'''
|
|26
|2L 17s
|31
|36
|41
|46
|51
|56
|-
|-
|1L 11s
!4
|1L 11s
|10L 11s
|
|
|
|
|
|
|3L 25s
|
|
|
|
|
|
|
|
|2L 19s
|'''28'''
|33
|38
|43
|48
|53
|58
|-
|-
|1L 12s
!5
|1L 12s
|31edo
|
|
|
|
|
Line 3,374: Line 813:
|
|
|
|
|31edo
|'''35'''
|
|40
|
|45
|
|50
|
|55
|2L 21s
|60
|-
|-
|1L 13s
!6
|1L 13s
|
|
|
|
|
|
Line 3,391: Line 827:
|
|
|
|
|
|'''42'''
|
|47
|
|52
|
|57
|2L 23s
|62
|-
|-
|1L 14s
!7
|1L 14s
|
|
|
|
Line 3,406: Line 841:
|
|
|
|
|
|'''49'''
|
|54
|
|59
|
|64
|
|2L 25s
|-
|-
|1L 15s
!8
|15L 1s
|
|
|
|
|
|
|
|
Line 3,427: Line 855:
|
|
|
|
|2L 27s
|'''56'''
|61
|66
|-
|-
|1L 16s
!9
|31edo
|
|
|
|
|
Line 3,441: Line 869:
|
|
|
|
|
|'''63'''
|
|68
|31edo
|-
|-
|1L 17s
!10
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|-
|1L 18s
|
|
|
|
|
|
|
|
Line 3,476: Line 883:
|
|
|
|
|'''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.
{| class="wikitable"
! colspan="2" rowspan="2" |Edos of 5L 2s
! colspan="11" |Large step size
|-
|-
|1L 19s
!0
|
!1
|
!2
|
!3
|
!4
|
!5
|
!6
|
!7
|
!8
|
!9
|
!10
|
|
|
|
|-
|-
|1L 20s
! rowspan="11" |Small step size
|
!0
|
|''0''
|
|''5''
|
|''10''
|
|''15''
|
|''20''
|
|''25''
|
|''30''
|
|''35''
|
|''40''
|
|''45''
|
|''50''
|
|
|-
|-
|1L 21s
!1
|
|''7''
|
|'''12'''
|
|'''17'''
|
|22
|
|27
|
|32
|
|37
|
|42
|
|47
|
|52
|
|57
|
|
|
|-
|-
|1L 22s
!2
|
|''14''
|
|'''19'''
|
|'''24'''
|
|29
|
|'''34'''
|
|39
|
|44
|
|49
|
|54
|
|59
|
|64
|
|
|
|-
|-
|1L 23s
!3
|
|''21''
|
|26
|
|31
|
|'''36'''
|
|41
|
|46
|
|'''51'''
|
|56
|
|61
|
|66
|
|71
|
|
|
|-
|-
|1L 24s
!4
|
|''28''
|
|33
|
|'''38'''
|
|43
|
|'''48'''
|
|53
|
|58
|
|63
|
|'''68'''
|
|73
|
|78
|
|
|
|-
|-
|1L 25s
!5
|
|''35''
|
|40
|
|45
|
|50
|
|55
|
|'''60'''
|
|65
|
|70
|
|75
|
|80
|
|'''85'''
|
|
|
|-
|-
|1L 26s
!6
|
|''42''
|
|47
|
|52
|
|'''57'''
|
|62
|
|67
|
|'''72'''
|
|77
|
|82
|
|87
|
|92
|
|
|
|-
|-
|1L 27s
!7
|
|''49''
|
|54
|
|59
|
|64
|
|69
|
|74
|
|79
|
|'''84'''
|
|89
|
|94
|
|99
|
|
|
|-
|-
|1L 28s
!8
|
|''56''
|
|61
|
|66
|
|71
|
|'''76'''
|
|81
|
|86
|
|91
|
|'''96'''
|
|101
|
|106
|
|
|
|-
|-
|1L 29s
!9
|
|''63''
|
|68
|
|73
|
|78
|
|83
|
|88
|
|93
|
|98
|
|103
|
|'''108'''
|
|113
|
|
|
|-
|-
|31edo
!10
|
|''70''
|
|75
|
|80
|
|85
|
|90
|
|'''95'''
|
|100
|
|105
|
|110
|
|115
|
|'''120'''
|
|
|
|}
|}

Revision as of 09:13, 8 March 2023

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

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

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 archeotonic
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 superdiatonic
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, diminished
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 Large step size
0 1 2 3 4 5 6 7 8 9 10
Small step size 0 0 5 10 15 20 25 30 35 40 45 50
1 7 12 17 22 27 32 37 42 47 52
2 14 19 24 29 34 39 44 49 54
3 21 26 31 36 41 46 51 56
4 28 33 38 43 48 53 58
5 35 40 45 50 55 60
6 42 47 52 57 62
7 49 54 59 64
8 56 61 66
9 63 68
10 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.

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