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→Mos-temperament table: Table broke, was also similar to the scale table in a way
Ganaram inukshuk (talk | contribs)
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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'''
|
|
|
|}
|}
Retrieved from "https://en.xen.wiki/w/User:Ganaram_inukshuk/Tables"