List of MOS scales in 17edo: Difference between revisions

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=Moment of Symmetry Scales of [[17edo|17edo]]=
Since 17 is a prime number, any interval can be repeatedly stacked to produce new intervals until all 17 tones are included. This page lists and visualizes the scales produced this way.


See [[MOSScales|moment of symmetry scales]] for background on this type of linear scale.
==Diagram of mosses of [[17edo]]==
 
The following diagram is a visualization of some of the mosses available in 17edo. See [[MOSScales|moment of symmetry scales]] for background on this type of linear scale, and see [[horogram]] for background on this type of diagram.


[[File:17edo_horograms.jpg|alt=17edo_horograms.jpg|17edo_horograms.jpg]]
[[File:17edo_horograms.jpg|alt=17edo_horograms.jpg|17edo_horograms.jpg]]
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See also: [[17edo_neutral_scale|17edo neutral scale]]
See also: [[17edo_neutral_scale|17edo neutral scale]]
== Mosses by generator pair ==
The following is a table that sorts all possible moment-of-symmetry scales by generator pair, including mos information, temperament-agnostic information, and temperament information. A few notes:
* The table denotes each family using a [[Horogram#Rectangular%20Horogram|rectangular horogram]], starting with 1L 1s and [[MOS Diagrams|adding notes]] until every note is added.
* For scales whose order of steps, from read left-to-right, starts with a large step and ends with a small step, the smaller of the two generators is the chroma-positive generator; otherwise, the larger of the two is the chroma-positive generator.
* [[TAMNAMS]] names are used wherever possible. Scales with at least four notes have clickable links to their corresponding mos page.
{| class="wikitable"
! colspan="21" |Single-Period Scales for 17 Equal Division of the Octave
|-
! colspan="17" |Steps for Generators 16\17 and 1\17
!Mos
!Step Ratio
!TAMNAMS Name
!Temperament
|-
| colspan="16" |16
|1
|1L 1s
|16:1
|
|
|-
| colspan="15" |15
|1
|1
|1L 2s
|15:1
|
|
|-
| colspan="14" |14
|1
|1
|1
|[[1L 3s]]
|14:1
|
|
|-
| colspan="13" |13
|1
|1
|1
|1
|[[1L 4s]]
|13:1
|
|
|-
| colspan="12" |12
|1
|1
|1
|1
|1
|[[1L 5s]]
|12:1
|
|
|-
| colspan="11" |11
|1
|1
|1
|1
|1
|1
|[[1L 6s]]
|11:1
|
|
|-
| colspan="10" |10
|1
|1
|1
|1
|1
|1
|1
|[[1L 7s]]
|10:1
|
|
|-
| colspan="9" |9
|1
|1
|1
|1
|1
|1
|1
|1
|[[1L 8s]]
|9:1
|
|
|-
| colspan="8" |8
|1
|1
|1
|1
|1
|1
|1
|1
|1
|[[1L 9s]]
|8:1
|
|
|-
| colspan="7" |7
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|[[1L 10s]]
|7:1
|
|
|-
| colspan="6" |6
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|[[1L 11s]]
|6:1
|
|
|-
| colspan="5" |5
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|[[1L 12s]]
|5:1
|
|
|-
| colspan="4" |4
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|[[1L 13s]]
|4:1
|
|
|-
| colspan="3" |3
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|[[1L 14s]]
|3:1
|
|
|-
| colspan="2" |2
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|[[1L 15s]]
|2:1
|
|
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|17edo
|1
|
|
|-
! colspan="17" |Steps for Generators 15\17 and 2\17
!Mos
!Step Ratio
!TAMNAMS Name
!Temperament
|-
| colspan="15" |15
| colspan="2" |2
|1L 1s
|15:2
|
|
|-
| colspan="13" |13
| colspan="2" |2
| colspan="2" |2
|1L 2s
|13:2
|
|
|-
| colspan="11" |11
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[1L 3s]]
|11:2
|
|bleu[3]
|-
| colspan="9" |9
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[1L 4s]]
|9:2
|
|bleu[4]
|-
| colspan="7" |7
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[1L 5s]]
|7:2
|
|bleu[5]
|-
| colspan="5" |5
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[1L 6s]]
|5:2
|
|bleu[6]
|-
| colspan="3" |3
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|[[1L 7s]]
|3:2
|
|bleu[7]
|-
|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
|[[8L 1s]]
|2:1
|subneutralic
|bleu[8]
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|17edo
|1
|
|
|-
! colspan="17" |Steps for Generators 14\17 and 3\17
!Mos
!Step Ratio
!TAMNAMS Name
!Temperament
|-
| colspan="14" |14
| colspan="3" |3
|1L 1s
|14:3
|
|
|-
| colspan="11" |11
| colspan="3" |3
| colspan="3" |3
|1L 2s
|11:3
|
|
|-
| colspan="8" |8
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
|[[1L 3s]]
|8:3
|
|machine[3]
|-
| colspan="5" |5
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
|[[1L 4s]]
|5:3
|
|machine[4]
|-
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
|[[5L 1s]]
|3:2
|machinoid
|machine[5]
|-
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
|[[6L 5s]]
|2:1
|
|machine[6]
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|17edo
|1
|
|
|-
! colspan="17" |Steps for Generators 13\17 and 4\17
!Mos
!Step Ratio
!TAMNAMS Name
!Temperament
|-
| colspan="13" |13
| colspan="4" |4
|1L 1s
|13:4
|
|
|-
| colspan="9" |9
| colspan="4" |4
| colspan="4" |4
|1L 2s
|9:4
|
|
|-
| colspan="5" |5
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
|[[1L 3s]]
|5:4
|
|huxley[3]
|-
|1
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
|[[4L 1s]]
|4:1
|manic
|huxley[4]
|-
|1
|1
| colspan="3" |3
|1
| colspan="3" |3
|1
| colspan="3" |3
|1
| colspan="3" |3
|[[4L 5s]]
|3:1
|orwelloid
|huxley[5]
|-
|1
|1
|1
| colspan="2" |2
|1
|1
| colspan="2" |2
|1
|1
| colspan="2" |2
|1
|1
| colspan="2" |2
|[[4L 9s]]
|2:1
|
|huxley[9]
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|17edo
|1
|
|
|-
! colspan="17" |Steps for Generators 12\17 and 5\17
!Mos
!Step Ratio
!TAMNAMS Name
!Temperament
|-
| colspan="12" |12
| colspan="5" |5
|1L 1s
|12:5
|
|
|-
| colspan="7" |7
| colspan="5" |5
| colspan="5" |5
|1L 2s
|7:5
|
|
|-
| colspan="2" |2
| colspan="5" |5
| colspan="5" |5
| colspan="5" |5
|[[3L 1s]]
|5:2
|
|maqamic/hemif[3]
|-
| colspan="2" |2
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
|[[3L 4s]]
|3:2
|mosh
|maqamic/hemif[4]
|-
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
| colspan="2" |2
| colspan="2" |2
|1
|[[7L 3s]]
|2:1
|dicotonic
|maqamic/hemif[7]
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|17edo
|1
|
|
|-
! colspan="17" |Steps for  Generators 11\17 and 6\17
!Mos
!Step Ratio
!TAMNAMS Name
!Temperament
|-
| colspan="11" |11
| colspan="6" |6
|1L 1s
|11:6
|
|
|-
| colspan="5" |5
| colspan="6" |6
| colspan="6" |6
|2L 1s
|6:5
|
|
|-
| colspan="5" |5
| colspan="5" |5
|1
| colspan="5" |5
|1
|3L 2s
|5:1
|antipentic
|sqwares[3]
|-
| colspan="4" |4
|1
| colspan="4" |4
|1
|1
| colspan="4" |4
|1
|1
|3L 5s
|4:1
|sensoid
|sqwares[5]
|-
| colspan="3" |3
|1
|1
| colspan="3" |3
|1
|1
|1
| colspan="3" |3
|1
|1
|1
|3L 8s
|3:1
|
|sqwares[8]
|-
| colspan="2" |2
|1
|1
|1
| colspan="2" |2
|1
|1
|1
|1
| colspan="2" |2
|1
|1
|1
|1
|3L 11s
|2:1
|
|sqwares[11]
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|17edo
|1
|
|
|-
! colspan="17" |Steps for Generators 10\17 and 7\17
!Mos
!Step Ratio
!TAMNAMS Name
!Temperament
|-
| colspan="10" |10
| colspan="7" |7
|1L 1s
|10:7
|
|
|-
| colspan="3" |3
| colspan="7" |7
| colspan="7" |7
|2L 1s
|7:3
|
|
|-
| colspan="3" |3
| colspan="3" |3
| colspan="4" |4
| colspan="3" |3
| colspan="4" |4
|[[2L 3s]]
|4:3
|pentic
|supra[3]
|-
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
|1
| colspan="3" |3
| colspan="3" |3
|1
|[[5L 2s]]
|3:1
|diatonic
|supra[5]
|-
| colspan="2" |2
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
|1
| colspan="2" |2
|1
| colspan="2" |2
|1
|1
|[[5L 7s]]
|2:1
|p-chromatic
|supra[7]
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|17edo
|1
|
|
|-
! colspan="17" |Steps for Generators 9\17 and 8\17
!Mos
!Step Ratio
!TAMNAMS Name
!Temperament
|-
| colspan="9" |9
| colspan="8" |8
|1L 1s
|9:8
|
|
|-
|1
| colspan="8" |8
| colspan="8" |8
|2L 1s
|8:1
|
|
|-
|1
|1
| colspan="7" |7
|1
| colspan="7" |7
|[[2L 3s]]
|7:1
|pentic
|progress[3]
|-
|1
|1
|1
| colspan="6" |6
|1
|1
| colspan="6" |6
|[[2L 5s]]
|6:1
|antidiatonic
|progress[5]
|-
|1
|1
|1
|1
| colspan="5" |5
|1
|1
|1
| colspan="5" |5
|[[2L 7s]]
|5:1
|joanatonic
|progress[7]
|-
|1
|1
|1
|1
|1
| colspan="4" |4
|1
|1
|1
|1
| colspan="4" |4
|[[2L 9s]]
|4:1
|
|progress[9]
|-
|1
|1
|1
|1
|1
|1
| colspan="3" |3
|1
|1
|1
|1
|1
| colspan="3" |3
|[[2L 11s]]
|3:1
|
|progress[11]
|-
|1
|1
|1
|1
|1
|1
|1
| colspan="2" |2
|1
|1
|1
|1
|1
|1
| colspan="2" |2
|[[2L 13s]]
|2:1
|
|progress[13]
|-
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|1
|17edo
|1
|
|
|}

Revision as of 06:19, 29 July 2022

Since 17 is a prime number, any interval can be repeatedly stacked to produce new intervals until all 17 tones are included. This page lists and visualizes the scales produced this way.

Diagram of mosses of 17edo

The following diagram is a visualization of some of the mosses available in 17edo. See moment of symmetry scales for background on this type of linear scale, and see horogram for background on this type of diagram.

17edo_horograms.jpg

17edo horograms.pdf

generator temperament
2\17 Bleu
3\17 Machine
4\17 Huxley
5\17 Maqamic/hemif
6\17 Skwares
7\17 Supra
8\17 Progress

See also: 17edo neutral scale

Mosses by generator pair

The following is a table that sorts all possible moment-of-symmetry scales by generator pair, including mos information, temperament-agnostic information, and temperament information. A few notes:

  • The table denotes each family using a rectangular horogram, starting with 1L 1s and adding notes until every note is added.
  • For scales whose order of steps, from read left-to-right, starts with a large step and ends with a small step, the smaller of the two generators is the chroma-positive generator; otherwise, the larger of the two is the chroma-positive generator.
  • TAMNAMS names are used wherever possible. Scales with at least four notes have clickable links to their corresponding mos page.
Single-Period Scales for 17 Equal Division of the Octave
Steps for Generators 16\17 and 1\17 Mos Step Ratio TAMNAMS Name Temperament
16 1 1L 1s 16:1
15 1 1 1L 2s 15:1
14 1 1 1 1L 3s 14:1
13 1 1 1 1 1L 4s 13:1
12 1 1 1 1 1 1L 5s 12:1
11 1 1 1 1 1 1 1L 6s 11:1
10 1 1 1 1 1 1 1 1L 7s 10:1
9 1 1 1 1 1 1 1 1 1L 8s 9:1
8 1 1 1 1 1 1 1 1 1 1L 9s 8:1
7 1 1 1 1 1 1 1 1 1 1 1L 10s 7:1
6 1 1 1 1 1 1 1 1 1 1 1 1L 11s 6:1
5 1 1 1 1 1 1 1 1 1 1 1 1 1L 12s 5:1
4 1 1 1 1 1 1 1 1 1 1 1 1 1 1L 13s 4:1
3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1L 14s 3:1
2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1L 15s 2:1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 17edo 1
Steps for Generators 15\17 and 2\17 Mos Step Ratio TAMNAMS Name Temperament
15 2 1L 1s 15:2
13 2 2 1L 2s 13:2
11 2 2 2 1L 3s 11:2 bleu[3]
9 2 2 2 2 1L 4s 9:2 bleu[4]
7 2 2 2 2 2 1L 5s 7:2 bleu[5]
5 2 2 2 2 2 2 1L 6s 5:2 bleu[6]
3 2 2 2 2 2 2 2 1L 7s 3:2 bleu[7]
1 2 2 2 2 2 2 2 2 8L 1s 2:1 subneutralic bleu[8]
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 17edo 1
Steps for Generators 14\17 and 3\17 Mos Step Ratio TAMNAMS Name Temperament
14 3 1L 1s 14:3
11 3 3 1L 2s 11:3
8 3 3 3 1L 3s 8:3 machine[3]
5 3 3 3 3 1L 4s 5:3 machine[4]
2 3 3 3 3 3 5L 1s 3:2 machinoid machine[5]
2 2 1 2 1 2 1 2 1 2 1 6L 5s 2:1 machine[6]
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 17edo 1
Steps for Generators 13\17 and 4\17 Mos Step Ratio TAMNAMS Name Temperament
13 4 1L 1s 13:4
9 4 4 1L 2s 9:4
5 4 4 4 1L 3s 5:4 huxley[3]
1 4 4 4 4 4L 1s 4:1 manic huxley[4]
1 1 3 1 3 1 3 1 3 4L 5s 3:1 orwelloid huxley[5]
1 1 1 2 1 1 2 1 1 2 1 1 2 4L 9s 2:1 huxley[9]
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 17edo 1
Steps for Generators 12\17 and 5\17 Mos Step Ratio TAMNAMS Name Temperament
12 5 1L 1s 12:5
7 5 5 1L 2s 7:5
2 5 5 5 3L 1s 5:2 maqamic/hemif[3]
2 2 3 2 3 2 3 3L 4s 3:2 mosh maqamic/hemif[4]
2 2 2 1 2 2 1 2 2 1 7L 3s 2:1 dicotonic maqamic/hemif[7]
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 17edo 1
Steps for Generators 11\17 and 6\17 Mos Step Ratio TAMNAMS Name Temperament
11 6 1L 1s 11:6
5 6 6 2L 1s 6:5
5 5 1 5 1 3L 2s 5:1 antipentic sqwares[3]
4 1 4 1 1 4 1 1 3L 5s 4:1 sensoid sqwares[5]
3 1 1 3 1 1 1 3 1 1 1 3L 8s 3:1 sqwares[8]
2 1 1 1 2 1 1 1 1 2 1 1 1 1 3L 11s 2:1 sqwares[11]
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 17edo 1
Steps for Generators 10\17 and 7\17 Mos Step Ratio TAMNAMS Name Temperament
10 7 1L 1s 10:7
3 7 7 2L 1s 7:3
3 3 4 3 4 2L 3s 4:3 pentic supra[3]
3 3 3 1 3 3 1 5L 2s 3:1 diatonic supra[5]
2 1 2 1 2 1 1 2 1 2 1 1 5L 7s 2:1 p-chromatic supra[7]
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 17edo 1
Steps for Generators 9\17 and 8\17 Mos Step Ratio TAMNAMS Name Temperament
9 8 1L 1s 9:8
1 8 8 2L 1s 8:1
1 1 7 1 7 2L 3s 7:1 pentic progress[3]
1 1 1 6 1 1 6 2L 5s 6:1 antidiatonic progress[5]
1 1 1 1 5 1 1 1 5 2L 7s 5:1 joanatonic progress[7]
1 1 1 1 1 4 1 1 1 1 4 2L 9s 4:1 progress[9]
1 1 1 1 1 1 3 1 1 1 1 1 3 2L 11s 3:1 progress[11]
1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 2L 13s 2:1 progress[13]
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 17edo 1
Retrieved from "https://en.xen.wiki/index.php?title=List_of_MOS_scales_in_17edo&oldid=93687"