List of MOS scales in 17edo: Difference between revisions

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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.
{{MOSes in EDO|EDO=17}}
 
== 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.


== Gallery ==
[[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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{| class="wikitable"
{| class="wikitable"
|-
|-
! generator
! Generator
! temperament
! Temperament
|-
|-
| 2\17
| 2\17
Line 21: Line 18:
|-
|-
| 4\17
| 4\17
| [[Huxley]]
| [[Huxley]]/[[Subklei]]
|-
|-
| 5\17
| 5\17
| [[Maqamic]]/[[Hemif]]
| [[Neutrominant]]/[[Hemif]]
|-
|-
| 6\17
| 6\17
Line 36: Line 33:
|}
|}


See also: [[17edo neutral scale]]
== 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 [[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, except for scales with 4 or fewer notes and 1L ns scales for tidiness. 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[4]
|-
| colspan="9" |9
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| [[1L 4s]]
| 9:2
|
| bleu[5]
|-
| colspan="7" |7
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| [[1L 5s]]
| 7:2
|
| bleu[6]
|-
| 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[7]
|-
| 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[8]
|-
| 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[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 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[4]
|-
| colspan="5" |5
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| [[1L 4s]]
| 5:3
|
| machine[5]
|-
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| [[5L 1s]]
| 3:2
| machinoid
| machine[6]
|-
| 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[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 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[4]
|-
| 1
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
| [[4L 1s]]
| 4:1
| manual
| huxley[5]
|-
| 1
| 1
| colspan="3" |3
| 1
| colspan="3" |3
| 1
| colspan="3" |3
| 1
| colspan="3" |3
| [[4L 5s]]
| 3:1
| gramitonic
| huxley[9]
|-
| 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[13]
|-
| 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
| tetric
| maqamic/hemif[4]
|-
| 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[7]
|-
| 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[10]
|-
| 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[5]
|-
| colspan="4" |4
| 1
| colspan="4" |4
| 1
| 1
| colspan="4" |4
| 1
| 1
| [[3L 5s]]
| 4:1
| checkertonic
| sqwares[8]
|-
| colspan="3" |3
| 1
| 1
| colspan="3" |3
| 1
| 1
| 1
| colspan="3" |3
| 1
| 1
| 1
| [[3L 8s]]
| 3:1
|
| sqwares[11]
|-
| 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[14]
|-
| 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[5]
|-
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| 1
| colspan="3" |3
| colspan="3" |3
| 1
| [[5L 2s]]
| 3:1
| diatonic
| supra[7]
|-
| 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
|
| supra[12]
|-
| 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[5]
|-
| 1
| 1
| 1
| colspan="6" |6
| 1
| 1
| colspan="6" |6
| [[2L 5s]]
| 6:1
| antidiatonic
| progress[7]
|-
| 1
| 1
| 1
| 1
| colspan="5" |5
| 1
| 1
| 1
| colspan="5" |5
| [[2L 7s]]
| 5:1
| balzano
| progress[9]
|-
| 1
| 1
| 1
| 1
| 1
| colspan="4" |4
| 1
| 1
| 1
| 1
| colspan="4" |4
| [[2L 9s]]
| 4:1
|
| progress[11]
|-
| 1
| 1
| 1
| 1
| 1
| 1
| colspan="3" |3
| 1
| 1
| 1
| 1
| 1
| colspan="3" |3
| [[2L 11s]]
| 3:1
|
| progress[13]
|-
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| colspan="2" |2
| 1
| 1
| 1
| 1
| 1
| 1
| colspan="2" |2
| [[2L 13s]]
| 2:1
|
| progress[15]
|-
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 17edo
| 1
|
|
|}
 
[[Category:17edo]]
[[Category:MOS]]

Latest revision as of 12:08, 21 May 2025

This page lists all moment of symmetry scales in 17edo.

Single-period MOS scales

Generators 9\17 and 8\17
Step visualization MOS (name) Step sizes Step ratio
├────────┼───────┤ 1L 1s 9, 8 9:8
├┼───────┼───────┤ 2L 1s 8, 1 8:1
├┼┼──────┼┼──────┤ 2L 3s 7, 1 7:1
├┼┼┼─────┼┼┼─────┤ 2L 5s (antidiatonic) 6, 1 6:1
├┼┼┼┼────┼┼┼┼────┤ 2L 7s (balzano) 5, 1 5:1
├┼┼┼┼┼───┼┼┼┼┼───┤ 2L 9s 4, 1 4:1
├┼┼┼┼┼┼──┼┼┼┼┼┼──┤ 2L 11s 3, 1 3:1
├┼┼┼┼┼┼┼─┼┼┼┼┼┼┼─┤ 2L 13s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 17edo 1, 1 1:1
Generators 10\17 and 7\17
Step visualization MOS (name) Step sizes Step ratio
├─────────┼──────┤ 1L 1s 10, 7 10:7
├──┼──────┼──────┤ 2L 1s 7, 3 7:3
├──┼──┼───┼──┼───┤ 2L 3s 4, 3 4:3
├──┼──┼──┼┼──┼──┼┤ 5L 2s (diatonic) 3, 1 3:1
├─┼┼─┼┼─┼┼┼─┼┼─┼┼┤ 5L 7s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 17edo 1, 1 1:1
Generators 11\17 and 6\17
Step visualization MOS (name) Step sizes Step ratio
├──────────┼─────┤ 1L 1s 11, 6 11:6
├────┼─────┼─────┤ 2L 1s 6, 5 6:5
├────┼────┼┼────┼┤ 3L 2s 5, 1 5:1
├───┼┼───┼┼┼───┼┼┤ 3L 5s (checkertonic) 4, 1 4:1
├──┼┼┼──┼┼┼┼──┼┼┼┤ 3L 8s 3, 1 3:1
├─┼┼┼┼─┼┼┼┼┼─┼┼┼┼┤ 3L 11s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 17edo 1, 1 1:1
Generators 12\17 and 5\17
Step visualization MOS (name) Step sizes Step ratio
├───────────┼────┤ 1L 1s 12, 5 12:5
├──────┼────┼────┤ 1L 2s 7, 5 7:5
├─┼────┼────┼────┤ 3L 1s 5, 2 5:2
├─┼─┼──┼─┼──┼─┼──┤ 3L 4s (mosh) 3, 2 3:2
├─┼─┼─┼┼─┼─┼┼─┼─┼┤ 7L 3s (dicoid) 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 17edo 1, 1 1:1
Generators 13\17 and 4\17
Step visualization MOS (name) Step sizes Step ratio
├────────────┼───┤ 1L 1s 13, 4 13:4
├────────┼───┼───┤ 1L 2s 9, 4 9:4
├────┼───┼───┼───┤ 1L 3s 5, 4 5:4
├┼───┼───┼───┼───┤ 4L 1s 4, 1 4:1
├┼┼──┼┼──┼┼──┼┼──┤ 4L 5s (gramitonic) 3, 1 3:1
├┼┼┼─┼┼┼─┼┼┼─┼┼┼─┤ 4L 9s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 17edo 1, 1 1:1
Generators 14\17 and 3\17
Step visualization MOS (name) Step sizes Step ratio
├─────────────┼──┤ 1L 1s 14, 3 14:3
├──────────┼──┼──┤ 1L 2s 11, 3 11:3
├───────┼──┼──┼──┤ 1L 3s 8, 3 8:3
├────┼──┼──┼──┼──┤ 1L 4s 5, 3 5:3
├─┼──┼──┼──┼──┼──┤ 5L 1s (machinoid) 3, 2 3:2
├─┼─┼┼─┼┼─┼┼─┼┼─┼┤ 6L 5s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 17edo 1, 1 1:1
Generators 15\17 and 2\17
Step visualization MOS (name) Step sizes Step ratio
├──────────────┼─┤ 1L 1s 15, 2 15:2
├────────────┼─┼─┤ 1L 2s 13, 2 13:2
├──────────┼─┼─┼─┤ 1L 3s 11, 2 11:2
├────────┼─┼─┼─┼─┤ 1L 4s 9, 2 9:2
├──────┼─┼─┼─┼─┼─┤ 1L 5s (antimachinoid) 7, 2 7:2
├────┼─┼─┼─┼─┼─┼─┤ 1L 6s (onyx) 5, 2 5:2
├──┼─┼─┼─┼─┼─┼─┼─┤ 1L 7s (antipine) 3, 2 3:2
├┼─┼─┼─┼─┼─┼─┼─┼─┤ 8L 1s (subneutralic) 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 17edo 1, 1 1:1
Generators 16\17 and 1\17
Step visualization MOS (name) Step sizes Step ratio
├───────────────┼┤ 1L 1s 16, 1 16:1
├──────────────┼┼┤ 1L 2s 15, 1 15:1
├─────────────┼┼┼┤ 1L 3s 14, 1 14:1
├────────────┼┼┼┼┤ 1L 4s 13, 1 13:1
├───────────┼┼┼┼┼┤ 1L 5s (antimachinoid) 12, 1 12:1
├──────────┼┼┼┼┼┼┤ 1L 6s (onyx) 11, 1 11:1
├─────────┼┼┼┼┼┼┼┤ 1L 7s (antipine) 10, 1 10:1
├────────┼┼┼┼┼┼┼┼┤ 1L 8s (antisubneutralic) 9, 1 9:1
├───────┼┼┼┼┼┼┼┼┼┤ 1L 9s (antisinatonic) 8, 1 8:1
├──────┼┼┼┼┼┼┼┼┼┼┤ 1L 10s 7, 1 7:1
├─────┼┼┼┼┼┼┼┼┼┼┼┤ 1L 11s 6, 1 6:1
├────┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 12s 5, 1 5:1
├───┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 13s 4, 1 4:1
├──┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 14s 3, 1 3:1
├─┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 1L 15s 2, 1 2:1
├┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┼┤ 17edo 1, 1 1:1

Gallery

17edo_horograms.jpg

17edo horograms.pdf

Generator Temperament
2\17 Bleu
3\17 Machine
4\17 Huxley/Subklei
5\17 Neutrominant/Hemif
6\17 Skwares
7\17 Supra
8\17 Progress

See also

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