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* Every MOS scale has two ''child MOS'' scales. The two children of the MOS scale ''a''L ''b''s are {{nowrap| (''a'' + ''b'')L ''a''s }} (generated by generators of soft-of-basic ''a''L ''b''s) and {{nowrap| ''a''L (''a'' + ''b'')s }} (generated by generators of hard-of-basic ''a''L'' b''s).
* Every MOS scale has two ''child MOS'' scales. The two children of the MOS scale ''a''L ''b''s are {{nowrap| (''a'' + ''b'')L ''a''s }} (generated by generators of soft-of-basic ''a''L ''b''s) and {{nowrap| ''a''L (''a'' + ''b'')s }} (generated by generators of hard-of-basic ''a''L'' b''s).
* Every MOS scale (with a specified [[equave]] ''Ɛ''), excluding {{nowrap|''a''L ''a''s{{angbr|''Ɛ''}} }}, has a ''parent MOS''. If {{nowrap| ''a'' > ''b'' }}, the parent of ''a''L&nbsp;''b''s is {{nowrap| ''b''L (''a'' − ''b'')s }}; if {{nowrap| ''a'' < ''b'' }}, the parent of ''a''L&nbsp;''b''s is {{nowrap| ''a''L (''b'' − ''a'')s }}.
* Every MOS scale (with a specified [[equave]] ''Ɛ''), excluding {{nowrap|''a''L ''a''s{{angbr|''Ɛ''|-)}} }}, has a ''parent MOS''. If {{nowrap| ''a'' > ''b'' }}, the parent of ''a''L&nbsp;''b''s is {{nowrap| ''b''L (''a'' − ''b'')s }}; if {{nowrap| ''a'' < ''b'' }}, the parent of ''a''L&nbsp;''b''s is {{nowrap| ''a''L (''b'' − ''a'')s }}.


=== Advanced discussion ===
=== Advanced discussion ===
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* [[MOS diagrams]], visualizations of the MOS process.
* [[MOS diagrams]], visualizations of the MOS process.
* [http://x31eq.com/temper/method.html How to Find Linear Temperaments], by [[Graham Breed]]
* [http://x31eq.com/temper/method.html How to Find Linear Temperaments], by [[Graham Breed]]
== Individual pages for MOS scales ==
''See also: [[Catalog of MOS]]''
=== L ≤ 12, s ≤ 12 ===
{| class="wikitable center-all"
|+ style="font-size: 105%; white-space: nowrap;" | Pages for MOS scales ({{nowrap|L ≤ 12|s ≤ 12}})
|-
| [[1L&nbsp;1s]]
| [[1L&nbsp;2s]]
| [[1L&nbsp;3s]]
| [[1L&nbsp;4s]]
| [[1L&nbsp;5s]]
| [[1L&nbsp;6s]]
| [[1L&nbsp;7s]]
| [[1L&nbsp;8s]]
| [[1L&nbsp;9s]]
| [[1L&nbsp;10s]]
| [[1L&nbsp;11s]]
| [[1L&nbsp;12s]]
|-
| [[2L&nbsp;1s]]
| [[2L&nbsp;2s]]
| [[2L&nbsp;3s]]
| [[2L&nbsp;4s]]
| [[2L&nbsp;5s]]
| [[2L&nbsp;6s]]
| [[2L&nbsp;7s]]
| [[2L&nbsp;8s]]
| [[2L&nbsp;9s]]
| [[2L&nbsp;10s]]
| [[2L&nbsp;11s]]
| [[2L&nbsp;12s]]
|-
| [[3L&nbsp;1s]]
| [[3L&nbsp;2s]]
| [[3L&nbsp;3s]]
| [[3L&nbsp;4s]]
| [[3L&nbsp;5s]]
| [[3L&nbsp;6s]]
| [[3L&nbsp;7s]]
| [[3L&nbsp;8s]]
| [[3L&nbsp;9s]]
| [[3L&nbsp;10s]]
| [[3L&nbsp;11s]]
| [[3L&nbsp;12s]]
|-
| [[4L&nbsp;1s]]
| [[4L&nbsp;2s]]
| [[4L&nbsp;3s]]
| [[4L&nbsp;4s]]
| [[4L&nbsp;5s]]
| [[4L&nbsp;6s]]
| [[4L&nbsp;7s]]
| [[4L&nbsp;8s]]
| [[4L&nbsp;9s]]
| [[4L&nbsp;10s]]
| [[4L&nbsp;11s]]
| [[4L&nbsp;12s]]
|-
| [[5L&nbsp;1s]]
| [[5L&nbsp;2s]]
| [[5L&nbsp;3s]]
| [[5L&nbsp;4s]]
| [[5L&nbsp;5s]]
| [[5L&nbsp;6s]]
| [[5L&nbsp;7s]]
| [[5L&nbsp;8s]]
| [[5L&nbsp;9s]]
| [[5L&nbsp;10s]]
| [[5L&nbsp;11s]]
| [[5L&nbsp;12s]]
|-
| [[6L&nbsp;1s]]
| [[6L&nbsp;2s]]
| [[6L&nbsp;3s]]
| [[6L&nbsp;4s]]
| [[6L&nbsp;5s]]
| [[6L&nbsp;6s]]
| [[6L&nbsp;7s]]
| [[6L&nbsp;8s]]
| [[6L&nbsp;9s]]
| [[6L&nbsp;10s]]
| [[6L&nbsp;11s]]
| [[6L&nbsp;12s]]
|-
| [[7L&nbsp;1s]]
| [[7L&nbsp;2s]]
| [[7L&nbsp;3s]]
| [[7L&nbsp;4s]]
| [[7L&nbsp;5s]]
| [[7L&nbsp;6s]]
| [[7L&nbsp;7s]]
| [[7L&nbsp;8s]]
| [[7L&nbsp;9s]]
| [[7L&nbsp;10s]]
| [[7L&nbsp;11s]]
| [[7L&nbsp;12s]]
|-
| [[8L&nbsp;1s]]
| [[8L&nbsp;2s]]
| [[8L&nbsp;3s]]
| [[8L&nbsp;4s]]
| [[8L&nbsp;5s]]
| [[8L&nbsp;6s]]
| [[8L&nbsp;7s]]
| [[8L&nbsp;8s]]
| [[8L&nbsp;9s]]
| [[8L&nbsp;10s]]
| [[8L&nbsp;11s]]
| [[8L&nbsp;12s]]
|-
| [[9L&nbsp;1s]]
| [[9L&nbsp;2s]]
| [[9L&nbsp;3s]]
| [[9L&nbsp;4s]]
| [[9L&nbsp;5s]]
| [[9L&nbsp;6s]]
| [[9L&nbsp;7s]]
| [[9L&nbsp;8s]]
| [[9L&nbsp;9s]]
| [[9L&nbsp;10s]]
| [[9L&nbsp;11s]]
| [[9L&nbsp;12s]]
|-
| [[10L&nbsp;1s]]
| [[10L&nbsp;2s]]
| [[10L&nbsp;3s]]
| [[10L&nbsp;4s]]
| [[10L&nbsp;5s]]
| [[10L&nbsp;6s]]
| [[10L&nbsp;7s]]
| [[10L&nbsp;8s]]
| [[10L&nbsp;9s]]
| [[10L&nbsp;10s]]
| [[10L&nbsp;11s]]
| [[10L&nbsp;12s]]
|-
| [[11L&nbsp;1s]]
| [[11L&nbsp;2s]]
| [[11L&nbsp;3s]]
| [[11L&nbsp;4s]]
| [[11L&nbsp;5s]]
| [[11L&nbsp;6s]]
| [[11L&nbsp;7s]]
| [[11L&nbsp;8s]]
| [[11L&nbsp;9s]]
| [[11L&nbsp;10s]]
| [[11L&nbsp;11s]]
| [[11L&nbsp;12s]]
|-
| [[12L&nbsp;1s]]
| [[12L&nbsp;2s]]
| [[12L&nbsp;3s]]
| [[12L&nbsp;4s]]
| [[12L&nbsp;5s]]
| [[12L&nbsp;6s]]
| [[12L&nbsp;7s]]
| [[12L&nbsp;8s]]
| [[12L&nbsp;9s]]
| [[12L&nbsp;10s]]
| [[12L&nbsp;11s]]
| [[12L&nbsp;12s]]
|}
=== L ≤ 12, 13 ≤ s ≤ 24 ===
{| class="wikitable mw-collapsible mw-collapsed center-all"
|+ style="font-size: 105%; white-space: nowrap;" | Pages for MOS scales ({{nowrap|L ≤ 12|13 ≤ s ≤ 24}})
|-
| [[1L&nbsp;13s]]
| [[1L&nbsp;14s]]
| [[1L&nbsp;15s]]
| [[1L&nbsp;16s]]
| [[1L&nbsp;17s]]
| [[1L&nbsp;18s]]
| [[1L&nbsp;19s]]
| [[1L&nbsp;20s]]
| [[1L&nbsp;21s]]
| [[1L&nbsp;22s]]
| [[1L&nbsp;23s]]
| [[1L&nbsp;24s]]
|-
| [[2L&nbsp;13s]]
| [[2L&nbsp;14s]]
| [[2L&nbsp;15s]]
| [[2L&nbsp;16s]]
| [[2L&nbsp;17s]]
| [[2L&nbsp;18s]]
| [[2L&nbsp;19s]]
| [[2L&nbsp;20s]]
| [[2L&nbsp;21s]]
| [[2L&nbsp;22s]]
| [[2L&nbsp;23s]]
| [[2L&nbsp;24s]]
|-
| [[3L&nbsp;13s]]
| [[3L&nbsp;14s]]
| [[3L&nbsp;15s]]
| [[3L&nbsp;16s]]
| [[3L&nbsp;17s]]
| [[3L&nbsp;18s]]
| [[3L&nbsp;19s]]
| [[3L&nbsp;20s]]
| [[3L&nbsp;21s]]
| [[3L&nbsp;22s]]
| [[3L&nbsp;23s]]
| [[3L&nbsp;24s]]
|-
| [[4L&nbsp;13s]]
| [[4L&nbsp;14s]]
| [[4L&nbsp;15s]]
| [[4L&nbsp;16s]]
| [[4L&nbsp;17s]]
| [[4L&nbsp;18s]]
| [[4L&nbsp;19s]]
| [[4L&nbsp;20s]]
| [[4L&nbsp;21s]]
| [[4L&nbsp;22s]]
| [[4L&nbsp;23s]]
| [[4L&nbsp;24s]]
|-
| [[5L&nbsp;13s]]
| [[5L&nbsp;14s]]
| [[5L&nbsp;15s]]
| [[5L&nbsp;16s]]
| [[5L&nbsp;17s]]
| [[5L&nbsp;18s]]
| [[5L&nbsp;19s]]
| [[5L&nbsp;20s]]
| [[5L&nbsp;21s]]
| [[5L&nbsp;22s]]
| [[5L&nbsp;23s]]
| [[5L&nbsp;24s]]
|-
| [[6L&nbsp;13s]]
| [[6L&nbsp;14s]]
| [[6L&nbsp;15s]]
| [[6L&nbsp;16s]]
| [[6L&nbsp;17s]]
| [[6L&nbsp;18s]]
| [[6L&nbsp;19s]]
| [[6L&nbsp;20s]]
| [[6L&nbsp;21s]]
| [[6L&nbsp;22s]]
| [[6L&nbsp;23s]]
| [[6L&nbsp;24s]]
|-
| [[7L&nbsp;13s]]
| [[7L&nbsp;14s]]
| [[7L&nbsp;15s]]
| [[7L&nbsp;16s]]
| [[7L&nbsp;17s]]
| [[7L&nbsp;18s]]
| [[7L&nbsp;19s]]
| [[7L&nbsp;20s]]
| [[7L&nbsp;21s]]
| [[7L&nbsp;22s]]
| [[7L&nbsp;23s]]
| [[7L&nbsp;24s]]
|-
| [[8L&nbsp;13s]]
| [[8L&nbsp;14s]]
| [[8L&nbsp;15s]]
| [[8L&nbsp;16s]]
| [[8L&nbsp;17s]]
| [[8L&nbsp;18s]]
| [[8L&nbsp;19s]]
| [[8L&nbsp;20s]]
| [[8L&nbsp;21s]]
| [[8L&nbsp;22s]]
| [[8L&nbsp;23s]]
| [[8L&nbsp;24s]]
|-
| [[9L&nbsp;13s]]
| [[9L&nbsp;14s]]
| [[9L&nbsp;15s]]
| [[9L&nbsp;16s]]
| [[9L&nbsp;17s]]
| [[9L&nbsp;18s]]
| [[9L&nbsp;19s]]
| [[9L&nbsp;20s]]
| [[9L&nbsp;21s]]
| [[9L&nbsp;22s]]
| [[9L&nbsp;23s]]
| [[9L&nbsp;24s]]
|-
| [[10L&nbsp;13s]]
| [[10L&nbsp;14s]]
| [[10L&nbsp;15s]]
| [[10L&nbsp;16s]]
| [[10L&nbsp;17s]]
| [[10L&nbsp;18s]]
| [[10L&nbsp;19s]]
| [[10L&nbsp;20s]]
| [[10L&nbsp;21s]]
| [[10L&nbsp;22s]]
| [[10L&nbsp;23s]]
| [[10L&nbsp;24s]]
|-
| [[11L&nbsp;13s]]
| [[11L&nbsp;14s]]
| [[11L&nbsp;15s]]
| [[11L&nbsp;16s]]
| [[11L&nbsp;17s]]
| [[11L&nbsp;18s]]
| [[11L&nbsp;19s]]
| [[11L&nbsp;20s]]
| [[11L&nbsp;21s]]
| [[11L&nbsp;22s]]
| [[11L&nbsp;23s]]
| [[11L&nbsp;24s]]
|-
| [[12L&nbsp;13s]]
| [[12L&nbsp;14s]]
| [[12L&nbsp;15s]]
| [[12L&nbsp;16s]]
| [[12L&nbsp;17s]]
| [[12L&nbsp;18s]]
| [[12L&nbsp;19s]]
| [[12L&nbsp;20s]]
| [[12L&nbsp;21s]]
| [[12L&nbsp;22s]]
| [[12L&nbsp;23s]]
| [[12L&nbsp;24s]]
|}
=== 13 ≤ L ≤ 24, s ≤ 12 ===
{| class="wikitable mw-collapsible mw-collapsed center-all"
|+ style="font-size: 105%; white-space: nowrap;" | Pages for MOS scales ({{nowrap|13 ≤ L ≤ 24|s ≤ 12}})
|-
| [[13L&nbsp;1s]]
| [[13L&nbsp;2s]]
| [[13L&nbsp;3s]]
| [[13L&nbsp;4s]]
| [[13L&nbsp;5s]]
| [[13L&nbsp;6s]]
| [[13L&nbsp;7s]]
| [[13L&nbsp;8s]]
| [[13L&nbsp;9s]]
| [[13L&nbsp;10s]]
| [[13L&nbsp;11s]]
| [[13L&nbsp;12s]]
|-
| [[14L&nbsp;1s]]
| [[14L&nbsp;2s]]
| [[14L&nbsp;3s]]
| [[14L&nbsp;4s]]
| [[14L&nbsp;5s]]
| [[14L&nbsp;6s]]
| [[14L&nbsp;7s]]
| [[14L&nbsp;8s]]
| [[14L&nbsp;9s]]
| [[14L&nbsp;10s]]
| [[14L&nbsp;11s]]
| [[14L&nbsp;12s]]
|-
| [[15L&nbsp;1s]]
| [[15L&nbsp;2s]]
| [[15L&nbsp;3s]]
| [[15L&nbsp;4s]]
| [[15L&nbsp;5s]]
| [[15L&nbsp;6s]]
| [[15L&nbsp;7s]]
| [[15L&nbsp;8s]]
| [[15L&nbsp;9s]]
| [[15L&nbsp;10s]]
| [[15L&nbsp;11s]]
| [[15L&nbsp;12s]]
|-
| [[16L&nbsp;1s]]
| [[16L&nbsp;2s]]
| [[16L&nbsp;3s]]
| [[16L&nbsp;4s]]
| [[16L&nbsp;5s]]
| [[16L&nbsp;6s]]
| [[16L&nbsp;7s]]
| [[16L&nbsp;8s]]
| [[16L&nbsp;9s]]
| [[16L&nbsp;10s]]
| [[16L&nbsp;11s]]
| [[16L&nbsp;12s]]
|-
| [[17L&nbsp;1s]]
| [[17L&nbsp;2s]]
| [[17L&nbsp;3s]]
| [[17L&nbsp;4s]]
| [[17L&nbsp;5s]]
| [[17L&nbsp;6s]]
| [[17L&nbsp;7s]]
| [[17L&nbsp;8s]]
| [[17L&nbsp;9s]]
| [[17L&nbsp;10s]]
| [[17L&nbsp;11s]]
| [[17L&nbsp;12s]]
|-
| [[18L&nbsp;1s]]
| [[18L&nbsp;2s]]
| [[18L&nbsp;3s]]
| [[18L&nbsp;4s]]
| [[18L&nbsp;5s]]
| [[18L&nbsp;6s]]
| [[18L&nbsp;7s]]
| [[18L&nbsp;8s]]
| [[18L&nbsp;9s]]
| [[18L&nbsp;10s]]
| [[18L&nbsp;11s]]
| [[18L&nbsp;12s]]
|-
| [[19L&nbsp;1s]]
| [[19L&nbsp;2s]]
| [[19L&nbsp;3s]]
| [[19L&nbsp;4s]]
| [[19L&nbsp;5s]]
| [[19L&nbsp;6s]]
| [[19L&nbsp;7s]]
| [[19L&nbsp;8s]]
| [[19L&nbsp;9s]]
| [[19L&nbsp;10s]]
| [[19L&nbsp;11s]]
| [[19L&nbsp;12s]]
|-
| [[20L&nbsp;1s]]
| [[20L&nbsp;2s]]
| [[20L&nbsp;3s]]
| [[20L&nbsp;4s]]
| [[20L&nbsp;5s]]
| [[20L&nbsp;6s]]
| [[20L&nbsp;7s]]
| [[20L&nbsp;8s]]
| [[20L&nbsp;9s]]
| [[20L&nbsp;10s]]
| [[20L&nbsp;11s]]
| [[20L&nbsp;12s]]
|-
| [[21L&nbsp;1s]]
| [[21L&nbsp;2s]]
| [[21L&nbsp;3s]]
| [[21L&nbsp;4s]]
| [[21L&nbsp;5s]]
| [[21L&nbsp;6s]]
| [[21L&nbsp;7s]]
| [[21L&nbsp;8s]]
| [[21L&nbsp;9s]]
| [[21L&nbsp;10s]]
| [[21L&nbsp;11s]]
| [[21L&nbsp;12s]]
|-
| [[22L&nbsp;1s]]
| [[22L&nbsp;2s]]
| [[22L&nbsp;3s]]
| [[22L&nbsp;4s]]
| [[22L&nbsp;5s]]
| [[22L&nbsp;6s]]
| [[22L&nbsp;7s]]
| [[22L&nbsp;8s]]
| [[22L&nbsp;9s]]
| [[22L&nbsp;10s]]
| [[22L&nbsp;11s]]
| [[22L&nbsp;12s]]
|-
| [[23L&nbsp;1s]]
| [[23L&nbsp;2s]]
| [[23L&nbsp;3s]]
| [[23L&nbsp;4s]]
| [[23L&nbsp;5s]]
| [[23L&nbsp;6s]]
| [[23L&nbsp;7s]]
| [[23L&nbsp;8s]]
| [[23L&nbsp;9s]]
| [[23L&nbsp;10s]]
| [[23L&nbsp;11s]]
| [[23L&nbsp;12s]]
|-
| [[24L&nbsp;1s]]
| [[24L&nbsp;2s]]
| [[24L&nbsp;3s]]
| [[24L&nbsp;4s]]
| [[24L&nbsp;5s]]
| [[24L&nbsp;6s]]
| [[24L&nbsp;7s]]
| [[24L&nbsp;8s]]
| [[24L&nbsp;9s]]
| [[24L&nbsp;10s]]
| [[24L&nbsp;11s]]
| [[24L&nbsp;12s]]
|}
=== Larger MOS scales ===
[[7L&nbsp;34s]], [[9L&nbsp;29s]], [[12L&nbsp;29s]], [[12L&nbsp;41s]], [[13L&nbsp;14s]], [[14L&nbsp;13s]], [[17L&nbsp;14s]], [[25L&nbsp;6s]], [[41L&nbsp;12s]]


== Variations ==
== Variations ==
Line 163: Line 652:


== See also ==
== See also ==
* Pailiaq's [https://www.pailiaq.com/xen/mos-explorer MOS explorer], an interactive tool for visualizing MOSses and the MOS spectrum.
* [[Diamond-mos notation]], a microtonal [[notation]] system focused on MOS scales
* [[Diamond-mos notation]], a microtonal [[notation]] system focused on MOS scales
* [[Metallic MOS]], an article focusing on MOS scales based on metallic means, such as [[phi]]
* [[Metallic MOS]], an article focusing on MOS scales based on metallic means, such as [[phi]]
Line 168: Line 658:
* [[:Category:MOS scales|Category:MOS scales]], the category including all MOS-related articles on this wiki
* [[:Category:MOS scales|Category:MOS scales]], the category including all MOS-related articles on this wiki
* [[Gallery of MOS patterns]]
* [[Gallery of MOS patterns]]
* [[Gral method]], a method for calculating MOS


== Notes ==
== Notes ==
Retrieved from "https://en.xen.wiki/w/MOS_scale"