User:BudjarnLambeth/Breuddwyd scale: Difference between revisions

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{{Editable user page|Feel free to add examples of music made with these scales, and feel free to add any new scales, approaches or other concepts you develop based on these ideas.}}

A '''breuddwyd scale'''{{idiosyncratic}} (''pronounced "braid wood"'') is any [[polymicrotonal]] scale which combines four scales, the first scale with 5 tones per [[equave]], the second with 11, the third with 13 and the fourth with 31.

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A '''sonhar tuning'''{{idiosyncratic}} (''pronounced "sonyar"'') is any scale or [[temperament]] which uses or approximates the JI [[subgroup]] 5.11.13.31.

A '''wijzerplaat scale'''{{idiosyncratic}} (''pronounced "why ~~zher platt~~"'') is any scale which is built by combining a ~~[[MOS~~ scale]] generated by 5\31, a ~~MOS~~ scale generated by 11\31, and a ~~MOS~~ scale generated by 13\31. (''Where n\31 is n steps of [[31edo]] or another 31-tone [[equal tuning]]''.)

A '''wijzerplaat scale'''{{idiosyncratic}} (''pronounced "why, ser as in deserve, plat as in platypus"'') is any scale which is built by combining a scale generated by 5\31, a scale generated by 11\31, and a scale generated by 13\31. (''Where n\31 is n steps of [[31edo]] or another 31-tone [[equal tuning]]''.) Often but not always the three scales are [[MOS scale]]s.

== History and etymology ==

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"Breuddwyd" is Welsh for "dream". "Sonhar" is Brazilian Portugese for "dream". "Wijzerplaat" is Dutch for "clock face".

[[File:BreuddwydDisc.jpeg|none|thumb|309x309px|A recreation of the disc from the dream.]]

== Breuddwyd scales ==

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| [[:Category:57-tone scales|57 tones]] [[Category:57-tone scales]]

| 57/octave

| Polymicrotonal scale of [[5afdo]], [[11afdo]], [[13afdo]] and [[31afdo]]

| Polymicrotonal scale of [[5afdo]], [[11afdo]], [[13afdo]] and [[31afdo]]

| The scale of all [[rational interval]]s with 5, 11, 13 or 31 in the denominator

| The scale of all [[rational interval]]s with 5, 11, 13 or 31 in the denominator

| [[22165afdo]]

| 7/6, 6/5, 5/4, 4/3 (weak), 7/5, 3/2 (weak), 5/3, 7/4, 2/1, 7/3, 5/2, 3/1 (weak), 7/2, 4/1, 5/1, 6/1 (weak), 7/1

| 7/6, 6/5, 5/4, 4/3 (weak), 7/5, 3/2 (very weak), 5/3, 7/4, 2/1, 7/3, 5/2, 3/1 (very weak), 7/2, 4/1, 5/1, 6/1 (very weak), 7/1

|-

| 5&11&13&31ifdo (''Breuddwyd inverse'')

| 5&11&13&31ifdo (''Breuddwyd inverse'') '''Main article: [[Breuddwyd inverse]]'''

| Just

| 2/1

| 57 tones

| 57/octave

| Polymicrotonal scale of [[5ifdo]], [[11ifdo]], [[13ifdo]] and [[31ifdo]]

| Polymicrotonal scale of [[5ifdo]], [[11ifdo]], [[13ifdo]] and [[31ifdo]]

| The scale of all [[rational interval]]s with 5, 11, 13 or 31, or any of their octave multiples (e.g. 10, 22, 26, 62 or 20, 44, 52, 124 or so on) in the numerator

| The scale of all [[rational interval]]s with 5, 11, 13 or 31, or any of their octave multiples (e.g. 10, 22, 26, 62 or 20, 44, 52, 124 or so on) in the numerator

| [[22165ifdo]]

| 7/6, 6/5, 5/4, 4/3 (weak), 7/5, 3/2 (weak), 5/3, 7/4, 2/1, 7/3, 5/2, 3/1 (weak), 7/2, 4/1, 5/1, 6/1 (weak), 7/1

| 7/6, 6/5, 5/4, 4/3 (very weak), 7/5, 3/2 (weak), 5/3, 7/4, 2/1, 7/3, 5/2, 3/1 (weak), 7/2, 4/1, 5/1, 6/1 (weak), 7/1

|-

| 5&11&13&31edo (''Breuddwyd-2'')

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| 2/1

| 57 tones

| 60/octave

| 57/octave

| Polymicrotonal scale of [[5edo]], [[11edo]], [[13edo]] and [[31edo]]

| Polymicrotonal scale of [[5edo]], [[11edo]], [[13edo]] and [[31edo]]

|

| [[22165edo]]

| 7/6, 6/5, 5/4, 4/3, 7/5, 3/2, 5/3, 7/4, 2/1, 7/3, 5/2, 3/1, 7/2, 4/1, 5/1, 6/1, 7/1

| 7/6, 6/5, 5/4, 4/3, 7/5, 3/2, 5/3, 7/4, 2/1, 7/3, 5/2, 3/1, 7/2, 4/1, 5/1, 6/1, 7/1

|-

| 5&11&13&31edt (''Breuddwyd-3'')

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| 57 tones

| ~36/octave

| Polymicrotonal scale of [[5edt]], [[11edt]], [[13edt]] and [[31edt]]

| Polymicrotonal scale of [[5edt]], [[11edt]], [[13edt]] and [[31edt]]

|

| [[22165edt]]

| 7/6, 6/5, 5/4, 4/3, 7/5, 3/2, 5/3, 7/4, 2/1, 7/3, 5/2, 3/1, 7/2, 4/1, 5/1, 6/1, 7/1

| 7/6, 6/5, 5/4, 4/3, 7/5, 3/2, 5/3, 7/4, 2/1, 7/3, 5/2, 3/1, 7/2, 4/1, 5/1, 6/1, 7/1

|-

| 5&11&13&31ed4 (''Breuddwyd-4'')

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| 57 tones

| ~29/octave

| Polymicrotonal scale of [[5ed4]], [[11ed4]], [[13ed4]] and [[31ed4]]

| Polymicrotonal scale of [[5ed4]], [[11ed4]], [[13ed4]] and [[31ed4]]

|

| [[22165ed4]]

| 6/5, 5/4, 4/3 (weak), 3/2, 5/3, 7/4, 7/3, 3/1 (weak), 7/2, 4/1, 5/1, 6/1, 7/1

| 6/5, 5/4, 4/3 (weak), 3/2, 5/3, 7/4, 7/3, 3/1 (weak), 7/2, 4/1, 5/1, 6/1, 7/1

|-

| 5&11&13&31ed5 (''Breuddwyd-5'')

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| 57 tones

| ~25/octave

| Polymicrotonal scale of [[5ed5]], [[11ed5]], [[13ed5]] and [[31ed5]]

| Polymicrotonal scale of [[5ed5]], [[11ed5]], [[13ed5]] and [[31ed5]]

|

| [[22165ed5]]

| 7/6, 4/3, 3/2 (weak), 5/3, 7/4, 7/2, 5/1, 7/1 (weak)

| 7/6, 4/3, 3/2 (weak), 5/3, 7/4, 7/2, 5/1, 7/1 (weak)

|-

| 5&11&13&31ed6 (''Breuddwyd-6'')

| 5&11&13&31ed6 (''Breuddwyd-6'') '''Main article: [[Breuddwyd6]]'''

| Tempered

| [[6/1]]

| 57 tones

| ~19/octave

| Polymicrotonal scale of [[5ed6]], [[11ed6]], [[13ed6]] and [[31ed6]]

| Polymicrotonal scale of [[5ed6]], [[11ed6]], [[13ed6]] and [[31ed6]]

|

| [[22165ed6]]

| 7/6, 6/5, 5/4, 4/3, 7/5, 3/2, 5/3, 7/4, 2/1, 5/2, 3/1, 4/1, 5/1, 6/1, 7/1

| 7/6, 6/5, 5/4, 4/3, 7/5, 3/2, 5/3, 7/4, 2/1, 5/2, 3/1, 4/1, 5/1, 6/1, 7/1

|-

| 5&11&13&31ed14/3 (''Breuddwyd-14/3'')

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| 57 tones

| ~26/octave

| Polymicrotonal scale of [[5ed14/3]], [[11ed14/3]], [[13ed14/3]] and [[31ed14/3]]

| Polymicrotonal scale of [[5ed14/3]], [[11ed14/3]], [[13ed14/3]] and [[31ed14/3]]

|

| [[22165ed14/3]]

| 7/6, 4/3 (weak), 7/5, 3/2 (weak), 5/3 (weak), 7/4, 2/1, 7/3, 5/2, 3/1 (weak), 7/2, 4/1, 6/1, 7/1

| 7/6, 4/3 (weak), 7/5, 3/2 (weak), 5/3 (weak), 7/4, 2/1, 7/3, 5/2, 3/1 (weak), 7/2, 4/1, 6/1, 7/1

|}

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| [[hexatonic|6 tones]]

| 6/octave

| The [[hexany]] generated by 5/1, 11/1, 13/1 and 31/1

| The [[hexany]] generated by 5/1, 11/1, 13/1 and 31/1

| The octave-repeating harmonic series subset 220:260:286:310:341:403:440

| The octave-repeating harmonic series subset 220:260:286:310:341:403:440

| [[220afdo]]

| (allowing rotations) 7/6, 6/5, 7/5, 5/3, 2/1, 7/3, 4/1

| (allowing rotations) 7/6, 6/5, 7/5, 5/3, 2/1, 7/3, 4/1

|}

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{| class="wikitable sortable mw-collapsible"}}

|+ Tempered sonhar tunings

|+ Tempered sonhar tunings

|-

! Systematic name (& idiosyncratic common name)

! Equave

~~! Harmonics mapped~~

! Equal temp mapping

! Reduced mapping

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! TE tuning map (¢)

! TE mistunings (¢)

! Complexity, adjusted error TE error

! Complexity, adjusted error, TE error

! Unison vectors

! Recommended ETs

! Recommended ETs (warts in brackets)

! (~~x31 notation~~)

|-

| c2 & c37 (''Sonhar A'')

| c2 & c37 (''Sonhar A'')

| [[5/1]]

| 5/1

| ~~'''~~5,11,13,31~~'''~~

| 5,11,13,31 [<2,3,3,4] <37,55,59,79]>

| [<2,3,3,4] <37,55,59,79]>

| 5,11,13,31 [<1,2,-2,-3] <0,-1,7,10]>

| [<1,2,-2,-3] <0,-1,7,10]>

| 2789.3304, 1431.2645

| 2789.3304, 1431.2645

| 40.49033, 73.19864

| 40.49033, 73.19864

| 2789.330, 4147.396, 4440.191, 5944.654

| 2789.330, 4147.396, 4440.191, 5944.654

| 3.017, -3.922, -0.337, -0.382

| 3.017, -3.922, -0.337, -0.382

| 0.454182, 4.281341, 0.864185

| 0.454182, 4.281341, 0.864185

| [-2,1,3,-2>, [-5,3,-1,1>, [-7,4,2,-1>, [-3,2,-4,3>

| [-2,1,3,-2>, [-5,3,-1,1>, [-7,4,2,-1>, [-3,2,-4,3>

| [[39ed5]], [[37ed5]], [[41ed5]], [[35ed5]], [[76ed5]], [[78ed5]], [[74ed5]], [[43ed5]](fk)

| [[39ed5]], [[37ed5]], [[41ed5]], [[35ed5]], [[76ed5]], [[78ed5]], [[74ed5]], [[43ed5]](fk)

~~| c39, c37, c41, c35, c76, c78, c74, c43fk~~

|}

== Wijzerplaat scales ==

All of these scales ~~are octave-repeating subsets of [[31edo]]. They~~ are tempered by definition. Sometimes multiple ~~MOSes~~ may generate the same tone, which is why when ~~you combine~~ an x-tone, y-tone and z-tone ~~MOS~~, the total number of tones/octave may still be less than (x+y+z).

All of these scales are tempered by definition. Sometimes multiple scales may generate the same tone, which is why when one combines an x-tone, y-tone and z-tone scale, the total number of tones/octave may still be less than (x+y+z).

This list is not exhaustive. There are many other possible wijzerplaat scales.

~~The scale names are [[Template:Idiosyncratic|idisyncratic]]~~.

{| class="wikitable sortable mw-collapsible"}}

|+ The wijzerplaat scales

|-

! ~~Name~~

! Systematic name (& idiosyncratic common name)

! Parent tuning used

! Tones per period used

! Scale pattern

! Tones generated by 5\31, 11\31, 13\31

! Tones generated by 5\31, 11\31, 13\31 (mos or no?)

! 5\31 generators up:down, 11\31 up:down, 13\31 up:down

! 7 integer limit intervals approximated within 15¢

|-

| PolyMOS 5\31(~~up2down1~~) 11\31(~~up0down2~~) 13\31(~~up1down1~~)

| PolyMOS <5\31(u2d0), <11\31(u0d4), 13\31(u1d3)> (''Oclock'') '''Main article: [[Oclock]]'''

| [[31edo]]

| [[:Category:9-tone scales|9 tones]] per 31\31 [[Category:9-tone scales]]

| 5 4 1 3 5 2 ~~1 5 5~~

| 5 4 1 3 5 2 3 6 2

| 5, ~~3, 3~~

| 3(mos), 5(mos), 5(mos)

| 2:2, 2:2, 2:2

| 2:0, 0:4, 1:3

| 5/4, 4/3, 3/2, 2/1, 5/2, 3/1, 4/1, 5/1, 6/1

| 5/4, 4/3, 3/2, 5/3, 2/1, 5/2, 3/1, 4/1, 5/1, 6/1

|}

[[Category:Scales by family]]

@@ Line 1: / Line 1: @@
 {{Novelty}}
+{{Editable user page|Feel free to add examples of music made with these scales, and feel free to add any new scales, approaches or other concepts you develop based on these ideas.}}
 A '''breuddwyd scale'''{{idiosyncratic}} (''pronounced "braid wood"'') is any [[polymicrotonal]] scale which combines four scales, the first scale with 5 tones per [[equave]], the second with 11, the third with 13 and the fourth with 31.
@@ Line 5: / Line 7: @@
 A '''sonhar tuning'''{{idiosyncratic}} (''pronounced "sonyar"'') is any scale or [[temperament]] which uses or approximates the JI [[subgroup]] 5.11.13.31.
-A '''wijzerplaat scale'''{{idiosyncratic}} (''pronounced "why zher platt"'') is any scale which is built by combining a [[MOS scale]] generated by 5\31, a MOS scale generated by 11\31, and a MOS scale generated by 13\31. (''Where n\31 is n steps of [[31edo]] or another 31-tone [[equal tuning]]''.)
+A '''wijzerplaat scale'''{{idiosyncratic}} (''pronounced "why, ser as in deserve, plat as in platypus"'') is any scale which is built by combining a scale generated by 5\31, a scale generated by 11\31, and a scale generated by 13\31. (''Where n\31 is n steps of [[31edo]] or another 31-tone [[equal tuning]]''.) Often but not always the three scales are [[MOS scale]]s.
 == History and etymology ==
@@ Line 13: / Line 15: @@
 "Breuddwyd" is Welsh for "dream". "Sonhar" is Brazilian Portugese for "dream". "Wijzerplaat" is Dutch for "clock face".
+[[File:BreuddwydDisc.jpeg|none|thumb|309x309px|A recreation of the disc from the dream.]]
 == Breuddwyd scales ==
@@ Line 35: / Line 38: @@
 | [[:Category:57-tone scales|57 tones]] [[Category:57-tone scales]]
 | 57/octave
-| Polymicrotonal scale of [[5afdo]], [[11afdo]], [[13afdo]] and [[31afdo]]
+| <small>Polymicrotonal scale of [[5afdo]], [[11afdo]], [[13afdo]] and [[31afdo]]</small>
-| The scale of all [[rational interval]]s with 5, 11, 13 or 31 in the denominator
+| <small>The scale of all [[rational interval]]s with 5, 11, 13 or 31 in the denominator</small>
 | [[22165afdo]]
-| 7/6, 6/5, 5/4, 4/3 (weak), 7/5, 3/2 (weak), 5/3, 7/4, 2/1, 7/3, 5/2, 3/1 (weak), 7/2, 4/1, 5/1, 6/1 (weak), 7/1
+| <small>7/6, 6/5, 5/4, 4/3 (weak), 7/5, 3/2 (very weak), 5/3, 7/4, 2/1, 7/3, 5/2, 3/1 (very weak), 7/2, 4/1, 5/1, 6/1 (very weak), 7/1</small>
 |-
-| 5&11&13&31ifdo <br>(''Breuddwyd inverse'')
+| 5&11&13&31ifdo <br>(''Breuddwyd inverse'')  <br><br>'''Main article: [[Breuddwyd inverse]]'''
 | Just
 | 2/1
 | 57 tones
 | 57/octave
-| Polymicrotonal scale of [[5ifdo]], [[11ifdo]], [[13ifdo]] and [[31ifdo]]
+| <small>Polymicrotonal scale of [[5ifdo]], [[11ifdo]], [[13ifdo]] and [[31ifdo]]</small>
-| The scale of all [[rational interval]]s with 5, 11, 13 or 31, or any of their octave multiples (e.g. 10, 22, 26, 62 or 20, 44, 52, 124 or so on) in the numerator
+| <small>The scale of all [[rational interval]]s with 5, 11, 13 or 31, or any of their octave multiples (e.g. 10, 22, 26, 62 or 20, 44, 52, 124 or so on) in the numerator</small>
 | [[22165ifdo]]
-| 7/6, 6/5, 5/4, 4/3 (weak), 7/5, 3/2 (weak), 5/3, 7/4, 2/1, 7/3, 5/2, 3/1 (weak), 7/2, 4/1, 5/1, 6/1 (weak), 7/1
+| <small>7/6, 6/5, 5/4, 4/3 (very weak), 7/5, 3/2 (weak), 5/3, 7/4, 2/1, 7/3, 5/2, 3/1 (weak), 7/2, 4/1, 5/1, 6/1 (weak), 7/1</small>
 |-
 | 5&11&13&31edo <br>(''Breuddwyd-2'')
@@ Line 54: / Line 57: @@
 | 2/1
 | 57 tones
-| 60/octave
+| 57/octave
-| Polymicrotonal scale of [[5edo]], [[11edo]], [[13edo]] and [[31edo]]
+| <small>Polymicrotonal scale of [[5edo]], [[11edo]], [[13edo]] and [[31edo]]</small>
 |
 | [[22165edo]]
-| 7/6, 6/5, 5/4, 4/3, 7/5, 3/2, 5/3, 7/4, 2/1, 7/3, 5/2, 3/1, 7/2, 4/1, 5/1, 6/1, 7/1
+| <small>7/6, 6/5, 5/4, 4/3, 7/5, 3/2, 5/3, 7/4, 2/1, 7/3, 5/2, 3/1, 7/2, 4/1, 5/1, 6/1, 7/1</small>
 |-
 | 5&11&13&31edt <br>(''Breuddwyd-3'')
@@ Line 65: / Line 68: @@
 | 57 tones
 | ~36/octave
-| Polymicrotonal scale of [[5edt]], [[11edt]], [[13edt]] and [[31edt]]
+| <small>Polymicrotonal scale of [[5edt]], [[11edt]], [[13edt]] and [[31edt]]</small>
 |
 | [[22165edt]]
-| 7/6, 6/5, 5/4, 4/3, 7/5, 3/2, 5/3, 7/4, 2/1, 7/3, 5/2, 3/1, 7/2, 4/1, 5/1, 6/1, 7/1
+| <small>7/6, 6/5, 5/4, 4/3, 7/5, 3/2, 5/3, 7/4, 2/1, 7/3, 5/2, 3/1, 7/2, 4/1, 5/1, 6/1, 7/1</small>
 |-
 | 5&11&13&31ed4 <br>(''Breuddwyd-4'')
@@ Line 75: / Line 78: @@
 | 57 tones
 | ~29/octave
-| Polymicrotonal scale of [[5ed4]], [[11ed4]], [[13ed4]] and [[31ed4]]
+| <small>Polymicrotonal scale of [[5ed4]], [[11ed4]], [[13ed4]] and [[31ed4]]</small>
 |
 | [[22165ed4]]
-| 6/5, 5/4, 4/3 (weak), 3/2, 5/3, 7/4, 7/3, 3/1 (weak), 7/2, 4/1, 5/1, 6/1, 7/1
+| <small>6/5, 5/4, 4/3 (weak), 3/2, 5/3, 7/4, 7/3, 3/1 (weak), 7/2, 4/1, 5/1, 6/1, 7/1</small>
 |-
 | 5&11&13&31ed5 <br>(''Breuddwyd-5'')
@@ Line 85: / Line 88: @@
 | 57 tones
 | ~25/octave
-| Polymicrotonal scale of [[5ed5]], [[11ed5]], [[13ed5]] and [[31ed5]]
+| <small>Polymicrotonal scale of [[5ed5]], [[11ed5]], [[13ed5]] and [[31ed5]]</small>
 |
 | [[22165ed5]]
-| 7/6, 4/3, 3/2 (weak), 5/3, 7/4, 7/2, 5/1, 7/1 (weak)
+| <small>7/6, 4/3, 3/2 (weak), 5/3, 7/4, 7/2, 5/1, 7/1 (weak)</small>
 |-
-| 5&11&13&31ed6 <br>(''Breuddwyd-6'')
+| 5&11&13&31ed6 <br>(''Breuddwyd-6'') <br><br>'''Main article: [[Breuddwyd6]]'''
 | Tempered
 | [[6/1]]
 | 57 tones
 | ~19/octave
-| Polymicrotonal scale of [[5ed6]], [[11ed6]], [[13ed6]] and [[31ed6]]
+| <small>Polymicrotonal scale of [[5ed6]], [[11ed6]], [[13ed6]] and [[31ed6]]</small>
 |
 | [[22165ed6]]
-| 7/6, 6/5, 5/4, 4/3, 7/5, 3/2, 5/3, 7/4, 2/1, 5/2, 3/1, 4/1, 5/1, 6/1, 7/1
+| <small>7/6, 6/5, 5/4, 4/3, 7/5, 3/2, 5/3, 7/4, 2/1, 5/2, 3/1, 4/1, 5/1, 6/1, 7/1</small>
 |-
 | 5&11&13&31ed14/3 <br>(''Breuddwyd-14/3'')
@@ Line 105: / Line 108: @@
 | 57 tones
 | ~26/octave
-| Polymicrotonal scale of [[5ed14/3]], [[11ed14/3]], [[13ed14/3]] and [[31ed14/3]]
+| <small>Polymicrotonal scale of [[5ed14/3]], [[11ed14/3]], [[13ed14/3]] and [[31ed14/3]]</small>
 |
 | [[22165ed14/3]]
-| 7/6, 4/3 (weak), 7/5, 3/2 (weak), 5/3 (weak), 7/4, 2/1, 7/3, 5/2, 3/1 (weak), 7/2, 4/1, 6/1, 7/1
+| <small>7/6, 4/3 (weak), 7/5, 3/2 (weak), 5/3 (weak), 7/4, 2/1, 7/3, 5/2, 3/1 (weak), 7/2, 4/1, 6/1, 7/1</small>
 |}
@@ Line 133: / Line 136: @@
 | [[hexatonic|6 tones]]
 | 6/octave
-| The [[hexany]] generated by 5/1, 11/1, 13/1 and 31/1
+| <small>The [[hexany]] generated by 5/1, 11/1, 13/1 and 31/1</small>
-| The octave-repeating harmonic series subset 220:260:286:310:341:403:440
+| <small>The octave-repeating harmonic series subset 220:260:286:310:341:403:440</small>
 | [[220afdo]]
-| (allowing rotations) 7/6, 6/5, 7/5, 5/3, 2/1, 7/3, 4/1
+| <small>(allowing rotations) 7/6, 6/5, 7/5, 5/3, 2/1, 7/3, 4/1</small>
 |}
@@ Line 143: / Line 146: @@
 {| class="wikitable sortable mw-collapsible"}}
-|+ Tempered sonhar tunings
+|+ <small>Tempered sonhar tunings</small>
 |-
 ! Systematic name <br>(& idiosyncratic common name)
 ! Equave
-! Harmonics mapped
 ! Equal temp mapping
 ! Reduced mapping
@@ Line 154: / Line 156: @@
 ! TE tuning map (¢)
 ! TE mistunings (¢)
-! Complexity, <br>adjusted error <br>TE error
+! Complexity, <br>adjusted error, <br>TE error</small>
 ! Unison vectors
-! Recommended ETs
+! Recommended ETs <br>(warts in brackets)
-! (x31 notation)
 |-
-| c2 & c37 <br>(''Sonhar A'')
+| <small>c2 & c37 <br>(''Sonhar A'')</small>
-| [[5/1]]
+| <small>5/1</small>
-| '''5,11,13,31'''
+| <small>5,11,13,31 <br>[<2,3,3,4] <br> <37,55,59,79]></small>
-| [<2,3,3,4] <br> <37,55,59,79]>
+| <small>5,11,13,31 <br>[<1,2,-2,-3] <br> <0,-1,7,10]></small>
-| [<1,2,-2,-3] <br> <0,-1,7,10]>
+| <small>2789.3304, 1431.2645</small>
-| 2789.3304, 1431.2645
+| <small>40.49033, 73.19864</small>
-| 40.49033, 73.19864
+| <small>2789.330, 4147.396, 4440.191, 5944.654</small>
-| 2789.330, 4147.396, 4440.191, 5944.654
+| <small>3.017, -3.922, -0.337, -0.382</small>
-| 3.017, -3.922, -0.337, -0.382
+| <small>0.454182, <br>4.281341, <br>0.864185</small>
-| 0.454182, <br>4.281341, <br>0.864185
+| <small>[-2,1,3,-2>, [-5,3,-1,1>, [-7,4,2,-1>, [-3,2,-4,3></small>
-| [-2,1,3,-2>, [-5,3,-1,1>, [-7,4,2,-1>, [-3,2,-4,3>
+| <small>[[39ed5]], [[37ed5]], [[41ed5]], [[35ed5]], [[76ed5]], [[78ed5]], [[74ed5]], [[43ed5]](fk)</small>
-| [[39ed5]], [[37ed5]], [[41ed5]], [[35ed5]], [[76ed5]], [[78ed5]], [[74ed5]], [[43ed5]](fk)
-| c39, c37, c41, c35, c76, c78, c74, c43fk
 |}
 == Wijzerplaat scales ==
-All of these scales are octave-repeating subsets of [[31edo]]. They are tempered by definition. Sometimes multiple MOSes may generate the same tone, which is why when you combine an x-tone, y-tone and z-tone MOS, the total number of tones/octave may still be less than (x+y+z).
+All of these scales are tempered by definition. Sometimes multiple scales may generate the same tone, which is why when one combines an x-tone, y-tone and z-tone scale, the total number of tones/octave may still be less than (x+y+z).
 This list is not exhaustive. There are many other possible wijzerplaat scales.
-The scale names are [[Template:Idiosyncratic|idisyncratic]].
 {| class="wikitable sortable mw-collapsible"}}
 |+ The wijzerplaat scales
 |-
-! Name
+! Systematic name <br>(& idiosyncratic common name)
 ! Parent tuning used
 ! Tones per period used
 ! Scale pattern
-! Tones generated by 5\31, 11\31, 13\31
+! Tones generated by 5\31, 11\31, 13\31 (mos or no?)
 ! 5\31 generators up:down, <br>11\31 up:down, <br>13\31 up:down
 ! 7 integer limit intervals approximated within 15¢
 |-
-| PolyMOS 5\31(up2down1) 11\31(up0down2) 13\31(up1down1)
+| <small>PolyMOS <5\31(u2d0), <11\31(u0d4), 13\31(u1d3)> </small><br>(''Oclock'')  <br><br>'''Main article: [[Oclock]]'''
 | [[31edo]]
 | [[:Category:9-tone scales|9 tones]] per 31\31 [[Category:9-tone scales]]
-| 5 4 1 3 5 2 1 5 5
+| 5 4 1 3 5 2 3 6 2
-| 5, 3, 3
+| 3(mos), 5(mos), 5(mos)
-| 2:2, <br>2:2, <br>2:2
+| 2:0, <br>0:4, <br>1:3
-| 5/4, 4/3, 3/2, 2/1, 5/2, 3/1, 4/1, 5/1, 6/1
+| <small>5/4, 4/3, 3/2, 5/3, 2/1, 5/2, 3/1, 4/1, 5/1, 6/1</small>
 |}
 [[Category:Scales by family]]