User:BudjarnLambeth/Breuddwyd scale: Difference between revisions

(13 intermediate revisions by 2 users not shown)

Line 1:

{{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.}}

Line 6:

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, ser as in deserve, plat as in platypus"'') 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 40:

Line 41:

| 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

Line 50:

Line 51:

| 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'')

Line 92:

Line 93:

| 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]]

Line 147:

Line 148:

|+ Tempered sonhar tunings

|-

! ~~~~Systematic name (& idiosyncratic common name)~~~~

! Systematic name (& idiosyncratic common name)

! ~~~~Equave~~~~

! Equave

! ~~~~Equal temp mapping~~~~

! Equal temp mapping

! ~~~~Reduced mapping~~~~

! Reduced mapping

! ~~~~TE generator tunings (¢)~~~~

! TE generator tunings (¢)

! ~~~~TE step tunings (¢)~~~~

! TE step tunings (¢)

! ~~~~TE tuning map (¢)~~~~

! TE tuning map (¢)

! ~~~~TE mistunings (¢)~~~~

! TE mistunings (¢)

! ~~~~Complexity, adjusted error, TE error

! Complexity, adjusted error, TE error

! ~~~~Unison vectors~~~~

! Unison vectors

! ~~~~Recommended ETs<~~/small>~~

! Recommended ETs (warts in brackets)

~~! <small~~>(~~x31 notation~~)~~~~

|-

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

| [[5/1]]

| 5/1

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

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

Line 171:

| [-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)

~~| 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|idiosyncratic]]~~.

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

{| 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(~~up2down2~~), <~~br>~~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, 0:2, 1:1

| 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.}}
@@ Line 6: / 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, ser as in deserve, plat as in platypus"'') 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 40: / Line 41: @@
 | <small>The scale of all [[rational interval]]s with 5, 11, 13 or 31 in the denominator</small>
 | [[22165afdo]]
-| <small>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>
+| <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
@@ Line 50: / Line 51: @@
 | <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]]
-| <small>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>
+| <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 92: / Line 93: @@
 | <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]]
@@ Line 147: / Line 148: @@
 |+ <small>Tempered sonhar tunings</small>
 |-
-! <small>Systematic name <br>(& idiosyncratic common name)</small>
+! Systematic name <br>(& idiosyncratic common name)
-! <small>Equave</small>
+! Equave
-! <small>Equal temp mapping</small>
+! Equal temp mapping
-! <sup>Reduced mapping</sup>
+! Reduced mapping
-! <small>TE generator tunings (¢)</small>
+! TE generator tunings (¢)
-! <small>TE step tunings (¢)</small>
+! TE step tunings (¢)
-! <small>TE tuning map (¢)</small>
+! TE tuning map (¢)
-! <small>TE mistunings (¢)</small>
+! TE mistunings (¢)
-! <small>Complexity, <br>adjusted error, <br>TE error</small>
+! Complexity, <br>adjusted error, <br>TE error</small>
-! <small>Unison vectors</small>
+! Unison vectors
-! <small>Recommended ETs</small>
+! Recommended ETs <br>(warts in brackets)
-! <small>(x31 notation)</small>
 |-
 | <small>c2 & c37 <br>(''Sonhar A'')</small>
-| <small>[[5/1]]</small>
+| <small>5/1</small>
 | <small>5,11,13,31 <br>[<2,3,3,4] <br> <37,55,59,79]></small>
 | <small>5,11,13,31 <br>[<1,2,-2,-3] <br> <0,-1,7,10]></small>
@@ Line 171: / Line 171: @@
 | <small>[-2,1,3,-2>, [-5,3,-1,1>, [-7,4,2,-1>, [-3,2,-4,3></small>
 | <small>[[39ed5]], [[37ed5]], [[41ed5]], [[35ed5]], [[76ed5]], [[78ed5]], [[74ed5]], [[43ed5]](fk)</small>
-| <small>c39, c37, c41, c35, c76, c78, c74, c43fk</small>
 |}
 == 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|idiosyncratic]].
+This list is not exhaustive. There are many other possible wijzerplaat scales.
 {| 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(up2down2), <br>11\31(up0down2), <br>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>0:2, <br>1:1
+| 2:0, <br>0:4, <br>1:3
-| <small>5/4, 4/3, 3/2, 2/1, 5/2, 3/1, 4/1, 5/1, 6/1</small>
+| <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]]