Syntonic–rastmic subchroma notation: Difference between revisions

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== Connections to interval naming ==
== Connections to interval naming ==
Courtesy of collaboration between Aura and [[Lillian Hearne]], syntonic-rastmic subchroma notation also has connections to [[SKULO interval names]] in which raising by the rastma is represented by "R" and lowering by the rastma is represented by "r".


Courtesy of collaboration between Aura and [[Lillian Hearne]], syntonic-rastmic subchroma notation also has connections to [[SKULO interval names]] in which raising by the rastma is represented by "R" and lowering by the rastma is represented by "r".
== Notation guide for common tunings ==
Due to enharmonic equivalences, each tuning system can take many accidental settings. Each case shown in the tables below is only one of them. Users should choose the combination in question according to the semantics.
 
Equal temperaments are shown if the corresponding edo has {1, 3, 9}-diamond consistency. Others can be notated as subsets or be extrapolated.
 
=== Neutral tunings ===
{| class="wikitable center-1"
|+ Neutral tunings
|-
! Sharpness !! Accidentals !! Temperament !! Equal temperaments
|-
| 2 || t, # || Mohaha || 10e, 17, 24, 31, 38
|-
| 4 || ↑, t, #↓, # || Tetracot || 27e, 34, 41, 48, 55c
|-
| 6 || ↑, t↓, t, t↑, #↓, # || Larry || 51ce, 58, 65, 72, 79
|-
| 8 || ↑, ↑↑, t↓, t, t↑, #↓↓, #↓, # || 7 & 89 || 82c, 89, 96
|}
55 can be notated as a mohaha tuning. 75 can be notated as a tetracot tuning. 123 and 137 can be notated as larry tunings.
 
=== Protomere tunings ===
{| class="wikitable center-1"
|+ Protomere tunings – order 1
|-
! Sharpness !! Accidentals !! Temperament !! Equal temperaments
|-
| 3 || t<, t>, # || Porcupine restriction || 15, 22, 29, 36ce
|-
| 5 || ↑, t<, t>, #↓, # || Hitchcock restriction || 39, 46, 53, 60e
|-
| 7 || ↑, ↑↑, t<, t>, #↓↓, #↓, # || Absurdity extension || 63c, 70, 77, 84e
|}
 
{| class="wikitable center-1"
|+ Protomere tunings – order 2
|-
! Sharpness !! Accidentals !! Temperament !! Equal temperaments
|-
| 6 || >, t<, t, t>, #<, # || Neutral porcupine restriction || 51, 58ce
|-
| 8 || >, ↑, t<, t, t>, #↓, #<, # || Tetracot extension || 68, 75, 82e
|-
| 10 || >, ↑, ↑>, t<, t, t>, #↓<, #↓, #<, # || Neutral hitchcock restriction || 92, 99, 106e
|}
 
51 and 99 can be notated as either order 1 or order 2.
 
=== Deuteromere tunings ===
{| class="wikitable center-1"
|+ Deuteromere tunings – order 1
|-
! Sharpness !! Accidentals !! Temperament !! Equal temperaments
|-
| 7 || /, ↑, t<, t>, #↓, #\, # || Sevond extension || 56, 63, 70c
|-
| 9 || /, ↑, ↑/, t<, t>, #↓\, #↓, #\, # || 7 & 87 || 80, 87, 94, 101c
|-
| 11 || /, ↑, ↑/, ↑↑, t<, t>, #↓↓, #↓\, #↓, #\, # || Twentcufo || 104c, 111, 118, 125, 132e
|-
| 13 || /, ↑, ↑/, ↑↑, ↑↑/, t<, t>, #↓↓\, #↓↓, #↓\, #↓, #\, # || 7 & 149 || 135c, 142, 149, 156e
|}
 
{| class="wikitable center-1"
|+ Deuteromere tunings – order 2
|-
! Sharpness !! Accidentals !! Temperament !! Equal temperaments
|-
| 18 || >, /, ↑<, ↑, ↑>, ↑/, ↑↑<, t<, t, <br>t>, #↓↓>, #↓\, #↓<, #↓, #↓>, #\, #<, # || Neutral 7 & 87 || 174, 181, 188c
|-
| 20 || >, /, ↑<, ↑, ↑>, ↑/, ↑↑<, ↑↑, t<, t, <br>t>, #↓↓, #↓↓>, #↓\, #↓<, #↓, #↓>, #\, #<, # || 7 & 205 || 198, 205, 212, 219ce
|-
| 22 || >, /, ↑<, ↑, ↑>, ↑/, ↑↑<, ↑↑, ↑↑>, t<, <br>t, t>, #↓↓<, #↓↓, #↓↓>, #↓\, #↓<, #↓, #↓>, #\, #<, # || Neutral twentcufo || 222c, 229, 236, 243e
|}
 
181, 229, and 243e can be notated as either order 1 or order 2.  
 
=== Tritomere tunings ===
{| class="wikitable center-1"
|+ Tritomere tunings – order 1
|-
! Sharpness !! Accidentals !! Temperament !! Equal temperaments
|-
| 13 || /, ↑\, ↑, ↑/, ↑↑\, t<, t>, #↓↓/, #↓\, #↓, #↓/, #\, # || 7 & 121 || 121, 128, 135, 142c
|-
| 15 || /, ↑\, ↑, ↑/, ↑↑\, ↑↑, t<, t>, #↓↓, #↓↓/, #↓\, #↓, #↓/, #\, # || Trinity restriction || 145, 152, 159, 166, 173c
|-
| 17 || /, ↑\, ↑, ↑/, ↑↑\, ↑↑, ↑↑/, t<, t>, #↓↓\, #↓↓, #↓↓/, #↓\, #↓, #↓/, #\, # || 7 & 183 || 169c, 176, 183, 190, 197e
|-
| 19 || /, ↑\, ↑, ↑/, ↑↑\, ↑↑, ↑↑/, ↑↑//, t<, t>, #↓↓\\, #↓↓\, #↓↓, #↓↓/, #↓\, #↓, #↓/, #\, # || 7 & 207 || 200c, 207, 214
|}
 
{| class="wikitable center-1"
|+ Tritomere tunings – order 2
|-
! Sharpness !! Accidentals !! Temperament !! Equal temperaments
|-
| 28 || >, /, />, ↑\, ↑<, ↑, ↑>, ↑/, ↑/>, ↑↑\, ↑↑<, ↑↑, t<, t, <br>t>, #↓↓, #↓↓>, #↓↓/, #↓\<, #↓\, #↓<, #↓, #↓>, #↓/, #\<, #\, #<, # || 7 & 280 || 280, 287, 294c
|-
| 30 || >, /, />, ↑\, ↑<, ↑, ↑>, ↑/, ↑/>, ↑↑\, ↑↑<, ↑↑, ↑↑>, t<, t, <br>t>, #↓↓<, #↓↓, #↓↓>, #↓↓/, #↓\<, #↓\, #↓<, #↓, #↓>, #↓/, #\<, #\, #<, # || Neutral trinity restriction || 304, 311, 318, 325c
|-
| 32 || >, /, />, ↑\, ↑<, ↑, ↑>, ↑/, ↑/>, ↑↑\, ↑↑<, ↑↑, ↑↑>, ↑↑/, t<, t, <br>t>, #↓↓\, #↓↓<, #↓↓, #↓↓>, #↓↓/, #↓\<, #↓\, #↓<, #↓, #↓>, #↓/, #\<, #\, #<, # || 7 & 335 || 321ce, 328, 335, 342, 349, 356ce
|-
| 34 || >, /, />, ↑\, ↑<, ↑, ↑>, ↑/, ↑/>, ↑↑\, ↑↑<, ↑↑, ↑↑>, ↑↑/, ↑↑/>, t<, t, <br>t>, #↓↓\<, #↓↓\, #↓↓<, #↓↓, #↓↓>, #↓↓/, #↓\<, #↓\, #↓<, #↓, #↓>, #↓/, #\<, #\, #<, # || 7 & 359 || 352c, 359, 366, 373
|-
| 36 || >, /, />, ↑\, ↑<, ↑, ↑>, ↑/, ↑/>, ↑↑\, ↑↑<, ↑↑, ↑↑>, ↑↑/, ↑↑/>, ↑↑//, t<, t, <br>t>, #↓↓\\, #↓↓\<, #↓↓\, #↓↓<, #↓↓, #↓↓>, #↓↓/, #↓\<, #↓\, #↓<, #↓, #↓>, #↓/, #\<, #\, #<, # || 7 & 390 || 383c, 390, 397
|}
 
311, 325c, 359 and 373 can be notated as either order 1 or order 2.
 
=== Hemitritomere tunings ===
{| class="wikitable center-1"
|+ Hemitritomere tunings
|-
! Sharpness !! Accidentals !! Temperament !! Equal temperaments
|-
| 12 || >, ↑<, ↑, ↑>, t<, t, t>, #↓<, #↓, #↓>, #<, # || 7 & 109 || 109, 116, 123ce
|-
| 14 || >, ↑<, ↑, ↑>, ↑/, t<, t, t>, #↓\, #↓<, #↓, #↓>, #<, # || 7 & 140 || 133, 140, 147e
|-
| 16 || >, ↑<, ↑, ↑>, ↑↑<, ↑↑, t<, t, t>, #↓↓, #↓↓>, #↓<, #↓, #↓>, #<, # || 7 & 157 || 157, 164, 171e
|}
 
=== Tetartomere tunings ===
{| class="wikitable center-1"
|+ Tetartomere tunings – order 1
|-
! Sharpness !! Accidentals !! Temperament !! Equal temperaments
|-
| 19 || /, //, ↑\, ↑, ↑/, ↑//, ↑↑\, ↑↑, t<, t>, #↓↓, #↓↓/, #↓\\, #↓\, #↓, #↓/, #\\, #\, # || 7 & 193 || 186e, 193, 200, 207c
|-
| 21 || /, //, ↑\, ↑, ↑/, ↑//, ↑↑\, ↑↑, ↑↑/, t<, t>, #↓↓\, #↓↓, #↓↓/, #↓\\, #↓\, #↓, #↓/, #\\, #\, # || Brahmagupta restriction || 210e, 217, 224, 231, 238c
|-
| 23 || /, //, ↑\, ↑, ↑/, ↑//, ↑↑\, ↑↑, ↑↑/, ↑↑//, t<, t>, #↓↓\\, #↓↓\, #↓↓, #↓↓/, #↓\\, #↓\, #↓, #↓/, #\\, #\, # || 7 & 241 || 234c, 241, 248, 255
|}
 
=== Pemptomere tunings ===
{| class="wikitable center-1"
|+ Pemptomere tunings – order 1
|-
! Sharpness !! Accidentals !! Temperament !! Equal temperaments
|-
| 25 || /, //, ↑\\, ↑\, ↑, ↑/, ↑//, ↑↑\\, ↑↑\, ↑↑, ↑↑/, t<, t>, #↓↓\, #↓↓, #↓↓/, #↓↓//, #↓\\, #↓\, #↓, #↓/, #↓//, #\\, #\, # || 7 & 258 || 251e, 258, 265, 272c
|-
| 27 || /, //, ↑\\, ↑\, ↑, ↑/, ↑//, ↑↑\\, ↑↑\, ↑↑, ↑↑/, ↑↑//, t<, t>, #↓↓\\, #↓↓\, #↓↓, #↓↓/, #↓↓//, #↓\\, #↓\, #↓, #↓/, #↓//, #\\, #\, # || 7 & 289 || 275e, 282, 289, 296, 303c
|}
 
=== Hemipemptomere tunings ===
{| class="wikitable center-1"
|+ Hemipemptomere tunings
|-
! Sharpness !! Accidentals !! Temperament !! Equal temperaments
|-
| 24 || >, /, ↑\, ↑<, ↑, ↑>, ↑/, ↑↑\, ↑↑<, ↑↑, t<, t, t>, #↓↓, #↓↓>, #↓↓/, #↓\, #↓<, #↓, #↓>, #↓/, #\, #<, # || 7 & 246 || 239, 246, 253, 260c
|-
| 26 || >, /, ↑\, ↑<, ↑, ↑>, ↑/, ↑↑\, ↑↑<, ↑↑, ↑↑>, t<, t, t>, #↓↓<, #↓↓, #↓↓>, #↓↓/, #↓\, #↓<, #↓, #↓>, #↓/, #\, #<, # || 7 & 270 || 256c, 263, 270, 277, 284, 291ce
|-
| 28 || >, /, ↑\, ↑<, ↑, ↑>, ↑/, ↑↑\, ↑↑<, ↑↑, ↑↑>, ↑↑/, t<, t, t>, #↓↓\, #↓↓<, #↓↓, #↓↓>, #↓↓/, #↓\, #↓<, #↓, #↓>, #↓/, #\, #<, # || 7 & 294 || 287c, 294, 301, 308e
|}


== Notes ==
== Notes ==