Syntonic–rastmic subchroma notation: Difference between revisions

The '''syntonic-rastmic subchroma notation''' is a notation scheme developed by [[Aura]] et al.<ref>Other contributors include [[Flora Canou]] and [[User:SupahstarSaga|HEHEHE I AM A SUPAHSTAR SAGA]].</ref> that is an expansion to the [[neutral circle-of-fifths notation]].  

While the neutral circle-of-fifths notation models the 2.3 [[subgroup]] of [[just intonation]], with the neutral intervals capable of roughly modeling the harmonic 11, the syntonic-rastmic subchroma notation accurately captures the characteristics of the 2.3.5.11 subgroup, and is fit for a wider variety of equal temperaments and multirank temperaments.  As it tries to strike a balance between the number and semantic consistency of the accidentals, it has the following three basic building blocks of accidentals: the conventional accidentals, the syntonic and demisyntonic accidentals, and the rastmic and demirastmic accidentals, detailed below.  

|+Series of conventional accidentals

! Name !! Ratio !! Monzo !! Textual<br>Representation

| Demiflat || (2187/2048)^-1/2 || {{monzo| 11/2 -7/2 }} || d

| Flat || (2187/2048)^-1 || {{monzo| 11 -7 }} || b

| Sesquiflat || (2187/2048)^-3/2 || {{monzo| 33/2 -21/2 }} || db

| Double flat || (2187/2048)^-2 || {{monzo| 22 -14 }} || bb

|+Series of syntonic accidentals

! Name !! Ratio !! Monzo !! Textual<br>Representation*

| Synsharp || (81/80)¹ || {{monzo| -4 4 -1 }} || +

| Demisynsharp || (81/80)^1/2 || {{monzo| -2 2 -1/2 }} || ↑

| Demisynflat || (81/80)^-1/2 || {{monzo| 2 -2 1/2 }} || ↓

| Synflat || (81/80)^-1 || {{monzo| 4 -4 1 }} || ɔ

|+Series of rastmic and demirastmic accidentals

! Name !! Ratio !! Subgroup Monzo<br>(2.3.5.11) !! Textual<br>Representation

| Demiraflat || (243/242)^-1/2 || {{monzo| 1/2 -5/2 0 1 }} || <

| Raflat || (243/242)^-1 || {{monzo| 1 -5 0 2 }} || \

| Sesquiraflat || (243/242)^-3/2 || {{monzo| 3/2 -15/2 0 3 }} || <\

| Double raflat || (243/242)^-2 || {{monzo| 2 -10 0 4 }} || \\

|+ Overview of accidentals

! Name !! Ratio !! Subgroup Monzo<br>(2.3.5.11) !! Textual<br>Representation

The natural accidental cancels all pitch alterations.  

The syntonic-rastmic subchroma notation is closely related to the [[syntonic-rastmic equivalence continuum]], in that the accidental settings are similar among tunings of a particular equivalence number. Due to enharmonic equivalences, however, 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.  

|+ Neutral tunings

| 4 || +, t, #ɔ, # || Tetracot || 27e, 34, 41, 48, 55c

| 6 || +, tɔ, t, t+, #ɔ, # || Larry || 51ce, 58, 65, 72, 79

| 8 || +, ++, tɔ, t, t+, #ɔɔ, #ɔ, # || 7 & 89 || 82c, 89, 96

|+ Protomere tunings – order 1

| 5 || +, t<, t>, #ɔ, # || Hitchcock restriction || 39, 46, 53, 60e

| 7 || +, ++, t<, t>, #ɔɔ, #ɔ, # || Absurdity extension || 63c, 70, 77, 84e

|+ Protomere tunings – order 2

| 8 || >, +, t<, t, t>, #ɔ, #<, # || Tetracot extension || 68, 75, 82e

| 10 || >, +, +>, t<, t, t>, #ɔ<, #ɔ, #<, # || Neutral hitchcock restriction || 92, 99, 106e

|+ Deuteromere tunings – order 1

| 7 || /, +, t<, t>, #ɔ, #\, # || Sevond extension || 56, 63, 70c

| 9 || /, +, +/, t<, t>, #ɔ\, #ɔ, #\, # || 7 & 87 || 80, 87, 94, 101c

| 11 || /, +, +/, ++, t<, t>, #ɔɔ, #ɔ\, #ɔ, #\, # || Twentcufo || 104c, 111, 118, 125, 132e

| 13 || /, +, +/, ++, ++/, t<, t>, #ɔɔ\, #ɔɔ, #ɔ\, #ɔ, #\, # || 7 & 149 || 135c, 142, 149, 156e

|+ Deuteromere tunings – order 2

| 18 || >, /, +<, +, +>, +/, ++<, t<, t, <br>t>, #ɔɔ>, #ɔ\, #ɔ<, #ɔ, #ɔ>, #\, #<, # || Neutral 7 & 87 || 174, 181, 188c

| 20 || >, /, +<, +, +>, +/, ++<, ++, t<, t, <br>t>, #ɔɔ, #ɔɔ>, #ɔ\, #ɔ<, #ɔ, #ɔ>, #\, #<, # || 7 & 205 || 198, 205, 212, 219ce

| 22 || >, /, +<, +, +>, +/, ++<, ++, ++>, t<, <br>t, t>, #ɔɔ<, #ɔɔ, #ɔɔ>, #ɔ\, #ɔ<, #ɔ, #ɔ>, #\, #<, # || Neutral twentcufo || 222c, 229, 236, 243e

|+ Tritomere tunings – order 1

| 13 || /, +\, +, +/, ++\, t<, t>, #ɔɔ/, #ɔ\, #ɔ, #ɔ/, #\, # || 7 & 121 || 121, 128, 135, 142c

| 15 || /, +\, +, +/, ++\, ++, t<, t>, #ɔɔ, #ɔɔ/, #ɔ\, #ɔ, #ɔ/, #\, # || Trinity restriction || 145, 152, 159, 166, 173c

| 17 || /, +\, +, +/, ++\, ++, ++/, t<, t>, #ɔɔ\, #ɔɔ, #ɔɔ/, #ɔ\, #ɔ, #ɔ/, #\, # || 7 & 183 || 169c, 176, 183, 190, 197e

| 19 || /, +\, +, +/, ++\, ++, ++/, ++//, t<, t>, #ɔɔ\\, #ɔɔ\, #ɔɔ, #ɔɔ/, #ɔ\, #ɔ, #ɔ/, #\, # || 7 & 207 || 200c, 207, 214

|+ Tritomere tunings – order 2

| 28 || >, /, />, +\, +<, +, +>, +/, +/>, ++\, ++<, ++, t<, t, <br>t>, #ɔɔ, #ɔɔ>, #ɔɔ/, #ɔ\<, #ɔ\, #ɔ<, #ɔ, #ɔ>, #ɔ/, #\<, #\, #<, # || 7 & 280 || 280, 287, 294c

| 30 || >, /, />, +\, +<, +, +>, +/, +/>, ++\, ++<, ++, ++>, t<, t, <br>t>, #ɔɔ<, #ɔɔ, #ɔɔ>, #ɔɔ/, #ɔ\<, #ɔ\, #ɔ<, #ɔ, #ɔ>, #ɔ/, #\<, #\, #<, # || Neutral trinity restriction || 304, 311, 318, 325c

| 32 || >, /, />, +\, +<, +, +>, +/, +/>, ++\, ++<, ++, ++>, ++/, t<, t, <br>t>, #ɔɔ\, #ɔɔ<, #ɔɔ, #ɔɔ>, #ɔɔ/, #ɔ\<, #ɔ\, #ɔ<, #ɔ, #ɔ>, #ɔ/, #\<, #\, #<, # || 7 & 335 || 321ce, 328, 335, 342, 349, 356ce

| 34 || >, /, />, +\, +<, +, +>, +/, +/>, ++\, ++<, ++, ++>, ++/, ++/>, t<, t, <br>t>, #ɔɔ\<, #ɔɔ\, #ɔɔ<, #ɔɔ, #ɔɔ>, #ɔɔ/, #ɔ\<, #ɔ\, #ɔ<, #ɔ, #ɔ>, #ɔ/, #\<, #\, #<, # || 7 & 359 || 352c, 359, 366, 373

| 36 || >, /, />, +\, +<, +, +>, +/, +/>, ++\, ++<, ++, ++>, ++/, ++/>, ++//, t<, t, <br>t>, #ɔɔ\\, #ɔɔ\<, #ɔɔ\, #ɔɔ<, #ɔɔ, #ɔɔ>, #ɔɔ/, #↓\<, #ɔ\, #ɔ<, #ɔ, #ɔ>, #ɔ/, #\<, #\, #<, # || 7 & 390 || 383c, 390, 397

|+ Hemitritomere tunings

| 12 || >, +<, +, +>, t<, t, t>, #ɔ<, #ɔ, #ɔ>, #<, # || 7 & 109 || 109, 116, 123ce

| 14 || >, +<, +, +>, +/, t<, t, t>, #ɔ\, #ɔ<, #ɔ, #ɔ>, #<, # || 7 & 140 || 133, 140, 147e

| 16 || >, +<, +, +>, ++<, ++, t<, t, t>, #ɔɔ, #ɔɔ>, #ɔ<, #ɔ, #ɔ>, #<, # || 7 & 157 || 157, 164, 171e

|+ Tetartomere tunings – order 1

| 19 || /, //, +\, +, +/, +//, ++\, ++, t<, t>, #ɔɔ, #ɔɔ/, #ɔ\\, #ɔ\, #ɔ, #ɔ/, #\\, #\, # || 7 & 193 || 186e, 193, 200, 207c

| 21 || /, //, +\, +, +/, +//, ++\, ++, ++/, t<, t>, #ɔɔ\, #ɔɔ, #ɔɔ/, #ɔ\\, #ɔ\, #ɔ, #ɔ/, #\\, #\, # || Brahmagupta restriction || 210e, 217, 224, 231, 238c

| 23 || /, //, +\, +, +/, +//, ++\, ++, ++/, ++//, t<, t>, #ɔɔ\\, #ɔɔ\, #ɔɔ, #ɔɔ/, #ɔ\\, #ɔ\, #ɔ, #ɔ/, #\\, #\, # || 7 & 241 || 234c, 241, 248, 255

|+ Tetartomere tunings – order 2

| 40 || >, /, />, //, +\<, +\, +<, +, +>, +/, +/>, +//, ++\<, ++\, ++<, ++, ++>, ++/, t<, t, <br>t>, #ɔɔ\, #ɔɔ<, #ɔɔ, #ɔɔ>, #ɔɔ/, #ɔɔ/>, #ɔ\\, #ɔ\<, #ɔ\, #ɔ<, #ɔ, #ɔ>, #ɔ/, #ɔ/>, #\\, #\<, #\, #<, # || 7 & 417 || 410e, 417, 424, 431c

| 42 || >, /, />, //, +\<, +\, +<, +, +>, +/, +/>, +//, ++\<, ++\, ++<, ++, ++>, ++/, ++/>, t<, t, <br>t>, #ɔɔ\<, #ɔɔ\, #ɔɔ<, #ɔɔ, #ɔɔ>, #ɔɔ/, #ɔɔ/>, #ɔ\\, #ɔ\<, #ɔ\, #ɔ<, #ɔ, #ɔ>, #ɔ/, #ɔ/>, #\\, #\<, #\, #<, # || Neutral brahmagupta restriction || 434e, 441, 448, 455

| 44 || >, /, />, //, +\<, +\, +<, +, +>, +/, +/>, +//, ++\<, ++\, ++<, ++, ++>, ++/, ++/>, ++//, t<, t, <br>t>, #ɔɔ\\, #ɔɔ\<, #ɔɔ\, #ɔɔ<, #ɔɔ, #ɔɔ>, #ɔɔ/, #ɔɔ/>, #ɔ\\, #ɔ\<, #ɔ\, #ɔ<, #ɔ, #ɔ>, #ɔ/, #ɔ/>, #\\, #\<, #\, #<, # || 7 & 472 || 458ce, 465, 472, 479

|+ Pemptomere tunings – order 1

| 25 || /, //, +\\, +\, +, +/, +//, ++\\, ++\, ++, ++/, t<, t>, #ɔɔ\, #ɔɔ, #ɔɔ/, #ɔɔ//, #ɔ\\, #ɔ\, #ɔ, #ɔ/, #ɔ//, #\\, #\, # || 7 & 258 || 251e, 258, 265, 272c

| 27 || /, //, +\\, +\, +, +/, +//, ++\\, ++\, ++, ++/, ++//, t<, t>, #ɔɔ\\, #ɔɔ\, #ɔɔ, #ɔɔ/, #ɔɔ//, #ɔ\\, #ɔ\, #ɔ, #ɔ/, #ɔ//, #\\, #\, # || 7 & 289 || 275e, 282, 289, 296, 303c

|+ Pemptomere tunings – order 2

| 52 || >, /, />, //, //>, +\\, +\<, +\, +<, +, +>, +/, +/>, +//, +//>, ++\\, ++\<, ++\, ++<, ++, ++>, ++/, ++/>, ++//, t<, t, <br>t>, #ɔɔ\\, #ɔɔ\<, #ɔɔ\, #ɔɔ<, #ɔɔ, #ɔɔ>, #ɔɔ/, #ɔɔ/>, #ɔ\\<, #ɔ\\, #ɔ\<, #ɔ\, #ɔ<, #ɔ, #ɔ>, #ɔ/, #ɔ/>, #\\<, #\\, #\<, #\, #<, # || 7 & 554 || 547e, 554, 561c

| 54 || >, /, />, //, //>, +\\, +\<, +\, +<, +, +>, +/, +/>, +//, +//>, ++\\, ++\<, ++\, ++<, ++, ++>, ++/, ++/>, ++//, ++//>, t<, t, <br>t>, #ɔɔ\\<, #ɔɔ\\, #ɔɔ\<, #ɔɔ\, #ɔɔ<, #ɔɔ, #ɔɔ>, #ɔɔ/, #ɔɔ/>, #ɔ\\<, #ɔ\\, #ɔ\<, #ɔ\, #ɔ<, #ɔ, #ɔ>, #ɔ/, #ɔ/>, #\\<, #\\, #\<, #\, #<, # || Neutral 7 & 289 || 571e, 578, 585

|+ Hemipemptomere tunings

| 24 || >, /, +\, +<, +, +>, +/, ++\, ++<, ++, t<, t, t>, #ɔɔ, #ɔɔ>, #ɔɔ/, #ɔ\, #ɔ<, #ɔ, #ɔ>, #ɔ/, #\, #<, # || 7 & 246 || 239, 246, 253, 260c

| 26 || >, /, +\, +<, +, +>, +/, ++\, ++<, ++, ++>, t<, t, t>, #ɔɔ<, #ɔɔ, #ɔɔ>, #ɔɔ/, #ɔ\, #ɔ<, #ɔ, #ɔ>, #ɔ/, #\, #<, # || 7 & 270 || 256c, 263, 270, 277, 284, 291ce

| 28 || >, /, +\, +<, +, +>, +/, ++\, ++<, ++, ++>, ++/, t<, t, t>, #ɔɔ\, #ɔɔ<, #ɔɔ, #ɔɔ>, #ɔɔ/, #ɔ\, #ɔ<, #ɔ, #ɔ>, #ɔ/, #\, #<, # || 7 & 294 || 287c, 294, 301, 308e

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".

<references/>