Syntonic–rastmic subchroma notation: Difference between revisions

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~~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]].

'''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 accidentals, and the rastmic and demirastmic accidentals, detailed below.

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.

== Accidentals ==

Line 8:

{| class="wikitable center-4"

|+Series of conventional accidentals

|+ style="font-size: 105%;" | Series of conventional accidentals

|-

! Name !! Ratio !! Monzo !! Textual Representation

! Name !! Ratio !! Monzo !! Textual Representation

|-

| … || … || … || …

Line 16:

| Double sharp || (2187/2048)2 || {{monzo| -22 14 }} || x

|-

| Sesquisharp || (2187/2048)3/2 || {{monzo| -33/2 21/2 }} || +#

| Sesquisharp || (2187/2048)3/2 || {{monzo| -33/2 21/2 }} || t#

|-

| Sharp || (2187/2048)1 || {{monzo| -11 7 }} || #

|-

| Demisharp || (2187/2048)1/2 || {{monzo| -11/2 7/2 }} || +

| Demisharp || (2187/2048)1/2 || {{monzo| -11/2 7/2 }} || t

|-

| (None) || (2187/2048)0 || {{monzo| 0 }} ||

|-

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

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

|-

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

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

|-

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

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

|-

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

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

|-

| … || … || … || …

|}

=== Syntonic accidentals ===

=== Syntonic and demisyntonic accidentals ===

[[File:Syntonic Accidentals.png|thumb|Syntonic accidentals]]

[[File:Demisyntonic Accidentals.PNG|thumb|Demisyntonic accidentals (WIP)]]

The syntonic accidentals model the harmonic 5. The synsharp raises the pitch by a syntonic comma. The synflat lowers the pitch by the same amount.

The syntonic and demisyntonic accidentals model the harmonic 5. The synsharp raises the pitch by a syntonic comma. The synflat lowers the pitch by the same amount.

{| class="wikitable center-4"

|+Series of syntonic accidentals

|+ style="font-size: 105%;" | Series of syntonic accidentals

|-

! Name !! Ratio !! Monzo !! Textual Representation*

! Name !! Ratio !! Monzo !! Textual Representation

|-

| … || … || … || …

|-

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

|-

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

|-

| (None) || (81/80)0 || {{monzo| 0 }} ||

|-

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

| Demisynflat || (81/80)−1/2 || {{monzo| 2 -2 1/2 }} || v

|-

| Synflat || (81/80)−1 || {{monzo| 4 -4 1 }} || ↓

|-

| … || … || … || …

|}

~~<nowiki>*</nowiki> "^" and "v" are acceptable variants of textual representation. Those are handy when input of non-ASCII characters are not available.~~

=== Rastmic and demirastmic accidentals ===

[[File:Rastmic Accidentals.png|thumb|Rastmic accidentals]]

[[File:Demirastmic Accidentals.png|thumb|Demirastmic accidentals ~~(WIP)~~]]

[[File:Demirastmic Accidentals.png|thumb|Demirastmic accidentals]]

The rastmic and demirastmic accidentals model the harmonic 11. The demirasharp raises the pitch by half a rastma. The demiraflat lowers the pitch by the same amount~~. '''Note''': The graphical forms of demirastmic accidentals are work in progress~~.

The rastmic and demirastmic accidentals model the harmonic 11. The demirasharp raises the pitch by half a rastma. The demiraflat lowers the pitch by the same amount.

{| class="wikitable center-4"

|+Series of rastmic and demirastmic accidentals

|+ style="font-size: 105%;" | Series of rastmic and demirastmic accidentals

|-

! Name !! Ratio !! Subgroup Monzo (2.3.5.11) !! Textual Representation

! Name !! Ratio !! Subgroup Monzo (2.3.5.11) !! Textual Representation

|-

| … || … || … || …

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| Double rasharp || (243/242)2 || {{monzo| -2 10 0 -4 }} || //

|-

| Sesquirasharp || (243/242)3/2 || {{monzo| -3/2 15/2 0 -3 }} || />

| Sesquirasharp || (243/242)3/2 || {{monzo| -3/2 15/2 0 -3 }} || >/

|-

| Rasharp || (243/242)1 || {{monzo| -1 5 0 -2 }} || /

Line 81:

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| (None) || (243/242)0 || {{monzo| 0 }} ||

|-

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

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

|-

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

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

|-

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

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

|-

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

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

|-

| … || … || … || …

Line 93:

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=== Combined accidentals ===

The demisharp/demiflat and the demirasharp/demiraflat are rarely used alone since they are irrational. They are usually combined for the following accidentals. These are the most common quartertones.

[[File:Quartertone Accidentals.png|thumb|Combined quartertone-demirastmic accidentals]]

The demisharp/demiflat and the demirasharp/demiraflat are rarely used alone since they are irrational. They are usually combined for the following accidentals. These are the most common quartertones.

{| class="wikitable center-all"

|+ Overview of accidentals

|+ style="font-size: 105%;" | Overview of accidentals

|-

! Name !! Ratio !! Subgroup Monzo (2.3.5.11) !! Textual Representation

! Name !! Ratio !! Subgroup Monzo (2.3.5.11) !! Textual Representation

|-

| Tendodemisharp || 729/704 || {{monzo| -6 6 0 -1 }} || +>

| Tendodemisharp || 729/704 || {{monzo| -6 6 0 -1 }} || t>

|-

| Artodemisharp || 33/32 || {{monzo| -5 1 0 1 }} || <+

| Artodemisharp || 33/32 || {{monzo| -5 1 0 1 }} || t<

|-

| Tendodemiflat || 32/33 || {{monzo| 5 -1 0 -1 }} || d>

|-

| Artodemiflat || 704/729 || {{monzo| 6 -6 0 1 }} || <d

| Artodemiflat || 704/729 || {{monzo| 6 -6 0 1 }} || d<

|}

=== Natural accidental ===

The natural accidental cancels all pitch alterations.

== Notation guide for common tunings ==

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.

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"

|+ style="font-size: 105%;" | 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"

|+ style="font-size: 105%;" | 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"

|+ style="font-size: 105%;" | 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"

|+ style="font-size: 105%;" | 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"

|+ style="font-size: 105%;" | Deuteromere tunings—order 2

|-

! Sharpness !! Accidentals !! Temperament !! Equal temperaments

|-

| 18 || >, /, ↑<, ↑, ↑>, ↑/, ↑↑<, t<, t, t>, #↓↓>, #↓\, #↓<, #↓, #↓>, #\, #<, # || Neutral 7 & 87 || 174, 181, 188c

|-

| 20 || >, /, ↑<, ↑, ↑>, ↑/, ↑↑<, ↑↑, t<, t, t>, #↓↓, #↓↓>, #↓\, #↓<, #↓, #↓>, #\, #<, # || 7 & 205 || 198, 205, 212, 219ce

|-

| 22 || >, /, ↑<, ↑, ↑>, ↑/, ↑↑<, ↑↑, ↑↑>, t<, 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"

|+ style="font-size: 105%;" | 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"

|+ style="font-size: 105%;" | Tritomere tunings—order 2

|-

! Sharpness !! Accidentals !! Temperament !! Equal temperaments

|-

| 28 || >, /, />, ↑\, ↑<, ↑, ↑>, ↑/, ↑/>, ↑↑\, ↑↑<, ↑↑, t<, t, t>, #↓↓, #↓↓>, #↓↓/, #↓\<, #↓\, #↓<, #↓, #↓>, #↓/, #\<, #\, #<, # || 7 & 280 || 280, 287, 294c

|-

| 30 || >, /, />, ↑\, ↑<, ↑, ↑>, ↑/, ↑/>, ↑↑\, ↑↑<, ↑↑, ↑↑>, t<, t, t>, #↓↓<, #↓↓, #↓↓>, #↓↓/, #↓\<, #↓\, #↓<, #↓, #↓>, #↓/, #\<, #\, #<, # || Neutral trinity restriction || 304, 311, 318, 325c

|-

| 32 || >, /, />, ↑\, ↑<, ↑, ↑>, ↑/, ↑/>, ↑↑\, ↑↑<, ↑↑, ↑↑>, ↑↑/, t<, t, t>, #↓↓\, #↓↓<, #↓↓, #↓↓>, #↓↓/, #↓\<, #↓\, #↓<, #↓, #↓>, #↓/, #\<, #\, #<, # || 7 & 335 || 321ce, 328, 335, 342, 349, 356ce

|-

| 34 || >, /, />, ↑\, ↑<, ↑, ↑>, ↑/, ↑/>, ↑↑\, ↑↑<, ↑↑, ↑↑>, ↑↑/, ↑↑/>, t<, t, t>, #↓↓\<, #↓↓\, #↓↓<, #↓↓, #↓↓>, #↓↓/, #↓\<, #↓\, #↓<, #↓, #↓>, #↓/, #\<, #\, #<, # || 7 & 359 || 352c, 359, 366, 373

|-

| 36 || >, /, />, ↑\, ↑<, ↑, ↑>, ↑/, ↑/>, ↑↑\, ↑↑<, ↑↑, ↑↑>, ↑↑/, ↑↑/>, ↑↑//, t<, t, 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"

|+ style="font-size: 105%;" | 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"

|+ style="font-size: 105%;" | 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

|}

{| class="wikitable center-1"

|+ style="font-size: 105%;" | Tetartomere tunings—order 2

|-

! Sharpness !! Accidentals !! Temperament !! Equal temperaments

|-

| 40 || >, /, />, //, ↑\<, ↑\, ↑<, ↑, ↑>, ↑/, ↑/>, ↑//, ↑↑\<, ↑↑\, ↑↑<, ↑↑, ↑↑>, ↑↑/, t<, t, t>, #↓↓\, #↓↓<, #↓↓, #↓↓>, #↓↓/, #↓↓/>, #↓\\, #↓\<, #↓\, #↓<, #↓, #↓>, #↓/, #↓/>, #\\, #\<, #\, #<, # || 7 & 417 || 410e, 417, 424, 431c

|-

| 42 || >, /, />, //, ↑\<, ↑\, ↑<, ↑, ↑>, ↑/, ↑/>, ↑//, ↑↑\<, ↑↑\, ↑↑<, ↑↑, ↑↑>, ↑↑/, ↑↑/>, t<, t, t>, #↓↓\<, #↓↓\, #↓↓<, #↓↓, #↓↓>, #↓↓/, #↓↓/>, #↓\\, #↓\<, #↓\, #↓<, #↓, #↓>, #↓/, #↓/>, #\\, #\<, #\, #<, # || Neutral brahmagupta restriction || 434e, 441, 448, 455

|-

| 44 || >, /, />, //, ↑\<, ↑\, ↑<, ↑, ↑>, ↑/, ↑/>, ↑//, ↑↑\<, ↑↑\, ↑↑<, ↑↑, ↑↑>, ↑↑/, ↑↑/>, ↑↑//, t<, t, t>, #↓↓\\, #↓↓\<, #↓↓\, #↓↓<, #↓↓, #↓↓>, #↓↓/, #↓↓/>, #↓\\, #↓\<, #↓\, #↓<, #↓, #↓>, #↓/, #↓/>, #\\, #\<, #\, #<, # || 7 & 472 || 458ce, 465, 472, 479

|}

441 and 455 can be notated as either order 1 or order 2.

=== Pemptomere tunings ===

{| class="wikitable center-1"

|+ style="font-size: 105%;" | 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

|}

{| class="wikitable center-1"

|+ style="font-size: 105%;" | Pemptomere tunings—order 2

|-

! Sharpness !! Accidentals !! Temperament !! Equal temperaments

|-

| 52 || >, /, />, //, //>, ↑\\, ↑\<, ↑\, ↑<, ↑, ↑>, ↑/, ↑/>, ↑//, ↑//>, ↑↑\\, ↑↑\<, ↑↑\, ↑↑<, ↑↑, ↑↑>, ↑↑/, ↑↑/>, ↑↑//, t<, t, t>, #↓↓\\, #↓↓\<, #↓↓\, #↓↓<, #↓↓, #↓↓>, #↓↓/, #↓↓/>, #↓\\<, #↓\\, #↓\<, #↓\, #↓<, #↓, #↓>, #↓/, #↓/>, #\\<, #\\, #\<, #\, #<, # || 7 & 554 || 547e, 554, 561c

|-

| 54 || >, /, />, //, //>, ↑\\, ↑\<, ↑\, ↑<, ↑, ↑>, ↑/, ↑/>, ↑//, ↑//>, ↑↑\\, ↑↑\<, ↑↑\, ↑↑<, ↑↑, ↑↑>, ↑↑/, ↑↑/>, ↑↑//, ↑↑//>, t<, t, t>, #↓↓\\<, #↓↓\\, #↓↓\<, #↓↓\, #↓↓<, #↓↓, #↓↓>, #↓↓/, #↓↓/>, #↓\\<, #↓\\, #↓\<, #↓\, #↓<, #↓, #↓>, #↓/, #↓/>, #\\<, #\\, #\<, #\, #<, # || Neutral 7 & 289 || 571e, 578, 585

|}

571e and 585 can be notated as either order 1 or order 2.

=== Hemipemptomere tunings ===

{| class="wikitable center-1"

|+ style="font-size: 105%;" | 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

|}

== 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".

== Notes ==

~~[[Category:Notation]]~~

@@ Line 1: / Line 1: @@
-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]].
+'''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 accidentals, and the rastmic and demirastmic accidentals, detailed below.
+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.
 == Accidentals ==
@@ Line 8: / Line 8: @@
 {| class="wikitable center-4"
-|+Series of conventional accidentals
+|+ style="font-size: 105%;" | Series of conventional accidentals
 |-
-! Name !! Ratio !! Monzo !! Textual<br>Representation
+! Name !! Ratio !! Monzo !! Textual<br />Representation
 |-
 | … || … || … || …
@@ Line 16: / Line 16: @@
 | Double sharp || (2187/2048)<sup>2</sup> || {{monzo| -22 14 }} || x
 |-
-| Sesquisharp || (2187/2048)<sup>3/2</sup> || {{monzo| -33/2 21/2 }} || +#
+| Sesquisharp || (2187/2048)<sup>3/2</sup> || {{monzo| -33/2 21/2 }} || t#
 |-
 | Sharp || (2187/2048)<sup>1</sup> || {{monzo| -11 7 }} || #
 |-
-| Demisharp || (2187/2048)<sup>1/2</sup> || {{monzo| -11/2 7/2 }} || +
+| Demisharp || (2187/2048)<sup>1/2</sup> || {{monzo| -11/2 7/2 }} || t
 |-
 | (None) || (2187/2048)<sup>0</sup> || {{monzo| 0 }} ||
 |-
-| Demiflat || (2187/2048)<sup>-1/2</sup> || {{monzo| 11/2 -7/2 }} || d
+| Demiflat || (2187/2048)<sup>&minus;1/2</sup> || {{monzo| 11/2 -7/2 }} || d
 |-
-| Flat || (2187/2048)<sup>-1</sup> || {{monzo| 11 -7 }} || b
+| Flat || (2187/2048)<sup>&minus;1</sup> || {{monzo| 11 -7 }} || b
 |-
-| Sesquiflat || (2187/2048)<sup>-3/2</sup> || {{monzo| 33/2 -21/2 }} || db
+| Sesquiflat || (2187/2048)<sup>&minus;3/2</sup> || {{monzo| 33/2 -21/2 }} || db
 |-
-| Double flat || (2187/2048)<sup>-2</sup> || {{monzo| 22 -14 }} || bb
+| Double flat || (2187/2048)<sup>&minus;2</sup> || {{monzo| 22 -14 }} || bb
 |-
 | … || … || … || …
 |}
-=== Syntonic accidentals ===
+=== Syntonic and demisyntonic accidentals ===
 [[File:Syntonic Accidentals.png|thumb|Syntonic accidentals]]
+[[File:Demisyntonic Accidentals.PNG|thumb|Demisyntonic accidentals (WIP)]]
-The syntonic accidentals model the harmonic 5. The synsharp raises the pitch by a syntonic comma. The synflat lowers the pitch by the same amount.
+The syntonic and demisyntonic accidentals model the harmonic 5. The synsharp raises the pitch by a syntonic comma. The synflat lowers the pitch by the same amount.
 {| class="wikitable center-4"
-|+Series of syntonic accidentals
+|+ style="font-size: 105%;" | Series of syntonic accidentals
 |-
-! Name !! Ratio !! Monzo !! Textual<br>Representation*
+! Name !! Ratio !! Monzo !! Textual<br />Representation
 |-
 | … || … || … || …
 |-
 | Synsharp || (81/80)<sup>1</sup> || {{monzo| -4 4 -1 }} || ↑
+|-
+| Demisynsharp || (81/80)<sup>1/2</sup> || {{monzo| -2 2 -1/2 }} || ^
 |-
 | (None) || (81/80)<sup>0</sup> || {{monzo| 0 }} ||
 |-
-| Synflat || (81/80)<sup>-1</sup> || {{monzo| 4 -4 1 }} || ↓
+| Demisynflat || (81/80)<sup>&minus;1/2</sup> || {{monzo| 2 -2 1/2 }} || v
+|-
+| Synflat || (81/80)<sup>&minus;1</sup> || {{monzo| 4 -4 1 }} || ↓
 |-
 | … || … || … || …
 |}
-<nowiki>*</nowiki> "^" and "v" are acceptable variants of textual representation. Those are handy when input of non-ASCII characters are not available.
 === Rastmic and demirastmic accidentals ===
 [[File:Rastmic Accidentals.png|thumb|Rastmic accidentals]]
-[[File:Demirastmic Accidentals.png|thumb|Demirastmic accidentals (WIP)]]
+[[File:Demirastmic Accidentals.png|thumb|Demirastmic accidentals]]
-The rastmic and demirastmic accidentals model the harmonic 11. The demirasharp raises the pitch by half a rastma. The demiraflat lowers the pitch by the same amount. '''Note''': The graphical forms of demirastmic accidentals are work in progress.
+The rastmic and demirastmic accidentals model the harmonic 11. The demirasharp raises the pitch by half a rastma. The demiraflat lowers the pitch by the same amount.
 {| class="wikitable center-4"
-|+Series of rastmic and demirastmic accidentals
+|+ style="font-size: 105%;" | Series of rastmic and demirastmic accidentals
 |-
-! Name !! Ratio !! Subgroup Monzo<br>(2.3.5.11) !! Textual<br>Representation
+! Name !! Ratio !! Subgroup Monzo<br />(2.3.5.11) !! Textual<br />Representation
 |-
 | … || … || … || …
@@ Line 73: / Line 76: @@
 | Double rasharp || (243/242)<sup>2</sup> || {{monzo| -2 10 0 -4 }} || //
 |-
-| Sesquirasharp || (243/242)<sup>3/2</sup> || {{monzo| -3/2 15/2 0 -3 }} || />
+| Sesquirasharp || (243/242)<sup>3/2</sup> || {{monzo| -3/2 15/2 0 -3 }} || >/
 |-
 | Rasharp || (243/242)<sup>1</sup> || {{monzo| -1 5 0 -2 }} || /
@@ Line 81: / Line 84: @@
 | (None) || (243/242)<sup>0</sup> || {{monzo| 0 }} ||
 |-
-| Demiraflat || (243/242)<sup>-1/2</sup> || {{monzo| 1/2 -5/2 0 1 }} || <
+| Demiraflat || (243/242)<sup>&minus;1/2</sup> || {{monzo| 1/2 -5/2 0 1 }} || <
 |-
-| Raflat || (243/242)<sup>-1</sup> || {{monzo| 1 -5 0 2 }} || \
+| Raflat || (243/242)<sup>&minus;1</sup> || {{monzo| 1 -5 0 2 }} || \
 |-
-| Sesquiraflat || (243/242)<sup>-3/2</sup> || {{monzo| 3/2 -15/2 0 3 }} || <\
+| Sesquiraflat || (243/242)<sup>&minus;3/2</sup> || {{monzo| 3/2 -15/2 0 3 }} || <\
 |-
-| Double raflat || (243/242)<sup>-2</sup> || {{monzo| 2 -10 0 4 }} || \\
+| Double raflat || (243/242)<sup>&minus;2</sup> || {{monzo| 2 -10 0 4 }} || \\
 |-
 | … || … || … || …
@@ Line 93: / Line 96: @@
 === Combined accidentals ===
-The demisharp/demiflat and the demirasharp/demiraflat are rarely used alone since they are irrational. They are usually combined for the following accidentals. These are the most common quartertones.
+[[File:Quartertone Accidentals.png|thumb|Combined quartertone-demirastmic accidentals]]
+The demisharp/demiflat and the demirasharp/demiraflat are rarely used alone since they are irrational. They are usually combined for the following accidentals. These are the most common quartertones.
 {| class="wikitable center-all"
-|+ Overview of accidentals
+|+ style="font-size: 105%;" | Overview of accidentals
 |-
-! Name !! Ratio !! Subgroup Monzo<br>(2.3.5.11) !! Textual<br>Representation
+! Name !! Ratio !! Subgroup Monzo<br />(2.3.5.11) !! Textual<br />Representation
 |-
-| Tendodemisharp || 729/704 || {{monzo| -6 6 0 -1 }} || +>
+| Tendodemisharp || 729/704 || {{monzo| -6 6 0 -1 }} || t>
 |-
-| Artodemisharp || 33/32 || {{monzo| -5 1 0 1 }} || <+
+| Artodemisharp || 33/32 || {{monzo| -5 1 0 1 }} || t<
 |-
 | Tendodemiflat || 32/33 || {{monzo| 5 -1 0 -1 }} || d>
 |-
-| Artodemiflat || 704/729 || {{monzo| 6 -6 0 1 }} || <d
+| Artodemiflat || 704/729 || {{monzo| 6 -6 0 1 }} || d<
 |}
 === Natural accidental ===
 The natural accidental cancels all pitch alterations.
+== Notation guide for common tunings ==
+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.
+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"
+|+ style="font-size: 105%;" | 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
+|}
+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"
+|+ style="font-size: 105%;" | Protomere tunings&mdash;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"
+|+ style="font-size: 105%;" | Protomere tunings&mdash;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
+|}
+and 99 can be notated as either order 1 or order 2.
+=== Deuteromere tunings ===
+{| class="wikitable center-1"
+|+ style="font-size: 105%;" | Deuteromere tunings&mdash;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"
+|+ style="font-size: 105%;" | Deuteromere tunings&mdash;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
+|}
+, 229, and 243e can be notated as either order 1 or order 2.
+=== Tritomere tunings ===
+{| class="wikitable center-1"
+|+ style="font-size: 105%;" | Tritomere tunings&mdash;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"
+|+ style="font-size: 105%;" | Tritomere tunings&mdash;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
+|}
+, 325c, 359 and 373 can be notated as either order 1 or order 2.
+=== Hemitritomere tunings ===
+{| class="wikitable center-1"
+|+ style="font-size: 105%;" | 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"
+|+ style="font-size: 105%;" | Tetartomere tunings&mdash;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
+|}
+{| class="wikitable center-1"
+|+ style="font-size: 105%;" | Tetartomere tunings&mdash;order 2
+|-
+! Sharpness !! Accidentals !! Temperament !! Equal temperaments
+|-
+| 40 || >, /, />, //, ↑\<, ↑\, ↑<, ↑, ↑>, ↑/, ↑/>, ↑//, ↑↑\<, ↑↑\, ↑↑<, ↑↑, ↑↑>, ↑↑/, t<, t, <br />t>, #↓↓\, #↓↓<, #↓↓, #↓↓>, #↓↓/, #↓↓/>, #↓\\, #↓\<, #↓\, #↓<, #↓, #↓>, #↓/, #↓/>, #\\, #\<, #\, #<, # || 7 & 417 || 410e, 417, 424, 431c
+|-
+| 42 || >, /, />, //, ↑\<, ↑\, ↑<, ↑, ↑>, ↑/, ↑/>, ↑//, ↑↑\<, ↑↑\, ↑↑<, ↑↑, ↑↑>, ↑↑/, ↑↑/>, t<, t, <br />t>, #↓↓\<, #↓↓\, #↓↓<, #↓↓, #↓↓>, #↓↓/, #↓↓/>, #↓\\, #↓\<, #↓\, #↓<, #↓, #↓>, #↓/, #↓/>, #\\, #\<, #\, #<, # || Neutral brahmagupta restriction || 434e, 441, 448, 455
+|-
+| 44 || >, /, />, //, ↑\<, ↑\, ↑<, ↑, ↑>, ↑/, ↑/>, ↑//, ↑↑\<, ↑↑\, ↑↑<, ↑↑, ↑↑>, ↑↑/, ↑↑/>, ↑↑//, t<, t, <br />t>, #↓↓\\, #↓↓\<, #↓↓\, #↓↓<, #↓↓, #↓↓>, #↓↓/, #↓↓/>, #↓\\, #↓\<, #↓\, #↓<, #↓, #↓>, #↓/, #↓/>, #\\, #\<, #\, #<, # || 7 & 472 || 458ce, 465, 472, 479
+|}
+and 455 can be notated as either order 1 or order 2.
+=== Pemptomere tunings ===
+{| class="wikitable center-1"
+|+ style="font-size: 105%;" | Pemptomere tunings&mdash;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
+|}
+{| class="wikitable center-1"
+|+ style="font-size: 105%;" | Pemptomere tunings&mdash;order 2
+|-
+! Sharpness !! Accidentals !! Temperament !! Equal temperaments
+|-
+| 52 || >, /, />, //, //>, ↑\\, ↑\<, ↑\, ↑<, ↑, ↑>, ↑/, ↑/>, ↑//, ↑//>, ↑↑\\, ↑↑\<, ↑↑\, ↑↑<, ↑↑, ↑↑>, ↑↑/, ↑↑/>, ↑↑//, t<, t, <br />t>, #↓↓\\, #↓↓\<, #↓↓\, #↓↓<, #↓↓, #↓↓>, #↓↓/, #↓↓/>, #↓\\<, #↓\\, #↓\<, #↓\, #↓<, #↓, #↓>, #↓/, #↓/>, #\\<, #\\, #\<, #\, #<, # || 7 & 554 || 547e, 554, 561c
+|-
+| 54 || >, /, />, //, //>, ↑\\, ↑\<, ↑\, ↑<, ↑, ↑>, ↑/, ↑/>, ↑//, ↑//>, ↑↑\\, ↑↑\<, ↑↑\, ↑↑<, ↑↑, ↑↑>, ↑↑/, ↑↑/>, ↑↑//, ↑↑//>, t<, t, <br />t>, #↓↓\\<, #↓↓\\, #↓↓\<, #↓↓\, #↓↓<, #↓↓, #↓↓>, #↓↓/, #↓↓/>, #↓\\<, #↓\\, #↓\<, #↓\, #↓<, #↓, #↓>, #↓/, #↓/>, #\\<, #\\, #\<, #\, #<, # || Neutral 7 & 289 || 571e, 578, 585
+|}
+e and 585 can be notated as either order 1 or order 2.
+=== Hemipemptomere tunings ===
+{| class="wikitable center-1"
+|+ style="font-size: 105%;" | 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
+|}
+== 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".
 == Notes ==
-<references/>
+<references />
-[[Category:Notation]]
+{{Navbox notation}}