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! Approximated [[Just intonation|JI]] Intervals<ref group="note">{{sg|limit=2.3.5.7.13 subgroup}}</ref>
! Approximated [[Just intonation|JI]] Intervals<ref group="note">{{sg|limit=2.3.5.7.13 subgroup}}</ref>
! [[Solfege]]
! [[Solfege]]
! colspan="2" | [[SKULO interval names|SKULO Interval]]
|-
|-
| 0
| 0
Line 60: Line 59:
| [[1/1]]
| [[1/1]]
| Do
| Do
| unison
| P1
|-
|-
| 1
| 1
Line 68: Line 65:
| [[25/24]], [[26/25]], [[28/27]]
| [[25/24]], [[26/25]], [[28/27]]
| Di/Ro
| Di/Ro
| super unison, subminor second
| S1, sm2
|-
|-
| 2
| 2
Line 76: Line 71:
| [[13/12]], [[14/13]], [[15/14]], [[16/15]]
| [[13/12]], [[14/13]], [[15/14]], [[16/15]]
| Ra
| Ra
| minor second
| m2
|-
|-
| 3
| 3
Line 84: Line 77:
| [[9/8]], [[10/9]]
| [[9/8]], [[10/9]]
| Re
| Re
| major second
| M2
|-
|-
| 4
| 4
Line 92: Line 83:
| [[7/6]], [[8/7]], [[15/13]]
| [[7/6]], [[8/7]], [[15/13]]
| Ri/Ma
| Ri/Ma
| supermajor second, subminor third
| SM2, sm3
|-
|-
| 5
| 5
Line 100: Line 89:
| [[6/5]]
| [[6/5]]
| Me
| Me
| minor third
| m3
|-
|-
| 6
| 6
Line 108: Line 95:
| [[5/4]], [[16/13]], [[56/45]]
| [[5/4]], [[16/13]], [[56/45]]
| Mi
| Mi
| major third
| M3
|-
|-
| 7
| 7
Line 116: Line 101:
| [[9/7]], [[13/10]], [[32/25]]
| [[9/7]], [[13/10]], [[32/25]]
| Mo/Fe
| Mo/Fe
| supermajor third, sub fourth
| SM3, s4
|-
|-
| 8
| 8
Line 124: Line 107:
| [[4/3]], [[75/56]]
| [[4/3]], [[75/56]]
| Fa
| Fa
| perfect fourth
| P4
|-
|-
| 9
| 9
Line 132: Line 113:
| [[7/5]], [[18/13]], [[25/18]]
| [[7/5]], [[18/13]], [[25/18]]
| Fi
| Fi
| augmented fourth
| A4
|-
|-
| 10
| 10
Line 140: Line 119:
| [[10/7]], [[13/9]], [[36/25]]
| [[10/7]], [[13/9]], [[36/25]]
| Se
| Se
| diminished fifth
| d5
|-
|-
| 11
| 11
Line 148: Line 125:
| [[3/2]], [[112/75]]
| [[3/2]], [[112/75]]
| So
| So
| perfect fifth
| P5
|-
|-
| 12
| 12
Line 156: Line 131:
| [[14/9]], [[20/13]], [[25/16]]
| [[14/9]], [[20/13]], [[25/16]]
| Si/Lo
| Si/Lo
| super fifth, subminor sixth
| S5, sm6
|-
|-
| 13
| 13
Line 164: Line 137:
| [[8/5]], [[13/8]], [[45/28]]
| [[8/5]], [[13/8]], [[45/28]]
| Le
| Le
| minor sixth
| m6
|-
|-
| 14
| 14
Line 172: Line 143:
| [[5/3]]
| [[5/3]]
| La
| La
| major sixth
| M6
|-
|-
| 15
| 15
Line 180: Line 149:
| [[7/4]], [[12/7]], [[26/15]]
| [[7/4]], [[12/7]], [[26/15]]
| Li/Ta
| Li/Ta
| supermajor sixth, subminor seventh
| SM6, sm7
|-
|-
| 16
| 16
Line 188: Line 155:
| [[9/5]], [[16/9]]
| [[9/5]], [[16/9]]
| Te
| Te
| minor seventh
| m7
|-
|-
| 17
| 17
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| [[13/7]], [[15/8]], [[24/13]], [[28/15]]
| [[13/7]], [[15/8]], [[24/13]], [[28/15]]
| Ti
| Ti
| major seventh
| M7
|-
|-
| 18
| 18
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| [[25/13]], [[27/14]], [[48/25]]
| [[25/13]], [[27/14]], [[48/25]]
| To/Da
| To/Da
| supermajor seventh, sub octave
| SM7, s8
|-
|-
| 19
| 19
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| [[2/1]]
| [[2/1]]
| Do
| Do
| octave
| P8
|}
=== Interval quality and chord names in color notation ===
Using [[color notation]], qualities can be loosely associated with colors:
{| class="wikitable" style="text-align: center;"
|-
! Quality
! [[Color name|Color Name]]
! Monzo Format
! Examples
|-
| diminished
| zo
| (a, b, 0, 1)
| 7/6, 7/4
|-
| rowspan="2" | minor
| fourthward wa
| (a, b), b &lt; -1
| 32/27, 16/9
|-
| gu
| (a, b, -1)
| 6/5, 9/5
|-
| rowspan="2" | major
| yo
| (a, b, 1)
| 5/4, 5/3
|-
| fifthward wa
| (a, b), b &gt; 1
| 9/8, 27/16
|-
| augmented
| ru
| (a, b, 0, -1)
| 9/7, 12/7
|}
Key signatures are the same, but with the extra notes and different enharmonic equivalents, some key signatures can get messy.  For example, the key of B&#x1D12B; would have double-flats on B and E, and flats on C, D, F, G, and A.  Thinking of rewriting this key as A&#x266F; might seem better, but then the key signature would contain double-sharps on C, F, and G, and sharps on A, B, D, and E, which is actually worse.
All 19edo chords can be named using conventional methods, expanded to include augmented and diminished 2nd, 3rds, 6ths and 7ths. Here are the zo, gu, yo and ru triads:
{| class="wikitable center-1 center-2 center-3 center-4"
|-
! [[Kite's color notation|Color of the 3rd]]
! JI Chord
! Edosteps
! Notes of C Chord
! Written Name
! Spoken Name
|-
| zo (7-over)
| 6:7:9
| 0–4–11
| C–E&#x1D12B;–G
| Cm(&#x266D;3) or Cmin(&#x266D;3) or C(d3)
| C subminor, C minor flat-three, C dim-three
|-
| gu (5-under)
| 10:12:15
| 0–5–11
| C–E&#x266D;–G
| Cm or Cmin
| C minor
|-
| yo (5-over)
| 4:5:6
| 0–6–11
| C–E–G
| C or Cmaj
| C, C major
|-
| ru (7-under)
| 14:18:21
| 0–7–11
| C–E&#x266F;–G
| C(&#x266F;3) or Cmaj(&#x266F;3) or C(A3)
| C supermajor, C major sharp-three, C aug-three
|-
| yo (5-over)
| 4:5:6:7
| 0–6–11–15
| C–E–G–B&#x1D12B;
| Ch7 or C,d7 or Cadd(d7)
| C harmonic 7, C (major) add dim-seven
|-
| gu (5-under)
| 12:10:8:7 or 1:6/5:3/2:12/7
| 0–5–11–15
| C–E&#x266D;–G–A&#x266F;
| Cm&#x266F;6 or CmA6 or Cm(add(&#x266F;6)) or Cm(add(A6))
| C minor (add) sharp-six, C minor (add) aug-six
|}
The last two chords illustrate how the 15\19 interval can be considered as either 7/4 or 12/7, and how 19edo conflates zo and ru ratios.
For a more complete list, see [[19edo Chord Names]] and [[Ups and downs notation #Chords and Chord Progressions]].
== Notation ==
=== Standard notation ===
Standard 12edo notation can be used, whether it is staff notation (with five lines), letter [[chain-of-fifths notation]] (with standard accidentals), solfege, or sargam. Note that D# and Eb are two different notes.
Any 19edo note or interval can be [[Enharmonic unison|respelled enharmonically]] by adding a double-diminished 2nd to it or subtracting one from it. Adding a dd2 is equivalent to finding the 12edo equivalent with a higher degree, then diminishing it. For example, C# becomes Db, which is diminished to become Dbb.
{| class="wikitable right-1 right-2 center-3 center-4"
|+ style="font-size: 105%;" | Notation of 19edo
|-
! rowspan="2" | [[Degree]]
! rowspan="2" | [[Cent]]s
! colspan="2" | [[Chain-of-fifths notation|Standard Notation]]
|-
! [[5L 2s|Diatonic Interval Names]]
! Note Names<br />on D
|-
| 0
| 0.00
| '''Perfect unison (P1)'''
| '''D'''
|-
| 1
| 63.16
| Augmented unison (A1)<br />Diminished second (d2)
| D#<br />Ebb
|-
| 2
| 126.32
| Doubly augmented unison (AA1)<br />Minor second (m2)
| Dx<br />Eb
|-
| 3
| 189.47
| '''Major second (M2)'''<br />Doubly diminished third (dd3)
| '''E'''<br />Fbb
|-
| 4
| 252.63
| Augmented second (A2)<br />Diminished third (d3)
| E#<br />Fb
|-
| 5
| 315.79
| Doubly augmented second (AA2)<br />'''Minor third (m3)'''
| Ex<br />'''F'''
|-
| 6
| 378.95
| '''Major third (M3)'''<br />Doubly diminished fourth (dd4)
| '''F#'''<br />Gbb
|-
| 7
| 442.11
| Augmented third (A3)<br />Diminished fourth (d4)
| Fx<br />Gb
|-
| 8
| 505.26
| '''Perfect fourth (P4)'''
| '''G'''
|-
| 9
| 568.42
| Augmented fourth (A4)<br />Doubly diminished fifth (dd5)
| G#<br />Abb
|-
| 10
| 631.58
| Doubly augmented fourth (AA4)<br />Diminished fifth (d5)
| Gx<br />Ab
|-
| 11
| 694.74
| '''Perfect fifth (P5)'''
| '''A'''
|-
| 12
| 757.89
| Augmented fifth (A5)<br />Diminished sixth (d6)
| A#<br />Bbb
|-
| 13
| 821.05
| Doubly augmented fifth (AA5)<br />Minor sixth (m6)
| Ax<br />Bb
|-
| 14
| 884.21
| '''Major sixth (M6)'''<br />Doubly diminished seventh (dd7)
| '''B'''<br />Cbb
|-
| 15
| 947.37
| Augmented sixth (A6)<br />Diminished seventh (d7)
| B#<br />Cb
|-
| 16
| 1010.53
| Doubly augmented sixth (AA6)<br />'''Minor seventh (m7)'''
| Bx<br />'''C'''
|-
| 17
| 1073.68
| Major seventh (M7)<br />Doubly diminished octave (dd8)
| C#<br />Dbb
|-
| 18
| 1136.84
| Augmented seventh (A7)<br />Diminished octave (d8)
| Cx<br />Db
|-
| 19
| 1200.00
| '''Perfect octave (P8)'''
| '''D'''
|}
|}


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</imagemap>
</imagemap>


Because it includes no Sagittal symbols, this Evo Sagittal notation is also a conventional notation.
Because it includes no Sagittal symbols, this Evo Sagittal notation is also a conventional  
 
==== Revo flavor ====
<imagemap>
File:19-EDO_Revo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 367 0 527 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
default [[File:19-EDO_Revo_Sagittal.svg]]
</imagemap>
 
=== Dodecatonic notation ===
{| class="wikitable right-1 right-2 mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | Dodecatonic Notation of 19edo
|-
! [[Degree]]
! [[Cent]]s
! Interval Names
|-
| 0
| 0.00
| P1
|-
| 1
| 63.16
| A1, m2
|-
| 2
| 126.32
| M2, m3
|-
| 3
| 189.47
| M3
|-
| 4
| 252.63
| m4, A3
|-
| 5
| 315.79
| M4, m5
|-
| 6
| 378.95
| M5
|-
| 7
| 442.11
| A5, d6
|-
| 8
| 505.26
| P6
|-
| 9
| 568.42
| A6, m7
|-
| 10
| 631.58
| M7, d8
|-
| 11
| 694.74
| P8
|-
| 12
| 757.89
| A8, m9
|-
| 13
| 821.05
| M9, m10
|-
| 14
| 884.21
| M10
|-
| 15
| 947.37
| m11, A10
|-
| 16
| 1010.53
| M11, m12
|-
| 17
| 1073.68
| M12
|-
| 18
| 1136.84
| A12, d13
|-
| 19
| 1200.00
| P13
|}


== Approximation to JI ==
== Approximation to JI ==
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