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19edo: Difference between revisions

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{| class="wikitable right-1 right-2 center-5 center-8"
{| class="wikitable right-1 right-2 center-5 center-8"
|-
|-
! [[Degree]]
! [[Degree|#]]
! [[Cent]]s
! [[Cent]]s
! [[Interval region|Interval Region]]
! [[Interval category|Interval categories]]
! Approximated [[Just intonation|JI]] Intervals<ref group="note">{{sg|limit=2.3.5.7.13 subgroup}}</ref>
! Approximated ratios<ref group="note">As a [[2.3.5.7.13 subgroup|2.3.5.7.13-]][[subgroup]] temperament.</ref>
! [[Solfege]]
! colspan="2" | [[SKULO interval names|SKULO Interval]]
|-
|-
| 0
| 0
| 0.00
| 0.0
| Unison (prime)
| Unison (prime)
| [[1/1]]
| [[1/1]]
|-
| 1
| 63.2
| Augmented unison
| [[25/24]], [[26/25]], [[27/26]], [[28/27]]
|-
| 2
| 126.3
| Minor second
| [[13/12]], [[14/13]], [[15/14]], [[16/15]]
|-
| 3
| 189.5
| Major second
| [[9/8]], [[10/9]]
|-
| 4
| 252.6
| Augmented second<br />Diminished third
| [[7/6]], [[8/7]], [[15/13]]
|-
| 5
| 315.8
| Minor third
| [[6/5]]
|-
| 6
| 378.9
| Major third
| [[5/4]], [[16/13]], [[56/45]]
|-
| 7
| 442.1
| Augmented third
| [[9/7]], [[13/10]], [[21/16]], [[32/25]]
|-
| 8
| 505.3
| Perfect fourth
| [[4/3]], [[75/56]]
|-
| 9
| 568.4
| Augmented fourth<br>(Small [[tritone]])
| [[7/5]], [[18/13]], [[25/18]]
|-
| 10
| 631.6
| Diminished fifth<br>(Large [[tritone]])
| [[10/7]], [[13/9]], [[36/25]]
|-
| 11
| 694.7
| Perfect fifth
| [[3/2]], [[112/75]]
|-
| 12
| 757.9
| Augmented fifth
| [[14/9]], [[20/13]], [[25/16]], [[32/21]]
|-
| 13
| 821.1
| Minor sixth
| [[8/5]], [[13/8]], [[45/28]]
|-
| 14
| 884.2
| Major sixth
| [[5/3]]
|-
| 15
| 947.4
| Augmented sixth<br>Diminished seventh
| [[7/4]], [[12/7]], [[26/15]]
|-
| 16
| 1010.5
| Minor seventh
| [[9/5]], [[16/9]]
|-
| 17
| 1073.7
| Major seventh
| [[13/7]], [[15/8]], [[24/13]], [[28/15]]
|-
| 18
| 1136.8
| Augmented seventh
| [[25/13]], [[27/14]], [[48/25]], [[52/27]]
|-
| 19
| 1200.0
| Octave
| [[2/1]]
|}
<references group="note"/>
=== Proposed interval names and solfèges ===
{| class="wikitable right-1 right-2 center-3 center-5 mw-collapsible mw-collapsed"
|+ style="white-space: nowrap;" | Table of proposed interval names and solfèges
|-
! #
! Cents
! [[Solfège]]
! colspan="2" | [[SKULO interval names]]
|-
| 0
| 0.0
| Do
| Do
| unison
| Unison
| P1
| P1
|-
|-
| 1
| 1
| 63.16
| 63.2
| Augmented unison
| [[25/24]], [[26/25]], [[27/26]], [[28/27]]
| Di/Ro
| Di/Ro
| super unison, subminor second
| Super unison, subminor second
| S1, sm2
| S1, sm2
|-
|-
| 2
| 2
| 126.32
| 126.3
| Ra
| Minor second
| Minor second
| [[13/12]], [[14/13]], [[15/14]], [[16/15]]
| Ra
| minor second
| m2
| m2
|-
|-
| 3
| 3
| 189.47
| 189.5
| Re
| Major second
| Major second
| [[9/8]], [[10/9]]
| Re
| major second
| M2
| M2
|-
|-
| 4
| 4
| 252.63
| 252.6
| Augmented second<br />Diminished third
| [[7/6]], [[8/7]], [[15/13]]
| Ri/Ma
| Ri/Ma
| supermajor second, subminor third
| Supermajor second, subminor third
| SM2, sm3
| SM2, sm3
|-
|-
| 5
| 5
| 315.79
| 315.8
| Me
| Minor third
| Minor third
| [[6/5]]
| Me
| minor third
| m3
| m3
|-
|-
| 6
| 6
| 378.95
| 378.9
| Mi
| Major third
| Major third
| [[5/4]], [[16/13]], [[56/45]]
| Mi
| major third
| M3
| M3
|-
|-
| 7
| 7
| 442.11
| 442.1
| Augmented third
| [[9/7]], [[13/10]], [[21/16]], [[32/25]]
| Mo/Fe
| Mo/Fe
| supermajor third, sub fourth
| Supermajor third, sub fourth
| SM3, s4
| SM3, s4
|-
|-
| 8
| 8
| 505.26
| 505.3
| Fa
| Perfect fourth
| Perfect fourth
| [[4/3]], [[75/56]]
| Fa
| perfect fourth
| P4
| P4
|-
|-
| 9
| 9
| 568.42
| 568.4
| Augmented fourth<br />(Small [[tritone]])
| [[7/5]], [[18/13]], [[25/18]]
| Fi
| Fi
| augmented fourth
| Augmented fourth
| A4
| A4
|-
|-
| 10
| 10
| 631.58
| 631.6
| Diminished fifth<br />(Large [[tritone]])
| [[10/7]], [[13/9]], [[36/25]]
| Se
| Se
| diminished fifth
| Diminished fifth
| d5
| d5
|-
|-
| 11
| 11
| 694.74
| 694.7
| So
| Perfect fifth
| Perfect fifth
| [[3/2]], [[112/75]]
| So
| perfect fifth
| P5
| P5
|-
|-
| 12
| 12
| 757.89
| 757.9
| Augmented fifth
| [[14/9]], [[20/13]], [[25/16]], [[32/21]]
| Si/Lo
| Si/Lo
| super fifth, subminor sixth
| Super fifth, subminor sixth
| S5, sm6
| S5, sm6
|-
|-
| 13
| 13
| 821.05
| 821.1
| Le
| Minor sixth
| Minor sixth
| [[8/5]], [[13/8]], [[45/28]]
| Le
| minor sixth
| m6
| m6
|-
|-
| 14
| 14
| 884.21
| 884.2
| La
| Major sixth
| Major sixth
| [[5/3]]
| La
| major sixth
| M6
| M6
|-
|-
| 15
| 15
| 947.37
| 947.4
| Augmented sixth<br />Diminished seventh
| [[7/4]], [[12/7]], [[26/15]]
| Li/Ta
| Li/Ta
| supermajor sixth, subminor seventh
| Supermajor sixth, subminor seventh
| SM6, sm7
| SM6, sm7
|-
|-
| 16
| 16
| 1010.53
| 1010.5
| Te
| Minor seventh
| Minor seventh
| [[9/5]], [[16/9]]
| Te
| minor seventh
| m7
| m7
|-
|-
| 17
| 17
| 1073.68
| 1073.7
| Ti
| Major seventh
| Major seventh
| [[13/7]], [[15/8]], [[24/13]], [[28/15]]
| Ti
| major seventh
| M7
| M7
|-
|-
| 18
| 18
| 1136.84
| 1136.8
| Augmented seventh
| [[25/13]], [[27/14]], [[48/25]], [[52/27]]
| To/Da
| To/Da
| supermajor seventh, sub octave
| Supermajor seventh, sub octave
| SM7, s8
| SM7, s8
|-
|-
| 19
| 19
| 1200.00
| 1200.0
| Do
| Octave
| Octave
| [[2/1]]
| Do
| octave
| P8
| P8
|}
|}
<references group="note" />


=== Interval quality and chord names in color notation ===
=== Interval quality and chord names in color notation ===
Using [[color notation]], qualities can be loosely associated with colors:
Using [[Kite's color notation]], qualities can be loosely associated with colors:


{| class="wikitable" style="text-align: center;"
{| class="wikitable" style="text-align: center;"
|-
|-
! Quality
! Quality
! [[Color name|Color Name]]
! Color name
! Monzo Format
! Monzo format
! Examples
! Examples
|-
|-
| diminished
| Diminished
| zo
| zo
| (a,&nbsp;b,&nbsp;0,&nbsp;1)
| {{nowrap|(''a'', ''b'', 0, 1)}}
| 7/6, 7/4
| 7/6, 7/4
|-
|-
| rowspan="2" | minor
| rowspan="2" | Minor
| fourthward wa
| fourthward wa
| (a,&nbsp;b), {{nowrap|b &lt; −1}}
| (''a'',&nbsp;''b''), {{nowrap|''b'' < −1}}
| 32/27, 16/9
| 32/27, 16/9
|-
|-
| gu
| gu
| (a,&nbsp;b,&nbsp;−1)
| {{nowrap|(''a'', ''b'', −1)}}
| 6/5, 9/5
| 6/5, 9/5
|-
|-
| rowspan="2" | major
| rowspan="2" | Major
| yo
| yo
| (a,&nbsp;b,&nbsp;1)
| {{nowrap|(''a'', ''b'', 1)}}
| 5/4, 5/3
| 5/4, 5/3
|-
|-
| fifthward wa
| fifthward wa
| (a,&nbsp;b), {{nowrap|b &gt; 1}}
| (''a'',&nbsp;''b''), {{nowrap| ''b'' > 1 }}
| 9/8, 27/16
| 9/8, 27/16
|-
|-
| augmented
| Augmented
| ru
| ru
| (a,&nbsp;b,&nbsp;0,&nbsp;−1)
| {{nowrap|(''a'', ''b'', 0, −1)}}
| 9/7, 12/7
| 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.
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𝄫 would have double-flats on B and E, and flats on C, D, F, G, and A. Thinking of rewriting this key as A♯ 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:
All 19edo chords can be named using conventional methods, expanded to include augmented and diminished seconds, thirds, sixths and sevenths. Here are the zo, gu, yo and ru triads:


{| class="wikitable center-1 center-2 center-3 center-4"
{| class="wikitable center-1 center-2 center-3 center-4"
|-
|-
! [[Kite's color notation|Color of the 3rd]]
! Color of the third
! JI Chord
! JI chord
! Edosteps
! Edosteps
! Notes of C Chord
! Notes of C chord
! Written Name
! Written name
! Spoken Name
! Spoken name
|-
|-
| zo (7-over)
| zo (7-over)
| 6:7:9
| 6:7:9
| 0–4–11
| 0–4–11
| C–E&#x1D12B;–G
| C–E𝄫–G
| Cm(&#x266D;3) or Cmin(&#x266D;3) or C(d3)
| Cm(♭3) or Cmin(♭3) or C(d3)
| C subminor, C minor flat-three, C dim-three
| C subminor, C minor flat-three, C dim-three
|-
|-
Line 289: Line 357:
| 10:12:15
| 10:12:15
| 0–5–11
| 0–5–11
| C–E&#x266D;–G
| C–E♭–G
| Cm or Cmin
| Cm or Cmin
| C minor
| C minor
Line 303: Line 371:
| 14:18:21
| 14:18:21
| 0–7–11
| 0–7–11
| C–E&#x266F;–G
| C–E♯–G
| C(&#x266F;3) or Cmaj(&#x266F;3) or C(A3)
| C(♯3) or Cmaj(♯3) or C(A3)
| C supermajor, C major sharp-three, C aug-three
| C supermajor, C major sharp-three, C aug-three
|-
|-
Line 310: Line 378:
| 4:5:6:7
| 4:5:6:7
| 0–6–11–15
| 0–6–11–15
| C–E–G–B&#x1D12B;
| C–E–G–B𝄫
| Ch7 or C,d7 or Cadd(d7)
| Ch7 or C,d7 or Cadd(d7)
| C harmonic 7, C (major) add dim-seven
| C harmonic 7, C (major) add dim-seven
Line 317: Line 385:
| 12:10:8:7 or 1:6/5:3/2:12/7
| 12:10:8:7 or 1:6/5:3/2:12/7
| 0–5–11–15
| 0–5–11–15
| C–E&#x266D;–G–A&#x266F;
| C–E♭–G–A♯
| Cm&#x266F;6 or CmA6 or Cm(add(&#x266F;6)) or Cm(add(A6))
| Cm♯6 or CmA6 or Cm(add(♯6)) or Cm(add(A6))
| C minor (add) sharp-six, C minor (add) aug-six
| C minor (add) sharp-six, C minor (add) aug-six
|}
|}
Line 324: Line 392:
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.
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]].
For a more complete list, see [[19edo chords #Ups and downs notation]] and [[Kite's ups and downs notation #Chords and chord progressions]].


== Notation ==
== Notation ==
Retrieved from "https://en.xen.wiki/w/19edo"