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== Theory ==
== Theory ==
19edo is the second edo, after [[12edo]] which is able to approximate [[5-limit]] intervals and chords with tolerable accuracy (unless you count [[15edo]], which has a 18-cent-sharp fifth). Having an almost just minor third and perfect fifths and major thirds about 7 cents flat, it serves as a good tuning for [[meantone]]. Unlike 12edo, where [[enharmonic]] notes are conflated, 19edo distinguishes them, and differs from [[17edo]] in that its [[diatonic semitone]] is wider than the [[chromatic semitone]], rather than narrower. In fact, it is nearly identical to the enharmonic scale of [[1/3-comma meantone]], and can be considered a closed form thereof.  
19edo is the second edo, after [[12edo]], which is able to approximate [[5-limit]] intervals and chords with tolerable accuracy (unless you count [[15edo]], which has a 18-[[cent]]-sharp fifth). Having an almost just minor third and perfect fifths and major thirds about 7 cents flat, it serves as a good tuning for [[meantone]]. Unlike 12edo, where [[enharmonic]] notes are conflated, 19edo distinguishes them, and differs from [[17edo]] in that its [[diatonic semitone]] is wider than the [[chromatic semitone]], rather than narrower. In fact, it is nearly identical to the enharmonic scale of [[1/3-comma meantone]], and can be considered a closed form thereof.  


It is less successful in the [[7-limit]] as it conflates the septimal subminor third ([[7/6]]) with the septimal whole tone ([[8/7]]), but it is still better than 12edo on average.  
It is less successful in the [[7-limit]] as it conflates the septimal subminor third ([[7/6]]) with the septimal whole tone ([[8/7]]), but it is still better than 12edo overall.  


=== Prime harmonics ===
=== Prime harmonics ===
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== Intervals ==
== Intervals ==
{| class="wikitable right-1 right-2 center-5 center-8"
{| class="wikitable center-1 right-2"
|-
|-
! [[Degree|#]]
! [[Degree|#]]
! [[Cent]]s
! [[Cent]]s
! [[Interval category|Interval categories]]
! Note
! Approximated ratios<ref group="note">As a [[2.3.5.7.13 subgroup|2.3.5.7.13-]][[subgroup]] temperament.</ref>
! Approximated ratios<ref group="note">As a [[2.3.5.7.13 subgroup|2.3.5.7.13-subgroup]] temperament</ref>
! [[Interval category]]
|-
|-
| 0
| 0
| 0.0
| 0.0
| D
| [[1/1]]
| Unison (prime)
| Unison (prime)
| [[1/1]]
|-
|-
| 1
| 1
| 63.2
| 63.2
| D♯
| [[25/24]], [[26/25]], [[27/26]], [[28/27]]
| Augmented unison
| Augmented unison
| [[25/24]], [[26/25]], [[27/26]], [[28/27]]
|-
|-
| 2
| 2
| 126.3
| 126.3
| E♭
| [[13/12]], [[14/13]], [[15/14]], [[16/15]]
| Minor second
| Minor second
| [[13/12]], [[14/13]], [[15/14]], [[16/15]]
|-
|-
| 3
| 3
| 189.5
| 189.5
| E
| [[9/8]], [[10/9]]
| Major second
| Major second
| [[9/8]], [[10/9]]
|-
|-
| 4
| 4
| 252.6
| 252.6
| Augmented second<br />Diminished third
| E♯/F♭
| [[7/6]], [[8/7]], [[15/13]]
| [[7/6]], [[8/7]], [[15/13]]
| Augmented second/<br>Diminished third
|-
|-
| 5
| 5
| 315.8
| 315.8
| F
| [[6/5]]
| Minor third
| Minor third
| [[6/5]]
|-
|-
| 6
| 6
| 378.9
| 378.9
| F♯
| [[5/4]], [[16/13]], [[56/45]]
| Major third
| Major third
| [[5/4]], [[16/13]], [[56/45]]
|-
|-
| 7
| 7
| 442.1
| 442.1
| Augmented third
| F𝄪/G♭
| [[9/7]], [[13/10]], [[21/16]], [[32/25]]
| [[9/7]], [[13/10]], [[21/16]], [[32/25]]
| Augmented third/<br>Diminished fourth
|-
|-
| 8
| 8
| 505.3
| 505.3
| G
| [[4/3]], [[75/56]]
| Perfect fourth
| Perfect fourth
| [[4/3]], [[75/56]]
|-
|-
| 9
| 9
| 568.4
| 568.4
| G♯
| [[7/5]], [[18/13]], [[25/18]]
| Augmented fourth<br>(Small [[tritone]])
| Augmented fourth<br>(Small [[tritone]])
| [[7/5]], [[18/13]], [[25/18]]
|-
|-
| 10
| 10
| 631.6
| 631.6
| A♭
| [[10/7]], [[13/9]], [[36/25]]
| Diminished fifth<br>(Large [[tritone]])
| Diminished fifth<br>(Large [[tritone]])
| [[10/7]], [[13/9]], [[36/25]]
|-
|-
| 11
| 11
| 694.7
| 694.7
| A
| [[3/2]], [[112/75]]
| Perfect fifth
| Perfect fifth
| [[3/2]], [[112/75]]
|-
|-
| 12
| 12
| 757.9
| 757.9
| Augmented fifth
| A♯/B𝄫
| [[14/9]], [[20/13]], [[25/16]], [[32/21]]
| [[14/9]], [[20/13]], [[25/16]], [[32/21]]
| Augmented fifth/<br>Diminished sixth
|-
|-
| 13
| 13
| 821.1
| 821.1
| B♭
| [[8/5]], [[13/8]], [[45/28]]
| Minor sixth
| Minor sixth
| [[8/5]], [[13/8]], [[45/28]]
|-
|-
| 14
| 14
| 884.2
| 884.2
| B
| [[5/3]]
| Major sixth
| Major sixth
| [[5/3]]
|-
|-
| 15
| 15
| 947.4
| 947.4
| B♯/C♭
| [[7/4]], [[12/7]], [[26/15]]
| Augmented sixth<br>Diminished seventh
| Augmented sixth<br>Diminished seventh
| [[7/4]], [[12/7]], [[26/15]]
|-
|-
| 16
| 16
| 1010.5
| 1010.5
| C
| [[9/5]], [[16/9]]
| Minor seventh
| Minor seventh
| [[9/5]], [[16/9]]
|-
|-
| 17
| 17
| 1073.7
| 1073.7
| C♯
| [[13/7]], [[15/8]], [[24/13]], [[28/15]]
| Major seventh
| Major seventh
| [[13/7]], [[15/8]], [[24/13]], [[28/15]]
|-
|-
| 18
| 18
| 1136.8
| 1136.8
| D♭
| [[25/13]], [[27/14]], [[48/25]], [[52/27]]
| Augmented seventh
| Augmented seventh
| [[25/13]], [[27/14]], [[48/25]], [[52/27]]
|-
|-
| 19
| 19
| 1200.0
| 1200.0
| D
| [[2/1]]
| Octave
| Octave
| [[2/1]]
|}
|}
<references group="note"/>
<references group="note"/>
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|-
|-
| gu (5-under)
| gu (5-under)
| 12:10:8:7 or 1:6/5:3/2:12/7
| 1/(12:10:8:7)<br>(1–6/5–3/2–12/7)
| 0–5–11–15
| 0–5–11–15
| C–E♭–G–A♯
| C–E♭–G–A♯
Line 393: Line 414:


For a more complete list, see [[19edo chords #Ups and downs notation]] and [[Kite's 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 ==
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| 23
| 23
| [[70/69]]
| [[70/69]]
| {{monzo| 1 -1 1 1 0 0 0 0 -}}
| {{monzo| 1 -1 1 1 0 0 0 0 -1 }}
| 24.91
| 24.91
| Twethuzoyo
| Twethuzoyo
Line 1,037: Line 1,059:
| M2
| M2
| [[1L&nbsp;5s]], [[6L&nbsp;1s]], [[6L&nbsp;7s]]
| [[1L&nbsp;5s]], [[6L&nbsp;1s]], [[6L&nbsp;7s]]
| [[Deutone]]<br>[[Spell]]
| [[Deutone]] <br>[[Xenial]] / [[Sensamagic clan #Xenia|Xenia]] <br>[[Spell]]
|-
|-
| 4
| 4
Line 1,043: Line 1,065:
| A2, d3
| A2, d3
| [[1L&nbsp;3s]], [[4L&nbsp;1s]], <br>[[5L&nbsp;4s]], [[5L&nbsp;9s]]
| [[1L&nbsp;3s]], [[4L&nbsp;1s]], <br>[[5L&nbsp;4s]], [[5L&nbsp;9s]]
| [[Godzilla]]
| [[Godzilla]] / [[Helayo]]
|-
|-
| 5
| 5
Line 1,073: Line 1,095:
| A4
| A4
| [[2L&nbsp;3s]], [[2L&nbsp;5s]], [[2L&nbsp;7s]], <br>[[2L&nbsp;9s]], [[2L&nbsp;11s]], [[2L&nbsp;13s]], <br>[[2L&nbsp;15s]]
| [[2L&nbsp;3s]], [[2L&nbsp;5s]], [[2L&nbsp;7s]], <br>[[2L&nbsp;9s]], [[2L&nbsp;11s]], [[2L&nbsp;13s]], <br>[[2L&nbsp;15s]]
| [[Liese]] / [[pycnic]]<br>[[Triton]]
| [[Liese]] <br>[[Triton]] / [[pycnic]]
|}
|}


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