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Interest in this tuning system goes back to the sixteenth century, when composer Guillaume Costeley used it in his chanson [[Seigneur Dieu ta pitié]] of 1558. Costeley understood and desired the circulating aspect of this tuning, which he defined as dividing the just major second into three approximately equal parts. Costeley had other compositions that made use of intervals, such as the diminished third, which have a meaningful context in 19edo, but not in other tuning systems contemporary with the work.
Interest in this tuning system goes back to the sixteenth century, when composer Guillaume Costeley used it in his chanson [[Seigneur Dieu ta pitié]] of 1558. Costeley understood and desired the circulating aspect of this tuning, which he defined as dividing the just major second into three approximately equal parts. Costeley had other compositions that made use of intervals, such as the diminished third, which have a meaningful context in 19edo, but not in other tuning systems contemporary with the work.


In 1577 music theorist Francisco de Salinas proposed [[1/3-comma meantone|{{frac|1|3}}-comma meantone]], in which the fifth is 694.786{{c}}; the fifth of 19edo is 694.737{{c}}, which is only a twentieth of a cent flatter. Salinas suggested tuning nineteen tones to the octave to this tuning, which comes within less than one cent of closing exactly, so that his suggestion is effectively 19edo.
In 1577, music theorist Francisco de Salinas proposed [[1/3-comma meantone]], in which the fifth is 694.786{{c}}; the fifth of 19edo is 694.737{{c}}, which is only a twentieth of a cent flatter. Salinas suggested tuning nineteen tones to the octave to this tuning, which comes within less than one cent of closing exactly, so that his suggestion is effectively 19edo.


In 1835, mathematician and music theorist Wesley Woolhouse proposed it as a more practical alternative to meantone tunings he regarded as better, such as [[50edo|50 equal temperament]] ([http://www.tonalsoft.com/sonic-arts/monzo/woolhouse/essay.htm summary of Woolhouse's essay]).
In 1835, mathematician and music theorist Wesley Woolhouse proposed it as a more practical alternative to meantone tunings he regarded as better, such as [[50edo|50 equal temperament]] ([http://www.tonalsoft.com/sonic-arts/monzo/woolhouse/essay.htm summary of Woolhouse's essay]).


== Theory ==
== Theory ==
Having an almost just minor third and perfect fifths and major thirds about 7 cents flat, 19edo 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 overall.
 
=== Prime harmonics ===
{{Harmonics in equal|19|columns=12}}


=== As an approximation of other temperaments ===
=== As an approximation of other temperaments ===
Besides meantone, 19edo is also suitable for [[magic|magic/muggles]] temperament, because five of its major thirds are equivalent to one of its twelfths. Its 7-step supermajor third can be used for [[sensi]], whose generator is a very sharp major third, two of which make an approximate 5/3 major sixth.  
Besides meantone, 19edo is also suitable for [[magic]]/[[muggles]] temperament, because five of its major thirds are equivalent to one of its twelfths. Its 7-step supermajor third can be used for [[sensi]], whose generator is a very sharp major third, two of which make an approximate 5/3 major sixth.  


For all of these there are more optimal tunings: the fifth of 19edo is flatter than the usual for meantone, and [[31edo]] is more optimal. Similarly, the generating interval of magic temperament is a major third, and again 19edo's is flatter; [[41edo]] more closely matches it. It does make for a good tuning for muggles, but in 19edo it is the same as magic. Finally, 19edo can be used as a tuning for sensi, though [[46edo]] provides a better sensi tuning.
For all of these there are more optimal tunings: the fifth of 19edo is flatter than the usual for meantone, and [[31edo]] is more optimal. Similarly, the generating interval of magic temperament is a major third, and again 19edo's is flatter; [[41edo]] more closely matches it. It does make for a good tuning for muggles, but in 19edo it is the same as magic. Finally, 19edo can be used as a tuning for sensi, though [[46edo]] provides a better sensi tuning.


However, for all of these 19edo has the practical advantage of requiring fewer pitches, which makes it easier to implement in physical instruments, and many 19edo instruments have been built. 19edo is in fact 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). It is less successful in the [[7-limit]] (but still better than 12edo), as it conflates the septimal subminor third ([[7/6]]) with the septimal whole tone ([[8/7]]). 19edo also has the advantage of being excellent for [[negri]], [[keemun]], [[godzilla]], muggles, and [[triton]]/[[liese]]. Keemun and negri are of particular note for being very simple 7-limit temperaments, with their [[mos scale]]s in 19edo offering a great abundance of septimal tetrads. The [[Graham complexity]] of a 7-limit tetrad is 6 for keemun, 7 for negri, 8 for godzilla, 10 for meantone, 11 for triton, 12 for magic/muggles, and 13 for sensi.
However, for all of these 19edo has the practical advantage of requiring fewer pitches, which makes it easier to implement in physical instruments, and many 19edo instruments have been built. 19edo also has the advantage of being excellent for [[negri]], [[keemun]], [[godzilla]], muggles, and [[triton]]/[[liese]]. Keemun and negri are of particular note for being very simple 7-limit temperaments, with their [[mos scale]]s in 19edo offering a great abundance of septimal tetrads. The [[Graham complexity]] of the [[4:5:6:7|7-odd-limit tetrad]] is 6 for keemun, 7 for negri, 8 for godzilla, 10 for meantone, 11 for triton, 12 for magic/muggles, and 13 for sensi.


=== As a means of extending harmony ===
=== As a means of extending harmony ===
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Due to the narrow whole tones and wide diatonic semitones, 19edo's diatonic scale tends to sound somewhat dull compared to 12edo, but the pentatonic scale is said by many to sound much more expressive owing to the significantly larger contrast between the narrow whole tone and wide minor third. While 12edo has an expressive diatonic and dull pentatonic, the reverse is true in 19. Pentatonicism thus becomes more important in 19edo, and one option is to use the pentatonic scale as a sort of "super-chord", with "chord progressions" being modulations between pentatonic subsets of the superdiatonic scale.
Due to the narrow whole tones and wide diatonic semitones, 19edo's diatonic scale tends to sound somewhat dull compared to 12edo, but the pentatonic scale is said by many to sound much more expressive owing to the significantly larger contrast between the narrow whole tone and wide minor third. While 12edo has an expressive diatonic and dull pentatonic, the reverse is true in 19. Pentatonicism thus becomes more important in 19edo, and one option is to use the pentatonic scale as a sort of "super-chord", with "chord progressions" being modulations between pentatonic subsets of the superdiatonic scale.


=== Prime harmonics ===
=== Adaptive tuning ===
{{Harmonics in equal|19|columns=12}}
 
=== Adaptive tuning and octave stretch ===
The no-11's 13-limit is represented relatively well and consistently. 19edo's negri, sensi and godzilla scales have many 13-limit chords. (You can think of the Sensi[8] [[3L 5s]] mos scale as 19edo's answer to the diminished scale. Both are made of two diminished seventh chords, but Sensi[8] gives you additional ratios of 7 and 13.) Its diminished fifth is also a very accurate approximation of the 23rd harmonic, being only 3.3{{c}} off [[23/16]].
The no-11's 13-limit is represented relatively well and consistently. 19edo's negri, sensi and godzilla scales have many 13-limit chords. (You can think of the Sensi[8] [[3L 5s]] mos scale as 19edo's answer to the diminished scale. Both are made of two diminished seventh chords, but Sensi[8] gives you additional ratios of 7 and 13.) Its diminished fifth is also a very accurate approximation of the 23rd harmonic, being only 3.3{{c}} off [[23/16]].


Practically 19edo can be used ''adaptively'' on instruments which allow you to bend notes up: by different amounts, the 3rd, 5th, 7th, and 13th harmonics are all tuned flat. This is in contrast to 12edo, where this is not possible since the 5th and 7th harmonics are not only much farther from just than they are in 19edo, but fairly sharp already.  
Practically 19edo can be used ''adaptively'' on instruments which allow you to bend notes up: by different amounts, the 3rd, 5th, 7th, and 13th harmonics are all tuned flat. This is in contrast to 12edo, where this is not possible since the 5th and 7th harmonics are not only much farther from just than they are in 19edo, but fairly sharp already.  


Another option would be to use [[octave stretching]], which has similar benefits to adaptive use, but it also works for fixed-pitch Instruments. For more on that see the section: [[19edo#Octave stretch]].
Another option would be to use [[octave stretching]], which has similar benefits to adaptive use, but it also works for fixed-pitch Instruments. For more on that see the [[19edo#Octave stretch or compression|section on octave stretch]].


=== Subsets and supersets ===
=== Subsets and supersets ===
Line 49: Line 51:


[[38edo]], which doubles 19edo, provides an approximation of harmonic 11 that works well with the flat tendency of its 5-limit mapping. See [[undevigintone]]. [[57edo]] effectively corrects the harmonic 7 to just, although it is [[76edo]] that fits the best. See [[meanmag]].
[[38edo]], which doubles 19edo, provides an approximation of harmonic 11 that works well with the flat tendency of its 5-limit mapping. See [[undevigintone]]. [[57edo]] effectively corrects the harmonic 7 to just, although it is [[76edo]] that fits the best. See [[meanmag]].
=== Miscellaneous properties ===
19edo has the flattest possible fifth of any edo that can possibly be [[diamond monotone]] in the [[15-odd-limit]]. Using 11\19 as the fifth, the sharpest possible mapping of [[5/4]] where [[10/9]] is no greater than [[9/8]] is 6\19, so the sharpest possible [[15/8]] is 17\19. Here [[16/15]] is a quarter of [[4/3]] (as in any [[negri]] tuning), so [[15/14]], [[14/13]], and [[13/12]] must all be equated with [[16/15]] to 2\19 for them to be monotone in size. If the fifth were any flatter, 5/4 and 15/8 would have to be flatter, and 16/15 would have to be sharper, so diamond monotone in the 15-odd-limit becomes impossible. 19edo is, in fact, diamond monotone in the 15-odd-limit, and even the [[17-odd-limit]] (see [[Monotonicity limits of small EDOs]]). The sharpest fifth where 15-odd-limit is possible is [[37edo#Miscellaneous properties|22\37]].


== Intervals ==
== Intervals ==
{| class="wikitable right-1 right-2 center-5 center-8"
{| class="wikitable right-1 right-2"
|-
|-
! [[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]], [[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]], [[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]]
| 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]]
| 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
|}
|}


=== 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 283: 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 297: 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 304: 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
|-
|-
| 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&#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 318: 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 ==
=== Standard 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.
Standard 12edo notation can be used, whether it is staff notation (with five lines), letter [[chain-of-fifths notation]] (with standard accidentals), solfège, 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.
Any 19edo note or interval can be [[enharmonic unison|respelled enharmonically]] by adding a double-diminished second 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"
{| class="wikitable right-1 right-2 center-3 center-4"
|+ style="font-size: 105%;" | Notation of 19edo
|+ style="font-size: 105%;" | Notation of 19edo
|-
|-
! rowspan="2" | [[Degree]]
! rowspan="2" | [[Degree|#]]
! rowspan="2" | [[Cent]]s
! rowspan="2" | [[Cent]]s
! colspan="2" | [[Chain-of-fifths notation|Standard Notation]]
! colspan="2" | [[Chain-of-fifths notation|Standard notation]]
|-
|-
! [[5L 2s|Diatonic Interval Names]]
! [[5L 2s|Diatonic interval names]]
! Note Names<br />on D
! Note names<br>on D
|-
|-
| 0
| 0
| 0.00
| 0.0
| '''Perfect unison (P1)'''
| '''Perfect unison (P1)'''
| '''D'''
| '''D'''
|-
|-
| 1
| 1
| 63.16
| 63.2
| Augmented unison (A1)<br />Diminished second (d2)
| Augmented unison (A1)<br>Diminished second (d2)
| D#<br />Ebb
| D#<br>Ebb
|-
|-
| 2
| 2
| 126.32
| 126.3
| Doubly augmented unison (AA1)<br />Minor second (m2)
| Doubly augmented unison (AA1)<br>Minor second (m2)
| Dx<br />Eb
| Dx<br>Eb
|-
|-
| 3
| 3
| 189.47
| 189.5
| '''Major second (M2)'''<br />Doubly diminished third (dd3)
| '''Major second (M2)'''<br>Doubly diminished third (dd3)
| '''E'''<br />Fbb
| '''E'''<br>Fbb
|-
|-
| 4
| 4
| 252.63
| 252.6
| Augmented second (A2)<br />Diminished third (d3)
| Augmented second (A2)<br>Diminished third (d3)
| E#<br />Fb
| E#<br>Fb
|-
|-
| 5
| 5
| 315.79
| 315.8
| Doubly augmented second (AA2)<br />'''Minor third (m3)'''
| Doubly augmented second (AA2)<br>'''Minor third (m3)'''
| Ex<br />'''F'''
| Ex<br>'''F'''
|-
|-
| 6
| 6
| 378.95
| 378.9
| '''Major third (M3)'''<br />Doubly diminished fourth (dd4)
| '''Major third (M3)'''<br>Doubly diminished fourth (dd4)
| '''F#'''<br />Gbb
| '''F#'''<br>Gbb
|-
|-
| 7
| 7
| 442.11
| 442.1
| Augmented third (A3)<br />Diminished fourth (d4)
| Augmented third (A3)<br>Diminished fourth (d4)
| Fx<br />Gb
| Fx<br>Gb
|-
|-
| 8
| 8
| 505.26
| 505.3
| '''Perfect fourth (P4)'''
| '''Perfect fourth (P4)'''
| '''G'''
| '''G'''
|-
|-
| 9
| 9
| 568.42
| 568.4
| Augmented fourth (A4)<br />Doubly diminished fifth (dd5)
| Augmented fourth (A4)<br>Doubly diminished fifth (dd5)
| G#<br />Abb
| G#<br>Abb
|-
|-
| 10
| 10
| 631.58
| 631.6
| Doubly augmented fourth (AA4)<br />Diminished fifth (d5)
| Doubly augmented fourth (AA4)<br>Diminished fifth (d5)
| Gx<br />Ab
| Gx<br>Ab
|-
|-
| 11
| 11
| 694.74
| 694.7
| '''Perfect fifth (P5)'''
| '''Perfect fifth (P5)'''
| '''A'''
| '''A'''
|-
|-
| 12
| 12
| 757.89
| 757.9
| Augmented fifth (A5)<br />Diminished sixth (d6)
| Augmented fifth (A5)<br>Diminished sixth (d6)
| A#<br />Bbb
| A#<br>Bbb
|-
|-
| 13
| 13
| 821.05
| 821.1
| Doubly augmented fifth (AA5)<br />Minor sixth (m6)
| Doubly augmented fifth (AA5)<br>Minor sixth (m6)
| Ax<br />Bb
| Ax<br>Bb
|-
|-
| 14
| 14
| 884.21
| 884.2
| '''Major sixth (M6)'''<br />Doubly diminished seventh (dd7)
| '''Major sixth (M6)'''<br>Doubly diminished seventh (dd7)
| '''B'''<br />Cbb
| '''B'''<br>Cbb
|-
|-
| 15
| 15
| 947.37
| 947.4
| Augmented sixth (A6)<br />Diminished seventh (d7)
| Augmented sixth (A6)<br>Diminished seventh (d7)
| B#<br />Cb
| B#<br>Cb
|-
|-
| 16
| 16
| 1010.53
| 1010.5
| Doubly augmented sixth (AA6)<br />'''Minor seventh (m7)'''
| Doubly augmented sixth (AA6)<br>'''Minor seventh (m7)'''
| Bx<br />'''C'''
| Bx<br>'''C'''
|-
|-
| 17
| 17
| 1073.68
| 1073.7
| Major seventh (M7)<br />Doubly diminished octave (dd8)
| Major seventh (M7)<br>Doubly diminished octave (dd8)
| C#<br />Dbb
| C#<br>Dbb
|-
|-
| 18
| 18
| 1136.84
| 1136.8
| Augmented seventh (A7)<br />Diminished octave (d8)
| Augmented seventh (A7)<br>Diminished octave (d8)
| Cx<br />Db
| Cx<br>Db
|-
|-
| 19
| 19
| 1200.00
| 1200.0
| '''Perfect octave (P8)'''
| '''Perfect octave (P8)'''
| '''D'''
| '''D'''
Line 439: Line 513:
In 19edo:
In 19edo:
* [[Ups and downs notation]] is identical to standard notation;
* [[Ups and downs notation]] is identical to standard notation;
* Mixed [[sagittal notation]] is identical to standard notation, but pure sagittal notation exchanges sharps (&#x266F;) and flats (&#x266D;) for sagittal sharp ([[File:Sagittal sharp.png]]) and sagittal flat ([[File:Sagittal flat.png]]) respectively.
* Mixed [[sagittal notation]] is identical to standard notation, but pure sagittal notation exchanges sharps (♯) and flats (♭) for sagittal sharp ([[File:Sagittal sharp.png]]) and sagittal flat ([[File:Sagittal flat.png]]) respectively.


{{Sharpness-sharp1}}
{{Sharpness-sharp1}}


=== Sagittal notation ===
=== Sagittal notation ===
This notation uses the same sagittal sequence as EDOs [[5edo#Sagittal notation|5]], [[12edo#Sagittal notation|12]], and [[26edo#Sagittal notation|26]], and is a subset of the notations for EDOs [[38edo#Sagittal notation|38]], [[57edo#Sagittal notation|57]], and [[76edo#Sagittal notation|76]].
This notation uses the same sagittal sequence as edos [[5edo #Sagittal notation|5]], [[12edo #Sagittal notation|12]], and [[26edo #Sagittal notation|26]], and is a subset of the notations for edos [[38edo #Sagittal notation|38]], [[57edo #Sagittal notation|57]], and [[76edo #Sagittal notation|76]].


==== Evo flavor ====
==== Evo flavor ====
<imagemap>
{{Sagittal chart|Evo}}
File:19-EDO_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 327 0 487 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
default [[File:19-EDO_Evo_Sagittal.svg]]
</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 identical to conventional notation.


==== Revo flavor ====
==== Revo flavor ====
<imagemap>
{{Sagittal chart}}
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 ===
=== Dodecatonic notation ===
{| class="wikitable right-1 right-2 mw-collapsible mw-collapsed"
{| class="wikitable right-1 right-2 mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | Dodecatonic Notation of 19edo
|+ style="font-size: 105%; white-space: nowrap;" | Dodecatonic notation of 19edo
|-
|-
! [[Degree]]
! [[Degree|#]]
! [[Cent]]s
! [[Cent]]s
! Interval Names
! Interval names
|-
|-
| 0
| 0
| 0.00
| 0.0
| P1
| P1
|-
|-
| 1
| 1
| 63.16
| 63.2
| A1, m2
| A1, m2
|-
|-
| 2
| 2
| 126.32
| 126.3
| M2, m3
| M2, m3
|-
|-
| 3
| 3
| 189.47
| 189.5
| M3
| M3
|-
|-
| 4
| 4
| 252.63
| 252.6
| m4, A3
| m4, A3
|-
|-
| 5
| 5
| 315.79
| 315.8
| M4, m5
| M4, m5
|-
|-
| 6
| 6
| 378.95
| 378.9
| M5
| M5
|-
|-
| 7
| 7
| 442.11
| 442.1
| A5, d6
| A5, d6
|-
|-
| 8
| 8
| 505.26
| 505.3
| P6
| P6
|-
|-
| 9
| 9
| 568.42
| 568.4
| A6, m7
| A6, m7
|-
|-
| 10
| 10
| 631.58
| 631.6
| M7, d8
| M7, d8
|-
|-
| 11
| 11
| 694.74
| 694.7
| P8
| P8
|-
|-
| 12
| 12
| 757.89
| 757.9
| A8, m9
| A8, m9
|-
|-
| 13
| 13
| 821.05
| 821.1
| M9, m10
| M9, m10
|-
|-
| 14
| 14
| 884.21
| 884.2
| M10
| M10
|-
|-
| 15
| 15
| 947.37
| 947.4
| m11, A10
| m11, A10
|-
|-
| 16
| 16
| 1010.53
| 1010.5
| M11, m12
| M11, m12
|-
|-
| 17
| 17
| 1073.68
| 1073.7
| M12
| M12
|-
|-
| 18
| 18
| 1136.84
| 1136.8
| A12, d13
| A12, d13
|-
|-
| 19
| 19
| 1200.00
| 1200.0
| P13
| P13
|}
|}
Line 894: Line 956:
| 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 941: Line 1,003:
| Triaphonisma
| Triaphonisma
|}
|}
<references group="note" />


=== Linear temperaments ===
=== Linear temperaments ===
Line 974: Line 1,037:
| 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 980: Line 1,043:
| 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 1,010: Line 1,073:
| 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]]
|}
|}


== Octave stretch ==
== Octave stretch or compression ==
 
19edo is a promising option as a meantone tuning for pianos if split sharps are acceptable, since pianos are frequently tuned with stretched octaves due to the slight [[inharmonicity]] inherent in their strings. It also works well with harpsichords, since many have been, and are, built with split sharps.
== Octave stretch ==
Pianos are frequently tuned with stretched octaves anyway due to the slight inharmonicity inherent in their strings, which makes 19edo a promising option for pianos with split sharps.
 
Octave stretching also means that an out-of-tune interval can be replaced with a compounded or inverted version of it which is near-[[just]]. For example, if we are using [[49ed6]] or [[30ed3]] (which tune 6:1 and 3:1 just and have octaves stretched by 2.8 and 4.57{{c}}, respectively), then we have near-just minor thirds (6:5), compound major thirds (as 5:1), and compound fifths (as 6:1), giving us versions of everything in the 5-limit [[tonality diamond]]. The compound major and minor triads (1:5:6 and 30:6:5) are near-just as well.
 
What follows is a comparison of stretched-octave 19edo tunings.
 
; 19edo
* Step size: 63.158{{c}}, octave size: 1200.0{{c}}
Pure-octaves 19edo approximates all harmonics up to 16 within 21.5{{c}}.
{{Harmonics in equal|19|2|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 19edo}}
{{Harmonics in equal|19|2|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 19edo (continued)}}
 
; [[WE|19et, 2.3.5.11 WE tuning]]
* Step size: 63.192{{c}}, octave size: 1200.6{{c}}
Stretching the octave of 19edo by around half a cent results in [[JND|just noticeably]] improved primes 3, 5, 7 and 13, but a just noticeably worse prime 11. This approximates all harmonics up to 16 within 19.6{{c}}. Its 2.3.5.11 WE tuning and 2.3.5.11 [[TE]] tuning both do this.
{{Harmonics in cet|63.192|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 19et, 2.3.5.11 WE tuning}}
{{Harmonics in cet|63.192|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 19et, 2.3.5.11 WE tuning (continued)}}
 
; [[WE|19et, 13-limit WE tuning]]
* Step size: 63.291{{c}}, octave size: 1202.5{{c}}
Stretching the octave of 19edo by around 2.5{{c}} results in greatly improved primes 3, 5, 7 and 13, but a greatly worse prime 11. This approximates all harmonics up to 16 within 25.9{{c}}. Its 13-limit WE tuning and 13-limit [[TE]] tuning both do this.
{{Harmonics in cet|63.291|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 19et, 13-limit WE tuning}}
{{Harmonics in cet|63.291|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 19et, 13-limit WE tuning (continued)}}
 
; [[49ed6]]
* Step size: NNN{{c}}, octave size: 1202.8{{c}}
Stretching the octave of 19edo by just under 3{{c}} results in greatly improved primes 3, 5, 7 and 13, but a greatly worse prime 11. This approximates all harmonics up to 16 within 26.8{{c}}. The tuning 49ed6 does this.
{{Harmonics in equal|49|6|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 49ed6}}
{{Harmonics in equal|49|6|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 49ed6 (continued)}}
 
; [[zpi|65zpi]]
* Step size: 63.331{{c}}, octave size: 1203.3{{c}}
Stretching the octave of 19edo by around 3.5{{c}} results in greatly improved primes 3, 5, 7 and 13, but a greatly worse prime 11. This approximates all harmonics up to 16 within 28.5{{c}}. The tuning 65zpi does this.
{{Harmonics in cet|63.331|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 65zpi}}
{{Harmonics in cet|63.331|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 65zpi (continued)}}


; [[30edt]]  
Octave stretching also means that an out-of-tune interval can be replaced with a compounded or inverted version of it which is near-[[just]]. For example, if we are using [[49ed6]] or [[30edt]] (which tune 6:1 and 3:1 just and have octaves stretched by 2.8 and 4.57{{c}}, respectively), then we have near-just minor thirds (6:5), compound major thirds (as 5:1), and compound fifths (as 6:1), giving us versions of everything in the 5-odd-limit [[tonality diamond]]. The compound major and minor triads (1:5:6 and 30:6:5) are near-just as well. Another possible choice is [[ZPI|65zpi]].
* Step size: NNN{{c}}, octave size: 1204.6{{c}}
Stretching the octave of 19edo by around 4.5{{c}} has similar results to 65zpi, but it "overshoot", meaning the improvements are less and the drawbacks are greater compared to 65zpi. The damage to the octave has also started to become [[JND|noticeable]] when it is stretched this far. This approximates all harmonics up to 16 within 30.4{{c}}. The tuning 30edt does this.
{{Harmonics in equal|30|3|1|columns=11|collapsed=true|intervals=integer|title=Approximation of harmonics in 30edt}}
{{Harmonics in equal|30|3|1|columns=12|start=12|collapsed=true|intervals=integer|title=Approximation of harmonics in 30edt (continued)}}
 
One can stretch the octave even further - 12.5 cents - to get the tuning [[11edf]], but its approximations of most harmonics are worse than pure-octaves 19. So it is hard to see a use case for 11edf.


== Scales ==
== Scales ==
Line 1,065: Line 1,086:


==== Octave-equivalent mosses ====
==== Octave-equivalent mosses ====
* [[meantone]] pentatonic, [[2L 3s]] (gen = 11\19): 3 3 5 3 5
* [[Meantone]] pentic, [[2L 3s]] (gen = 11\19): 3 3 5 3 5
* [[meantone]] diatonic, [[5L 2s]] (gen = 11\19): 3 3 2 3 3 3 2
* [[Meantone]] diatonic, [[5L 2s]] (gen = 11\19): 3 3 2 3 3 3 2
* [[meantone]] chromatic, [[7L 5s]] (gen = 11\19): 2 1 2 1 2 2 1 2 1 2 1 2
* [[Meantone]] chromatic, [[7L 5s]] (gen = 11\19): 2 1 2 1 2 2 1 2 1 2 1 2
* [[semaphore]][5], [[4L 1s]] (gen = 4\19): 4 4 3 4 4
* [[Semaphore]][5], [[4L 1s]] (gen = 4\19): 4 4 3 4 4
* [[semaphore]][9], [[5L 4s]] (gen = 4\19): 3 1 3 1 3 3 1 3 1
* [[Semaphore]][9], [[5L 4s]] (gen = 4\19): 3 1 3 1 3 3 1 3 1
* [[semaphore]][14], [[5L 9s]] (gen = 4\19): 2 1 2 1 1 2 1 1 2 1 1 2 1 1
* [[Semaphore]][14], [[5L 9s]] (gen = 4\19): 2 1 2 1 1 2 1 1 2 1 1 2 1 1
* [[sensi]][5], [[2L 3s]] (gen = 7\19): 5 2 5 2 5
* [[Sensi]][5], [[2L 3s]] (gen = 7\19): 5 2 5 2 5
* [[sensi]][8], [[3L 5s]] (gen = 7\19): 2 3 2 2 3 2 2 3
* [[Sensi]][8], [[3L 5s]] (gen = 7\19): 2 3 2 2 3 2 2 3
* [[sensi]][11], [[8L 3s]] (gen = 7\19): 2 2 1 2 2 2 1 2 2 2 1
* [[Sensi]][11], [[8L 3s]] (gen = 7\19): 2 2 1 2 2 2 1 2 2 2 1
* [[negri]][9], [[1L 8s]] (gen = 2\19): 2 2 2 2 3 2 2 2 2
* [[Negri]][9], [[1L 8s]] (gen = 2\19): 2 2 2 2 3 2 2 2 2
* [[negri]][10], [[9L 1s]] (gen = 2\19): 2 2 2 2 2 1 2 2 2 2
* [[Negri]][10], [[9L 1s]] (gen = 2\19): 2 2 2 2 2 1 2 2 2 2
* [[kleismic]][7], [[4L 3s]] (gen = 5\19): 1 4 1 4 1 4 4
* [[Kleismic]][7], [[4L 3s]] (gen = 5\19): 1 4 1 4 1 4 4
* [[kleismic]][11], [[4L 7s]] (gen = 5\19): 1 3 1 1 3 1 1 3 1 3 1
* [[Kleismic]][11], [[4L 7s]] (gen = 5\19): 1 3 1 1 3 1 1 3 1 3 1
* [[kleismic]][15], [[4L 11s]] (gen = 5\19): 1 2 1 1 1 2 1 1 1 2 1 1 2 1 1
* [[Kleismic]][15], [[4L 11s]] (gen = 5\19): 1 2 1 1 1 2 1 1 1 2 1 1 2 1 1
* [[magic]][7], [[3L 4s]] (gen = 6\19): 5 1 5 1 5 1 1
* [[Magic]][7], [[3L 4s]] (gen = 6\19): 5 1 5 1 5 1 1
* [[magic]][10], [[3L 7s]] (gen = 6\19): 4 1 1 4 1 1 4 1 1 1
* [[Magic]][10], [[3L 7s]] (gen = 6\19): 4 1 1 4 1 1 4 1 1 1
* [[magic]][13], [[3L 10s]] (gen = 6\19): 3 1 1 1 3 1 1 1 3 1 1 1 1
* [[Magic]][13], [[3L 10s]] (gen = 6\19): 3 1 1 1 3 1 1 1 3 1 1 1 1
* [[magic]][16], [[3L 13s]] (gen = 6\19): 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1
* [[Magic]][16], [[3L 13s]] (gen = 6\19): 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1
* [[liese]][17], [[2L 15s]] (gen = 9\19): 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1
* [[Liese]][17], [[2L 15s]] (gen = 9\19): 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1


=== Other scales ===
=== Other scales ===
{{Main|19edo modes}}
* Meantone harmonic minor: 3 2 3 3 2 4 2
* Meantone harmonic minor: 3 2 3 3 2 4 2
* Meantone melodic minor: 3 2 3 3 3 3 2
* Meantone melodic minor: 3 2 3 3 3 3 2 (ascending), 3 2 3 3 2 3 3 (descending)
* Meantone harmonic major: 3 3 2 3 2 4 2
* Meantone harmonic major: 3 3 2 3 2 4 2
* chromatic octave species - Meantone / [[marvel double harmonic major]] (subset of Negri[9]): 2 4 2 3 2 4 2
* Chromatic octave species – meantone / [[marvel double harmonic major]] (subset of Negri[9]): 2 4 2 3 2 4 2
* chromatic octave species (subset of Negri[9]): 2 2 4 3 2 2 4
* Chromatic octave species (subset of Negri[9]): 2 2 4 3 2 2 4
* chromatic octave species - [[Sahara]] septatonic (subset of Negri[9]): 4 2 2 3 4 2 2
* Chromatic octave species - [[Sahara]] septatonic (subset of Negri[9]): 4 2 2 3 4 2 2
* [[Marvel hexatonic]] (subset of Negri[9]): 4 2 5 2 4 2
* [[Marvel hexatonic]] (subset of Negri[9]): 4 2 5 2 4 2
* enharmonic pentatonic: 2 6 3 2 6
* Enharmonic pentatonic: 2 6 3 2 6
* enharmonic pentatonic: 6 2 3 6 2
* Enharmonic pentatonic: 6 2 3 6 2
* enharmonic octave species: 1 1 6 3 1 1 6
* Enharmonic octave species: 1 1 6 3 1 1 6
* enharmonic octave species: 6 1 1 3 6 1 1
* Enharmonic octave species: 6 1 1 3 6 1 1
* enharmonic octave species: 1 6 1 3 1 6 1
* Enharmonic octave species: 1 6 1 3 1 6 1
* [[Pinetone#Pinetone octatonic scales|Pinetone major-harmonic octatonic]]: 3 2 3 1 2 3 2 3 (subset of Meantone[12])
* [[Pinetone #Pinetone octatonic scales|Pinetone major-harmonic octatonic]]: 3 2 3 1 2 3 2 3 (subset of Meantone[12])
* [[Pinetone#Pinetone octatonic scales|Pinetone minor-harmonic octatonic]]: 3 2 1 3 2 3 3 2 (subset of Meantone[12])
* [[Pinetone #Pinetone octatonic scales|Pinetone minor-harmonic octatonic]]: 3 2 1 3 2 3 3 2 (subset of Meantone[12])
* [[Pinetone#Pinetone diminished octatonic|Pinetone diminished octatonic]] / [[Porcusmine]]: 2 3 1 3 2 3 2 3
* [[Pinetone #Pinetone diminished octatonic|Pinetone diminished octatonic]] / [[Porcusmine]]: 2 3 1 3 2 3 2 3
* [[Pinetone#Pinetone harmonic diminished octatonic|Pinetone harmonic diminished]]: 2 3 1 4 1 3 2 3
* [[Pinetone #Pinetone harmonic diminished octatonic|Pinetone harmonic diminished]]: 2 3 1 4 1 3 2 3
* [[Blackville]] / [[SNS ((2/1, 3/2)-5, 16/15)-10|5-limit dipentatonic]] (superset of Meantone[7]): 1 2 3 2 1 2 3 2 1 2
* [[Blackville]] / [[SNS ((2/1, 3/2)-5, 16/15)-10|5-limit dipentatonic]] (superset of Meantone[7]): 1 2 3 2 1 2 3 2 1 2
* [[Antipental blues]]: 4 4 1 2 4 4
* [[Antipental blues]]: 4 4 1 2 4 4
Line 1,144: Line 1,167:
* [[Bostjan Zupancic]]'s [https://sites.google.com/site/bostjanzupancickhereb/home/bostjan/microtones/19edo 19-EDO pages]  
* [[Bostjan Zupancic]]'s [https://sites.google.com/site/bostjanzupancickhereb/home/bostjan/microtones/19edo 19-EDO pages]  
* [https://sites.google.com/view/19edoscales Catalog of all 19edo heptatonic scales]
* [https://sites.google.com/view/19edoscales Catalog of all 19edo heptatonic scales]
=== Notes ===
<references group="note" />


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