19edo: Difference between revisions

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.

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.  

[[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]].

{| class="wikitable right-1 right-2 center-5 center-8"

! [[Degree]]

! [[Interval region|Interval Region]]

! Approximated [[Just intonation|JI]] Intervals<ref group="note">{{sg|limit=2.3.5.7.13 subgroup}}</ref>

! [[Solfege]]

! colspan="2" | [[SKULO interval names|SKULO Interval]]

| 0.00

| [[1/1]]

| unison

| 63.16

| super unison, subminor second

| 126.32

| 189.47

| 252.63

| [[7/6]], [[8/7]], [[15/13]]

| supermajor second, subminor third

| 315.79

| 378.95

| 442.11

| supermajor third, sub fourth

| 505.26

| 568.42

| augmented fourth

| 631.58

| diminished fifth

| 694.74

| 757.89

| [[14/9]], [[20/13]], [[25/16]], [[32/21]]

| super fifth, subminor sixth

| 821.05

| 884.21

| 947.37

| [[7/4]], [[12/7]], [[26/15]]

| supermajor sixth, subminor seventh

| 1010.53

| 1073.68

| 1136.84

| supermajor seventh, sub octave

| 1200.00

Using [[color notation]], qualities can be loosely associated with colors:

! [[Color name|Color Name]]

! Monzo Format

| diminished

| (a,&nbsp;b,&nbsp;0,&nbsp;1)

| rowspan="2" | minor

| (a,&nbsp;b), {{nowrap|b &lt; −1}}

| (a,&nbsp;b,&nbsp;−1)

| rowspan="2" | major

| (a,&nbsp;b,&nbsp;1)

| (a,&nbsp;b), {{nowrap|b &gt; 1}}

| augmented

| (a,&nbsp;b,&nbsp;0,&nbsp;−1)

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:

! [[Kite's color notation|Color of the 3rd]]

! JI Chord

! Notes of C Chord

! Written Name

! Spoken Name

| C–E&#x1D12B;–G

| Cm(&#x266D;3) or Cmin(&#x266D;3) or C(d3)

| C–E&#x266D;–G

| C–E&#x266F;–G

| C(&#x266F;3) or Cmaj(&#x266F;3) or C(A3)

| C–E–G–B&#x1D12B;

| 12:10:8:7 or 1:6/5:3/2:12/7

| C–E&#x266D;–G–A&#x266F;

| Cm&#x266F;6 or CmA6 or Cm(add(&#x266F;6)) or Cm(add(A6))

For a more complete list, see [[19edo Chord Names]] and [[Ups and downs notation #Chords and Chord Progressions]].

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.

! rowspan="2" | [[Degree]]

! colspan="2" | [[Chain-of-fifths notation|Standard Notation]]

! [[5L 2s|Diatonic Interval Names]]

! Note Names<br />on D

| 0.00

| 63.16

| Augmented unison (A1)<br />Diminished second (d2)

| D#<br />Ebb

| 126.32

| Doubly augmented unison (AA1)<br />Minor second (m2)

| Dx<br />Eb

| 189.47

| '''Major second (M2)'''<br />Doubly diminished third (dd3)

| '''E'''<br />Fbb

| 252.63

| Augmented second (A2)<br />Diminished third (d3)

| E#<br />Fb

| 315.79

| Doubly augmented second (AA2)<br />'''Minor third (m3)'''

| Ex<br />'''F'''

| 378.95

| '''Major third (M3)'''<br />Doubly diminished fourth (dd4)

| '''F#'''<br />Gbb

| 442.11

| Augmented third (A3)<br />Diminished fourth (d4)

| Fx<br />Gb

| 505.26

| 568.42

| Augmented fourth (A4)<br />Doubly diminished fifth (dd5)

| G#<br />Abb

| 631.58

| Doubly augmented fourth (AA4)<br />Diminished fifth (d5)

| Gx<br />Ab

| 694.74

| 757.89

| Augmented fifth (A5)<br />Diminished sixth (d6)

| A#<br />Bbb

| 821.05

| Doubly augmented fifth (AA5)<br />Minor sixth (m6)

| Ax<br />Bb

| 884.21

| '''Major sixth (M6)'''<br />Doubly diminished seventh (dd7)

| '''B'''<br />Cbb

| 947.37

| Augmented sixth (A6)<br />Diminished seventh (d7)

| B#<br />Cb

| 1010.53

| Doubly augmented sixth (AA6)<br />'''Minor seventh (m7)'''

| Bx<br />'''C'''

| 1073.68

| Major seventh (M7)<br />Doubly diminished octave (dd8)

| C#<br />Dbb

| 1136.84

| Augmented seventh (A7)<br />Diminished octave (d8)

| Cx<br />Db

| 1200.00

* 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.

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]].

Because it includes no Sagittal symbols, this Evo Sagittal notation is also a conventional notation.

|+ style="font-size: 105%; white-space: nowrap;" | Dodecatonic Notation of 19edo

! [[Degree]]

! Interval Names

| 0.00

| 63.16

| 126.32

| 189.47

| 252.63

| 315.79

| 378.95

| 442.11

| 505.26

| 568.42

| 631.58

| 694.74

| 757.89

| 821.05

| 884.21

| 947.37

| 1010.53

| 1073.68

| 1136.84

| 1200.00

| {{monzo| 1 -1 1 1 0 0 0 0 -}}

| [[Deutone]]<br>[[Spell]]

| [[Godzilla]]

| [[Liese]] / [[pycnic]]<br>[[Triton]]

* [[meantone]] pentatonic, [[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]] 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]][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

* [[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]][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]][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]][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

* [[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]][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

* [[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

* Meantone melodic minor: 3 2 3 3 3 3 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 - [[Sahara]] septatonic (subset of Negri[9]): 4 2 2 3 4 2 2

* enharmonic pentatonic: 2 6 3 2 6

* enharmonic pentatonic: 6 2 3 6 2

* enharmonic octave species: 1 1 6 3 1 1 6

* enharmonic octave species: 6 1 1 3 6 1 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 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 harmonic diminished octatonic|Pinetone harmonic diminished]]: 2 3 1 4 1 3 2 3