19 equal temperament
{{Short description|Musical tuning system with 19 pitches per octave}}
{{More citations needed|date=July 2024}}File:Syntonic tuning continuum.svg|author3=Plamondon, J. |url=http://www.mitpressjournals.org/doi/pdf/10.1162/comj.2007.31.4.15 |title=Isomorphic controllers and dynamic tuning: Invariant fingerings across a tuning continuum |journal=Computer Music Journal|date=Winter 2007 |volume=31 |issue=4 |pages=15–32|doi=10.1162/comj.2007.31.4.15 |s2cid=27906745 |doi-access=free }}]]
In music, 19 equal temperament, called 19 TET, 19 EDO ("Equal Division of the Octave"), 19-ED2 ("Equal Division of 2:1) or 19 ET, is the tempered scale derived by dividing the octave into 19 equal steps (equal frequency ratios). Each step represents a frequency ratio of {{radic|2|19}}, or 63.16 cents ({{audio|1 step in 19-et on C.mid|Play}}).
{{stack|File:19 equal temperament keyboard.png}}
The fact that traditional western music maps unambiguously onto this scale (unless it presupposes 12-EDO enharmonic equivalences) makes it easier to perform such music in this tuning than in many other tunings.
File:19 equal temperament keyboard Yasser.png's 19 equal temperament keyboard layout{{cite web |url=http://www.musanim.com/Yasser/ |author=Joseph Yasser|title=A Theory of Evolving Tonality |website=MusAnim.com}}]]
19 EDO is the tuning of the syntonic temperament in which the tempered perfect fifth is equal to 694.737 cents, as shown in Figure 1 (look for the label "19 TET"). On an isomorphic keyboard, the fingering of music composed in 19 EDO is precisely the same as it is in any other syntonic tuning (such as 12 EDO), so long as the notes are "spelled properly" – that is, with no assumption that the sharp below matches the flat immediately above it (enharmonicity).
File:Fretboard 19 Tone Mechanics .jpg
{{clear left}}
History and use
Division of the octave into 19 equal-width steps arose naturally out of Renaissance music theory. The ratio of four minor thirds to an octave ({{small|{{sfrac| 648 | 625 }}}} or 62.565 cents – the "greater" diesis) was almost exactly a nineteenth of an octave. Interest in such a tuning system goes back to the 16th 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.
In 1577, music theorist Francisco de Salinas discussed {{nobr|{{small|{{sfrac| 1 | 3 }} }}comma}} meantone, in which the tempered perfect fifth is 694.786 cents. Salinas proposed tuning nineteen tones to the octave to this fifth, which falls within one cent of closing. The fifth of 19 EDO is 694.737 cents, which is less than a twentieth of a cent narrower, imperceptible and less than tuning error, so Salinas' suggestion is, for purposes relating to human hearing, functionally identical to 19 EDO.
In the 19th century, mathematician and music theorist Wesley Woolhouse proposed it as a more practical alternative to meantone temperaments he regarded as better, such as 50 EDO.
The composer Joel Mandelbaum wrote on the properties of the 19 EDO tuning and advocated for its use in his Ph.D. thesis:
{{cite thesis
|last=Mandelbaum |first=M. Joel |author-link=Joel Mandelbaum
|year=1961
|title=Multiple Division of the Octave and the Tonal Resources of 19 Tone Temperament
|url=http://anaphoria.com/mandelbaum.html
|ref=Mandelbaum_1961
}}
Mandelbaum argued that it is the only viable system with a number of divisions between 12 and 22, and furthermore, that the next smallest number of divisions resulting in a significant improvement in approximating just intervals is 31 equal temperament.
{{cite journal
|last=Gamer |first=C. |author-link=Carlton Gamer
|date=Spring 1967
|title=Some combinational resources of equal-tempered systems
|journal=Journal of Music Theory
|volume=11 |issue=1 |pages=32–59
|doi=10.2307/842948 |jstor=842948
}}
Mandelbaum and Joseph Yasser have written music with 19 EDO.
{{cite journal
|last=Leedy |first=Douglas
|year=1991
|title=A venerable temperament rediscovered
|journal=Perspectives of New Music
|volume=29 |issue=2 |page=205
|doi=10.2307/833439 |jstor=833439
}}
: cited by
{{cite book
|last=Skinner |first=Myles Leigh
|year=2007
|title=Toward a Quarter-Tone Syntax: Analyses of selected works by Blackwood, Haba, Ives, and Wyschnegradsky
|page=51, footnote 6
|isbn=9780542998478}}
Easley Blackwood stated that 19 EDO makes possible "a substantial enrichment of the tonal repertoire".{{sfnp|Skinner|2007|p=76}}
Notation
File:19-tet scale on C.png{{sfnp|Skinner|2007|page=52}} and Wesley Woolhouse,
{{cite book
|last=Woolhouse |first=W.S.B. |author-link=Wesley S. B. Woolhouse
|year=1835
|url=https://archive.org/details/essayonmusicali00woolgoog
|title=Essay on Musical Intervals, Harmonics, and the Temperament of the Musical Scale, &c.
|publisher=J. Souter
|location=London, UK
}}
for 19 equal temperament: Intervals are notated similarly to the {{nobr|12 {{sc|tet}}}} intervals that approximate them. Aside from double sharps or double flats, only the note pairs E♯ & F♭ and B♯ & C♭ are enharmonic equivalents (modern sense).
{{cite web
|title=19 EDO
|website=TonalSoft.com
|url=http://tonalsoft.com/enc/number/19edo.aspx
}}
{{center|File:19-tet scale on C.mid}} ]]
19-EDO can be represented with the traditional letter names and system of sharps and flats simply by treating flats and sharps as distinct notes, as usual in standard musical practice; however, in 19-EDO the distinction is a real pitch difference, rather than a notational fiction. In 19-EDO only B♯ is enharmonic with C♭, and E♯ with F♭.
This article uses that re-adapted standard notation: Simply using conventionally enharmonic sharps and flats as distinct notes "as usual".
Interval size
Here are the sizes of some common intervals and comparison with the ratios arising in the harmonic series; the difference column measures in cents the distance from an exact fit to these ratios.
For reference, the difference from the perfect fifth in the widely used 12 TET is 1.955 cents flat, the difference from the major third is 13.686 cents sharp, the minor third is 15.643 cents flat, and the (lost) harmonic minor seventh is 31.174 cents sharp.
:
| class="wikitable" style="text-align:center;"
| bgcolor="#ffeeee" |Step (cents) | | colspan="2" bgcolor="#ffeeee" |63 | colspan="2" bgcolor="#ffeeee" |63 | colspan="2" bgcolor="#ffeeee" |63 | colspan="2" bgcolor="#ffeeee" |63 | colspan="2" bgcolor="#ffeeee" |63 | colspan="2" bgcolor="#ffeeee" |63 | colspan="2" bgcolor="#ffeeee" |63 | colspan="2" bgcolor="#ffeeee" |63 | colspan="2" bgcolor="#ffeeee" |63 | colspan="2" bgcolor="#ffeeee" |63 | colspan="2" bgcolor="#ffeeee" |63 | colspan="2" bgcolor="#ffeeee" |63 | colspan="2" bgcolor="#ffeeee" |63 | colspan="2" bgcolor="#ffeeee" |63 | colspan="2" bgcolor="#ffeeee" |63 | colspan="2" bgcolor="#ffeeee" |63 | colspan="2" bgcolor="#ffeeee" |63 | colspan="2" bgcolor="#ffeeee" |63 | colspan="2" bgcolor="#ffeeee" |63 | |
| bgcolor="#fffbee" |Note name
| colspan="2" bgcolor="#fffbee" |A | colspan="2" bgcolor="#fffbee" |A♯ | colspan="2" bgcolor="#fffbee" |B♭ | colspan="2" bgcolor="#fffbee" |B | colspan="2" bgcolor="#fffbee" |B♯ | colspan="2" bgcolor="#fffbee" |C | colspan="2" bgcolor="#fffbee" |C♯ | colspan="2" bgcolor="#fffbee" |D♭ | colspan="2" bgcolor="#fffbee" |D | colspan="2" bgcolor="#fffbee" |D♯ | colspan="2" bgcolor="#fffbee" |E♭ | colspan="2" bgcolor="#fffbee" |E | colspan="2" bgcolor="#fffbee" |E♯ | colspan="2" bgcolor="#fffbee" |F | colspan="2" bgcolor="#fffbee" |F♯ | colspan="2" bgcolor="#fffbee" |G♭ | colspan="2" bgcolor="#fffbee" |G | colspan="2" bgcolor="#fffbee" |G♯ | colspan="2" bgcolor="#fffbee" |A♭ | colspan="2" bgcolor="#fffbee" |A |
| bgcolor="#eeeeff" |Interval (cents)
| colspan="2" bgcolor="#eeeeff" |0 | colspan="2" bgcolor="#eeeeff" |63 | colspan="2" bgcolor="#eeeeff" |126 | colspan="2" bgcolor="#eeeeff" |189 | colspan="2" bgcolor="#eeeeff" |253 | colspan="2" bgcolor="#eeeeff" |316 | colspan="2" bgcolor="#eeeeff" |379 | colspan="2" bgcolor="#eeeeff" |442 | colspan="2" bgcolor="#eeeeff" |505 | colspan="2" bgcolor="#eeeeff" |568 | colspan="2" bgcolor="#eeeeff" |632 | colspan="2" bgcolor="#eeeeff" |695 | colspan="2" bgcolor="#eeeeff" |758 | colspan="2" bgcolor="#eeeeff" |821 | colspan="2" bgcolor="#eeeeff" |884 | colspan="2" bgcolor="#eeeeff" |947 | colspan="2" bgcolor="#eeeeff" |1011 | colspan="2" bgcolor="#eeeeff" |1074 | colspan="2" bgcolor="#eeeeff" |1137 | colspan="2" bgcolor="#eeeeff" |1200 |
:
| class="wikitable sortable" style="text-align:center;"
! Interval name ! Size ! Size ! Midi ! Just ratio ! Just ! Midi ! Error |
| Octave
| 19 | 1200{{0}}{{0}} | | 2:1 | 1200{{0}}{{0}} | | 0{{0}} |
| Septimal major seventh
| 18 | 1136.84 | | 27:14 | 1137.04 | | −{{0}}0.20 |
| Diminished octave
| 18 | 1136.84 | | 48:25 | 1129.33 | {{audio|Classic diminished octave on C.mid|Play}} | +{{0}}7.51 |
| Major seventh
| 17 | 1073.68 | | 15:8 | 1088.27 | {{audio|Just major seventh on C.mid|Play}} | −14.58 |
| Minor seventh
| 16 | 1010.53 | | 9:5 | 1017.60 | {{audio|Greater just minor seventh on C.mid|Play}} | −{{0}}7.07 |
| bgcolor = "D4D4D4"| Harmonic minor seventh
|bgcolor = "D4D4D4"| 15 |bgcolor = "D4D4D4"| {{0}}947.37 |bgcolor = "D4D4D4"| |bgcolor = "D4D4D4"| 7:4 |bgcolor = "D4D4D4"| {{0}}968.83 |bgcolor = "D4D4D4"| {{audio|Harmonic seventh on C.mid|Play}} |bgcolor = "D4D4D4"| −21.46 |
| Septimal major sixth
| 15 | {{0}}947.37 | | 12:7 | {{0}}933.13 | {{audio|Septimal major sixth on C.mid|Play}} | +14.24 |
| Major sixth
| 14 | {{0}}884.21 | | 5:3 | {{0}}884.36 | {{audio|Just major sixth on C.mid|Play}} | −{{0}}0.15 |
| Minor sixth
| 13 | {{0}}821.05 | | 8:5 | {{0}}813.69 | {{audio|Just minor sixth on C.mid|Play}} | +{{0}}7.37 |
| Augmented fifth
| 12 | {{0}}757.89 | | 25:16 | {{0}}772.63 | {{Audio|Just augmented fifth on C.mid|Play}} | −14.73 |
| Septimal minor sixth
| 12 | {{0}}757.89 | | 14:9 | {{0}}764.92 | | −{{0}}7.02 |
| Perfect fifth
| 11 | {{0}}694.74 | {{Audio|11 steps in 19-et on C.mid|Play}} | 3:2 | {{0}}701.96 | {{Audio|Just perfect fifth on C.mid|Play}} | −{{0}}7.22 |
| Greater tridecimal tritone
| 10 | {{0}}631.58 | | 13:9{{0}} | {{0}}636.62 | | −{{0}}5.04 |
| Greater septimal tritone, diminished fifth
| 10 | {{0}}631.58 | {{Audio|10 steps in 19-et on C.mid|Play}} | 10:7{{0}} | {{0}}617.49 | {{Audio|Greater septimal tritone on C.mid|Play}} | +14.09 |
| Lesser septimal tritone, augmented fourth
| {{0}}9 | {{0}}568.42 | {{Audio|9 steps in 19-et on C.mid|Play}} | 7:5 | {{0}}582.51 | | −14.09 |
| Lesser tridecimal tritone
| {{0}}9 | {{0}}568.42 | | 18:13 | {{0}}563.38 | | +{{0}}5.04 |
| Perfect fourth
| {{0}}8 | {{0}}505.26 | {{Audio|8 steps in 19-et on C.mid|Play}} | 4:3 | {{0}}498.04 | {{Audio|Just perfect fourth on C.mid|Play}} | +{{0}}7.22 |
| Augmented third
| {{0}}7 | {{0}}442.11 | | 125:96 | {{0}}456.99 | {{Audio|Just augmented third on C.mid|Play}} | −14.88 |
| Tridecimal major third
| {{0}}7 | {{0}}442.11 | | 13:10 | {{0}}454.12 | | −10.22 |
| Septimal major third
| {{0}}7 | {{0}}442.11 | {{Audio|7 steps in 19-et on C.mid|Play}} | 9:7 | {{0}}435.08 | {{Audio|Septimal major third on C.mid|Play}} | +{{0}}7.03 |
| Major third
| {{0}}6 | {{0}}378.95 | {{Audio|6 steps in 19-et on C.mid|Play}} | 5:4 | {{0}}386.31 | {{Audio|Just major third on C.mid|Play}} | −{{0}}7.36 |
| bgcolor = "D4D4D4"| Inverted 13th harmonic
|bgcolor = "D4D4D4"| {{0}}6 |bgcolor = "D4D4D4"| {{0}}378.95 |bgcolor = "D4D4D4"| |bgcolor = "D4D4D4"| 16:13 |bgcolor = "D4D4D4"| {{0}}359.47 |bgcolor = "D4D4D4"| |bgcolor = "D4D4D4"| +19.48 |
| Minor third
| {{0}}5 | {{0}}315.79 | {{Audio|5 steps in 19-et on C.mid|Play}} | 6:5 | {{0}}315.64 | {{Audio|Just minor third on C.mid|Play}} | +{{0}}0.15 |
| Septimal minor third
| {{0}}4 | {{0}}252.63 | | 7:6 | {{0}}266.87 | {{Audio|Septimal minor third on C.mid|Play}} | −14.24 |
| Tridecimal {{small|{{sfrac| 5 | 4 }}}} tone
| {{0}}4 | {{0}}252.63 | | 15:13 | {{0}}247.74 | | +{{0}}4.89 |
| bgcolor = "D4D4D4"| Septimal whole tone
|bgcolor = "D4D4D4"| {{0}}4 |bgcolor = "D4D4D4"| {{0}}252.63 |bgcolor = "D4D4D4"| {{Audio|4 steps in 19-et on C.mid|Play}} |bgcolor = "D4D4D4"| 8:7 |bgcolor = "D4D4D4"| {{0}}231.17 |bgcolor = "D4D4D4"| {{Audio|Septimal major second on C.mid|Play}} |bgcolor = "D4D4D4"| +21.46 |
| Whole tone, major tone
| {{0}}3 | {{0}}189.47 | | 9:8 | {{0}}203.91 | {{Audio|Major tone on C.mid|Play}} | −14.44 |
| Whole tone, minor tone
| {{0}}3 | {{0}}189.47 | {{Audio|3 steps in 19-et on C.mid|Play}} | 10:9{{0}} | {{0}}182.40 | {{Audio|Minor tone on C.mid|Play}} | +{{0}}7.07 |
| Greater tridecimal {{small|{{sfrac| 2 | 3 }}}}-tone
| {{0}}2 | {{0}}126.32 | | 13:12 | {{0}}138.57 | | −12.26 |
| Lesser tridecimal {{small|{{sfrac| 2 | 3 }}}}-tone
| {{0}}2 | {{0}}126.32 | | 14:13 | {{0}}128.30 | | −{{0}}1.98 |
| Septimal diatonic semitone
| {{0}}2 | {{0}}126.32 | | 15:14 | {{0}}119.44 | {{Audio|Septimal diatonic semitone on C.mid|Play}} | +{{0}}6.88 |
| Diatonic semitone, just
| {{0}}2 | {{0}}126.32 | | 16:15 | {{0}}111.73 | {{Audio|Just diatonic semitone on C.mid|Play}} | +14.59 |
| Septimal chromatic semitone
| {{0}}1 | {{0}}{{0}}63.16 | {{Audio|1 step in 19-et on C.mid|Play}} | 21:20 | {{0}}{{0}}84.46 | | −21.31 |
| Chromatic semitone, just
| {{0}}1 | {{0}}{{0}}63.16 | | 25:24 | {{0}}{{0}}70.67 | {{Audio|Just chromatic semitone on C.mid|Play}} | −{{0}}7.51 |
| Septimal third-tone
| {{0}}1 | {{0}}{{0}}63.16 | {{Audio|1 step in 19-et on C.mid|Play}} | 28:27 | {{0}}{{0}}62.96 | | +{{0}}0.20 |
A possible variant of 19-ED2 is 93-ED30, i.e. the division of 30:1 in 93 equal steps, corresponding to a stretching of the octave by 27.58¢, which improves the approximation of most natural ratios.
Scale diagram
File:19-TET circle of fifths.png in 19 tone equal temperament]]
Because 19 is a prime number, repeating any fixed interval in this tuning system cycles through all possible notes; just as one may cycle through 12-EDO on the circle of fifths, since a fifth is 7 semitones, and number 7 is coprime to 12.
= [[Mode (music)|Modes]] =
== [[Ionian mode]] ([[major scale]]) ==
| class="wikitable"
! colspan="7" | Scale !Number of sharps ! !Key signature ! colspan="7" | Scale !Number of flats |
| C major
|C |D |E |F |G |A |B |0 (no sharps or flats) | rowspan="5" | | rowspan="5" | | rowspan="5" colspan="7" | |
| G major
|G |A |B |C |D |E |F♯ |1 |
| D major
|D |E |F♯ |G |A |B |C♯ |2 |
| A major
|A |B |C♯ |D |E |F♯ |G♯ |3 |
| E major
|E |F♯ |G♯ |A |B |C♯ |D♯ |4 |
| B major
|B |C♯ |D♯ |E |F♯ |G♯ |A♯ |5 | |C𝄫 |D𝄫 |E𝄫 |F𝄫 |G𝄫 |A𝄫 |B𝄫 |14 |
| F♯ major
|F♯ |G♯ |A♯ |B |C♯ |D♯ |E♯ |6 | |G𝄫 |A𝄫 |B𝄫 |C𝄫 |D𝄫 |E𝄫 |F♭ |13 |
| C♯ major
|C♯ |D♯ |E♯ |F♯ |G♯ |A♯ |B♯ |7 | |D𝄫 |E𝄫 |F♭ |G𝄫 |A𝄫 |B𝄫 |C♭ |12 |
| G♯ major
|G♯ |A♯ |B♯ |C♯ |D♯ |E♯ |F𝄪 |8 | |A𝄫 |B𝄫 |C♭ |D𝄫 |E𝄫 |F♭ |G♭ |11 |
| D♯ major
|D♯ |E♯ |F𝄪 |G♯ |A♯ |B♯ |C𝄪 |9 | |E𝄫 |F♭ |G♭ |A𝄫 |B𝄫 |C♭ |D♭ |10 |
| A♯ major
|A♯ |B♯ |F𝄪 |D♯ |E♯ |F𝄪 |G𝄪 |10 | |B𝄫 |C♭ |D♭ |E𝄫 |F♭ |G♭ |A♭ |9 |
| E♯ major
|E♯ |F𝄪 |G𝄪 |A♯ |B♯ |F𝄪 |D𝄪 |11 | |F♭ |G♭ |A♭ |B𝄫 |C♭ |D♭ |E♭ |8 |
| B♯ major
|B♯ |C𝄪 |D𝄪 |E♯ |F𝄪 |G𝄪 |A𝄪 |12 | |C♭ |D♭ |E♭ |F♭ |G♭ |A♭ |B♭ |7 |
| F𝄪 major
|F𝄪 |G𝄪 |A𝄪 |B♯ |C𝄪 |D𝄪 |E𝄪 |13 | |G♭ |A♭ |B♭ |C♭ |D♭ |E♭ |F |6 |
| C𝄪 major
|C𝄪 |D𝄪 |E𝄪 |F𝄪 |G𝄪 |A𝄪 |B𝄪 |14 | |D♭ |E♭ |F |G♭ |A♭ |B♭ |C |5 |
| colspan="9" rowspan="5" |
| rowspan="5" | |A♭ |B♭ |C |D♭ |E♭ |F |G |4 |
| E♭ major
|E♭ |F |G |A♭ |B♭ |C |D |3 |
| B♭ major
|B♭ |C |D |E♭ |F |G |A |2 |
| F major
|F |G |A |B♭ |C |D |E |1 |
| C major
|C |D |E |F |G |A |B |0 (no flats or sharps) |
== [[Dorian mode]] ==
| class="wikitable"
! colspan="7" | Scale !Number of sharps ! !Key signature ! colspan="7" | Scale !Number of flats |
| D Dorian
|D |E |F |G |A |B |C |0 (no sharps or flats) | rowspan="5" | | rowspan="5" | | rowspan="5" colspan="7" | |
| A Dorian
|A |B |C |D |E |F♯ |G |1 |
| E Dorian
|E |F♯ |G |A |B |C♯ |D |2 |
| B Dorian
|B |C♯ |D |E |F♯ |G♯ |A |3 |
| F♯ Dorian
|F♯ |G♯ |A |B |C♯ |D♯ |E |4 |
| C♯ Dorian
|C♯ |D♯ |E |F♯ |G♯ |A♯ |B |5 | |D𝄫 Dorian |D𝄫 |E𝄫 |F𝄫 |G𝄫 |A𝄫 |B𝄫 |C𝄫 |14 |
| G♯ Dorian
|G♯ |A♯ |B |C♯ |D♯ |E♯ |F♯ |6 | |A𝄫 Dorian |A𝄫 |B𝄫 |C𝄫 |D𝄫 |E𝄫 |F♭ |G𝄫 |13 |
| D♯ Dorian
|D♯ |E♯ |F♯ |G♯ |A♯ |B♯ |C♯ |7 | |E𝄫 Dorian |E𝄫 |F♭ |G𝄫 |A𝄫 |B𝄫 |C♭ |D𝄫 |12 |
| A♯ Dorian
|A♯ |B♯ |C♯ |D♯ |E♯ |F𝄪 |G♯ |8 | |B𝄫 Dorian |B𝄫 |C♭ |D𝄫 |E𝄫 |F♭ |G♭ |A𝄫 |11 |
| E♯ Dorian
|E♯ |F𝄪 |G♯ |A♯ |B♯ |C𝄪 |D♯ |9 | |F♭ Dorian |F♭ |G♭ |A𝄫 |B𝄫 |C♭ |D♭ |E𝄫 |10 |
| B♯ Dorian
|B♯ |F𝄪 |D♯ |E♯ |F𝄪 |G𝄪 |A♯ |10 | |C♭ Dorian |C♭ |D♭ |E𝄫 |F♭ |G♭ |A♭ |B𝄫 |9 |
| F𝄪 Dorian
|F𝄪 |G𝄪 |A♯ |B♯ |F𝄪 |D𝄪 |E♯ |11 | |G♭ Dorian |G♭ |A♭ |B𝄫 |C♭ |D♭ |E♭ |F♭ |8 |
| C𝄪 Dorian
|C𝄪 |D𝄪 |E♯ |F𝄪 |G𝄪 |A𝄪 |B♯ |12 | |D♭ Dorian |D♭ |E♭ |F♭ |G♭ |A♭ |B♭ |C♭ |7 |
| G𝄪 Dorian
|G𝄪 |A𝄪 |B♯ |C𝄪 |D𝄪 |E𝄪 |F𝄪 |13 | |A♭ Dorian |A♭ |B♭ |C♭ |D♭ |E♭ |F |G♭ |6 |
| D𝄪 Dorian
|D𝄪 |E𝄪 |F𝄪 |G𝄪 |A𝄪 |B𝄪 |C𝄪 |14 | |E♭ Dorian |E♭ |F |G♭ |A♭ |B♭ |C |D♭ |5 |
| rowspan="5" colspan="9" |
| rowspan="5" | |B♭ Dorian |B♭ |C |D♭ |E♭ |F |G |A♭ |4 |
| F Dorian
|F |G |A♭ |B♭ |C |D |E♭ |3 |
| C Dorian
|C |D |E♭ |F |G |A |B♭ |2 |
| G Dorian
|G |A |B♭ |C |D |E |F |1 |
| D Dorian
|D |E |F |G |A |B |C |0 (no flats or sharps) |
== [[Phrygian mode]] ==
| class="wikitable"
! colspan="7" | Scale !Number of sharps ! !Key signature ! colspan="7"|Scale !Number of flats |
| E Phrygian
|E |F |G |A |B |C |D |0 (no sharps or flats) | rowspan="5" | | rowspan="5" | | rowspan="5" colspan="7" | |
| B Phrygian
|B |C |D |E |F♯ |G |A |1 |
| F♯ Phrygian
|F♯ |G |A |B |C♯ |D |E |2 |
| C♯ Phrygian
|C♯ |D |E |F♯ |G♯ |A |B |3 |
| G♯ Phrygian
|G♯ |A |B |C♯ |D♯ |E |F♯ |4 |
| D♯ Phrygian
|D♯ |E |F♯ |G♯ |A♯ |B |C♯ |5 | |E𝄫 Phrygian |E𝄫 |F𝄫 |G𝄫 |A𝄫 |B𝄫 |C𝄫 |D𝄫 |14 |
| A♯ Phrygian
|A♯ |B |C♯ |D♯ |E♯ |F♯ |G♯ |6 | |B𝄫 Phrygian |B𝄫 |C𝄫 |D𝄫 |E𝄫 |F♭ |G𝄫 |A𝄫 |13 |
| E♯ Phrygian
|E♯ |F♯ |G♯ |A♯ |B♯ |C♯ |D♯ |7 | |F♭ Phrygian |F♭ |G𝄫 |A𝄫 |B𝄫 |C♭ |D𝄫 |E𝄫 |12 |
| B♯ Phrygian
|B♯ |C♯ |D♯ |E♯ |F𝄪 |G♯ |A♯ |8 | |C♭ Phrygian |C♭ |D𝄫 |E𝄫 |F♭ |G♭ |A𝄫 |B𝄫 |11 |
| F𝄪 Phrygian
|F𝄪 |G♯ |A♯ |B♯ |C𝄪 |D♯ |E♯ |9 | |G♭ Phrygian |G♭ |A𝄫 |B𝄫 |C♭ |D♭ |E𝄫 |F♭ |10 |
| C𝄪 Phrygian
|C𝄪 |D♯ |E♯ |F𝄪 |G𝄪 |A♯ |B♯ |10 | |D♭ Phrygian |D♭ |E𝄫 |F♭ |G♭ |A♭ |B𝄫 |C♭ |9 |
| G𝄪 Phrygian
|G𝄪 |A♯ |B♯ |C𝄪 |D𝄪 |E♯ |F𝄪 |11 | |A♭ Phrygian |A♭ |B𝄫 |C♭ |D♭ |E♭ |F♭ |G♭ |8 |
| D𝄪 Phrygian
|D𝄪 |E♯ |F𝄪 |G𝄪 |A𝄪 |B♯ |C𝄪 |12 | |E♭ Phrygian |E♭ |F♭ |G♭ |A♭ |B♭ |C♭ |D♭ |7 |
| A𝄪 Phrygian
|A𝄪 |B♯ |C𝄪 |D𝄪 |E𝄪 |F𝄪 |G𝄪 |13 | |B♭ Phrygian |B♭ |C♭ |D♭ |E♭ |F |G♭ |A♭ |6 |
| E𝄪 Phrygian
|E𝄪 |F𝄪 |G𝄪 |A𝄪 |B𝄪 |C𝄪 |D𝄪 |14 | |F Phrygian |F |G♭ |A♭ |B♭ |C |D♭ |E♭ |5 |
| rowspan="5" colspan="9" |
| rowspan="5" | |C Phrygian |C |D♭ |E♭ |F |G |A♭ |B♭ |4 |
| G Phrygian
|G |A♭ |B♭ |C |D |E♭ |F |3 |
| D Phrygian
|D |E♭ |F |G |A |B♭ |C |2 |
| A Phrygian
|A |B♭ |C |D |E |F |G |1 |
| E Phrygian
|E |F |G |A |B |C |D |0 (no flats or sharps) |
== [[Lydian mode]] ==
| class="wikitable"
! colspan="7" |Scale !Number of sharps ! !Key signature ! colspan="7" |Scale !Number of flats |
| F Lydian
|F |G |A |B |C |D |E |0 (no sharps or flats) |rowspan="5"| |rowspan="5"| |rowspan="5" colspan="7"| |
| C Lydian
|C |D |E |F♯ |G |A |B |1 |
| G Lydian
|G |A |B |C♯ |D |E |F♯ |2 |
| D Lydian
|D |E |F♯ |G♯ |A |B |C♯ |3 |
| A Lydian
|A |B |C♯ |D♯ |E |F♯ |G♯ |4 |
| E Lydian
|E |F♯ |G♯ |A♯ |B |C♯ |D♯ |5 | |F𝄫 Lydian |F𝄫 |G𝄫 |A𝄫 |B𝄫 |C𝄫 |D𝄫 |E𝄫 |14 |
| B Lydian
|B |C♯ |D♯ |E♯ |F♯ |G♯ |A♯ |6 | |C𝄫 Lydian |C𝄫 |D𝄫 |E𝄫 |F♭ |G𝄫 |A𝄫 |B𝄫 |13 |
| F♯ Lydian
|F♯ |G♯ |A♯ |B♯ |C♯ |D♯ |E♯ |7 | |G𝄫 Lydian |G𝄫 |A𝄫 |B𝄫 |C♭ |D𝄫 |E𝄫 |F♭ |12 |
| C♯ Lydian
|C♯ |D♯ |E♯ |F𝄪 |G♯ |A♯ |B♯ |8 | |D𝄫 Lydian |D𝄫 |E𝄫 |F♭ |G♭ |A𝄫 |B𝄫 |C♭ |11 |
| G♯ Lydian
|G♯ |A♯ |B♯ |C𝄪 |D♯ |E♯ |F𝄪 |9 | |A𝄫 Lydian |A𝄫 |B𝄫 |C♭ |D♭ |E𝄫 |F♭ |G♭ |10 |
| D♯ Lydian
|D♯ |E♯ |F𝄪 |G𝄪 |A♯ |B♯ |C𝄪 |10 | |E𝄫 Lydian |E𝄫 |F♭ |G♭ |A♭ |B𝄫 |C♭ |D♭ |9 |
| A♯ Lydian
|A♯ |B♯ |C𝄪 |D𝄪 |E♯ |F𝄪 |G𝄪 |11 | |B𝄫 Lydian |B𝄫 |C♭ |D♭ |E♭ |F♭ |G♭ |A♭ |8 |
| E♯ Lydian
|E♯ |F𝄪 |G𝄪 |A𝄪 |B♯ |C𝄪 |D𝄪 |12 | |F♭ Lydian |F♭ |G♭ |A♭ |B♭ |C♭ |D♭ |E♭ |7 |
| B♯ Lydian
|B♯ |C𝄪 |D𝄪 |E𝄪 |F𝄪 |G𝄪 |A𝄪 |13 | |C♭ Lydian |C♭ |D♭ |E♭ |F |G♭ |A♭ |B♭ |6 |
| F𝄪 Lydian
|F𝄪 |G𝄪 |A𝄪 |B𝄪 |C𝄪 |D𝄪 |E𝄪 |14 | |G♭ Lydian |G♭ |A♭ |B♭ |C |D♭ |E♭ |F |5 |
| colspan="9" rowspan="5"|
|rowspan="5"| |D♭ Lydian |D♭ |E♭ |F |G |A♭ |B♭ |C |4 |
| A♭ Lydian
|A♭ |B♭ |C |D |E♭ |F |G |3 |
| E♭ Lydian
|E♭ |F |G |A |B♭ |C |D |2 |
| B♭ Lydian
|B♭ |C |D |E |F |G |A |1 |
| F Lydian
|F |G |A |B |C |D |E |0 (no flats or sharps) |
== [[Mixolydian mode]] ==
| class="wikitable"
!colspan="7"|Scale !Number of sharps ! !Key signature !colspan="7"|Scale !Number of flats |
| G Mixolydian
|G |A |B |C |D |E |F |0 (no sharps or flats) |rowspan="5"| |rowspan="5"| |rowspan="5" colspan="7"| |
| D Mixolydian
|D |E |F♯ |G |A |B |C |1 |
| A Mixolydian
|A |B |C♯ |D |E |F♯ |G |2 |
| E Mixolydian
|E |F♯ |G♯ |A |B |C♯ |D |3 |
| B Mixolydian
|B |C♯ |D♯ |E |F♯ |G♯ |A |4 |
| F♯ Mixolydian
|F♯ |G♯ |A♯ |B |C♯ |D♯ |E |5 | |G𝄫 Mixolydian |G𝄫 |A𝄫 |B𝄫 |C𝄫 |D𝄫 |E𝄫 |F𝄫 |14 |
| C♯ Mixolydian
|C♯ |D♯ |E♯ |F♯ |G♯ |A♯ |B |6 | |D𝄫 Mixolydian |D𝄫 |E𝄫 |F♭ |G𝄫 |A𝄫 |B𝄫 |C𝄫 |13 |
| G♯ Mixolydian
|G♯ |A♯ |B♯ |C♯ |D♯ |E♯ |F♯ |7 | |A𝄫 Mixolydian |A𝄫 |B𝄫 |C♭ |D𝄫 |E𝄫 |F♭ |G𝄫 |12 |
| D♯ Mixolydian
|D♯ |E♯ |F𝄪 |G♯ |A♯ |B♯ |C♯ |8 | |E𝄫 Mixolydian |E𝄫 |F♭ |G♭ |A𝄫 |B𝄫 |C♭ |D𝄫 |11 |
| A♯ Mixolydian
|A♯ |B♯ |C𝄪 |D♯ |E♯ |F𝄪 |G♯ |9 | |B𝄫 Mixolydian |B𝄫 |C♭ |D♭ |E𝄫 |F♭ |G♭ |A𝄫 |10 |
| E♯ Mixolydian
|E♯ |F𝄪 |G𝄪 |A♯ |B♯ |C𝄪 |D♯ |10 | |F♭ Mixolydian |F♭ |G♭ |A♭ |B𝄫 |C♭ |D♭ |E𝄫 |9 |
| B♯ Mixolydian
|B♯ |C𝄪 |D𝄪 |E♯ |F𝄪 |G𝄪 |A♯ |11 | |C♭ Mixolydian |C♭ |D♭ |E♭ |F♭ |G♭ |A♭ |B𝄫 |8 |
| F𝄪 Mixolydian
|F𝄪 |G𝄪 |A𝄪 |B♯ |C𝄪 |D𝄪 |E♯ |12 | |G♭ Mixolydian |G♭ |A♭ |B♭ |C♭ |D♭ |E♭ |F♭ |7 |
| C𝄪 Mixolydian
|C𝄪 |D𝄪 |E𝄪 |F𝄪 |G𝄪 |A𝄪 |B♯ |13 | |D♭ Mixolydian |D♭ |E♭ |F |G♭ |A♭ |B♭ |C♭ |6 |
| G𝄪 Mixolydian
|G𝄪 |A𝄪 |B𝄪 |C𝄪 |D𝄪 |E𝄪 |F𝄪 |14 | |A♭ Mixolydian |A♭ |B♭ |C |D♭ |E♭ |F |G♭ |5 |
| rowspan="5" colspan="9"|
|rowspan="5"| |E♭ Mixolydian |E♭ |F |G |A♭ |B♭ |C |D♭ |4 |
| B♭ Mixolydian
|B♭ |C |D |E♭ |F |G |A♭ |3 |
| F Mixolydian
|F |G |A |B♭ |C |D |E♭ |2 |
| C Mixolydian
|C |D |E |F |G |A |B♭ |1 |
| G Mixolydian
|G |A |B |C |D |E |F |0 (no flats or sharps) |
== [[Aeolian mode]] ([[natural minor scale]]) ==
| class="wikitable"
!colspan="7"|Scale !Number of sharps ! !Key signature !colspan="7"|Scale !Number of flats |
| A minor
|A |B |C |D |E |F |G |0 (no sharps or flats) |rowspan="5"| |rowspan="5"| |rowspan="5" colspan="7"| |
| E minor
|E |F♯ |G |A |B |C |D |1 |
| B minor
|B |C♯ |D |E |F♯ |G |A |2 |
| F♯ minor
|F♯ |G♯ |A |B |C♯ |D |E |3 |
| C♯ minor
|C♯ |D♯ |E |F♯ |G♯ |A |B |4 |
| G♯ minor
|G♯ |A♯ |B |C♯ |D♯ |E |F♯ |5 | |A𝄫 |B𝄫 |C𝄫 |D𝄫 |E𝄫 |F𝄫 |G𝄫 |14 |
| D♯ minor
|D♯ |E♯ |F♯ |G♯ |A♯ |B |C♯ |6 | |E𝄫 |F♭ |G𝄫 |A𝄫 |B𝄫 |C𝄫 |D𝄫 |13 |
| A♯ minor
|A♯ |B♯ |C♯ |D♯ |E♯ |F♯ |G♯ |7 | |B𝄫 |C♭ |D𝄫 |E𝄫 |F♭ |G𝄫 |A𝄫 |12 |
| E♯ minor
|E♯ |F𝄪 |G♯ |A♯ |B♯ |C♯ |D♯ |8 | |F♭ |G♭ |A𝄫 |B𝄫 |C♭ |D𝄫 |E𝄫 |11 |
| B♯ minor
|B♯ |C𝄪 |D♯ |E♯ |F𝄪 |G♯ |A♯ |9 | |C♭ |D♭ |E𝄫 |F♭ |G♭ |A𝄫 |B𝄫 |10 |
| F𝄪 minor
|F𝄪 |G𝄪 |A♯ |B♯ |C𝄪 |D♯ |E♯ |10 | |G♭ |A♭ |B𝄫 |C♭ |D♭ |E𝄫 |F♭ |9 |
| C𝄪 minor
|C𝄪 |D𝄪 |E♯ |F𝄪 |G𝄪 |A♯ |B♯ |11 | |D♭ |E♭ |F♭ |G♭ |A♭ |B𝄫 |C♭ |8 |
| G𝄪 minor
|G𝄪 |A𝄪 |B♯ |C𝄪 |D𝄪 |E♯ |F𝄪 |12 | |A♭ |B♭ |C♭ |D♭ |E♭ |F♭ |G♭ |7 |
| D𝄪 minor
|D𝄪 |E𝄪 |F𝄪 |G𝄪 |A𝄪 |B♯ |C𝄪 |13 | |E♭ |F |G♭ |A♭ |B♭ |C♭ |D♭ |6 |
| A𝄪 minor
|A𝄪 |B𝄪 |C𝄪 |D𝄪 |E𝄪 |F𝄪 |G𝄪 |14 | |B♭ |C |D♭ |E♭ |F |G♭ |A♭ |5 |
| colspan="9" rowspan="5"|
|rowspan="5"| |F |G |A♭ |B♭ |C |D♭ |E♭ |4 |
| C minor
|C |D |E♭ |F |G |A♭ |B♭ |3 |
| G minor
|G |A |B♭ |C |D |E♭ |F |2 |
| D minor
|D |E |F |G |A |B♭ |C |1 |
| A minor
|A |B |C |D |E |F |G |0 (no flats or sharps) |
== [[Locrian mode]] ==
| class="wikitable"
!colspan="7"|Scale !Number of sharps ! !Key signature !colspan="7"|Scale !Number of flats |
| B Locrian
|B |C |D |E |F |G |A |0 (no sharps or flats) |rowspan="5"| |rowspan="5"| |rowspan="5" colspan="7"| |
| F♯ Locrian
|F♯ |G |A |B |C |D |E |1 |
| C♯ Locrian
|C♯ |D |E |F♯ |G |A |B |2 |
| G♯ Locrian
|G♯ |A |B |C♯ |D |E |F♯ |3 |
| D♯ Locrian
|D♯ |E |F♯ |G♯ |A |B |C♯ |4 |
| A♯ Locrian
|A♯ |B |C♯ |D♯ |E |F♯ |G♯ |5 | |B𝄫 Locrian |B𝄫 |C𝄫 |D𝄫 |E𝄫 |F𝄫 |G𝄫 |A𝄫 |14 |
| E♯ Locrian
|E♯ |F♯ |G♯ |A♯ |B |C♯ |D♯ |6 | |F♭ Locrian |F♭ |G𝄫 |A𝄫 |B𝄫 |C𝄫 |D𝄫 |E𝄫 |13 |
| B♯ Locrian
|B♯ |C♯ |D♯ |E♯ |F♯ |G♯ |A♯ |7 | |C♭ Locrian |C♭ |D𝄫 |E𝄫 |F♭ |G𝄫 |A𝄫 |B𝄫 |12 |
| F𝄪 Locrian
|F𝄪 |G♯ |A♯ |B♯ |C♯ |D♯ |E♯ |8 | |G♭ Locrian |G♭ |A𝄫 |B𝄫 |C♭ |D𝄫 |E𝄫 |F♭ |11 |
| C𝄪 Locrian
|C𝄪 |D♯ |E♯ |F𝄪 |G♯ |A♯ |B♯ |9 | |D♭ Locrian |D♭ |E𝄫 |F♭ |G♭ |A𝄫 |B𝄫 |C♭ |10 |
| G𝄪 Locrian
|G𝄪 |A♯ |B♯ |C𝄪 |D♯ |E♯ |F𝄪 |10 | |A♭ Locrian |A♭ |B𝄫 |C♭ |D♭ |E𝄫 |F♭ |G♭ |9 |
| D𝄪 Locrian
|D𝄪 |E♯ |F𝄪 |G𝄪 |A♯ |B♯ |C𝄪 |11 | |E♭ Locrian |E♭ |F♭ |G♭ |A♭ |B𝄫 |C♭ |D♭ |8 |
| A𝄪 Locrian
|A𝄪 |B♯ |C𝄪 |D𝄪 |E♯ |F𝄪 |G𝄪 |12 | |B♭ Locrian |B♭ |C♭ |D♭ |E♭ |F♭ |G♭ |A♭ |7 |
| E𝄪 Locrian
|E𝄪 |F𝄪 |G𝄪 |A𝄪 |B♯ |C𝄪 |D𝄪 |13 | |F Locrian |F |G♭ |A♭ |B♭ |C♭ |D♭ |E♭ |6 |
| B𝄪 Locrian
|B𝄪 |C𝄪 |D𝄪 |E𝄪 |F𝄪 |G𝄪 |A𝄪 |14 | |C Locrian |C |D♭ |E♭ |F |G♭ |A♭ |B♭ |5 |
| rowspan="5" colspan="9"|
|rowspan="5"| |G Locrian |G |A♭ |B♭ |C |D♭ |E♭ |F |4 |
| D Locrian
|D |E♭ |F |G |A♭ |B♭ |C |3 |
| A Locrian
|A |B♭ |C |D |E♭ |F |G |2 |
| E Locrian
|E |F |G |A |B♭ |C |D |1 |
| B Locrian
|B |C |D |E |F |G |A |0 (no flats or sharps) |
See also
- Archicembalo, instrument with a double keyboard layout consisting of a 19 tone system close to 19tet in pitch with an additional 12 tone keyboard that is tuned approximately a quartertone in between the white keys of the 19 tone keyboard.
- Beta scale
- Elaine Walker (composer)
- Meantone temperament
- Musical temperament
- 23 tone equal temperament
- 31 tone equal temperament
References
{{reflist|25em}}
Further reading
- {{cite conference
|last1 = Bucht |first1 = Saku
|last2 = Huovinen |first2 = Erkki
|date = 15–18 April 2004
|title=Perceived consonance of harmonic intervals in 19 tone equal temperament
|editor1 = Parncutt, R.
|editor2 = Kessler, A.
|editor3 = Zimmer, F.
|conference = Conference on Interdisciplinary Musicology 2004
|book-title = Proceedings of the Conference on Interdisciplinary Musicology (CIM04)
|place = Graz, Austria
|url=http://www.uni-graz.at/richard.parncutt/cim04/CIM04_paper_pdf/Bucht_Huovinen_CIM04_proceedings.pdf
|access-date = 2014-03-12 |url-status = dead |via = uni-graz.at
|archive-url = https://web.archive.org/web/20131226014305/http://www.uni-graz.at/richard.parncutt/cim04/CIM04_paper_pdf/Bucht_Huovinen_CIM04_proceedings.pdf
|archive-date = 2013-12-26 |df=dmy-all
|conference-url = http://gewi.uni-graz.at/~cim04/
}}
- {{cite web
|last = Howe |first = Hubert S. Jr.
|title = 19 tone theory and applications
|series = Aaron Copland School of Music
|publisher = Queens College / City University of New York
|place = Queens, NY
|type = online journal
|url = http://journaliconi.com/index.php/iconi/article/view/110
}}
- {{cite book |last=Levy |first=Kenneth J. |year=1955 |title=Costeley's Chromatic Chanson |series=Annales Musicologiques: Moyen-Age et Renaissance |volume=III |pages=213–261}}
- {{cite magazine
|last = Sethares |first = W.A. |author-link = William Sethares
|date = April 1991
|title = Tunings for 19 tone equal tempered guitar
|magazine = Experimental Musical Instruments
|volume = VI |series = 6
|url = http://eceserv0.ece.wisc.edu/~sethares/tet19/guitarchords19.html
|via = U. Wisconsin
}}
External links
- {{cite web
|last = Darreg |first = Ivor
|title=A case for nineteen
|series = Sonic Arts
|website = tonalsoft.com
|url = http://tonalsoft.com/sonic-arts/darreg/case.htm
}}
- {{cite report
|first1 = Ingrid |last1 = Pearson |first2 = Graham |last2 = Hair
|first3 = Dougie |last3 = McGilvray |first4 = Nick |last4 = Bailey
|first5 = Amanda |last5 = Morrison |first6 = Richard |last6 = Parncutt
|date = 2014-09-19 |orig-year = 2006
|title = Rehearsing microtonal music: Grappling with performance and intonational problems
|editor = Bailey, Nick
|series = Microtonalism
|website = n-ism.org
|department = Project summary
|url = http://www.n-ism.org/Projects/microtonalism.php
|access-date = 2024-04-01 |df=dmy-all
}}
- {{cite AV media
|first = Elaine |last = Walker |author-link=Elaine Walker (composer)
|title = 19 TET downloadable MP3 files
|medium = music
|publisher = Zia and D.D.T.
|website = ZiaSpace.com
|url = http://www.ziaspace.com/ZIA/sections/music.html
}}
- {{cite web
|title=The Music of Jeff Harrington
|website=Parnasse.com
|url=http://www.parnasse.com/jh/blog/
}} — Jeff Harrington is a composer who has written several pieces for piano in the {{nobr|19 {{sc|TET}} }} tuning, and there are both scores and MP3's available for download on this site.
- {{cite AV media
|first = Chris |last = Vaisvil
|date = 10 December 2009
|title = GR-20 Hexaphonic 19 ET guitar improvisation
|medium = music
|url=http://chrisvaisvil.com/?p=25#
}}
- {{cite AV media
|first = Fabio |last = Costa
|date = 14 October 2018
|title = Meditation in 19 EDO
|medium = music
|url = https://www.youtube.com/watch?v=905sTmTNo_k
}}
{{Microtonal music}}
{{Musical tuning}}