19 equal temperament
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 19√2, or 63.16 cents (ⓘ).
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.
19 EDO is the tuning of the
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 ( 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 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 effectively 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.[2]
The composer Joel Mandelbaum wrote on the properties of the 19 EDO tuning and advocated for its use in his Ph.D. thesis:[5] 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 TET.[5][6] Mandelbaum and Joseph Yasser have written music with 19 EDO.[7] Easley Blackwood stated that 19 EDO makes possible "a substantial enrichment of the tonal repertoire".[8]
Notation
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
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.
Step (cents) 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 63 Note name A A♯ B♭ B B♯
C♭C C♯ D♭ D D♯ E♭ E E♯
F♭F F♯ G♭ G G♯ A♭ A Interval (cents) 0 63 126 189 253 316 379 442 505 568 632 695 758 821 884 947 1011 1074 1137 1200
Interval name Size
(steps)Size
(cents)Midi Just ratio Just
(cents)Midi Error
(cents)Octave 19 1200 2:1 1200 0 Septimal major seventh 18 1136.84 27:14 1137.04 − 0.20Diminished octave 18 1136.84 48:25 1129.33 ⓘ + 7.51Major seventh 17 1073.68 15:8 1088.27 ⓘ −14.58 Minor seventh 16 1010.53 9:5 1017.60 ⓘ − 7.07Harmonic minor seventh 15 947.37 7:4 968.83 ⓘ −21.46 Septimal major sixth 15 947.37 12:7 933.13 ⓘ +14.24 Major sixth 14 884.21 5:3 884.36 ⓘ − 0.15Minor sixth 13 821.05 8:5 813.69 ⓘ + 7.37Augmented fifth 12 757.89 25:16 772.63 ⓘ −14.73 Septimal minor sixth 12 757.89 14:9 764.92 − 7.02Perfect fifth 11 694.74 ⓘ 3:2 701.96 ⓘ − 7.22Greater tridecimal tritone 10 631.58 13:9 636.62 − 5.04Greater septimal tritone, diminished fifth 10 631.58 ⓘ 10:7 617.49 ⓘ +14.09 Lesser septimal tritone, augmented fourth 9 568.42 ⓘ 7:5 582.51 −14.09 Lesser tridecimal tritone 9 568.42 18:13 563.38 + 5.04Perfect fourth 8 505.26 ⓘ 4:3 498.04 ⓘ + 7.22Augmented third 7 442.11 125:96 456.99 ⓘ −14.88 Tridecimal major third7 442.11 13:10 454.12 −10.22 Septimal major third 7 442.11 ⓘ 9:7 435.08 ⓘ + 7.03Major third 6 378.95 ⓘ 5:4 386.31 ⓘ − 7.36Inverted 13th harmonic 6 378.95 16:13 359.47 +19.48 Minor third 5 315.79 ⓘ 6:5 315.64 ⓘ + 0.15Septimal minor third 4 252.63 7:6 266.87 ⓘ −14.24 Tridecimal 5 / 4 tone 4 252.63 15:13 247.74 + 4.89Septimal whole tone 4 252.63 ⓘ 8:7 231.17 ⓘ +21.46 major tone3 189.47 9:8 203.91 ⓘ −14.44 Whole tone, minor tone3 189.47 ⓘ 10:9 182.40 ⓘ + 7.07Greater tridecimal 2 / 3 -tone 2 126.32 13:12 138.57 −12.26 Lesser tridecimal 2 / 3 -tone 2 126.32 14:13 128.30 − 1.98Septimal diatonic semitone 2 126.32 15:14 119.44 ⓘ + 6.88Diatonic semitone, just2 126.32 16:15 111.73 ⓘ +14.59 Septimal chromatic semitone 1 63.16 ⓘ 21:20 84.46 −21.31 Chromatic semitone, just1 63.16 25:24 70.67 ⓘ − 7.51Septimal third-tone1 63.16 ⓘ 28:27 62.96 + 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
Because 19 is a
Modes
Ionian mode (major scale)
Key signature | Number of sharps |
Key signature | Number of flats | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
C major | C | D | E | F | G | A | B | 0 | ||||||||||
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𝄫 major | C𝄫 | D𝄫 | E𝄫 | F𝄫 | G𝄫 | A𝄫 | B𝄫 | 14 | |
F♯ major | F♯ | G♯ | A♯ | B | C♯ | D♯ | E♯ | 6 | G𝄫 major | G𝄫 | A𝄫 | B𝄫 | C𝄫 | D𝄫 | E𝄫 | F♭ | 13 | |
C♯ major | C♯ | D♯ | E♯ | F♯ | G♯ | A♯ | B♯ | 7 | D𝄫 major | D𝄫 | E𝄫 | F♭ | G𝄫 | A𝄫 | B𝄫 | C♭ | 12 | |
G♯ major | G♯ | A♯ | B♯ | C♯ | D♯ | E♯ | F𝄪 | 8 | A𝄫 major | A𝄫 | B𝄫 | C♭ | D𝄫 | E𝄫 | F♭ | G♭ | 11 | |
D♯ major | D♯ | E♯ | F𝄪 | G♯ | A♯ | B♯ | C𝄪 | 9 | E𝄫 major | E𝄫 | F♭ | G♭ | A𝄫 | B𝄫 | C♭ | D♭ | 10 | |
A♯ major | A♯ | B♯ | C𝄪 | D♯ | E♯ | F𝄪 | G𝄪 | 10 | B𝄫 major | B𝄫 | C♭ | D♭ | E𝄫 | F♭ | G♭ | A♭ | 9 | |
E♯ major | E♯ | F𝄪 | G𝄪 | A♯ | B♯ | C𝄪 | D𝄪 | 11 | F♭ major | F♭ | G♭ | A♭ | B𝄫 | C♭ | D♭ | E♭ | 8 | |
B♯ major | B♯ | C𝄪 | D𝄪 | E♯ | F𝄪 | G𝄪 | A𝄪 | 12 | C♭ major | C♭ | D♭ | E♭ | F♭ | G♭ | A♭ | B♭ | 7 | |
F𝄪 major | F𝄪 | G𝄪 | A𝄪 | B♯ | C𝄪 | D𝄪 | E𝄪 | 13 | G♭ major | G♭ | A♭ | B♭ | C♭ | D♭ | E♭ | F | 6 | |
C𝄪 major | C𝄪 | D𝄪 | E𝄪 | F𝄪 | G𝄪 | A𝄪 | B𝄪 | 14 | D♭ major | D♭ | E♭ | F | G♭ | A♭ | B♭ | C | 5 | |
A♭ major | 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 |
Dorian mode
Key signature | Number of sharps |
Key signature | Number of flats | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
D Dorian | D | E | F | G | A | B | C | 0 | ||||||||||
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♯ | C𝄪 | D♯ | E♯ | F𝄪 | G𝄪 | A♯ | 10 | C♭ Dorian | C♭ | D♭ | E𝄫 | F♭ | G♭ | A♭ | B𝄫 | 9 | |
F𝄪 Dorian | F𝄪 | G𝄪 | A♯ | B♯ | C𝄪 | 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 | |
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 |
Phrygian mode
Key signature | Number of sharps |
Key signature | Number of flats | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
E Phrygian | E | F | G | A | B | C | D | 0 | ||||||||||
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 | |
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 |
Lydian mode
Key signature | Number of sharps |
Key signature | Number of flats | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
F Lydian | F | G | A | B | C | D | E | 0 | ||||||||||
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 | |
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 |
Mixolydian mode
Key signature | Number of sharps |
Key signature | Number of flats | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
G Mixolydian | G | A | B | C | D | E | F | 0 | ||||||||||
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 | |
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 |
Aeolian mode (natural minor scale)
Key signature | Number of sharps |
Key signature | Number of flats | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A minor | A | B | C | D | E | F | G | 0 | ||||||||||
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𝄫 minor | A𝄫 | B𝄫 | C𝄫 | D𝄫 | E𝄫 | F𝄫 | G𝄫 | 14 | |
D♯ minor | D♯ | E♯ | F♯ | G♯ | A♯ | B | C♯ | 6 | E𝄫 minor | E𝄫 | F♭ | G𝄫 | A𝄫 | B𝄫 | C𝄫 | D𝄫 | 13 | |
A♯ minor | A♯ | B♯ | C♯ | D♯ | E♯ | F♯ | G♯ | 7 | B𝄫 minor | B𝄫 | C♭ | D𝄫 | E𝄫 | F♭ | G𝄫 | A𝄫 | 12 | |
E♯ minor | E♯ | F𝄪 | G♯ | A♯ | B♯ | C♯ | D♯ | 8 | F♭ minor | F♭ | G♭ | A𝄫 | B𝄫 | C♭ | D𝄫 | E𝄫 | 11 | |
B♯ minor | B♯ | C𝄪 | D♯ | E♯ | F𝄪 | G♯ | A♯ | 9 | C♭ minor | C♭ | D♭ | E𝄫 | F♭ | G♭ | A𝄫 | B𝄫 | 10 | |
F𝄪 minor | F𝄪 | G𝄪 | A♯ | B♯ | C𝄪 | D♯ | E♯ | 10 | G♭ minor | G♭ | A♭ | B𝄫 | C♭ | D♭ | E𝄫 | F♭ | 9 | |
C𝄪 minor | C𝄪 | D𝄪 | E♯ | F𝄪 | G𝄪 | A♯ | B♯ | 11 | D♭ minor | D♭ | E♭ | F♭ | G♭ | A♭ | B𝄫 | C♭ | 8 | |
G𝄪 minor | G𝄪 | A𝄪 | B♯ | C𝄪 | D𝄪 | E♯ | F𝄪 | 12 | A♭ minor | A♭ | B♭ | C♭ | D♭ | E♭ | F♭ | G♭ | 7 | |
D𝄪 minor | D𝄪 | E𝄪 | F𝄪 | G𝄪 | A𝄪 | B♯ | C𝄪 | 13 | E♭ minor | E♭ | F | G♭ | A♭ | B♭ | C♭ | D♭ | 6 | |
A𝄪 minor | A𝄪 | B𝄪 | C𝄪 | D𝄪 | E𝄪 | F𝄪 | G𝄪 | 14 | B♭ minor | B♭ | C | D♭ | E♭ | F | G♭ | A♭ | 5 | |
F minor | 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 |
Locrian mode
Key signature | Number of sharps |
Key signature | Number of flats | ||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
B Locrian | B | C | D | E | F | G | A | 0 | |||||||||||
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 | ||
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 |
See also
- quartertonein 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
- S2CID 27906745.
- ^ a b c Woolhouse, W.S.B. (1835). Essay on Musical Intervals, Harmonics, and the Temperament of the Musical Scale, &c. London, UK: J. Souter.
- ^ Joseph Yasser. "A Theory of Evolving Tonality". MusAnim.com.
- ^ Heino, Arto Juhani. "Artone 19 Guitar Design". Heino names the 19 note scale Parvatic.
- ^ a b Mandelbaum, M. Joel (1961). Multiple Division of the Octave and the Tonal Resources of 19 Tone Temperament (Thesis).
- ^
JSTOR 842948.
- ^
Leedy, Douglas (1991). "A venerable temperament rediscovered". JSTOR 833439.
- cited by
ISBN 9780542998478. - cited by
- ^ Skinner (2007), p. 76.
- ^ Skinner (2007), p. 52.
- ^ "19 EDO". TonalSoft.com.
Further reading
- Bucht, Saku; Huovinen, Erkki (15–18 April 2004). "Perceived consonance of harmonic intervals in 19 tone equal temperament" (PDF). In Parncutt, R.; Kessler, A.; Zimmer, F. (eds.). Proceedings of the Conference on Interdisciplinary Musicology (CIM04). Conference on Interdisciplinary Musicology 2004. Graz, Austria. Archived from the original (PDF) on 26 December 2013. Retrieved 12 March 2014 – via uni-graz.at.
- Howe, Hubert S. Jr. "19 tone theory and applications" (academic pers. site). Queens College / City University of New York.
- Levy, Kenneth J. (1955). Costeley's Chromatic Chanson. Annales Musicologues: Moyen-Age et Renaissance. Vol. III. pp. 213–261.
- U. Wisconsin.
External links
- Darreg, Ivor. "A case for nineteen". tonalsoft.com. Sonic Arts.
- Pearson, Ingrid; Hair, Graham; McGilvray, Dougie; Bailey, Nick; Morrison, Amanda; Parncutt, Richard (19 September 2014) [2006]. Bailey, Nick (ed.). Rehearsing microtonal music: Grappling with performance and intonational problems. Project summary. n-ism.org (Report). Microtonalism. Retrieved 1 April 2024.
- Walker, Elaine. 19 TET downloadable MP3 files. ZiaSpace.com (music). Zia and D.D.T.
- "The Music of Jeff Harrington". Parnasse.com. — Jeff Harrington is a composer who has written several pieces for piano in the 19 TET tuning, and there are both scores and MP3's available for download on this site.
- Vaisvil, Chris (10 December 2009). GR-20 Hexaphonic 19 ET guitar improvisation (music).
- Costa, Fabio (14 October 2018). Meditation in 19 EDO (music).