19 equal temperament

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File:Syntonic tuning continuum.svg
Figure 1: 19-TET on the syntonic temperament's tuning continuum at P5= 694.737 cents[1]

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 Template:Radic, or 63.16 cents (Template:ErrorTemplate:Category handler).

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File:19 equal temperament keyboard.png
19 equal temperament keyboard[2]

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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
Joseph Yasser's 19 equal temperament keyboard layout[3]

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
The comparison between a standard 12 tone classical guitar and a 19 tone guitar design. This is the preliminary data that Arto Juhani Heino used to develop the "Artone 19" guitar design. The measurements are in millimeters.[4]

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 (Template:SfracScript error: No such module "Check for unknown parameters". 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 Template:Sfrac Script error: No such module "Check for unknown parameters".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.[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 equal temperament|31 Template:Sc]].[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".Template:Sfnp

Notation

File:19-tet scale on C.png
Usual pitch notation, promoted by Easley BlackwoodTemplate:Sfnp and Wesley Woolhouse,[2] for 19 equal temperament: Intervals are notated similarly to the 12 Template:Sc 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).[8]
File:19-tet scale on C.mid
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File:19ed2.svg
Just intonation intervals approximated in 19 EDO

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

File:Diatonic scale on C.png
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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 −0.20
Diminished octave 18 1136.84 48:25 1129.33 Template:ErrorTemplate:Category handler +7.51
Major seventh 17 1073.68 15:8 1088.27 Template:ErrorTemplate:Category handler −14.58
Minor seventh 16 1010.53 9:5 1017.60 Template:ErrorTemplate:Category handler −7.07
Harmonic minor seventh 15 947.37 7:4 968.83 Template:ErrorTemplate:Category handler −21.46
Septimal major sixth 15 947.37 12:7 933.13 Template:ErrorTemplate:Category handler +14.24
Major sixth 14 884.21 5:3 884.36 Template:ErrorTemplate:Category handler −0.15
Minor sixth 13 821.05 8:5 813.69 Template:ErrorTemplate:Category handler +7.37
Augmented fifth 12 757.89 25:16 772.63 Template:ErrorTemplate:Category handler −14.73
Septimal minor sixth 12 757.89 14:9 764.92 −7.02
Perfect fifth 11 694.74 Template:ErrorTemplate:Category handler 3:2 701.96 Template:ErrorTemplate:Category handler −7.22
Greater tridecimal tritone 10 631.58 13:9 636.62 −5.04
Greater septimal tritone, diminished fifth 10 631.58 Template:ErrorTemplate:Category handler 10:7 617.49 Template:ErrorTemplate:Category handler +14.09
Lesser septimal tritone, augmented fourth 9 568.42 Template:ErrorTemplate:Category handler 7:5 582.51 −14.09
Lesser tridecimal tritone 9 568.42 18:13 563.38 +5.04
Perfect fourth 8 505.26 Template:ErrorTemplate:Category handler 4:3 498.04 Template:ErrorTemplate:Category handler +7.22
Augmented third 7 442.11 125:96 456.99 Template:ErrorTemplate:Category handler −14.88
Tridecimal major third 7 442.11 13:10 454.12 −10.22
Septimal major third 7 442.11 Template:ErrorTemplate:Category handler 9:7 435.08 Template:ErrorTemplate:Category handler +7.03
Major third 6 378.95 Template:ErrorTemplate:Category handler 5:4 386.31 Template:ErrorTemplate:Category handler −7.36
Inverted 13th harmonic 6 378.95 16:13 359.47 +19.48
Minor third 5 315.79 Template:ErrorTemplate:Category handler 6:5 315.64 Template:ErrorTemplate:Category handler +0.15
Septimal minor third 4 252.63 7:6 266.87 Template:ErrorTemplate:Category handler −14.24
Tridecimal Template:SfracScript error: No such module "Check for unknown parameters". tone 4 252.63 15:13 247.74 +4.89
Septimal whole tone 4 252.63 Template:ErrorTemplate:Category handler 8:7 231.17 Template:ErrorTemplate:Category handler +21.46
Whole tone, major tone 3 189.47 9:8 203.91 Template:ErrorTemplate:Category handler −14.44
Whole tone, minor tone 3 189.47 Template:ErrorTemplate:Category handler 10:9 182.40 Template:ErrorTemplate:Category handler +7.07
Greater tridecimal Template:SfracScript error: No such module "Check for unknown parameters".-tone 2 126.32 13:12 138.57 −12.26
Lesser tridecimal Template:SfracScript error: No such module "Check for unknown parameters".-tone 2 126.32 14:13 128.30 −1.98
Septimal diatonic semitone 2 126.32 15:14 119.44 Template:ErrorTemplate:Category handler +6.88
Diatonic semitone, just 2 126.32 16:15 111.73 Template:ErrorTemplate:Category handler +14.59
Septimal chromatic semitone 1 63.16 Template:ErrorTemplate:Category handler 21:20 84.46 −21.31
Chromatic semitone, just 1 63.16 25:24 70.67 Template:ErrorTemplate:Category handler −7.51
Septimal third-tone 1 63.16 Template:ErrorTemplate:Category handler 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

File:19-TET circle of fifths.png
Circle of fifths in 19 tone equal temperament
File:Major chord on C.png
Major chord on C in 19 equal temperament: All notes within 8 cents of just intonation (rather than 14 for 12 equal temperament). Template:ErrorTemplate:Category handler, Template:ErrorTemplate:Category handler, or Template:ErrorTemplate:Category handler

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.

Modes

Ionian mode (major scale)

Key signature Scale Number of sharps Key signature Scale Number of flats
C major C D E F G A B 0 (no sharps or flats)
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♯ F𝄪 D♯ E♯ F𝄪 G𝄪 10 B𝄫 major B𝄫 C♭ D♭ E𝄫 F♭ G♭ A♭ 9
E♯ major E♯ F𝄪 G𝄪 A♯ B♯ F𝄪 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 (no flats or sharps)

Dorian mode

Key signature Scale Number of sharps Key signature Scale Number of flats
D Dorian D E F G A B C 0 (no sharps or flats)
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
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

Key signature Scale Number of sharps Key signature Scale Number of flats
E Phrygian E F G A B C D 0 (no sharps or flats)
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 (no flats or sharps)

Lydian mode

Key signature Scale Number of sharps Key signature Scale Number of flats
F Lydian F G A B C D E 0 (no sharps or flats)
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 (no flats or sharps)

Mixolydian mode

Key signature Scale Number of sharps Key signature Scale Number of flats
G Mixolydian G A B C D E F 0 (no sharps or flats)
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 (no flats or sharps)

Aeolian mode (natural minor scale)

Key signature Scale Number of sharps Key signature Scale Number of flats
A minor A B C D E F G 0 (no sharps or flats)
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 (no flats or sharps)

Locrian mode

Key signature Scale Number of sharps Key signature Scale Number of flats
B Locrian B C D E F G A 0 (no sharps or flats)
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 (no flats or sharps)

See also

References

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  1. ↑ Script error: No such module "Citation/CS1".
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  3. ↑ Script error: No such module "citation/CS1".
  4. ↑ Script error: No such module "citation/CS1". Heino names the 19 note scale Parvatic.
  5. ↑ a b Template:Cite thesis
  6. ↑ Script error: No such module "Citation/CS1".
  7. ↑ Script error: No such module "Citation/CS1".
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Further reading

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External links

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  • Script error: No such module "citation/CS1". — Jeff Harrington is a composer who has written several pieces for piano in the 19 Template:Sc tuning, and there are both scores and MP3's available for download on this site.
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