Definitions of tuning terms
© 1998 by Joseph L. Monzo
All definitions by Joe Monzo unless otherwise cited
1/4-comma meantone
The most frequently encountered version of
meantone tuning.
This tuning narrows or flattens each
'5th' in a series of '5ths'
by 1/4 of a
syntonic comma,
hence its name.
This results in 'perfect 5ths' of approximately 697
cents or 6.97
Semitones.
Meantone tunings can be and have been extended to as many notes
per 'octave' as desired, but when used
for fretted strings or, especially, keyboards, they are usually
limited to 12 discrete pitches per 'octave'.
Regardless of how many notes the meantone has, comparing the
two notes at either end results in a
'wolf 5th' and a 'wolf 4th',
as can be seen in the following two tables. The 'wolves'
occur between the two '5ths' or '4ths' which bound the
notes at the end of the series of '5ths'.
In the tables below, the reference pitch
(1/1) is 'A', and the series of '5ths'
runs arbitrarily from 3-6 (= 'Eb') to
35 (= G#). The first table is an
interval matrix
of all possible intervals between any two pitches in this tuning.
The second table lists all available intervals and
the notes between which they can be found.
interval sizes given in Semitones
G#
G
F#
F
E
Eb
D
C#
C
B
Bb
A
3^x
5
-2
3
-4
1
-6
-1
4
-3
2
-5
0
G#
5
0.00
11.24
10.07
9.31
8.14
7.38
6.21
5.03
4.27
3.10
2.34
1.17
G
-2
0.76
0.00
10.83
10.07
8.90
8.14
6.97
5.79
5.03
3.86
3.10
1.93
F#
3
1.93
1.17
0.00
11.24
10.07
9.31
8.14
6.97
6.21
5.03
4.27
3.10
F
-4
2.69
1.93
0.76
0.00
10.83
10.07
8.90
7.73
6.97
5.79
5.03
3.86
E
1
3.86
3.10
1.93
1.17
0.00
11.24
10.07
8.90
8.14
6.97
6.21
5.03
Eb
-6
4.62
3.86
2.69
1.93
0.76
0.00
10.83
9.66
8.90
7.73
6.97
5.79
D
-1
5.79
5.03
3.86
3.10
1.93
1.17
0.00
10.83
10.07
8.90
8.14
6.97
C#
4
6.97
6.21
5.03
4.27
3.10
2.34
1.17
0.00
11.24
10.07
9.31
8.14
C
-3
7.73
6.97
5.79
5.03
3.86
3.10
1.93
0.76
0.00
10.83
10.07
8.90
B
2
8.90
8.14
6.97
6.21
5.03
4.27
3.10
1.93
1.17
0.00
11.24
10.07
Bb
-5
9.66
8.90
7.73
6.97
5.79
5.03
3.86
2.69
1.93
0.76
0.00
10.83
A
0
10.83
10.07
8.90
8.14
6.97
6.21
5.03
3.86
3.10
1.93
1.17
0.00
diminished 8ve
11.24
G#:G
F#:F
E:Eb
C#:C
B:Bb
major 7th
10.83
G:F#
F:E
Eb:D
D:C#
C:B
Bb:A
A:G#
minor 7th
10.07
G#:F#
G:F
F#:E
F:Eb
E:D
D:C
C#:B
C:Bb
B:A
A:G
augmented 6th
9.66
Eb:C#
Bb:G#
diminshed 7th
9.31
G#:F
F#:Eb
C#:Bb
major 6th
8.90
G:E
F:D
E:C#
Eb:C
D:B
C:A
B:G#
Bb:G
A:F#
minor 6th
8.14
G#:E
G:Eb
F#:D
E:C
D:B
C#:A
B:G
A:F
augmented 5th
7.73
F:C#
Eb:B
C:G#
Bb:F#
wolf 5th
7.38
G#:Eb
'perfect' 5th
6.97
G:D
F#:C#
F:C
E:B
Eb:Bb
D:A
C#:G#
C:G
B:F#
Bb:F
A:E
diminished 5th
6.21
G#:D
F#:C
E:Bb
C#:G
B:F
A:Eb
augmented 4th
5.79
G:C#
F:B
Eb:A
D:G#
C:F#
Bb:E
'perfect' 4th
5.03
G#:C#
G:C
F#:B
F:Bb
E:A
D:G
C#:F#
C:F
B:E
Bb:Eb
A:D
wolf 4th
4.62
Eb:G#
diminished 4th
4.27
G#:C
F#:Bb
C#:F
B:Eb
major 3rd
3.86
G:B
F:A
E:G#
Eb:G
D:F#
C:E
Bb:D
A:C#
minor 3rd
3.10
G#:B
G:Bb
F#:A
E:G
D:F
C#:E
C:Eb
B:D
A:C
augmented 2nd
2.69
F:G#
Eb:F#
Bb:C#
diminished 3rd
2.34
G#:Bb
C#:Eb
major 2nd
1.93
G:A
F#:G#
F:G
E:F#
Eb:F
D:E
C:D
B:C#
Bb:C
A:B
minor 2nd
1.17
G#:A
F#:G
E:F
D:Eb
C#:D
B:C
A:Bb
augmented unison
0.76
G:G#
F:F#
Eb:E
C:C#
Bb:B
unison / 8ve
0 or 12
G#:G#
G:G
F#:F#
F:F
E:E
Eb:Eb
D:D
C#:C#
C:C
B:B
Bb:Bb
A:A
Last Updated 2000.8.10
by Joe Monzo
(to download a zip file of the entire Dictionary, click here) |
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