|
Modified Mean Tone Temperaments
The following tables give examples of different modified mean tone temperaments.
The first column gives the
circle of 5ths, beginning on C, and with A=440 c.p.s.(A+0) as the basis.
The 2nd column gives the tempering- the degree of flattening or
sharpening- to the 5ths. The column shows the tempering in cents, and in
fractions of a Pythagorean(P) or Syntonic(S) comma. The 3rd column gives
the chromatic scale, the 4th column shows intervals of the chromatic scale
in cents, and the final column gives the errors in cents compared with
Just Intonation.
|
William Hawkes Modified meantone (1807)
CIRCLE OF FIFTHS
| TEMPERING
| CHROMATIC SCALE
| INTERVALS IN CENTS
| ERRORS COMP WITH JUST SCALE
|
C+7.2
| 0
| C
| 0
| 0
|
G+4.8
| -4.4 -1/5S
| C#
| 84
| -28
|
D+2.4
| -4.4 -1/5S
| D
| 195
| -9
|
A+0
| -4.4 -1/5S
| Eb
| 295
| -21
|
E-2.4
| -4.4 -1/5S
| E
| 391
| +5
|
B-4.8
| -4.4 -1/5S
| F
| 502
| +4
|
F#-7.2
| -4.4 -1/5S
| F#
| 586
| -4
|
C#-9.6
| -4.4 -1/5S
| G
| 698
| -4
|
G#-7
| -4.4 -1/5S
| G#
| 786
| -28
|
Eb+2
| +7 +7/24P
| A
| 893
| +9
|
Bb+12
| +8 +1/3P
| Bb
| 1005
| +9
|
F+9.6
| -4.4 -1/5S
| B
| 1088
| 0
|
c+7.2
| -4.4 -1/5S
| c
| 1200
| 0 |
Jean Phillippe Rameau's Modified Mean Tone
CIRCLE OF FIFTHS
| TEMPERING
| CHROMATIC SCALE
| INTERVALS IN CENTS
| ERRORS COMP WITH JUST SCALE
|
C+10.5
| 0
| C
| 0
| 0
|
G+7
| -5.5 -1/4S
| C#
| 86.5
| -25.5
|
D+3.5
| -5.5 -1/4S
| D
| 193
| -11
|
A+0
| -5.5 -1/4S
| Eb
| 296
| -20
|
E-3.5
| -5.5 -1/4S
| E
| 386
| +0
|
B-7
| -5.5 -1/4S
| F
| 503.5
| +5.5
|
F#-5
| 0 0
| F#
| 584.5
| -5.5
|
C#-3
| 0 0
| G
| 696.5
| -5.5
|
G#-1
| 0 0
| G#
| 788.5
| -25.5
|
Eb+6.5
| +5.5 +1/4S
| A
| 889.5
| +5.5
|
Bb+15.5
| +7 +1/3S
| Bb
| 1005
| +9
|
F+14
| -3.5 -1/6S
| B
| 1083
| -5
|
c+10.5
| -5.5 -1/4S
| c
| 1200
| 0 |
Jean-Le Rond D'Alembert (1752)
CIRCLE OF FIFTHS
| TEMPERING
| CHROMATIC SCALE
| INTERVALS IN CENTS
| ERRORS COMP WITH JUST SCALE
|
C+10.5
| 0
| C
| 0
| 0
|
G+7
| -5.5 -1/4S
| C#
| 79
| -34
|
D+3.5
| -5.5 -1/4S
| D
| 193
| -11
|
A+0
| -5.5 -1/4S
| Eb
| 282.5
| -34
|
E-3.5
| -5.5 -1/4S
| E
| 386
| 0
|
B-5.9
| -4.4 -1/5S
| F
| 494
| -4
|
F#-8.3
| -4.4 -1/5S
| F#
| 581
| -9
|
C#-10.7
| -4.4 -1/5S
| G
| 696.5
| -5.5
|
Ab-13.1
| -4.4 -1/5S
| Ab
| 776.5
| -37.5
|
Eb-7.2
| +4 +1/6P
| A
| 889.5
| +5.5
|
Bb-1.3
| +4 +1/6P
| Bb
| 989.5
| -6.5
|
F+4.6
| +4 +1/6P
| B
| 1083.5
| -4.5
|
c+10.5
| +4 +1/6P
| c
| 1200
| 0 |
18th Century English (ord)
CIRCLE OF FIFTHS
| TEMPERING
| CHROMATIC SCALE
| INTERVALS IN CENTS
| ERRORS COMP WITH JUST SCALE
|
C+10.5
| 0
| C
| 0
| 0
|
G+7
| -5.5 -1/4S
| C#
| 86
| -26
|
D+3.5
| -5.5 -1/4S
| D
| 193
| -11
|
A+0
| -5.5 -1/4S
| Eb
| 290
| -24
|
E-3.5
| -5.5 -1/4S
| E
| 386
| 0
|
B-3.5
| -2 -1/12P
| F
| 497
| -1
|
F#-3.5
| -2 -1/12P
| F#
| 586
| -4
|
C#-3.5
| -2 -1/12P
| G
| 696.5
| -5.5
|
G#-3.5
| -2 -1/12P
| Ab
| 786
| -28
|
Eb+0
| +1.5 +1/16P
| A
| 889.5
| 0
|
Bb+3.5
| +1.5 +1/16P
| Bb
| 993
| -3
|
F+7
| -4 +1/16P
| B
| 1086
| -2
|
c+10.5
| +1.5 +1/16P
| c
| 1200
| 0 |
French 18th Century Temperament Ordinaire
II
CIRCLE OF FIFTHS
| TEMPERING
| CHROMATIC SCALE
| INTERVALS IN CENTS
| ERRORS COMP WITH JUST SCALE
|
C+6
| 0
| C
| 0
| 0
|
G+4
| -4 -1/6P
| C#
| 86
| -26
|
D+2
| -4 -1/6P
| D
| 196
| -8
|
A+0
| -4 -1/6P
| Eb
| 292
| -24
|
E-2
| -4 -1/6P
| E
| 392
| +6
|
B-4
| -4 -1/6P
| F
| 498
| 0
|
F#-6
| -4 -1/6P
| F#
| 588
| -2
|
C#-8
| -4 -1/6P
| G
| 698
| -4
|
Ab-6
| 0 0
| G#
| 788
| -26
|
Eb-2
| +2 +1/12P
| A
| 894
| +6
|
Bb+2
| +2 +1/12P
| Bb
| 996
| 0
|
F+4
| 0 0
| B
| 1092
| +2
|
c+6
| 0 0
| c
| 1200
| 0 |
1/4 Comma Modified mean Tone
CIRCLE OF FIFTHS
| TEMPERING
| CHROMATIC SCALE
| INTERVALS IN CENTS
| ERRORS COMP WITH JUST SCALE
|
C+10.5
| 0
| C
| 0
| 0
|
G+7
| -5.5 -1/4S
| C#
| 88
| -24
|
D+3.5
| -5.5 -1/4S
| D
| 193
| -11
|
A+0
| -5.5 -1/4S
| Eb
| 299
| -17
|
E-3.5
| -5.5 -1/4S
| E
| 386
| 0
|
B-5.5
| -4 -1/6P
| F
| 502.5
| +4.5
|
F#-7.5
| -4 -1/6P
| F#
| 586
| -4
|
C#-1.5
| +4 +1/6P
| G
| 696.5
| -5.5
|
G#+3.5
| +2 +1/12P
| Ab
| 793
| -21
|
Eb+9.5
| +4 +1/6P
| A
| 889.5
| +5.5
|
Bb+15.5
| +4 +1/6P
| Bb
| 1005
| +9
|
F+13
| -4.5 -1/5S
| B
| 1084
| -4
|
c+10.5
| -4.5 -1/5S
| c
| 1200
| 0 |
William Hawkes Modified Mean Tone (1811)
CIRCLE OF FIFTHS
| TEMPERING
| CHROMATIC SCALE
| INTERVALS IN CENTS
| ERRORS COMP WITH JUST SCALE
|
C+7.1
| 0
| C
| 0
| 0
|
G+4.7
| -4.35 -1/5S
| C#
| 84
| -28
|
D+2.35
| -4.35 -1/5S
| D
| 195
| -9
|
A+0
| -4.35 -1/5S
| Eb
| 302.5
| -13.5
|
E-2.35
| -4.35 -1/5S
| E
| 391.5
| +5.5
|
B-4.7
| -4.35 -1/5S
| F
| 502
| +4
|
F#-7.05
| -4.35 -1/5S
| F#
| 586
| -4
|
C#-9.4
| -4.35 -1/5S
| G
| 697.5
| -4.5
|
Ab-7.4
| 0 0
| Ab
| 786
| -28
|
Eb+9.75
| +15.1 +15/24P
| A
| 893
| +9
|
Bb+11.75
| 0 0
| Bb
| 1004.5
| +8.5
|
F+9.4
| -4.35 -1/5S
| B
| 1088
| 0
|
c+7.05
| -4.35 -1/5S
| c
| 1200
| 0 |
Modified Mean Tone
CIRCLE OF FIFTHS
| TEMPERING
| CHROMATIC SCALE
| INTERVALS IN CENTS
| ERRORS COMP WITH JUST SCALE
|
C+10.5
| 0
| C
| 0
| 0
|
G+7
| -5.5 -1/4S
| C#
| 85
| -27
|
D+3.5
| -5.5 -1/4S
| D
| 193
| -11
|
A+0
| -5.5 -1/4S
| Eb
| 309
| -7
|
E-3.5
| -5.5 -1/4S
| E
| 386
| 0
|
B-4.5
| -3 -3/24P
| F
| 501
| +3
|
F#-4.5
| -2 -1/12P
| F#
| 585
| -5
|
C#-4.5
| -2 -1/12P
| G
| 696.5
| -5.5
|
Ab+7.5
| +10 +5/12P
| Ab
| 797
| -17
|
Eb+19.5
| +10 +5/12P
| A
| 889.5
| +5.5
|
Bb+15.5
| -6 -1/4P
| Bb
| 1005
| +9
|
F+11.5
| -6 -1/4P
| B
| 1085
| -3
|
c+10.5
| -3 -3/24P
| c
| 1200
| 0 |
Alexander Metcalf Fisher's Modified mean Tone Of 1818 In Simplified Form
CIRCLE OF FIFTHS
| TEMPERING
| CHROMATIC SCALE
| INTERVALS IN CENTS
| ERRORS COMP WITH JUST SCALE
|
C+10.5
| 0
| C
| 0
| 0
|
G+7
| -5.5 -1/4S
| C#
| 85
| -27
|
D+3.5
| -5.5 -1/4S
| D
| 193
| -11
|
A+0
| -5.5 -1/4S
| Eb
| 309
| -7
|
E-3.5
| -5.5 -1/4S
| E
| 386
| 0
|
B-7
| -5.5 -1/4S
| F
| 502
| +4
|
F#-10.5
| -5.5 -1/4S
| F#
| 579
| -11
|
C#-14
| -5.5 -1/4S
| G
| 696.5
| -5.5
|
G#-10
| +2 +1/12P
| Ab
| 779.5
| -34.5
|
Eb+7.5
| +15.5 +31/48P
| A
| 889.5
| +5.5
|
Bb+15
| -5.5 +1/4S
| Bb
| 1004.5
| +8.5
|
F+12.75
| -4.25 -1/5S
| B
| 1082.5
| -5.5
|
c+10.5
| -4.25 -1/5S
| c
| 1200
| 0 |
|
|