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