Mean Tone Temperaments

The following tables give examples of different 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.

1/3rd Comma Mean Tone ( From Salinas' 31 note Mean Tone)

CIRCLE
OF FIFTHS
TEMPERING CHROMATIC
SCALE
INTERVALS
IN CENTS
ERRORS
COMP WITH
JUST SCALE
C+15.75 0 C 0 0
G+10.5 -4
-1/3S
C# 63.5 -48.5
D+5.25 -4
-1/3S
D 189.5 -14.5
A+0 -4
-1/3S
Eb 315.75 -0
E-5.25 -4
-1/3S
E 379.25 -6.8
B-10.5 -4
-1/3S
F 505.25 +7.2
F#-15.75 -4
-1/3S
F# 568.75 -21.3
C#-21 -4
-1/3S
G 694.75 -5.2
Ab-26.25 -4
-1/3S
Ab 758.25 -55.8
Eb+31.5 -4
+2 3/8P
A 884.5 0
Bb+26.25 -4
-1/3S
Bb 1010.5 +14.5
F+21 -4
-1/3S
B 1074 -22
c+15.75 -4
-1/3S
c 1200 0


Lucy Tuning (From John Harrison's 31 note Mean Tone)

CIRCLE
OF FIFTHS
TEMPERING CHROMATIC
SCALE
INTERVALS
IN CENTS
ERRORS
COMP WITH
JUST SCALE
C+13.5 0 C 0 0
G+9 -6.5
-13/47P
C# 68.5 -43.5
D+4.5 -6.5
-13/47P
D 191 -13
A+0 -6.5
-13/47P
Eb 313.5 -2.5
E-4.5 -6.5
-13/47P
E 382 -4
B-9 -6.5
-13/47P
F 504.5 +6.5
F#-13.5 -6.5
-13/47P
F# 573 -17
C#-18 -6.5
-13/47P
G 695.5 -6.5
Ab-22.5 -6.5
-13/47P
Ab 764 -50
Eb+27 -6.5
+2P
A 886.5 +2.5
Bb+22.5 -6.5
-13/47P
Bb 1009 +13
F+18 -6.5
-13/47P
B 1077.5 -10.5
c+13.5 -6.5
-13/47P
c 1200 0


Gioseffo Zarlino's 2/7 Comma Mean Tone (1558)

CIRCLE
OF FIFTHS
TEMPERING CHROMATIC
SCALE
INTERVALS
IN CENTS
ERRORS
COMP WITH
JUST SCALE
C+12.3 0 C 0 0
G+8.2 -6.1
-2/7S
C# 71.3 -40.4
D+4.1 -6.1
-2/7S
D 191.8 -12.2
A+0 -6.1
-2/7S
Eb 312.3 -3.3
E-4.1 -6.1
-2/7S
E 383.6 -2.4
B-8.2 -6.1
-2/7S
F 504.1 +6.1
F#-12.3 -6.1
-2/7S
F# 575.4 -14.6
C#-16.4 -6.1
-2/7S
G 695.9 -6.1
Ab-20.5 -6.1
-2/7S
Ab 767.2 -46.5
Eb+24.6 +43.1
+1 3/4P
A 887.7 +3.3
Bb+20.5 -6.1
-2/7S
Bb 1008.2 +12.1
F+16.4 -6.1
-2/7S
B 1079.5 -8.5
c+12.3 -4.4
-2/7S
c 1200 0


Pietro Aaron's 1/4 Comma Mean Tone (1523)

CIRCLE
OF FIFTHS
TEMPERING CHROMATIC
SCALE
INTERVALS
IN CENTS
ERRORS
COMP WITH
JUST SCALE
C+10.5 0 C 0 0
G+7 -5.4
-1/4S
C# 76 -36
D+3.5 -5.4
-1/4S
D 193 -11
A+0 -5.4
-1/4S
Eb 310 -6
E-3.5 -5.4
-1/4S
E 386 0
B-7 -5.4
-1/4S
F 503.5 +5.5
F#-10.5 -5.4
-1/4S
F# 586 -4
C#-14 -5.4
-1/4S
G 696.5 -4
G#-17.5 -5.4
-1/4S
Ab 781 -32
Eb+21 +36.5
+1 1/2P
A 889.5 +9
Bb+17.5 -5.4
-1/4S
Bb 1006 +9
F+14 -5.4
-1/4S
B 1083 0
c+10.5 -5.4
-1/4S
c 1200 0


2/9 Comma Mean Tone

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
-2/9S
C# 84 -28
D+2.4 -4.4
-2/9S
D 195 -9
A+0 -4.4
-2/9S
Eb 307 -9
E-2.4 -4.4
-2/9S
E 391 +5
B-4.8 -4.4
-2/9S
F 502 +4
F#-7.2 -4.4
-2/9S
F# 586 -4
C#-9.6 -4.4
-2/9S
G 698 -4
G#-12 -4.4
-2/9S
Ab 781 -32
Eb+14.4 +24
+1 1/4P
A 893 +9
Bb+12 -4.4
-2/9S
Bb 1005 +9
F+9.6 -4.4
-2/9S
B 1088 0
c+7.2 -4.4
-2/9S
c 1200 0


1/5 Comma Mean Tone

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 307 -9
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#-12 -4.4
-1/5S
Ab 781 -32
Eb+14.4 +24
+1P
A 893 +9
Bb+12 -4.4
-1/5S
Bb 1005 +9
F+9.6 -4.4
-1/5S
B 1088 0
c+7.2 -4.4
-1/5S
c 1200 0


1/6th Comma Mean Tone (Silbermann)

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 306 -10
E-2 -4
-1/6P
E 392 +6
B-4 -4
-1/6P
F 502 +4
F#-6 -4
-1/6P
F# 588 -2
C#-8 -4
-1/6P
G 698 -4
G#-10 -4
-1/6P
Ab 784 -30
Eb+12 -4
+5/6P
A 894 +10
Bb+10 -4
-1/6P
Bb 1004 +8
F+8 -4
-1/6P
B 1090 +2
c+6 -4
-1/6P
c 1200 0


John Marsh's 4/25ths Comma mean Tone (1809)

CIRCLE
OF FIFTHS
TEMPERING CHROMATIC
SCALE
INTERVALS
IN CENTS
ERRORS
COMP WITH
JUST SCALE
C+4.5 0 C 0 0
G+3 -3.5
-4/25S
C# 89.5 -22.5
D+1.5 -3.5
-4/25S
D 197 -7
A+0 -3.5
-4/25S
Eb 304.5 -11.5
E-1.5 -3.5
-4/25S
E 394 +8
B-3 -3.5
-4/25S
F 501.5 +3.5
F#-4.5 -3.5
-4/25S
F# 591 +1
C#-6 -4
-4/25S
G 698.5 -3.5
G#-7.5 -3.5
-4/25S
Ab 788 -26
Eb+9 +14.5
+29/48P
A 895.5 +11.5
Bb+7.5 -3.5
-4/25S
Bb 1003 +7
F+6 -3.5
-4/25S
B 1092.5 +4.5
c+4.5 -3.5
-4/25S
c 1200 0