Yamaha HD-200 HD-200 Owners Manual - Page 25

Pitch ratio and cent values for the main pitches, Preset temperament cent list for C Major/a minor

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English Pitch ratio and cent values for the main pitches Pitch Octave Pure 5th 4th Major 3rd Minor 3rd Large Interval Whole Tone Small Interval Whole Tone Diatonic Scale Semi-tone Chromatic Scale Semi-tone Meantone Syntonic-Comma (S.C.) Pythagorean Comma (P.C.) Schisma Equal Semi-tone Pitch ratio Cent value Comments 2 3/2 4/3 5/4 6/5 9/8 10/9 16/15 25/24 5/2 81/80 12 2 1200.00 701.955 498.045 386.314 315.641 203.910 182.404 111.731 70.672 193.157 21.506 23.460 1.954 100.0 Difference between the 4th and major 3rd Difference between the major 3rd and minor 3rd Average between large and small interval whole tones Difference between large and small interval whole tones Difference between the pure 5th x12 and 7 octaves Difference between P.C. and S.C. Preset temperament cent list (for C Major/a minor) Display Temperament type Equal Equal Pure (Major) Pure Major pure (minor) Pure Minor Individual cent value (cent) C Db D Eb E F F# G Ab A Bb B 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -29.3 3.9 15.6 -13.7 -2.0 -31.3 2.0 -27.4 -15.6 17.6 -11.7 15.6 -13.7 -2.0 31.3 2.0 13.7 -15.6 17.6 -11.7 0.0 33.2 3.9 Reference The following temperaments are occasionally used. Temperament type Meatone Temperament Pythagoras Temperament Werkmeister I 3rd Variant Kirnberger III Vallotti & Young Individual cent value (cent) C Db D Eb E F F# G Ab A Bb B 0.0 -24.0 -6.8 10.3 -13.7 3.4 -20.5 -3.4 -27.4 -10.3 6.8 -17.1 0.0 13.7 3.9 -5.9 7.8 -2.0 11.7 2.0 15.6 5.9 -3.9 9.8 0.0 -9.8 -7.8 -5.9 -9.8 -2.0 -11.7 -3.9 -7.8 -11.7 -3.9 -7.8 0.0 -9.8 -6.8 -5.9 -13.7 -2.0 -9.8 -3.4 -7.8 -10.3 -3.9 -11.7 0.0 -9.8 -3.9 -5.9 -7.8 -2.0 -11.7 -2.0 -7.8 -5.9 -3.9 -9.8 20

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20
English
Pitch ratio and cent values for the main pitches
Preset temperament cent list (for C Major/a minor)
Reference
The following temperaments are occasionally used.
Pitch
Pitch ratio
Cent value
Comments
Octave
2
1200.00
Pure 5
th
3/2
701.955
4
th
4/3
498.045
Major 3
rd
5/4
386.314
Minor 3
rd
6/5
315.641
Large Interval Whole Tone
9/8
203.910
Small Interval Whole Tone
10/9
182.404
Diatonic Scale Semi-tone
16/15
111.731
Difference between the 4
th
and major 3
rd
Chromatic Scale Semi-tone
25/24
70.672
Difference between the major 3
rd
and minor 3
rd
Meantone
193.157
Average between large and small interval whole tones
Syntonic-Comma (S.C.)
81/80
21.506
Difference between large and small interval whole tones
Pythagorean Comma (P.C.)
23.460
Difference between the pure 5
th
x12 and 7 octaves
Schisma
1.954
Difference between P.C. and S.C.
Equal Semi-tone
100.0
Display
Temperament
type
Individual cent value (cent)
C
D
b
D
E
b
E
F
F
#
G
A
b
A
B
b
B
Equal
Equal
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Pure (Major)
Pure Major
0.0
-29.3
3.9
15.6
-13.7
-2.0
-31.3
2.0
-27.4
-15.6
17.6
-11.7
pure (minor)
Pure Minor
15.6
-13.7
-2.0
31.3
2.0
13.7
-15.6
17.6
-11.7
0.0
33.2
3.9
Temperament type
Individual cent value (cent)
C
D
b
D
E
b
E
F
F
#
G
A
b
A
B
b
B
Meatone Temperament
0.0
-24.0
-6.8
10.3
-13.7
3.4
-20.5
-3.4
-27.4
-10.3
6.8
-17.1
Pythagoras Temperament
0.0
13.7
3.9
-5.9
7.8
-2.0
11.7
2.0
15.6
5.9
-3.9
9.8
Werkmeister I 3rd Variant
0.0
-9.8
-7.8
-5.9
-9.8
-2.0
-11.7
-3.9
-7.8
-11.7
-3.9
-7.8
Kirnberger III
0.0
-9.8
-6.8
-5.9
-13.7
-2.0
-9.8
-3.4
-7.8
-10.3
-3.9
-11.7
Vallotti & Young
0.0
-9.8
-3.9
-5.9
-7.8
-2.0
-11.7
-2.0
-7.8
-5.9
-3.9
-9.8
5/2
12
2