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Temperaments
Equal and Pure Temperaments
Temperament
Equal
Temperament that divides one octave into 12 equal steps. The frequency ratio between neighboring notes is
12
2
(= 1.0594631).
Pure (Major)
The tuning preserves the pure mathematical intervals of the major scale, especially for the triad chords (in case of
the "C Major"; CEG, FAC, and GBD). Since this tuning includes the pure perfect 5th and pure major 3rd, both large
and small interval whole tones, and chromatic scale semi-tones, changing keys requires changing the pitch ratio of
every note in the scale, making it impractical for keyboard or fretted instruments.
Pure (minor)
Like the pure major, this tuning preserves the pure mathematical intervals of the minor scale (in case of "a minor";
ACE, DFA, EGB). Changing keys also requires changing the pitch of every note in the scale, making it impractical
for keyboard or fretted instruments.
Preset Temperaments Cent List (for C MAJOR/a minor)
Display
Temper-
ament
Type
C
Equal
Equal
0.0
Pure
Pure C
0.0
Major (C)
Pure
Pure a
15.6
Minor (a)
Other Temperaments Cent List (for reference)
The following temperaments can be set in the individual temperament mode.
Temperament
C
Meantone
0
Pythagoras
0
Werkmeister I 3rd
0
Variant
Kirnberger III
0
Valloti & Young
0
Difference from the equal temperament (cent)
b
b
D
D
E
E
0.0
0.0
0.0
0.0
-29.3
3.9
15.6
-13.7
-13.7
-2.0
31.3
2.0
Difference from the equal temperament (cent): When the root key is C
b
b
D
D
E
E
-24.0
-6.8
10.3
-13.7
13.7
3.9
-5.9
7.8
-9.8
-7.8
-5.9
-9.8
-9.8
-6.8
-5.9
-13.7
-9.8
-3.9
-5.9
-7.8
Description
b
F
F
G
A
0.0
0.0
0.0
0.0
-2.0
-31.3
2.0
-27.4
13.7
-15.6
17.6
-11.7
b
F
F
G
A
3.4
-20.5
-3.4
-27.4
-2.0
11.7
2
15.6
-2.0
-11.7
-3.9
-7.8
-2.0
-9.8
-3.4
-7.8
-2.0
-11.7
-2.0
-7.8
Appendix
b
b
A
B
B
0.0
0.0
0.0
-15.6
17.6
-11.7
0.0
33.2
3.9
b
b
A
B
B
-10.3
6.8
-17.1
5.9
-3.9
9.8
-11.7
-3.9
-7.8
-10.3
-3.9
-11.7
-5.9
-3.9
-9.8
HD-300 Owner's Manual
39
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