User Manual

Appendix
HD-300 Owner’s Manual
39
 Equal and Pure Temperaments
 Preset Temperaments Cent List (for C MAJOR/a minor)
 Other Temperaments Cent List (for reference)
The following temperaments can be set in the individual temperament mode.
Temperaments
Temperament Description
Equal Temperament that divides one octave into 12 equal steps. The frequency ratio between neighboring notes is
(= 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.
Display Temper-
ament
Type
Difference from the equal temperament (cent)
C D
b
D E
b
E F F
b
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 C
Pure
Major (C)
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 a
Pure
Minor (a)
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 Difference from the equal temperament (cent): When the root key is C
C D
b
D E
b
E F F
b
G A
b
A B
b
B
Meantone
0 -24.0 -6.8 10.3 -13.7 3.4 -20.5 -3.4 -27.4 -10.3 6.8 -17.1
Pythagoras
0 13.7 3.9 -5.9 7.8 -2.0 11.7 2 15.6 5.9 -3.9 9.8
Werkmeister I 3rd
Variant
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 -9.8 -6.8 -5.9 -13.7 -2.0 -9.8 -3.4 -7.8 -10.3 -3.9 -11.7
Valloti & Young
0 -9.8 -3.9 -5.9 -7.8 -2.0 -11.7 -2.0 -7.8 -5.9 -3.9 -9.8
2
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