Scale, Equal temperament, Pure major/pure minor – Yamaha PORTATONE PSR-1000 User Manual
Page 136: Pythagorean, Mean-tone, Werckmeister/kirnberger, Arabic
Making Global and Other Important Settings — Function
PSR-2000/1000
136
Scale
■ Equal Temperament
The pitch range of each octave is divided equally into twelve parts, with each half-step evenly spaced in pitch. This
is the most commonly used tuning in music today.
■ Pure Major/Pure Minor
These tunings preserve the pure mathematical intervals of each scale, especially for triad chords (root, third, fifth).
You can hear this best in actual vocal harmonies — such as choirs and acapella singing.
■ Pythagorean
This scale was devised by the famous Greek philosopher and is created from a series of perfect fifths, which are
collapsed into a single octave. The 3rd in this tuning are slightly unstable, but the 4th and 5th are beautiful and
suitable for some leads.
■ Mean-Tone
This scale was created as an improvement on the Pythagorean scale, by making the major third interval more “in
tune.” It was especially popular from the 16th century to the 18th century. Handel, among others, used this scale.
■ Werckmeister/Kirnberger
This composite scale combines the Werckmeister and Kirnberger systems, which were themselves improvements on
the mean-tone and Pythagorean scales. The main feature of this scale is that each key has its own unique character.
The scale was used extensively during the time of Bach and Beethoven, and even now it is often used when
performing period music on the harpsichord.
■ Arabic
Use these tunings when playing Arabic music.
Pitch settings for each scale (in cents; example scale of C)
C
C
D
E
E
F
F
G
A
A
B
B
Equal Temperament
0
.0
0
.0
0
.0
0
.0
0
.0
0
.0
0
.0
0
.0
0
.0
0
.0
0
.0
0
.0
PureMajor
0
.0
-29.7
3.9
15.6
-14.1
-2.3
-9.4
2.3
-27.3
-15.6
18.0
-11.7
PuoreMinor
0
.0
33.6
3.9
15.6
-14.1
-2.3
31.3
2.3
14.1
-15.6
18.0
-11.7
Pythagorean
0
.0
14.1
3.9
-6.3
7.8
-2.3
11.7
2.3
15.6
6.3
-3.9
10.2
Mean-Tone
0
.0
-24.2
-7.0
10.2
-14.1
3.1
-20.3
-3.1
-27.3
-10.2
7.0
-17.2
Werckmeister
0
.0
-10.2
-7.8
-6.3
-10.2
-2.3
-11.7
-3.9
-7.8
-11.7
-3.9
-7.8
Kirnberger
0
.0
-10.2
-7.0
-6.3
-14.1
-2.3
-10.2
-3.1
-7.8
-10.2
-3.9
-11.7
Arabic1
0
.0
0
-50
.0
0
.0
0
.0
0
.0
0
.0
0
.0
0
.0
-50
.0
0
.0
0
.0
Arabic2
0
.0
0
0
.0
0
.0
-50
.0
0
.0
0
.0
0
.0
0
.0
0
.0
0
.0
-50
.0