If we want to have a more finely tuned choir, we need to have an understanding of how intervals might sound. We are so entrenched in a modern system of tuning, i.e., equal temperament, that many of us are not even aware that there are other tuning possibilities.
Let’s compare Equal Temperament with its forefathers of tuning, Just and Pythagorean. (Note: In equal temperament a semitone is divided into 100 cents such that C à C# = 100 cents, C# à D = 100 cents, and so on.)
|
System
|
C
|
D
|
E
|
F
|
G
|
A
|
B
|
C
|
|
Just
|
0
|
204
|
386
|
498
|
702
|
884
|
1088
|
1200
|
|
Equal T
|
0
|
200
|
400
|
500
|
700
|
900
|
1100
|
1200
|
|
Pyth.
|
0
|
204
|
408
|
498
|
702
|
906
|
1110
|
1200
|
Since Pythagorean tuning is built on a system of perfectly tuned fifths, we should use that value (702) as our guide. Therefore, a true P5 should ring slightly higher than a P5 played on a piano.
For the fourth scale degree, the subdominant or fifth below the tonic, we arrive at a cent value of 498 by subtracting a P5 (702) from an octave (1200).
The cent value for the second scale degree (204) comes from stacking two fifths on top of one another.
C à G à D = 1404 cents
1404 – 1200 = 204
Since just intonation is built on the concept of really pure thirds, we use that system to find a truer value for intervals of a third. In equal temperament the major third (C à E) is 400 cents, but in just intonation the same major third is only 386 cents. A true M3, a just M3, is actually lower than we might imagine.
Let’s review.
|
Scale Degree
|
ET Cent Value
|
Target Cent Value
|
Adjustment
|
|
5
|
700
|
702
|
Slightly Higher
|
|
4
|
500
|
498
|
Slightly Lower
|
|
2
|
200
|
204
|
Slightly Higher
|
|
3
|
400
|
386
|
Fairly Lower
|
Bart Brush says