Ex. 3.
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A comparison of the Harmonic Series (
red box
) with a 12TET/piano (
gray box
) tuning.
Harmonic No.
1
2
3
4
5
6
7
8
9
10
11
12
Pitch name
C
2
C
3
G
3
C
4
E
4
G
4
(Bb
4
)
C
5
D
5
E
5
(F#
5
)
G
5
12TET freq. (Hz.)
Based on A
4
=440 Hz.
65.41
130.81
196.00
261.63
329.63
392.00
466.16
523.25
587.33
659.26
739.99
783.99
Difference in cents
0
0
+2
0
-14
+2
-31
0
+4
-14
-49
-2
Harmonic Series freq. (Hz.)
Based on C
2
=65.41 Hz.
65.41
130.82
196.23
261.64
327.05
392.46
457.87
523.28
588.69
654.1
719.51
784.92
C
4
= middle C - All frequency calculations are to the nearest 1/100 Hz.
The discrepancy is indicated in +/- cents and is intended to show how much the
Harmonic Series (natural intervals) differ from the 12TET intervals we use on a piano modern piano.
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