Apple Logic Express 8 User Manual

Page 968

968

Chapter 39

Project Settings and Preferences

For the rest of the scale: Tune the next fifth up: 150 x 3 = 450. Divide this by 2 to get
225 (which is more than an octave above the starting pitch, so you need to drop it
another octave to 112.5).

As you can see from the table above, there’s a problem!

Although the laws of physics dictate that the octave above C (100 Hz) is C (at 200 Hz),
the practical exercise of a (C to C) circle of perfectly tuned fifths results in a C at
202.7287 Hz. This is not a mathematical error. If this was a real instrument, the results
would be clear.

To work around the problem, you need to choose between the following options:

Â Each fifth is perfectly tuned, with octaves out of tune.
Â Perfectly tuned octaves with the final fifth (F to C) out of tune.

It goes without saying that detuned octaves are more noticeable to the ears.

Note

Frequency (Hz)

Notes

100

x 1.5 divided by 2.

106.7871