About tuning – Apple Logic Pro 8 User Manual

Page 945

Chapter 40

Project Settings and Preferences

945

About Tuning

Before looking at the Tuning settings, some basics and background information.

About Alternate Tunings

The twelve tone scale used in Western music is a development that took centuries.
Hidden in-between these twelve notes are a number of other microtones—different
frequency intervals between tones.

To explain, by looking at the harmonic series: Imagine that you have a starting (or
fundamental) frequency of 100 Hz (100 vibrations per second). The first harmonic is
double that, or 200 Hz. The second harmonic is found at 300 Hz, the third at 400 Hz,
and so on. Musically speaking, when the frequency doubles, pitch increases by exactly
one octave (in the 12 tone system). The second harmonic (300 Hz) is exactly one
octave—and a pure fifth—higher than the fundamental frequency (100 Hz).

From this, you could assume that tuning an instrument so that each fifth is pure would
be the way to go, right? In doing so, you would expect a perfectly tuned scale, as you
worked your way from C though to the C above or below. Close, but no cigar.

To simplify this example: Imagine that you are tuning an instrument, beginning with a
note called C at a frequency of 100 Hz (a real C would be closer to 130 Hz). The first fifth
would be tuned by adjusting the pitch until a completely clear tone is produced, with
no beats (beats are cyclic modulations in the tone). This will result in a G at exactly
150 Hz. This is derived from this calculation:

Â The fundamental (100 Hz) x 3 (= 300 Hz for the second harmonic).
Â Divided by 2 (to drop it back into the same octave as your starting pitch).

This frequency relationship is often expressed as a ratio of 3:2.

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).

Note

Frequency (Hz)

Notes

100

x 1.5 divided by 2.

106.7871