Tuning, Scales and Temperament Harmonic and Inharmonic ...
Tuning, Scales and Temperament Harmonic and Inharmonic ...
Tuning, Scales and Temperament Harmonic and Inharmonic ...
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scales<br />
http://www.anu.edu.au/ITA/ACAT/drw/PPofM/scales/scales3.html<br />
Construction of the Pythagorean Diatonic Scale<br />
The Pythagorean scale is developed from the interval of a perfect 5th.<br />
Step 1: Begin with an arbitrary tone of frequency represented by 1, <strong>and</strong> ascend in steps of perfect 5ths:<br />
if these were based on C4 the notes would be<br />
C4 G4 D5 A5 E6 B6<br />
Step 2: Reduce the ratios obtained in step 1 into the range of a single octave by descending from these<br />
notes in whole octave steps:<br />
Step 3: Arrange the notes obtained in step 2 in ascending order:<br />
Step 4: The above sequence of notes is missing one important note the one corresponding to a perfect<br />
4th from the beginning point. This can be obtained by descending from the beginning point by a perfect<br />
fifth (2/3) <strong>and</strong> then moving up one octave (2/3) x 2 = 4/3 = 1.3333.... Placing it in the ascending<br />
sequence as arranged in step 3, we have the following sequence:<br />
This is known as the Pythagorean diatonic scale. Examining the intervals between each step,<br />
We can see that the scale consists of the familiar major scale (where the whole step is 9/8 <strong>and</strong> the 1/2<br />
step is 256/243).<br />
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