History of Intervals

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Summary of what I have learned about tones:

tonos is greek for "stretch" or "tension" according to midicode.com/tunings

Assume that the basic note is an open string at normal length.

an "octave" interval is obtained by reducing a string to 1/2 length, therefore an octave is a 2 to 1 ratio

a "fifth" interval is obtained by reducing a string to 2/3 length therefore a fifth is a 3 to 2 ratio

a "fourth" interval is obtained by reducing a string to 3/4 length therefore a fourth is a 4 to 3 ratio

a "tone" interval on a string of the original size is obtained by subtracting the length of a fourth interval from the length of a fifth interval
The ratios of these most common intervals are:

2/1 = octave
3/2 = fifth
4/3 = fourth


The octave, fifth and fourth intervals are regarded as the most consonant.

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