Ancient Greek Tuning Theory

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Three Common Tuning Systems in Algebraic Shorthand

A “cent” (¢) is 1/1,200th of an octave,
the minimal theoretic unit of piano tuning.

GreekTuning

Ditonic Comma – 12 Fifths minus 7 Octaves
Schisma – 8 Fifths minus 5 Octaves plus 1 Major Third
Syntonic Comma – 4 Fifths minus 2 Octaves minus 1 Major Third

Syntonic Comma
+ Schisma
= Ditonic Comma

Octaves – VIII (12 half steps) – 2:1
Fifths – V (7 half steps) – 3:2
[Fourths – IV (5 half steps) – 4:3]
Major Thirds – III (4 half steps) – 5:4