A Dictionary of Music and Musicians/Comma

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COMMA. A comma is a very minute interval of sound, the difference resulting from the process of tuning up by several steps from one note to another in two different ways. There are two commas.

1. The common comma is found by tuning up four perfect fifths from a fixed note, on the one hand, and two octaves and a major third on the other, which ostensibly produce the same note, thus—

{ \override Score.TimeSignature #'stencil = ##f \clef bass \cadenzaOn <g, c,>1 ~ <g, d> ~ <d a> ~ <a e'> s <c, c> ~ <c c'> ~ <c' e'> }

or by multiplying the number of the vibrations of the lowest note by ⅔ for each fifth, by 2 for each octave, and by 54 for the perfect third. The result in each case will be found to be different, and the vibrations of the two sounds are found by the latter process to be in the ratio of 80:81. The difference between the two is a comma.

2. The comma maxima, or Pythagorean comma, is the difference resulting from the process of tuning up twelve perfect fifths on the one hand, and the corresponding number of octaves on the other; or, by multiplying the number of vibrations of the lowest note by 3/2 for every fifth, and by 2 for every octave. The difference will appear in the vibration of the two notes thus obtained in the ratio of 524,288:551,441, [App. p.595 "531,441"] or nearly 80:81.0915.

Other commas may be found by analogous processes, but the above two are the only ones usually taken account of.