COMMA. - The ratio of 80:81 - not an interval, but a fraction of an interval. [Scientific Basis and Build of Music, page 25]
As Ramsay points out a scale of tones beginning on a given fundamental can progressively evolve to higher frequencies. Yet when counting down beginning with the highest tone the counting does not arrive at the same fundamental. The difference between them is called a Comma or Pythagorean Comma with an interval ratio of 81:80 which is a very slight difference but considered very discordant.
Pythagorean Komma 81:80
The small interval between a major and a minor tone, that is whose ratio is 8:9 and one whose ratio is 9:10. The ratio of a comma is therefore 80:81. A Pythagorean comma is the difference between the note produced by taking 7 octaves upwards and 12 fifths.
"That is a complex ratio of 531441:524288 equal to 1.013643 or about 23.46 cents above the starting tone." [INTERFERENCE - A Grand Scientific Musical Theory, Richard Merrick, 2011, Third Edition]
See Also
Apotome Minor
Apotome
Diesis
Forty-seventh Proposition of Pythagoras
Golden Verses of Pythagoras
Interval
Pythagoras Kepler School
Pythagorean Comma
Pythagorean Komma
Pythagorean Tuning
Ramsay - The New Way of Reckoning a Pendulum Oscillation
comma