Ratio of the comma, Pythagorean Comma or Pythagorean Komma
Ramsay
And it is another very interesting fact that those numbers multiplied into each other always make 720, the number in the minor genesis which corresponds to 1 in the major; F1 being the generative root of the major, and B720 the generative top of the minor; so adjusted they place the two D's beside each other - D26 2/3 and D27 - and we see the comma of difference between these two numbers which are distinctive of the major and the minor; 26 2/3 x 3 = 80, and 27 x 3 = 81, and 80:81 is the ratio of the comma. This is the Ray and the Rah in which there lurks one of music's mysteries. Let him that is wise unravel it. It is symbolic of something in the spiritual realm of things; its full meaning is only found there. [Scientific Basis and Build of Music, page 88]
In the opening of the third measure the tune returns to its own key by striking the tonic. This case is a very simple illustration of how a composition will move with perfect naturalness in more keys than one, the keys so grow out of each other, and may either merely snatch a passing chord from a new key, or pass quite into it for a phrase or two, or for a whole measure, then return as naturally, either by a smooth and quiet or by a strongly contrasted turn, according to the chords between which the turn takes place. In such modulation there may or there may not be marked a #, ?, or ?, in the air itself; the note which Nature raises in the new key may occur in one of the other parts of the harmony. In Watchman it is A, the fourth, which is altered; from being ? it is made ?. The change which takes place in the sixth of the scale, which is C in Watchman, is only one comma, the ratio of 80 to 81, and it slips into the new key as if nothing had happened. No mark is placed to it, as the comma difference is never taken notice of, although it is really and regularly taking place, with all the precision of Nature, in every new key. It is, however, only the note which is altered four commas, which is marked by a #, ?, or ?, as the case may be. [Scientific Basis and Build of Music, page 94]
| Note | Frequency | Factors | Reduced |
| D27 | 80 | 2^4 * 5 | 2*2*2*2*5 |
| D26 2/3 | 81 | 3^4 | 3*3*3*3 |
See Also
comma
duality of D
Janus-faced center
Pythagorean Comma
Pythagorean Komma
Ramsay - The Two D's - The Rah and the Ray