Commas in 53-eq
Once you get deeper into 53-eq tuning, you will discover that the small intervals between the 53 steps take you much closer to just-intonation pitches of all kinds. The 12-eq commas we discussed above are like gross puns. The commas that are yet to be discovered in 53-eq are like subtle layers of meaning in a Shakespeare play by comparison. There is one set of commas that are very effective in 53-eq and is even occasionally evoked in 12-eq: the septimal commas. There are several septimal commas we will talk about in Chapter 14, but for now, an example of a true 53-eq comma is that of the 225:224 septimal/”ga-ga” (seventh harmonic vs. the spine two just thirds up from your tonic). From C to its seventh harmonic is 969 cents. The nearest 53-eq note is A2#/B1b, which is 973.5 cents, or 4 ½ cents sharp. That’s not perfect but pretty good, compared to the 12-eq Bb which is 1000 cents, or 39 cents sharp of the seventh harmonic. The 225/128 ratio created between C and the pure just A2# (two fifths up and two just thirds up) is 977 cents, about eight cents higher than the pure harmonic seventh. So the 53-eq A2# is right in the middle: 969 (7th harmonic), 973.5 (53-eq A2#/B1b), 977 (pure A2#). This means you can start with a septimal seventh going in and then change its harmonic usage to the ga-ga A2# going out for some extremely effective chord progressions. But, I tip my hand. In Chapter 14 I promise to make you a septimal magician with hundreds of new possible chord progressions exploiting this and other septimal commas. But this general principle applies to all commas in all tuning systems: to use commas to create harmonic ambiguity, you can always enter a note and give it a context where it has one harmonic meaning, and then leave that same pitch while giving it an entirely different harmonic meaning based on what follows.
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