Douglas Blumeyer's RTT How-To: Difference between revisions

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=== tuning & pure octaves ===

Now, because the octave is the interval of equivalence in terms of human pitch perception, it’s a major convenience to enforce pure octaves, and so many people prefer the first term to be exact. In fact, I’ll bet many readers have never even heard of or imagined impure octaves, if my own anecdotal experience is any indicator; the idea that I could detune octaves to optimize tunings came rather late to me.

Now, because the octave is the [[interval of equivalence]] in terms of human pitch perception, it’s a major convenience to enforce pure octaves, and so many people prefer the first term to be exact. In fact, I’ll bet many readers have never even heard of or imagined impure octaves, if my own anecdotal experience is any indicator; the idea that I could detune octaves to optimize tunings came rather late to me.

Well, you’ll notice that in the previous section, we did approximate the octave, using 1.998 instead of 2. But another thing {{val|12 19 28}} has going for it is that it excels at approximating 5-limit JI even if we constrain ourselves to pure octaves, locking g¹² to exactly 2: (¹²√2)¹⁹ ≈ 2.997 and (¹²√2)²⁸ ≈ 5.040. You can see that actually the approximation of 3 is even better here, marginally; it’s the damage to 5 which is lamentable.

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 === tuning & pure octaves ===
-Now, because the octave is the interval of equivalence in terms of human pitch perception, it’s a major convenience to enforce pure octaves, and so many people prefer the first term to be exact. In fact, I’ll bet many readers have never even heard of or imagined impure octaves, if my own anecdotal experience is any indicator; the idea that I could detune octaves to optimize tunings came rather late to me.
+Now, because the octave is the [[interval of equivalence]] in terms of human pitch perception, it’s a major convenience to enforce pure octaves, and so many people prefer the first term to be exact. In fact, I’ll bet many readers have never even heard of or imagined impure octaves, if my own anecdotal experience is any indicator; the idea that I could detune octaves to optimize tunings came rather late to me.
 Well, you’ll notice that in the previous section, we did approximate the octave, using 1.998 instead of 2. But another thing {{val|12 19 28}} has going for it is that it excels at approximating 5-limit JI even if we constrain ourselves to pure octaves, locking g¹² to exactly 2: (¹²√2)¹⁹ ≈ 2.997 and (¹²√2)²⁸ ≈ 5.040. You can see that actually the approximation of 3 is even better here, marginally; it’s the damage to 5 which is lamentable.