127834/1
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29-wood major 119th
(Shannon, [math]\sqrt{nd}[/math])
127834/1, the 127834th harmonic, or 29-wood supermajor 119th, is 16 octaves above 63917/32768. It is a part of 397-limit harmony, the 78th prime number.
The number appears in a sequence of fractional part of [math]1.5^n[/math] decreasing monotonically to zero, meaning the sequence offers progressively closer approximations to repeated stacks of 3/2. Indeed, this interval is close to a stack of perfect fifths by two parameters - both its fractional part decreases progressively, and it is also better than all the [math]1.5^k[/math] for [math]0\lt k\lt 29[/math]. The difference between the stack of 29 perfect fifths and 127834/1, which is the 68630377364883/68630356164608 comma is 0.534 millicents, or 1 in 2.24 million parts of an octave.
Equal divisions of the 127834/1
For practical purposes, 127834/1 is too complex and too large to be used as an equivalence interval, being over 100 times larger than the human hearing range.
- 29ed127834 - corresponds to Pythagorean tuning
- 261ed127834 - equivalent to Carlos Alpha
- 348ed127834 - equivalent to 12edo
Trivia
Prime numbers 23 and 397, having indices 9 and 78, are 69 prime numbers apart. Nice.