127834/1: Difference between revisions
Created page with "{{Infobox Interval | Ratio = 127834/1 | Monzo = 2 0 0 7 0<sup>4</sup> 23 0<sup>68</sup> 397 | Cents = 20356.6945 | Name = 127834th harmonic, 29-wood major 119th }} 127834/1, t..." |
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Revision as of 09:45, 28 December 2021
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29-wood major 119th
127834/1, the 127834th harmonic, or 29-wood major 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]\displaystyle{ 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]\displaystyle{ 1.5^k }[/math] for [math]\displaystyle{ 0\lt k\lt 29 }[/math]. The difference between the two is 0.534 millicents, or 1 in 2.24 million parts of an octave.
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.
Trivia
Prime numbers 23 and 397, having indices 9 and 78, are 69 prime numbers apart. Nice.