127834/1
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| Ratio | 127834/1 |
| Subgroup monzo | 2.7.23.397 [1 1 1 1⟩ |
| Size in cents | 20356.694¢ |
| Names | 127834th harmonic, 29-wood major 119th |
| Color name | c16397o23oz9 |
| FJS name | [math]\text{P120}^{7,23,397}[/math] |
| Special properties | harmonic |
| Tenney height (log2 nd) | 16.9639 |
| Weil height (log2 max(n, d)) | 33.9278 |
| Wilson height (sopfr(nd)) | 429 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~0 bits |
| open this interval in xen-calc | |
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.