127834/1
This page presents a novelty topic. It features ideas which are less likely to find practical applications in xenharmonic music. It may contain numbers that are impractically large, exceedingly complex or chosen arbitrarily. Novelty topics are often developed by a single person or a small group. As such, this page may also feature idiosyncratic terms, notations or conceptual frameworks. |
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 | c^{16}397o23oz9 |
FJS name | [math]\text{P120}^{7,23,397}[/math] |
Special properties | harmonic |
Tenney height (log_{2} nd) | 16.9639 |
Weil height (log_{2} 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.