1536/1

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.

Interval information

Ratio	1536/1
Factorization	29 × 3
Monzo	[9 1⟩
Size in cents	12701.955¢
Name	1536th harmonic
FJS name	[math]\text{P75}[/math]
Special properties	harmonic
Tenney height (log2 nd)	10.585
Weil height (log2 max(n, d))	21.1699
Wilson height (sopfr(nd))	21
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~0 bits
open this interval in xen-calc

1536/1, the 1536th harmonic, is the harmonic past 1535/1 and before 1537/1. It is about ten octaves and seven semitones in size. It is the largest interval allowed by MIDI without pitch bends, assume the note names follow Pythagorean tuning. The only occurrence of this interval in MIDI spans note 0 (C-1) to 127 (G9). If 12edo is used instead, such an interval will have a frequency ratio of about 1534.266….