3/1
The 3rd harmonic, tritave, triple, or perfect twelfth is the interval of frequency ratio 3/1. It is perhaps the most consonant interval after the octave. For this reason, it is used as an equave in some nonoctave systems, such as the Bohlen–Pierce scale.
| Interval information |
tritave,
triple,
perfect twelfth
prime harmonic
[sound info]
Etymology
The term tritave was coined by John Pierce[1]. It was derived from the word octave by replacing the perceived prefix octo- (eight, for the eighth degree of the diatonic scale) by tri- (three, for 3/1). However, the oct in octave is not a prefix, but part of the single-morpheme word derived from Latin octavus ("eighth"). In this sense, tritave is more of a contraction of tri- and octave than anything else. As such, the term usually refers to 3/1 as an interval of equivalence; in other contexts, it is more often called the perfect twelfth (after the 12th degree of the diatonic scale).
Triple is a proposed term which relates itself to the ancient Greek concept of multiples. It also fixes the problem of using part of the word octave.
Since the enneatonic 4L 5s⟨3/1⟩ ("Lambda") scale is the BP substitute for the diatonic scale, the term decade[2] or decim[citation needed] (tenth degree of the Lambda scale) has been proposed as an alternative to tritave, though decade almost always refers to ten times the frequency (10/1) in audio engineering.
See also
- EDT (equal divisions of the tritave/twelfth)
- No-twos 31-limit – non-octave 31-limit system containing neither 2 nor primes higher than 31
- Tritave complement – the analogue for octave complement