3/1

The 3rd harmonic, tritave, 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

Ratio	3/1
Factorization	3
Monzo	[0 1⟩
Size in cents	1901.955¢
Names	3rd harmonic, tritave, perfect twelfth
Color name	w12, wa 12th
FJS name	[math]\displaystyle{ \text{P12} }[/math]
Special properties	harmonic, prime harmonic
Tenney norm (log2 nd)	1.58496
Weil norm (log2 max(n, d))	3.16993
Wilson norm (sopfr(nd))	3
[sound info]
Open this interval in xen-calc

Etymology

The term tritave was coined by John Pierce. 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). It should be noted, however, that the oct in octave is not a prefix, but part of the single-morpheme word derived from Latin octavus ("eighth").

Since the enneatonic 4L 5s⟨3/1⟩ ("Lambda") scale is the BP substitute for the diatonic scale, the term decade or decim (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