3/1

The tritave, 3rd harmonic, 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	tritave, 3rd harmonic, 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]
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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).

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