3/1

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
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The tritave (interval ratio 3/1) is the interval between a fundamental tone and its 3rd harmonic. 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.

The tritave is one octave above 3/2, the perfect fifth. Therefore, in a diatonic context, 3/1 is also called the perfect twelfth.

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)
• No-twos 31-limit – non-octave 31-limit system containing neither 2 nor primes higher than 31
• Tritave complement – the analogue for octave complement