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Interval information
Ratio 12/1
Factorization 22 × 3
Monzo [2 1
Size in cents 4301.955¢
Name 12th harmonic
Color name c3w5, tricowa 5th
FJS name [math]\text{P26}[/math]
Special properties harmonic
Tenney height (log2 nd) 3.58496
Weil height (log2 max(n, d)) 7.16993
Wilson height (sopfr (nd)) 7
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~2.45478 bits

[sound info]
open this interval in xen-calc

12/1, the 12th harmonic, is the harmonic past 11/1 and before 13/1. It is three octaves above 3/2. Since 12 is a highly composite number, this harmonic can be approached in various ways of stacking, all the components being Pythagorean intervals. For example, stacking with octaves, fifths and fourths gives a consonant but simplistic skeleton across multiple registers: 1-2-3-4-6-12, on which higher-limit intervals can be added to enrich its colors.

See also