12/1
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Ratio | 12/1 |
Factorization | 2^{2} × 3 |
Monzo | [2 1⟩ |
Size in cents | 4301.955¢ |
Name | 12th harmonic |
Color name | c^{3}w5, tricowa 5th |
FJS name | [math]\text{P26}[/math] |
Special properties | harmonic |
Tenney height (log_{2} nd) | 3.58496 |
Weil height (log_{2} 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.