169/168
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Ratio | 169/168 |
Factorization | 2^{-3} × 3^{-1} × 7^{-1} × 13^{2} |
Monzo | [-3 -1 0 -1 0 2⟩ |
Size in cents | 10.274416¢ |
Name(s) | missing^{ ? } |
FJS name | [math]\text{d1}^{13,13}_{7}[/math] |
Special properties | square superparticular, reduced |
Tenney height (log_{2} n⋅d) | 14.7932 |
Weil height (max(n, d)) | 169 |
Benedetti height (n⋅d) | 28392 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.82268 bits |
open this interval in xen-calc |
169/168, is a superparticular ratio measuring about 10.3 cents. It is the difference between 13/12 and 14/13 semitones, and also between 224/169 and 4/3 perfect fourths.
Theory
169/168 is tempered out in a 13-0-2-8 chord of 19edo, which is a symmetrical relative to itself - it is the same when inverted. Such a chord consists of a stack of 16/13 - 13/12 - 16/13, which also intertwine two 4/3s between the 1st and 3rd, and 2nd and 4th notes. Tempering out 169/168 means that 14/13 can appear in this chord as well as 13/12.