169/168

From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Ratio 169/168
Factorization 2-3 × 3-1 × 7-1 × 132
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 (log2 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.