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Interval information
Ratio 225/128
Factorization 2-7 × 32 × 52
Monzo [-7 2 2
Size in cents 976.53743¢
Names marvel five-limit harmonic seventh,
Neapolitan augmented sixth
Color name Lyy6, layoyo 6th
FJS name [math]\text{A6}^{5,5}[/math]
Special properties reduced
Tenney height (log2 nd) 14.8138
Weil height (log2 max(n, d)) 15.6276
Wilson height (sopfr (nd)) 30
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.12647 bits

[sound info]
open this interval in xen-calc

The marvel five-limit harmonic seventh is the interval 225/128. It is the interval between the 5-limit minor second, 16/15, and the major seventh, 15/8, and, on account of this interval occurring in precisely this capacity in just Neapolitan scales, this interval can also be referred to as as the Neapolitan augmented sixth. It is a marvel comma, 225/224, sharp of the harmonic seventh, 7/4, and so tempering out 225/224, which is marvel temperament, equates the two. Marvel tempering is a useful method of tempering the 5-limit to include septimal harmony, making two minor seconds a supermajor second, 8/7 and two major seconds into 7/6.

See also