225/128: Difference between revisions

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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]].
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.


== See also ==
== See also ==

Latest revision as of 20:34, 29 October 2024

Interval information
Ratio 225/128
Factorization 2-7 × 32 × 52
Monzo [-7 2 2⟩
Size in cents 976.5374¢
Names marvel five-limit harmonic seventh,
Neapolitan augmented sixth
Color name Lyy6, layoyo 6th
FJS name [math]\displaystyle{ \text{A6}^{5,5} }[/math]
Special properties reduced,
reduced harmonic
Tenney height (log2 nd) 14.8138
Weil height (log2 max(n, d)) 15.6276
Wilson height (sopfr(nd)) 30

[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.

See also

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