225/128: Difference between revisions

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'''225/128'''
{{Infobox Interval
|-7 2 2>
| Name = diptolemaic augmented sixth, Neapolitan augmented sixth, marvel 5-limit harmonic seventh
| Color name = Lyy6, layoyo 6th
| Sound = jid_225_128_pluck_adu_dr220.mp3
}}


976.5374 cents
'''225/128''', the '''diptolemaic augmented sixth''' or '''Neapolitan augmented sixth''', is the interval between the [[5-limit]] minor second, [[16/15]], and the major seventh, [[15/8]]. It is flat of the [[59049/32768|Pythagorean augmented sixth]] by two syntonic commas, hence the first name, whereas the second name comes on account of this interval occurring in precisely this capacity in just Neapolitan scales.  


[[File:jid_225_128_pluck_adu_dr220.mp3]] [[:File:jid_225_128_pluck_adu_dr220.mp3|sound sample]]
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. As such, it can also be called the '''marvel 5-limit harmonic seventh'''.


The '''marvel five-limit harmonic seventh''' is the interval '''225/128'''.  It is the interval between the [[5-limit|5-limit]] minor second, [[16/15|16/15]], and the major seventh, [[15/8|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|7/4]], and so tempering out 225/224, which is [[Marvel|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|8/7]] and two major seconds into [[7/6|7/6]].
== See also ==
* [[256/225]] – its [[octave complement]]
* [[Gallery of just intervals]]
* [[:File:Ji-225-128-csound-foscil-220hz.mp3]] – another sound example
 
[[Category:Sixth]]
[[Category:Augmented sixth]]

Latest revision as of 09:01, 18 January 2026

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

[sound info]
Open this interval in xen-calc

225/128, the diptolemaic augmented sixth or Neapolitan augmented sixth, is the interval between the 5-limit minor second, 16/15, and the major seventh, 15/8. It is flat of the Pythagorean augmented sixth by two syntonic commas, hence the first name, whereas the second name comes on account of this interval occurring in precisely this capacity in just Neapolitan scales.

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. As such, it can also be called the marvel 5-limit harmonic seventh.

See also

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