125/96: Difference between revisions

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125/96 is the pythagorean augmented third flattened by 3 syntonic commas, not sharpened
 
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{{Infobox Interval
{{Infobox Interval
| Name = classic augmented third
| Name = classic(al) augmented third, triptolemaic augmented third
| Color name = y<sup>3</sup>3, triyo 3rd
| Color name = y<sup>3</sup>3, triyo 3rd
}}
}}
'''125/96''', the '''classic augmented third''', is a [[5-limit]] just interval of about 457 [[cent]]s. It differs from the classic major third [[5/4]] by [[25/24]] and [[13/10]] by [[625/624]].
'''125/96''', the '''classic(al) augmented third''' or '''triptolemaic augmented third''', is a [[5-limit]] just interval of about 457 [[cent]]s. It differs from the classic major third [[5/4]] by [[25/24]] and from [[13/10]] by [[625/624]]. It is also the Pythagorean augmented third (177147/131072) flattened by three [[81/80|syntonic commas]], which lends itself to the term ''triptolemaic''.  


== See also ==
== See also ==
* [[192/125]] – its [[octave complement]]
* [[192/125]] – its [[octave complement]]
* [[144/125]] – its [[fifth complement]]
* [[144/125]] – its [[fifth complement]]
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[[Category:Augmented third]]
[[Category:Augmented third]]
[[Category:Interseptimal intervals]]
[[Category:Interseptimal intervals]]
{{todo|improve synopsis|expand}}

Latest revision as of 20:15, 19 February 2025

Interval information
Ratio 125/96
Factorization 2-5 × 3-1 × 53
Monzo [-5 -1 3
Size in cents 456.9861¢
Names classic(al) augmented third,
triptolemaic augmented third
Color name y33, triyo 3rd
FJS name [math]\displaystyle{ \text{A3}^{5,5,5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 13.5507
Weil norm (log2 max(n, d)) 13.9316
Wilson norm (sopfr(nd)) 28
Open this interval in xen-calc

125/96, the classic(al) augmented third or triptolemaic augmented third, is a 5-limit just interval of about 457 cents. It differs from the classic major third 5/4 by 25/24 and from 13/10 by 625/624. It is also the Pythagorean augmented third (177147/131072) flattened by three syntonic commas, which lends itself to the term triptolemaic.

See also