40/21: Difference between revisions

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| Monzo = 3 -1 1 -1
| Monzo = 3 -1 1 -1
| Cents = 1115.53281
| Cents = 1115.53281
| Name = acute major seventh, <br>small septimal diminished octave
| Name = septimal acute major seventh, <br>small septimal diminished octave
| Color name =  
| Color name =  
| FJS name = M7<sup>5</sup><sub>7</sub>
| FJS name = M7<sup>5</sup><sub>7</sub>
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}}
}}


'''40/21''', the '''acute major seventh''', is a [[7-limit]] interval measuring about 1115.5 cents. Despite being approximated by the diminished octave in systems like [[septimal meantone]], and even being called the "'''small septimal diminished octave'''" by some musicians due to analogy with [[21/20]] being called the "large septimal chroma", 40/21 is a major seventh in both [[Helmholtz-Ellis notation]] and [[Functional Just System]] because it is sharp of the [[243/128|Pythagorean major seventh (243/128)]] by [[5120/5103]].  
'''40/21''', the '''septimal acute major seventh''', is a [[7-limit]] interval measuring about 1115.5 cents.  
 
== Terminology ==
Despite being approximated by the diminished octave in systems like [[septimal meantone]], and even being called the '''small septimal diminished octave''' by some musicians due to analogy with [[21/20]] being called the "large septimal chroma", 40/21 is a major seventh in just intonation notation systems such as [[Sagittal notation]], [[Helmholtz-Ellis notation]] and [[Functional Just System]], viewed as the [[243/128|Pythagorean major seventh (243/128)]] altered by [[5120/5103]].  


== See also ==
== See also ==
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[[Category:Seventh]]
[[Category:Seventh]]
[[Category:Major seventh]]
[[Category:Major seventh]]
[[Category:Pages with internal sound examples]]

Revision as of 16:13, 10 April 2021

Interval information
Ratio 40/21
Factorization 23 × 3-1 × 5 × 7-1
Monzo [3 -1 1 -1
Size in cents 1115.533¢
Names septimal acute major seventh,
small septimal diminished octave
FJS name [math]\displaystyle{ \text{M7}^{5}_{7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 9.71425
Weil norm (log2 max(n, d)) 10.6439
Wilson norm (sopfr(nd)) 21

[sound info]
Open this interval in xen-calc

40/21, the septimal acute major seventh, is a 7-limit interval measuring about 1115.5 cents.

Terminology

Despite being approximated by the diminished octave in systems like septimal meantone, and even being called the small septimal diminished octave by some musicians due to analogy with 21/20 being called the "large septimal chroma", 40/21 is a major seventh in just intonation notation systems such as Sagittal notation, Helmholtz-Ellis notation and Functional Just System, viewed as the Pythagorean major seventh (243/128) altered by 5120/5103.

See also