40/21: Difference between revisions

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+logical reasons for both d8 and M7 but let's just remove "small septimal diminished octave" since the term is out of nowhere
m Fix a link
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'''40/21''', is a [[7-limit]] interval measuring about 1115.5 cents. Despite being approximated by the diminished octave in systems like [[septimal meantone]], it is a major seventh in both [[Helmholtz-Ellis notation]] and [[Functional Just System]] because it is sharp of the [[Pythagorean major seventh (243/128)]] by [[5120/5103]].  
'''40/21''', is a [[7-limit]] interval measuring about 1115.5 cents. Despite being approximated by the diminished octave in systems like [[septimal meantone]], it 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]].  


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

Revision as of 10:27, 25 December 2020

Interval information
Ratio 40/21
Factorization 23 × 3-1 × 5 × 7-1
Monzo [3 -1 1 -1
Size in cents 1115.533¢
Name acute major seventh
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, is a 7-limit interval measuring about 1115.5 cents. Despite being approximated by the diminished octave in systems like septimal meantone, it is a major seventh in both Helmholtz-Ellis notation and Functional Just System because it is sharp of the Pythagorean major seventh (243/128) by 5120/5103.

See also