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 = small septimal suboctave
| Name = small septimal suboctave, <br> acute major seventh
| Color name =  
| Color name =  
| FJS name =  
| FJS name =  
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'''40/21''', the '''small septimal diminished octave''' is a [[7-limit]] interval, which despite being dubbed a "diminished octave", is actually a type of major seventh for much the same reason that [[21/20]] is actually a diatonic semitone of sorts.
'''40/21''', is a [[7-limit]] interval which despite being dubbed the '''small septimal diminished octave''', is actually a type of major seventh for much the same reason that [[21/20]] is actually a diatonic semitone of sorts, specifically is it dubbed the '''acute major seventh''' by the Huygens-Fokker Foundation.


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

Revision as of 23:37, 24 December 2020

Interval information
Ratio 40/21
Factorization 23 × 3-1 × 5 × 7-1
Monzo [3 -1 1 -1
Size in cents 1115.533¢
Names small septimal suboctave,
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 which despite being dubbed the small septimal diminished octave, is actually a type of major seventh for much the same reason that 21/20 is actually a diatonic semitone of sorts, specifically is it dubbed the acute major seventh by the Huygens-Fokker Foundation.

See also