28/15: Difference between revisions

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introduced infobox, added some information and cats
Replace "diatonic" by "grave" by analogy to 40/21 being called "acute" ("diatonic" here doesn't make any sense), and move this suboptimal name to the terminology section
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| Monzo = 2 -1 -1 1
| Monzo = 2 -1 -1 1
| Cents = 1080.55719
| Cents = 1080.55719
| Name = septimal diatonic major seventh
| Name = septimal grave major seventh
| Color name =  
| Color name =  
| FJS name = d8<sup>7</sup><sub>5</sub>
| FJS name = d8<sup>7</sup><sub>5</sub>
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}}
}}


'''28/15''', the '''septimal diatonic major seventh''', is a [[7-limit]] just interval of about 1080.6 [[cent]]s.
'''28/15''' is a [[7-limit]] just interval of about 1080.6 [[cent]]s. It is well approximated by [[10edo]] (9\10).
 
== Terminology ==
Despite being approximated by the major seventh in systems like [[septimal meantone]], and even being called the '''septimal grave major seventh''' by some musicians, 28/15 is a diminished octave in just intonation notation systems such as [[Sagittal notation]], [[Helmholtz-Ellis notation]] and [[Functional Just System]], viewed as the [[4096/2187|Pythagorean diminished octave (4096/2187)]] altered by [[5120/5103]].  


== See also ==
== See also ==
 
* [[15/14]] – its [[octave complement]]
* [[Gallery of just intervals]]
* [[Gallery of just intervals]]
* [[15/14]] – its [[octave complement]]
* [[10edo]] has a good approximation


[[Category:7-limit]]
[[Category:7-limit]]
[[Category:Interval ratio]]
[[Category:Interval]]
[[Category:Listen]]
[[Category:Ratio]]
[[Category:Seventh]]
[[Category:Seventh]]
[[Category:Major seventh]]
[[Category:Major seventh]]
[[Category:Pages with internal sound examples]]


[[Category:Todo:expand]]
{{todo| expand | improve synopsis | add color name }}
[[Category:Todo:improve synopsis]]
[[Category:Todo:add color name]]

Revision as of 16:23, 10 April 2021

Interval information
Ratio 28/15
Factorization 22 × 3-1 × 5-1 × 7
Monzo [2 -1 -1 1
Size in cents 1080.557¢
Name septimal grave major seventh
FJS name [math]\displaystyle{ \text{d8}^{7}_{5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 8.71425
Weil norm (log2 max(n, d)) 9.61471
Wilson norm (sopfr(nd)) 19

[sound info]
Open this interval in xen-calc

28/15 is a 7-limit just interval of about 1080.6 cents. It is well approximated by 10edo (9\10).

Terminology

Despite being approximated by the major seventh in systems like septimal meantone, and even being called the septimal grave major seventh by some musicians, 28/15 is a diminished octave in just intonation notation systems such as Sagittal notation, Helmholtz-Ellis notation and Functional Just System, viewed as the Pythagorean diminished octave (4096/2187) altered by 5120/5103.

See also