51/40: Difference between revisions

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| Monzo = -8 1 -1 0 0 0 1  
| Monzo = -8 1 -1 0 0 0 1  
| Cents = 420.59670
| Cents = 420.59670
| Name = lesser septendecimal supermajor third (?)
| Name = septendecimal major third
| Color name = 17og4, sogu 4th
| Color name = 17og4, sogu 4th
| Sound = Ji-{{#regex:{{PAGENAME}}|/(\S+)\/(\S+)/|\1-\2}}-csound-foscil-220hz.mp3
| Sound = Ji-{{#regex:{{PAGENAME}}|/(\S+)\/(\S+)/|\1-\2}}-csound-foscil-220hz.mp3
}}
}}


In [[17-limit]] [[just intonation]], '''51/40''' is the '''lesser septendecimal supermajor third'''.
In [[17-limit]] [[just intonation]], '''51/40''' is the '''septendecimal major third'''.  Although technically a type of supermajor third, there's already a septendecimal supermajor third in the form of [[22/17]], while this interval is the [[fifth complement]] of [[20/17]], which is the septendecimal minor third.


It is approximated by:
It is approximated by:
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== See also ==
== See also ==
 
* [[80/51]] – its [[octave complement]]
* [[22/17]] – Septendecimal supermajor third
* [[20/17]] – its [[fifth complement]]
* [[Gallery of just intervals]]
* [[Gallery of just intervals]]



Revision as of 15:18, 13 May 2022

Interval information
Ratio 51/40
Factorization 2-3 × 3 × 5-1 × 17
Monzo [-3 1 -1 0 0 0 1
Size in cents 420.5967¢
Name septendecimal major third
Color name 17og4, sogu 4th
FJS name [math]\displaystyle{ \text{d4}^{17}_{5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 10.9944
Weil norm (log2 max(n, d)) 11.3449
Wilson norm (sopfr(nd)) 31
[[File:Ji-{{#regex:51/40|/(\S+)\/(\S+)/|\1-\2}}-csound-foscil-220hz.mp3|270px]]
[[:File:Ji-{{#regex:51/40|/(\S+)\/(\S+)/|\1-\2}}-csound-foscil-220hz.mp3|[sound info]]]
Open this interval in xen-calc

In 17-limit just intonation, 51/40 is the septendecimal major third. Although technically a type of supermajor third, there's already a septendecimal supermajor third in the form of 22/17, while this interval is the fifth complement of 20/17, which is the septendecimal minor third.

It is approximated by:

See also