51/40: Difference between revisions

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m Normalising usage of Infobox Interval
Aura (talk | contribs)
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Changed name to reflect the name change of its minor counterpart.
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{{Infobox Interval
{{Infobox Interval
| Name = septendecimal major third
| Name = diatismic 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 '''septendecimal major third'''.  Although technically a type of supermajor third, there's already a septendecimal supermajor third in the form of [[22/17]], while 51/40 itself is the [[fifth complement]] of [[20/17]]- the septendecimal minor third.
In [[17-limit]] [[just intonation]], '''51/40''' is the '''diatismic major third'''.  It exceeds the [[81/64|Pythagorean major third (81/64)]] by a [[136/135|diatisma (136/135)]], hence the name.


It is approximated by:
It is approximated by:

Revision as of 18:12, 1 June 2024

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 diatismic 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 diatismic major third. It exceeds the Pythagorean major third (81/64) by a diatisma (136/135), hence the name.

It is approximated by:

See also

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