100/81: Difference between revisions

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Touched up comma names, added "diptolemaic" to its naming due to its containing of 25.
Separate the 13- and 17-limit equations, as they're not necessary to understand this 5-limit interval
 
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{{Infobox Interval
{{Infobox Interval
| Name = (classical/diptolemaic) grave major third
| Name = classical grave major third, diptolemaic major third
| Color name = yy3, yoyo 3rd
| Color name = yy3, yoyo 3rd
}}
}}
'''100/81''', the '''classical grave major third''' or '''diptolemaic major third''', is a [[81/80|syntonic comma (81/80)]] flat of [[5/4]]. It can be obtained by stacking two [[10/9|small whole tones (10/9)]].


'''100/81''', the (classical/diptolemaic) '''grave major third''', is a [[81/80|syntonic comma (81/80)]] flat of [[5/4]], a [[325/324|marveltwin comma (325/324)]] sharp of [[16/13]], and merely a [[1701/1700|palingenetic comma (1701/1700)]] flat of the interval [[21/17]]. It is obtained by stacking [[10/9|two small whole tones (10/9)]].
In the [[13-limit]], it is a [[325/324|marveltwin comma (325/324)]] sharp of [[16/13]], and in the [[17-limit]], merely a [[1701/1700|palingenetic comma (1701/1700)]] flat of the interval [[21/17]]


[[Category:Third]]
[[Category:Third]]
[[Category:Submajor third]]
[[Category:Submajor third]]

Latest revision as of 15:52, 1 September 2026

Interval information
Ratio 100/81
Factorization 22 × 3-4 × 52
Monzo [2 -4 2
Size in cents 364.8074 ¢
Names classical grave major third,
diptolemaic major third
Color name yy3, yoyo 3rd
FJS name [math]\displaystyle{ \text{M3}^{5,5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 12.9837
Weil norm (log2 max(n, d)) 13.2877
Wilson norm (sopfr(nd)) 26
Open this interval in xen-calc

100/81, the classical grave major third or diptolemaic major third, is a syntonic comma (81/80) flat of 5/4. It can be obtained by stacking two small whole tones (10/9).

In the 13-limit, it is a marveltwin comma (325/324) sharp of 16/13, and in the 17-limit, merely a palingenetic comma (1701/1700) flat of the interval 21/17