19/10: Difference between revisions

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m infoboxified
Expansion according to its octave complement
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| Monzo = -1 0 -1 0 0 0 0 1
| Monzo = -1 0 -1 0 0 0 0 1
| Cents = 1111.19930
| Cents = 1111.19930
| Name =  
| Name = undeviceismal diminished octave, <br>Eratosthenes' major seventh
| Color name =  
| Color name =  
| FJS name =  
| FJS name = d8<sup>19</sup><sub>5</sub>
| Sound = jid_19_10_pluck_adu_dr220.mp3
| Sound = jid_19_10_pluck_adu_dr220.mp3
}}
}}


'''19/10''' is a [[19-limit]] interval.
In [[19-limit]] [[just intonation]], '''19/10''' is the '''undevicesimal diminished octave''', measuring about 1111.2¢. In [[Functional Just System]] and [[Helmholtz-Ellis notation]], it is a ''diminished octave'', obtained by adding [[81/80]] and [[513/512]] to the [[4096/2187|Pythagorean diminished octave]], but it may be called the '''Eratosthenes' major seventh''' as it is sharp of the [[243/128|Pythagorean limma (256/243)]] by [[1216/1215]], the ''password'' aka ''Eratosthenes' comma''.  


[[category:Just interval]]
[[Category:19-limit]]
[[category:19-limit]]
[[Category:Interval]]
 
[[Category:Octave]]
[[Category:todo:expand]]
[[Category:Diminished octave]]
[[Category:Seventh]]
[[Category:Major seventh]]
[[Category:Eratosthenes]]

Revision as of 07:13, 6 February 2021

Interval information
Ratio 19/10
Subgroup monzo 2.5.19 [-1 -1 1
Size in cents 1111.199¢
Names undeviceismal diminished octave,
Eratosthenes' major seventh
FJS name [math]\displaystyle{ \text{d8}^{19}_{5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 7.56986
Weil norm (log2 max(n, d)) 8.49586
Wilson norm (sopfr(nd)) 26

[sound info]
Open this interval in xen-calc

In 19-limit just intonation, 19/10 is the undevicesimal diminished octave, measuring about 1111.2¢. In Functional Just System and Helmholtz-Ellis notation, it is a diminished octave, obtained by adding 81/80 and 513/512 to the Pythagorean diminished octave, but it may be called the Eratosthenes' major seventh as it is sharp of the Pythagorean limma (256/243) by 1216/1215, the password aka Eratosthenes' comma.