77/76: Difference between revisions

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Created page with "{{Infobox Interval | Name = small undevicesimal 1/9-tone | Color name = 19u1oz1, nulozo 1sn, <br>Nulozo comma | Comma = yes }} '''77/76''' is a superparticular interval o..."
 
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adjacent superparticulars
 
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'''77/76''' is a [[superparticular]] interval of about 22.6¢ which makes the difference between [[8/7]] and [[22/19]] in [[19-limit]] [[just intonation]]; it is also the difference between [[11/8]] and [[19/14]].
'''77/76''' is a [[superparticular]] interval of about 22.6¢ which makes the difference between [[8/7]] and [[22/19]] in [[19-limit]] [[just intonation]]; it is also the difference between [[11/8]] and [[19/14]].
The adjacent superparticulars [[76/75]] and [[78/77]] are also within the 19-limit, and 77/76 differs from them by [[5776/5775]] and [[5929/5928]] respectively.


== Temperaments ==
== Temperaments ==
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* [[Small comma]]
* [[Small comma]]
* [[List of superparticular intervals]]
* [[List of superparticular intervals]]
[[Category:Commas named after their interval size]]

Latest revision as of 04:05, 27 May 2026

Interval information
Ratio 77/76
Factorization 2-2 × 7 × 11 × 19-1
Monzo [-2 0 0 1 1 0 0 -1
Size in cents 22.63083¢
Name small undevicesimal 1/9-tone
Color name 19u1oz1, nulozo 1sn,
Nulozo comma
FJS name [math]\displaystyle{ \text{P1}^{7,11}_{19} }[/math]
Special properties superparticular,
reduced
Tenney norm (log2 nd) 12.5147
Weil norm (log2 max(n, d)) 12.5336
Wilson norm (sopfr(nd)) 41
Comma size small
Open this interval in xen-calc

77/76 is a superparticular interval of about 22.6¢ which makes the difference between 8/7 and 22/19 in 19-limit just intonation; it is also the difference between 11/8 and 19/14.

The adjacent superparticulars 76/75 and 78/77 are also within the 19-limit, and 77/76 differs from them by 5776/5775 and 5929/5928 respectively.

Temperaments

It is close to one step of 53edo, and the comma associating it with 1\53 is tempered out in notable high-prime-limit systems like 159edo and 742edo.

See also