3025/3024: Difference between revisions

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fixed a typo
We can also say it's the diff between 121/120 and 126/125
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'''3025/3024''', the '''lehmerisma''', is an [[11-limit]] [[unnoticeable comma]] measuring about 0.57 cents. It is the difference between [[55/54]] and [[56/55]], between [[385/384]] and [[441/440]], and between [[225/224]] and [[243/242]], as well as the amount by which two [[12/11]] neutral seconds falls short of [[25/21]], the quasi-tempered minor third.  
'''3025/3024''', the '''lehmerisma''', is an [[11-limit]] [[unnoticeable comma]] measuring about 0.57 cents. It is the difference between [[55/54]] and [[56/55]], between [[121/120]] and [[126/125]], between [[225/224]] and [[243/242]], and between [[385/384]] and [[441/440]], as well as the amount by which two [[12/11]] neutral seconds falls short of [[25/21]], the quasi-tempered minor third.  


Tempering it out leads to [[lehmerismic temperaments]], which splits [[28/27]] into two equal parts, each representing 55/54~56/55.  
Tempering it out leads to [[lehmerismic temperaments]], which splits [[28/27]] into two equal parts, each representing 55/54~56/55.  

Revision as of 10:33, 25 December 2020

Interval information
Ratio 3025/3024
Factorization 2-4 × 3-3 × 52 × 7-1 × 112
Monzo [-4 -3 2 -1 2
Size in cents 0.5724034¢
Name lehmerisma
FJS name [math]\displaystyle{ \text{m}{-2}^{5,5,11,11}_{7} }[/math]
Special properties square superparticular,
reduced
Tenney height (log2 nd) 23.125
Weil height (log2 max(n, d)) 23.1254
Wilson height (sopfr(nd)) 56
Open this interval in xen-calc

3025/3024, the lehmerisma, is an 11-limit unnoticeable comma measuring about 0.57 cents. It is the difference between 55/54 and 56/55, between 121/120 and 126/125, between 225/224 and 243/242, and between 385/384 and 441/440, as well as the amount by which two 12/11 neutral seconds falls short of 25/21, the quasi-tempered minor third.

Tempering it out leads to lehmerismic temperaments, which splits 28/27 into two equal parts, each representing 55/54~56/55.

It factors into two superparticular commas: 4375/4374 × 9801/9800.

See also