3025/3024: Difference between revisions

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'''3025/3024''', the '''lehmerisma''', is an [[11-limit]] [[~~unnoticeable~~ comma]] measuring about 0.57{{cent}}. 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.

'''3025/3024''', the '''lehmerisma''', is an [[unnoticeable comma|unnoticeable]] [[11-limit]] [[comma]] measuring about 0.57{{cent}}. 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.

It factors into two superparticular commas: ([[4375/4374]])([[9801/9800]]).

It factors into the two smallest superparticular commas in the 11-limit: 3025/3024 = ([[4375/4374]])([[9801/9800]]).

== Temperaments ==

Tempering it out leads to the '''lehmerismic temperament''', which splits [[28/27]] into two equal parts, each representing 55/54~56/55. See [[Rank-4 temperament #Lehmerismic (3025/3024)]] for some technical details. See [[Lehmerismic temperaments]] for a collection of rank-3 temperaments where it is tempered out.

[[Tempering out]] this comma leads to the '''lehmerismic temperament''', which splits [[28/27]] into two equal parts, each representing 55/54~56/55. See [[Rank-4 temperament #Lehmerismic (3025/3024)]] for some technical details. See [[Lehmerismic temperaments]] for a collection of rank-3 temperaments where it is tempered out.

== Etymology ==

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[[Category:Lehmerismic]]

[[Category:Commas named after mathematicians]]

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-'''3025/3024''', the '''lehmerisma''', is an [[11-limit]] [[unnoticeable comma]] measuring about 0.57{{cent}}. 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.
+'''3025/3024''', the '''lehmerisma''', is an [[unnoticeable comma|unnoticeable]] [[11-limit]] [[comma]] measuring about 0.57{{cent}}. 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.
-It factors into two superparticular commas: ([[4375/4374]])([[9801/9800]]).
+It factors into the two smallest superparticular commas in the 11-limit: 3025/3024 = ([[4375/4374]])([[9801/9800]]).
 == Temperaments ==
-Tempering it out leads to the '''lehmerismic temperament''', which splits [[28/27]] into two equal parts, each representing 55/54~56/55. See [[Rank-4 temperament #Lehmerismic (3025/3024)]] for some technical details. See [[Lehmerismic temperaments]] for a collection of rank-3 temperaments where it is tempered out.
+[[Tempering out]] this comma leads to the '''lehmerismic temperament''', which splits [[28/27]] into two equal parts, each representing 55/54~56/55. See [[Rank-4 temperament #Lehmerismic (3025/3024)]] for some technical details. See [[Lehmerismic temperaments]] for a collection of rank-3 temperaments where it is tempered out.
 == Etymology ==
@@ Line 27: / Line 27: @@
 [[Category:Lehmerismic]]
+[[Category:Commas named after mathematicians]]