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.

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

It factors into two superparticular commas: ([[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.

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.

== Etymology ==

This comma was named by [[Gene Ward Smith]] in 2004 after the American mathematician [[wikipedia: D. H. Lehmer|D. H. Lehmer]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10130.html Yahoo! Tuning Group | ''Re: [tuning-math] Digest Number 1011'']</ref>.

== See also ==

* [[Rank-4 temperament #Lehmerismic (3025/3024)]]

* [[Lehmerismic temperaments]], a collection of rank-3 temperaments where it is tempered out

* [[List of superparticular intervals]]

== Notes ==

[[Category:Lehmerismic]]

@@ Line 6: / Line 6: @@
 '''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.
-It factors into two superparticular commas: [[4375/4374]] × [[9801/9800]].
+It factors into two superparticular commas: ([[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.
+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.
+== Etymology ==
+This comma was named by [[Gene Ward Smith]] in 2004 after the American mathematician [[wikipedia: D. H. Lehmer|D. H. Lehmer]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10130.html Yahoo! Tuning Group | ''Re: [tuning-math] Digest Number 1011'']</ref>.
 == See also ==
-* [[Rank-4 temperament #Lehmerismic (3025/3024)]]
-* [[Lehmerismic temperaments]], a collection of rank-3 temperaments where it is tempered out
 * [[List of superparticular intervals]]
+== Notes ==
 [[Category:Lehmerismic]]