3025/3024: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

~~| Ratio = 3025/3024~~

~~| Monzo = -4 -3 2 -1 2~~

~~| Cents = 0.57249~~

| Name = lehmerisma

| Color name =

| Color name = 1ooryy-2, Loloruyoyo comma

| ~~FJS name =~~

| Comma = yes

~~| Sound~~ =

}}

'''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.

~~'''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~~.

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

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

== Temperaments ==

[[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.

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

== Etymology ==

This comma was named by [[Gene Ward Smith]] in 2004 after the American mathematician [[wikipedia: D. H. Lehmer|D. H. Lehmer]].

Or perhaps 3025/3024 is a better lehmerisma, as Lehmer mentions it on the first page of his paper. […] He was a wonderful gentlemen and a hell of a mathematician, and deserves

a comma as much as anyone.

</blockquote>

—Gene Ward Smith<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10130.html Yahoo! Tuning Group | ''Re: {{lbrack}}tuning-math{{rbrack}} Digest Number 1011'']</ref>

== See also ==

* [[Lehmerismic temperaments]]

* [[Unnoticeable comma]]

* [[List of superparticular intervals]]

~~[[Category:11-limit]]~~

== Notes ==

~~[[Category:Unnoticeable comma]]~~

~~[[Category:Ratio]]~~

~~[[Category:Superparticular]]~~

[[Category:Lehmerismic]]

[[Category:Commas named after mathematicians]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
-| Ratio = 3025/3024
-| Monzo = -4 -3 2 -1 2
-| Cents = 0.57249
 | Name = lehmerisma
-| Color name =
+| Color name = 1ooryy-2, Loloruyoyo comma
-| FJS name =
+| Comma = yes
-| Sound =
 }}
+'''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.
-'''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.
+It factors into the two smallest superparticular commas in the 11-limit: 3025/3024 = ([[4375/4374]])([[9801/9800]]).
-Tempering it out leads to [[lehmerismic temperaments]], which splits [[28/27]] into two equal parts, each representing 55/54~56/55.
+== Temperaments ==
+[[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.
-It factors into two superparticular commas: [[4375/4374]] × [[9801/9800]].
+== Etymology ==
+This comma was named by [[Gene Ward Smith]] in 2004 after the American mathematician [[wikipedia: D. H. Lehmer|D. H. Lehmer]].
+<blockquote>
+Or perhaps 3025/3024 is a better lehmerisma, as Lehmer mentions it on the first page of his paper. […] He was a wonderful gentlemen and a hell of a mathematician, and deserves
+a comma as much as anyone.
+</blockquote>
+—Gene Ward Smith<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10130.html Yahoo! Tuning Group | ''Re: {{lbrack}}tuning-math{{rbrack}} Digest Number 1011'']</ref>
 == See also ==
-* [[Lehmerismic temperaments]]
-* [[Unnoticeable comma]]
 * [[List of superparticular intervals]]
-[[Category:11-limit]]
+== Notes ==
-[[Category:Unnoticeable comma]]
-[[Category:Ratio]]
-[[Category:Superparticular]]
 [[Category:Lehmerismic]]
+[[Category:Commas named after mathematicians]]