Fynn's comma: Difference between revisions

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'''Fynn's comma''' ({{monzo|legend=1| 73 0 0 -26 }}, [[ratio]]: 9 444 732 965 739 290 427 392 / 9 387 480 337 647 754 305 649), or systematically, the '''26-7-comma''', is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 10.5 [[cent]]s. It is the amount by which twenty-one [[2/1|octaves]] exceed twenty-six [[7/1|harmonic sevenths]], or ~~2<sup>21</sup>~~/(7~~/4)<sup>26</sup>~~. It ~~is the comma between~~ the [[~~dilemma~~]] ~~and the~~ [[~~antidilemma~~]]~~, intervals describing the difference between 13~~ 7/~~4s and 10 or 11 octaves respectively, explaining the high accuracy of [[26edo~~]] ~~at harmonic 7~~.

'''Fynn's comma''' ({{monzo|legend=1| 73 0 0 -26 }}, [[ratio]]: 9 444 732 965 739 290 427 392 / 9 387 480 337 647 754 305 649), or systematically, the '''26-7-comma''', is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 10.5 [[cent]]s. It is the amount by which twenty-one [[2/1|octaves]] exceed twenty-six [[7/4|harmonic sevenths]], or the amount by which twenty-one [[8/7|septimal major seconds]] exceed five octaves. It explains the high accuracy of [[26edo]]'s approximate [[harmonic]] [[7/1|7]].

==Temperaments==

== Temperaments ==

[[Tempering out]] this comma splits the octave into 26 equal parts and maps 7/4 to 21\26, For edos ''N'' up to 1456, it is tempered out if and only if 26 divides ''N''.

~~Tempering out Fynn~~'s ~~comma splits~~ the ~~octave into 26 equal parts~~ and ~~maps~~ 7/4 ~~to 18\26, For edos ''N'' up to 1456~~, it ~~is tempered out if and only if 26 divides ''N''~~.

== Trivia ==

This interval is the difference between the [[dilemma]], the difference between thirteen 7/4's and 10 octaves, and the [[antidilemma]], difference between thirteen 7/4's and 11 octaves. Since 26edo has an accurate 7/4 not shared with any lower edo, [[13edo]] has almost 50% relative error on it.

==See also==

== See also ==

* [[26th-octave temperaments]]

[[~~26th-octave temperaments~~]]

[[Category:Commas someone named after themselves]]

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-'''Fynn's comma''' ({{monzo|legend=1| 73 0 0 -26 }}, [[ratio]]: 9 444 732 965 739 290 427 392 / 9 387 480 337 647 754 305 649), or systematically, the '''26-7-comma''', is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 10.5 [[cent]]s. It is the amount by which twenty-one [[2/1|octaves]] exceed twenty-six [[7/1|harmonic sevenths]], or 2<sup>21</sup>/(7/4)<sup>26</sup>. It is the comma between the [[dilemma]] and the [[antidilemma]], intervals describing the difference between 13 7/4s and 10 or 11 octaves respectively, explaining the high accuracy of [[26edo]] at harmonic 7.
+'''Fynn's comma''' ({{monzo|legend=1| 73 0 0 -26 }}, [[ratio]]: 9 444 732 965 739 290 427 392 / 9 387 480 337 647 754 305 649), or systematically, the '''26-7-comma''', is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 10.5 [[cent]]s. It is the amount by which twenty-one [[2/1|octaves]] exceed twenty-six [[7/4|harmonic sevenths]], or the amount by which twenty-one [[8/7|septimal major seconds]] exceed five octaves. It explains the high accuracy of [[26edo]]'s approximate [[harmonic]] [[7/1|7]].
-==Temperaments==
+== Temperaments ==
+[[Tempering out]] this comma splits the octave into 26 equal parts and maps 7/4 to 21\26, For edos ''N'' up to 1456, it is tempered out if and only if 26 divides ''N''.
-Tempering out Fynn's comma splits the octave into 26 equal parts and maps 7/4 to 18\26, For edos ''N'' up to 1456, it is tempered out if and only if 26 divides ''N''.
+== Trivia ==
+This interval is the difference between the [[dilemma]], the difference between thirteen 7/4's and 10 octaves, and the [[antidilemma]], difference between thirteen 7/4's and 11 octaves. Since 26edo has an accurate 7/4 not shared with any lower edo, [[13edo]] has almost 50% relative error on it.
-==See also==
+== See also ==
+* [[26th-octave temperaments]]
-[[26th-octave temperaments]]
+[[Category:Commas someone named after themselves]]