1216/1215: Difference between revisions

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== Temperaments ==

~~By tempering~~ out this comma ~~is defined the~~ '''eratosthenes temperament''', which enables ~~the~~ [[eratosthenes chords]]. Edos supporting this temperament includes {{Optimal ET sequence| 12, 29, 41, 53, 65, 77, 87, 94, 99, 106, 111, 118, 130, 140, 152, 159, 183, 193, 205, 217, 270, 282, 311, 323, 364, 400, 422, 581, and 692 }}.

Tempering out this comma defines '''eratosthenes temperament''', which enables [[eratosthenes chords]]. Edos supporting this temperament includes {{Optimal ET sequence| 12, 29, 41, 53, 65, 77, 87, 94, 99, 106, 111, 118, 130, 140, 152, 159, 183, 193, 205, 217, 270, 282, 311, 323, 364, 400, 422, 581, and 692 }}.

== Etymology ==

This comma was named after {{w|Eratosthenes}}, the Ancient Greek polymath. According to an analysis by [[Joseph Monzo]], Eratosthenes made use of this comma by employing "standard" [[3-limit]] pitches in his diatonic [[genus]], but substituting 19-limit ratios which are very close by in pitch in his chromatic and enharmonic genera.<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_26618.html Yahoo! Tuning Group | ''ratios in ancient Greek tetrachords (was: Byzantine and Serb Church Music)'']</ref>

The etymology for "password" is unknown, but it can be noted that it was at one point logged as ''password comma''.

== See also ==

* [[List of superparticular intervals]]

== ~~Notes~~ ==

== References ==

[[Category:Eratosthenes]]

[[Category:Commas named after polymaths]]

[[Category:Commas with unknown etymology]]~~{{todo|add etymology|comment=add etymology for “password”}}~~

[[Category:Commas with unknown etymology]]

@@ Line 28: / Line 28: @@
 == Temperaments ==
-By tempering out this comma is defined the '''eratosthenes temperament''', which enables the [[eratosthenes chords]]. Edos supporting this temperament includes {{Optimal ET sequence| 12, 29, 41, 53, 65, 77, 87, 94, 99, 106, 111, 118, 130, 140, 152, 159, 183, 193, 205, 217, 270, 282, 311, 323, 364, 400, 422, 581, and 692 }}.
+Tempering out this comma defines '''eratosthenes temperament''', which enables [[eratosthenes chords]]. Edos supporting this temperament includes {{Optimal ET sequence| 12, 29, 41, 53, 65, 77, 87, 94, 99, 106, 111, 118, 130, 140, 152, 159, 183, 193, 205, 217, 270, 282, 311, 323, 364, 400, 422, 581, and 692 }}.
 == Etymology ==
 This comma was named after {{w|Eratosthenes}}, the Ancient Greek polymath. According to an analysis by [[Joseph Monzo]], Eratosthenes made use of this comma by employing "standard" [[3-limit]] pitches in his diatonic [[genus]], but substituting 19-limit ratios which are very close by in pitch in his chromatic and enharmonic genera.<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_26618.html Yahoo! Tuning Group | ''ratios in ancient Greek tetrachords (was: Byzantine and Serb Church Music)'']</ref>
+The etymology for "password" is unknown, but it can be noted that it was at one point logged as ''password comma''.
 == See also ==
 * [[List of superparticular intervals]]
-== Notes ==
+== References ==
 [[Category:Eratosthenes]]
 [[Category:Commas named after polymaths]]
-[[Category:Commas with unknown etymology]]{{todo|add etymology|comment=add etymology for “password”}}
+[[Category:Commas with unknown etymology]]