1323/1280: Difference between revisions

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1323/1280, the septimal 2/7-tone, is a 7-limit ratio ~~very~~ close to the step of [[21edo]].

{{Infobox Interval

|Ratio = 1323/1280

|Name = larger breedsmic half-apotome, septimal 2/7-tone, septimal 21st-octave

|Color name = Lzzg2, lazozogu 2nd

|Comma = yes

}}

'''1323/1280''', the '''septimal 2/7-tone''', is a 7-limit ratio, the product of ([[405/392]])·([[2401/2400]]), extremely close to the step of [[21edo]] and less close but very close still to [[sqrt(2187/2048)]] a. It is also the difference between:

~~== Theory ==~~

* [[49/45]] and [[256/243]]

~~If taken as a comma to be tempered, it produces~~ [[~~greenwood~~]]~~. If it is taken as a period~~ and ~~assigned to 1\21 of the octave, it produces~~ [[~~akjayland~~]] and ~~temperaments like 441 & 1848.~~

* [[2187/2048]] and [[405/392]]

* [[9/8]] and [[160/147]]

{{Monzo|-169,63,-21,42}} is a comma that results from the difference of 21 instances of this interval with the octave. For EDOs N up to ~5000, it is tempered out if and only if 21 divides N.

== Temperaments ==

If taken as a comma to be tempered, it produces [[greenwood]]. If it is taken as a period and assigned to 1\21 of the octave, it serves as a period in the [[akjayland]] temperament.

{{Monzo|-169 63 -21 42}} is a comma that results from the difference of 21 instances of this interval with the octave. For EDOs N up to ~5000, it is tempered out if and only if 21 divides N.

Tempering out 2401/2400 equates 1323/1280 with 405/392 and merges them into half an apotome.

[[Category:Commas named after their interval size]]

@@ Line 1: / Line 1: @@
-/1280, the septimal 2/7-tone, is a 7-limit ratio very close to the step of [[21edo]].
+{{Infobox Interval
+|Ratio = 1323/1280
+|Name = larger breedsmic half-apotome, septimal 2/7-tone, septimal 21st-octave
+|Color name = Lzzg2, lazozogu 2nd
+|Comma = yes
+}}
+'''1323/1280''', the '''septimal 2/7-tone''', is a 7-limit ratio, the product of ([[405/392]])·([[2401/2400]]), extremely close to the step of [[21edo]] and less close but very close still to [[sqrt(2187/2048)]] a. It is also the difference between:
-== Theory ==
+* [[49/45]] and [[256/243]]
-If taken as a comma to be tempered, it produces [[greenwood]]. If it is taken as a period and assigned to 1\21 of the octave, it produces [[akjayland]] and temperaments like 441 & 1848.
+* [[2187/2048]] and [[405/392]]
+* [[9/8]] and [[160/147]]
-{{Monzo|-169,63,-21,42}} is a comma that results from the difference of 21 instances of this interval with the octave. For EDOs N up to ~5000, it is tempered out if and only if 21 divides N.
+== Temperaments ==
+If taken as a comma to be tempered, it produces [[greenwood]]. If it is taken as a period and assigned to 1\21 of the octave, it serves as a period in the [[akjayland]] temperament.
+{{Monzo|-169 63 -21 42}} is a comma that results from the difference of 21 instances of this interval with the octave. For EDOs N up to ~5000, it is tempered out if and only if 21 divides N.
+Tempering out 2401/2400 equates 1323/1280 with 405/392 and merges them into half an apotome.
+[[Category:Commas named after their interval size]]