2960edo: Difference between revisions

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== Theory ==

2960edo is ~~a dual~~-~~fifth system that~~ is ~~also an~~ excellent 2.5.9.11.17.19 subgroup ~~tuning.~~

2960edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1|3]] is about halfway between its steps. Otherwise it is excellent in approximating harmonics [[5/1|5]], [[9/1|9]], [[11/1|11]], [[17/1|17]], and [[19/1|19]], making it suitable for a 2.9.5.11.17.19 [[subgroup]] interpretation, with optional additions of [[7/1|7]] and [[23/1|23]], or [[21/1|21]] and [[13/1|13]].

~~2960dh val {{val|2960 4691 6873 '''8309''' 10240 10953 12099 '''12573'''}} is the unique mapping that supports both the 80th-octave temperament called~~ [[~~mercury~~]], and ~~the coincidentally similarly named~~ [[~~mercury meantone~~]], ~~which tunes the meantone steps to~~ [[19/17]] and [[15/14]].

In this case, 19/17 is mapped to 474 steps and 15/14 is mapped to 295 steps. This means that the fifth is mapped to 1717 steps, being 14 steps below the patent val fifth, therefore also meaning if such a temperament is realized via the regular temperament perspective, it will not be mapped to 3\2.

The 2960dh [[val]] {{val| 2960 4691 6873 '''8309''' 10240 10953 12099 '''12573''' }} is the unique mapping that supports both the 80th-octave temperament called [[mercury]], and the coincidentally similarly named [[mercury meantone]], which tunes the meantone steps to [[19/17]] and [[15/14]]. In this case, 19/17 is mapped to 474 steps and 15/14 is mapped to 295 steps. This means that the fifth is mapped to 1717 steps, being 14 steps below the [[patent val]] fifth, therefore also meaning if such a temperament is realized via the regular temperament perspective, it will not be mapped to 3/2.

From a regular temperament perspective, mercury meantone in 2960edo can be potentially realized as [[893edo|893]] & 2960dh temperament in the 19-limit, as it maps two generators to 19/17 and 2955 generators to 15/14, which is circularly equivalent to 5 steps down in 2960edo (2955 + 5 = 2960), corresponding to Phrygian and Locrian modes. Eliora proposes the name ''quicksilvertone'' for this regular temperament.

=== Odd harmonics ===

=== Subsets and supersets ===

Since 2960 factors into {{factorization|2960}}, 2960edo has subset edos {{EDOs| 2, 4, 5, 8, 10, 16, 20, 37, 40, 74, 80, 148, 185, 296, 370, 592, 740 and 1480 }}.

== Scales ==

* 474 474 295 474 474 474 295 - mercury meantone (major scale)

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 {{Infobox ET}}
 {{EDO intro|2960}}
 == Theory ==
-edo is a dual-fifth system that is also an excellent 2.5.9.11.17.19 subgroup tuning.
+edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1|3]] is about halfway between its steps. Otherwise it is excellent in approximating harmonics [[5/1|5]], [[9/1|9]], [[11/1|11]], [[17/1|17]], and [[19/1|19]], making it suitable for a 2.9.5.11.17.19 [[subgroup]] interpretation, with optional additions of [[7/1|7]] and [[23/1|23]], or [[21/1|21]] and [[13/1|13]].
-dh val {{val|2960 4691 6873 '''8309''' 10240 10953 12099 '''12573'''}} is the unique mapping that supports both the 80th-octave temperament called [[mercury]], and the coincidentally similarly named [[mercury meantone]], which tunes the meantone steps to [[19/17]] and [[15/14]].
-In this case, 19/17 is mapped to 474 steps and 15/14 is mapped to 295 steps. This means that the fifth is mapped to 1717 steps, being 14 steps below the patent val fifth, therefore also meaning if such a temperament is realized via the regular temperament perspective, it will not be mapped to 3\2.
+The 2960dh [[val]] {{val| 2960 4691 6873 '''8309''' 10240 10953 12099 '''12573''' }} is the unique mapping that supports both the 80th-octave temperament called [[mercury]], and the coincidentally similarly named [[mercury meantone]], which tunes the meantone steps to [[19/17]] and [[15/14]]. In this case, 19/17 is mapped to 474 steps and 15/14 is mapped to 295 steps. This means that the fifth is mapped to 1717 steps, being 14 steps below the [[patent val]] fifth, therefore also meaning if such a temperament is realized via the regular temperament perspective, it will not be mapped to 3/2.
 From a regular temperament perspective, mercury meantone in 2960edo can be potentially realized as [[893edo|893]] & 2960dh temperament in the 19-limit, as it maps two generators to 19/17 and 2955 generators to 15/14, which is circularly equivalent to 5 steps down in 2960edo (2955 + 5 = 2960), corresponding to Phrygian and Locrian modes. Eliora proposes the name ''quicksilvertone'' for this regular temperament.
 === Odd harmonics ===
-{{harmonics in equal|2960}}
+{{Harmonics in equal|2960}}
+=== Subsets and supersets ===
+Since 2960 factors into {{factorization|2960}}, 2960edo has subset edos {{EDOs| 2, 4, 5, 8, 10, 16, 20, 37, 40, 74, 80, 148, 185, 296, 370, 592, 740 and 1480 }}.
 == Scales ==
 * 474 474 295 474 474 474 295 - mercury meantone (major scale)
+{{Todo| review }}