5767168/5767125: Difference between revisions

Line 9:

== Temperaments ==

This comma is trivially tempered out in [[olympic]], as 4096/4095 and 4225/4224 are also tempered out there. Thus, any temperament of olympic also tempers it out. See [[Olympic clan|here]] for a compendium of temperaments and edos that temper out this comma due to being ~~olympian~~.

This comma is trivially tempered out in [[olympic|(tridecimal) olympic]], as 4096/4095 and 4225/4224 are also tempered out there. Thus, any temperament of olympic also tempers it out. See [[Olympic clan|here]] for a compendium of temperaments and edos that temper out this comma due to being olympic.

Other non-olympian edos that temper out the insanisma by patent val, but not either of S64 and S65 include {{EDOs| 35, 40, 49 }}, and some hyperfine edos like [[3395edo|3395]] and [[8539edo|8539]].

=== Insanismic ===

[[Subgroup]]: 2.3.5.7.11.13

[[Comma list]]: [[5767168/5767125]]

[[Mapping]]: [⟨ 1 0 0 0 2 7 ], ⟨ 0 1 0 0 0 0 ], ⟨ 0 0 1 0 0 -1 ], ⟨ 0 0 0 1 1 0 ], ⟨ 0 0 0 0 3 1 ]]

Mapping generators: ~2, ~3, ~5, ~7, ~65/128

[[Optimal tuning|Optimal tunings]]:

: [[WE]]: ~2 = 1199.999558¢, ~3/2 = 701.955501¢, ~5/4 = 386.314974¢, ~7/4 = 968.826974¢, ~65/128 = -1173.1542¢

: error map: -0.000442 0.000058 0.000376 0.000183 -0.000278 0.000955

: [[CWE]]: ~2 = 1200.¢, ~3/2 = 701.955606¢, ~5/4 = 386.315031¢, ~7/4 = 968.827097¢, ~65/128 = -1173.154680¢

: error map: 0.000000 0.000605 0.001318 0.001190 0.000720 0.002627

[[Optimal ET sequence]]: [[7edo|7]], [[10edo|10e]], [[12edo|12e]], [[30edo|30b]], [[31edo|31e]], [[34edo|34]], [[36edo|36]], [[41edo|41]], [[46edo|46]], [[53edo|53]], [[84edo|84]], [[87edo|87]], [[130edo|130]], [[183edo|183]], [[217edo|217]], [[224edo|224]], [[270edo|270]], [[494edo|494]], [[764edo|764]], [[935edo|935]], [[1075edo|1075]], [[1205edo|1205]], [[1609edo|1609]], [[1696edo|1696]], [[1920edo|1920]], [[2190edo|2190]], [[2684edo|2684]], [[3395edo|3395]], [[5144edo|5144]], [[5585edo|5585]], [[6079edo|6079]], [[8269edo|8269]], [[8539edo|8539]], [[11664edo|11664]], [[14124edo|14124]], [[14348edo|14348]], [[14618edo|14618]], [[20203edo|20203]]

Badness (Sintel): 0.241

== Etymology ==

This comma was named by [[Eufalesio]] in 2026, on the basis that tempering out this comma alone purportedly entails an ''insane'' level of precision.

This comma was named by [[Eufalesio]] in 2026, on the basis that tempering out this comma alone purportedly entails a ''insane'' level of precision.

[[Category:Insanismic]]

[[Category:Commas named for other reasons]]

@@ Line 9: / Line 9: @@
 == Temperaments ==
-This comma is trivially tempered out in [[olympic]], as 4096/4095 and 4225/4224 are also tempered out there. Thus, any temperament of olympic also tempers it out. See [[Olympic clan|here]] for a compendium of temperaments and edos that temper out this comma due to being olympian.
+This comma is trivially tempered out in [[olympic|(tridecimal) olympic]], as 4096/4095 and 4225/4224 are also tempered out there. Thus, any temperament of olympic also tempers it out. See [[Olympic clan|here]] for a compendium of temperaments and edos that temper out this comma due to being olympic.
 Other non-olympian edos that temper out the insanisma by patent val, but not either of S64 and S65 include {{EDOs| 35, 40, 49 }}, and some hyperfine edos like [[3395edo|3395]] and [[8539edo|8539]].
+=== Insanismic ===
+[[Subgroup]]: 2.3.5.7.11.13
+[[Comma list]]: [[5767168/5767125]]
+[[Mapping]]: [⟨ 1 0 0 0 2 7 ], ⟨ 0 1 0 0 0 0 ], ⟨ 0 0 1 0 0 -1 ], ⟨ 0 0 0 1 1 0 ], ⟨ 0 0 0 0 3 1 ]]
+Mapping generators: ~2, ~3, ~5, ~7, ~65/128
+[[Optimal tuning|Optimal tunings]]:
+: [[WE]]: ~2 = 1199.999558¢, ~3/2 = 701.955501¢, ~5/4 = 386.314974¢, ~7/4 = 968.826974¢, ~65/128 = -1173.1542¢
+: error map: -0.000442 0.000058 0.000376 0.000183 -0.000278 0.000955
+: [[CWE]]: ~2 = 1200.¢, ~3/2 = 701.955606¢, ~5/4 = 386.315031¢, ~7/4 = 968.827097¢, ~65/128 = -1173.154680¢
+: error map: 0.000000 0.000605 0.001318 0.001190 0.000720 0.002627
+[[Optimal ET sequence]]: [[7edo|7]], [[10edo|10e]], [[12edo|12e]], [[30edo|30b]], [[31edo|31e]], [[34edo|34]], [[36edo|36]], [[41edo|41]], [[46edo|46]], [[53edo|53]], [[84edo|84]], [[87edo|87]], [[130edo|130]], [[183edo|183]], [[217edo|217]], [[224edo|224]], [[270edo|270]], [[494edo|494]], [[764edo|764]], [[935edo|935]], [[1075edo|1075]], [[1205edo|1205]], [[1609edo|1609]], [[1696edo|1696]], [[1920edo|1920]], [[2190edo|2190]], [[2684edo|2684]], [[3395edo|3395]], [[5144edo|5144]], [[5585edo|5585]], [[6079edo|6079]], [[8269edo|8269]], [[8539edo|8539]], [[11664edo|11664]], [[14124edo|14124]], [[14348edo|14348]], [[14618edo|14618]], [[20203edo|20203]]
+Badness (Sintel): 0.241
 == Etymology ==
-This comma was named by [[Eufalesio]] in 2026, on the basis that tempering out this comma alone purportedly entails an ''insane'' level of precision.
+This comma was named by [[Eufalesio]] in 2026, on the basis that tempering out this comma alone purportedly entails a ''insane'' level of precision.
 [[Category:Insanismic]]
 [[Category:Commas named for other reasons]]