Septimal enneadeca - Revision history

Lériendil at 10:32, 25 August 2024

2024-08-25T10:32:08Z

← Older revision		Revision as of 10:32, 25 August 2024
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	\| Comma = yes		\| Comma = yes
	}}		}}
	The '''septimal enneadeca''' ({{monzo\|legend=1\| -37 57 0 -19 }}), is an interval of 2.~~816~~ [[cent]]s which is the amount by which nineteen [[28/27]]'s fall short of an octave, that is, 2/(28/27)<sup>19</sup>.		The '''septimal enneadeca''' ({{monzo\|legend=1\| -37 57 0 -19 }}), is an interval of 3.743 [[cent]]s which is the amount by which nineteen [[28/27]]'s fall short of an octave, that is, 2/(28/27)<sup>19</sup>.

	== Temperaments ==		== Temperaments ==

Godtone: remove name to increase clarity

2024-04-08T19:37:41Z

remove name to increase clarity

← Older revision		Revision as of 19:37, 8 April 2024
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	\| Ratio = 1 570 042 899 082 081 611 640 534 563 /<br>1 566 652 225 014 704 215 735 402 496		\| Ratio = 1 570 042 899 082 081 611 640 534 563 /<br>1 566 652 225 014 704 215 735 402 496
	\| Monzo = -37 57 0 -19		\| Monzo = -37 57 0 -19
	\| Name = septimal enneadeca~~, septienneadeca~~		\| Name = septimal enneadeca
	\| Comma = yes		\| Comma = yes
	}}		}}
	The '''septimal enneadeca~~''' or '''septienneadeca~~''' ({{monzo\|legend=1\| -37 57 0 -19 }}), is an interval of 2.816 [[cent]]s which is the amount by which nineteen [[28/27]]'s fall short of an octave, that is, 2/(28/27)<sup>19</sup>.		The '''septimal enneadeca''' ({{monzo\|legend=1\| -37 57 0 -19 }}), is an interval of 2.816 [[cent]]s which is the amount by which nineteen [[28/27]]'s fall short of an octave, that is, 2/(28/27)<sup>19</sup>.

	== Temperaments ==		== Temperaments ==

Godtone: avoid unnecessary temp distinction (i believe my original addition was in error)

2024-04-08T19:36:23Z

avoid unnecessary temp distinction (i believe my original addition was in error)

@@ Line 8: / Line 8: @@
 == Temperaments ==
-=== Septienneadecal ===
+Because of how accurately [[19edo]] approximates [[6/5]], there is no real reason to not also temper out the [[enneadeca]] with the septimal enneadeca, leading to the 7-limit version of [[enneadecal]].
 ==== Enneadecal ====

FloraC: Style for enormous ratio

2024-03-22T08:48:07Z

Style for enormous ratio

← Older revision		Revision as of 08:48, 22 March 2024
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	{{Infobox Interval		{{Infobox Interval
	\| Ratio = ~~1570042899082081611640534563~~/~~1566652225014704215735402496~~		\| Ratio = 1 570 042 899 082 081 611 640 534 563 /<br>1 566 652 225 014 704 215 735 402 496
	\| Monzo = -37 57 0 -19		\| Monzo = -37 57 0 -19
	\| Name = septimal enneadeca, septienneadeca		\| Name = septimal enneadeca, septienneadeca

ArrowHead294 at 17:44, 21 March 2024

2024-03-21T17:44:02Z

← Older revision		Revision as of 17:44, 21 March 2024
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	{{Infobox Interval		{{Infobox Interval
			\| Ratio = 1570042899082081611640534563/1566652225014704215735402496
	\| Monzo = -37 57 0 -19		\| Monzo = -37 57 0 -19
	\| Name = septimal enneadeca, septienneadeca		\| Name = septimal enneadeca, septienneadeca

FloraC: "Septimal enneadecal" can't be used to contrast "7-limit enneadecal", contracted to "septienneadecal"

2024-03-15T08:22:34Z

"Septimal enneadecal" can't be used to contrast "7-limit enneadecal", contracted to "septienneadecal"

← Older revision		Revision as of 08:22, 15 March 2024
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	{{Infobox Interval		{{Infobox Interval
	\| Monzo = -37 57 0 -19		\| Monzo = -37 57 0 -19
	\| Name = septimal enneadeca		\| Name = septimal enneadeca, septienneadeca
	\| Comma = yes		\| Comma = yes
	}}		}}
	~~{{Monzo\| -37 57 0 -19 }}, the~~ '''septimal enneadeca''' or '''~~19-tone-comma~~''', is an interval of 2.816 ~~cents~~ which is the amount by which nineteen [[28/27]]'s fall short of an octave, that is, 2/(28/27)<sup>19</sup>.		The '''septimal enneadeca''' or '''septienneadeca''' ({{monzo\|legend=1\| -37 57 0 -19 }}), is an interval of 2.816 [[cent]]s which is the amount by which nineteen [[28/27]]'s fall short of an octave, that is, 2/(28/27)<sup>19</sup>.

	== Temperaments ==		== Temperaments ==
	=== ~~Septimal enneadecal~~ ===		=== Septienneadecal ===
	This temperament is a no-5's temperament in the 7-limit; contrast with 7-limit [[enneadecal]], which adds a mapping for 5 by tempering the [[enneadeca]].		This temperament is a no-5's temperament in the 7-limit; contrast with 7-limit [[enneadecal]], which adds a mapping for 5 by tempering out the [[enneadeca]].

	[[Subgroup]]: 2.3.7		[[Subgroup]]: 2.3.7

	~~Mapping:~~ {{Mapping\| 19 0 -37 \| 0 1 3}}		{{Mapping\|legend=1\| 19 0 -37 \| 0 1 3 }}

	~~[[CTE]]~~ generators: ~28/27 ~~= 1\19~~, ~3 ~~= 1901.906~~		: mapping generators: ~28/27, ~3

	[[~~Patent val~~]] ~~EDOs < 400~~: 19, ~~152, 171, 190, 323~~		[[Optimal tuning]] ([[CTE]]): ~28/27 = 1\19, ~3/2 = 701.906 (~{{monzo\| 14 -23 0 8 }} = 6.969)

	=~~=== [[Enneadecal]] ====~~		{{Optimal ET sequence\|legend=1\| 19, …, 152, 171, 494, 665, 836, 1007, 1843, 2850, 6707, 9557 }}
	~~[[Subgroup]]: 2.3.5.7~~

	~~{{Mapping\|legend=1\| 19~~ 0 ~~14 -37 \| 0 1 1 3 }}~~		[[Badness]]: 0.00146

	See: [[Enneadecal]]		==== Enneadecal ====
			See [[Ragismic microtemperaments #Enneadecal]].

	== See also ==		== See also ==

Godtone: /* See also */ correction

2024-03-15T01:17:46Z

Godtone: Created page with "{{Infobox Interval | Monzo = -37 57 0 -19 | Name = septimal enneadeca | Comma = yes }} {{Monzo| -37 57 0 -19 }}, the '''septimal enneadeca''' or '''19-tone-comma''', is an int..."

2024-03-15T01:17:26Z

Created page with "{{Infobox Interval | Monzo = -37 57 0 -19 | Name = septimal enneadeca | Comma = yes }} {{Monzo| -37 57 0 -19 }}, the '''septimal enneadeca''' or '''19-tone-comma''', is an int..."

New page

{{Infobox Interval
| Monzo = -37 57 0 -19
| Name = septimal enneadeca
| Comma = yes
}}
{{Monzo| -37 57 0 -19 }}, the '''septimal enneadeca''' or '''19-tone-comma''', is an interval of 2.816 cents which is the amount by which nineteen [[28/27]]'s fall short of an octave, that is, 2/(28/27)<sup>19</sup>.

== Temperaments ==
=== Septimal enneadecal ===
This temperament is a no-5's temperament in the 7-limit; contrast with 7-limit [[enneadecal]], which adds a mapping for 5 by tempering the [[enneadeca]].

[[Subgroup]]: 2.3.7

Mapping: {{Mapping| 19 0 -37 | 0 1 3}}

[[CTE]] generators: ~28/27 = 1\19, ~3 = 1901.906

[[Patent val]] EDOs < 400: 19, 152, 171, 190, 323

==== [[Enneadecal]] ====
[[Subgroup]]: 2.3.5.7

{{Mapping|legend=1| 19 0 14 -37 | 0 1 1 3 }}

See: [[Enneadecal]]

== See also ==
* [[Unnoticeable comma]]
* [[Septimal enneadeca]]

[[Category:Enneadecal]]

← Older revision		Revision as of 01:17, 15 March 2024
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	== See also ==		== See also ==
	* [[Unnoticeable comma]]		* [[Unnoticeable comma]]
	* [[~~Septimal enneadeca~~]]		* [[Enneadeca]]

	[[Category:Enneadecal]]		[[Category:Enneadecal]]