User:BudjarnLambeth/Ed13/4 - Revision history

BudjarnLambeth: {{Editable user page}}

2025-05-18T02:58:48Z

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			{{Editable user page}}

	The '''equal division of 13/4''' ('''ed13/4''') is a [[tuning]] obtained by dividing the [[13/4\|tridecimal neutral thirteenth (13/4)]] into a number of [[equal]] steps.		The '''equal division of 13/4''' ('''ed13/4''') is a [[tuning]] obtained by dividing the [[13/4\|tridecimal neutral thirteenth (13/4)]] into a number of [[equal]] steps.

BudjarnLambeth: BudjarnLambeth moved page Ed13/4 to User:BudjarnLambeth/Ed13/4

2025-05-18T01:37:24Z

BudjarnLambeth moved page Ed13/4 to User:BudjarnLambeth/Ed13/4

← Older revision	Revision as of 01:37, 18 May 2025
(No difference)

BudjarnLambeth: /* Properties */

2025-01-12T12:00:33Z

Properties

← Older revision		Revision as of 12:00, 12 January 2025
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	Equivalence aside, the structural significance of thirteenths like 13/4 is apparent by being the the top of the upper structure of jazz voicings, as well as a fairly trivial point to split the difference between the [[3/1\|tritave]] and the [[4/1\|double octave]].		Equivalence aside, the structural significance of thirteenths like 13/4 is apparent by being the the top of the upper structure of jazz voicings, as well as a fairly trivial point to split the difference between the [[3/1\|tritave]] and the [[4/1\|double octave]].

	~~Ed15~~/4s are in the region where they may experience [[structural beating]] with the interval [[3/1]].		Ed13/4s are in the region where they may experience [[structural beating]] with the interval [[3/1]].

	== Notable ed13/4s==		== Notable ed13/4s==

BudjarnLambeth: /* Properties */ add line

2025-01-12T12:00:20Z

Properties: add line

← Older revision		Revision as of 12:00, 12 January 2025
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	Equivalence aside, the structural significance of thirteenths like 13/4 is apparent by being the the top of the upper structure of jazz voicings, as well as a fairly trivial point to split the difference between the [[3/1\|tritave]] and the [[4/1\|double octave]].		Equivalence aside, the structural significance of thirteenths like 13/4 is apparent by being the the top of the upper structure of jazz voicings, as well as a fairly trivial point to split the difference between the [[3/1\|tritave]] and the [[4/1\|double octave]].

			Ed15/4s are in the region where they may experience [[structural beating]] with the interval [[3/1]].

	== Notable ed13/4s==		== Notable ed13/4s==

BudjarnLambeth at 11:08, 12 January 2025

2025-01-12T11:08:29Z

← Older revision		Revision as of 11:08, 12 January 2025
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	== Properties ==		== Properties ==
	Division of 13/4 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed13/4 scales have a perceptually important false octave, with various degrees of accuracy.		Division of 13/4 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed13/4 scales have a perceptually important [[Pseudo-octave\|false octave]], with various degrees of accuracy.

	Equivalence aside, the structural significance of thirteenths like 13/4 is apparent by being the the top of the upper structure of jazz voicings, as well as a fairly trivial point to split the difference between the [[3/1\|tritave]] and the [[4/1\|double octave]].		Equivalence aside, the structural significance of thirteenths like 13/4 is apparent by being the the top of the upper structure of jazz voicings, as well as a fairly trivial point to split the difference between the [[3/1\|tritave]] and the [[4/1\|double octave]].

BudjarnLambeth: Created page with "The '''equal division of 13/4''' ('''ed13/4''') is a tuning obtained by dividing the tridecimal neutral thirteenth (13/4) into a number of equal steps. == P..."

2025-01-12T11:02:20Z

Created page with "The '''equal division of 13/4''' ('''ed13/4''') is a tuning obtained by dividing the tridecimal neutral thirteenth (13/4) into a number of equal steps. == P..."

New page

The '''equal division of 13/4''' ('''ed13/4''') is a [[tuning]] obtained by dividing the [[13/4|tridecimal neutral thirteenth (13/4)]] into a number of [[equal]] steps.

== Properties ==
Division of 13/4 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed13/4 scales have a perceptually important false octave, with various degrees of accuracy.

Equivalence aside, the structural significance of thirteenths like 13/4 is apparent by being the the top of the upper structure of jazz voicings, as well as a fairly trivial point to split the difference between the [[3/1|tritave]] and the [[4/1|double octave]].

== Notable ed13/4s==

=== 22ed13/4 ===
* 2.5.13.17.19.29.31 all within 14 cents
* Stretched [[13edo]]
* Much better 5.19.31 than 13edo
* Much worse 11.23 than 13edo
{{Harmonics in equal|22|13|4|intervals=prime}}
{{Harmonics in equal|13|2|1|intervals=prime|collapsed=1}}
; Intervals
{{Interval table|22ed13/4}}

=== 27ed13/4 ===
* 2.3.5.11.17.23.29 all within 14 cents
* Stretched [[16edo]]
* Much better 3.11.17.23.29 than 16edo
* Much worse 7.19 than 16edo
{{Harmonics in equal|27|13|4|intervals=prime}}
{{Harmonics in equal|16|2|1|intervals=prime|collapsed=1}}
; Intervals
{{Interval table|27ed13/4}}

=== 29ed13/4 ===
* 2.3.7.11.13.23.29 all within 11 cents
* Compressed [[17edo]]
* Much better 7.11.29 than 17edo
* Much worse 19.31 than 17edo
{{Harmonics in equal|29|13|4|intervals=prime}}
{{Harmonics in equal|17|2|1|intervals=prime|collapsed=1}}
; Intervals
{{Interval table|29ed13/4}}

=== 31ed13/4 ===
*2.3.7.11 all within 16 cents
* Compressed [[18edo]]
* Much better 3.7.11 than 17edo
* Much worse 2.5.31 than 17edo
{{Harmonics in equal|31|13|4|intervals=prime}}
{{Harmonics in equal|18|2|1|intervals=prime|collapsed=1}}
; Intervals
{{Interval table|31ed13/4}}

=== 32ed13/4 ===
* 2.3.7.11.17.19.23.31 all within 15 cents
* Stretched [[19edo]]
* Much better 7.11.17.19 than 19edo
* Much worse 2.5 than 19edo
{{Harmonics in equal|32|13|4|intervals=prime}}
{{Harmonics in equal|19|2|1|intervals=prime|collapsed=1}}
; Intervals
{{Interval table|32ed13/4}}

=== 33ed13/4 ===
* 3.5.11.13.23.31 all within 15 cents
* Compressed [[45ed5]]
* Much better 3.13.23 than 45ed5
* Much worse 17.29 than 45ed5
{{Harmonics in equal|33|13|4|intervals=prime}}
{{Harmonics in equal|45|5|1|intervals=prime|collapsed=1}}
; Intervals
{{Interval table|33ed13/4}}

=== 35ed13/4 ===
* 5.7.11.13.17.23.29.31 all within 13 cents
* Stretched [[48ed5]]
* Much better 11.13.17.23.29.31 than 48ed5
* Much worse 3.5.7.19 than 48ed5
{{Harmonics in equal|35|13|4|intervals=prime}}
{{Harmonics in equal|48|5|1|intervals=prime|collapsed=1}}
; Intervals
{{Interval table|35ed13/4}}

=== 43ed13/4 ===
* 2.3.5.7.29.31 all within 14 cents
* Compressed [[25edo]]
* Much better 3.7.29 than 48ed5
* Much worse 2.5.17.19.23 than 48ed5
{{Harmonics in equal|43|13|4|intervals=prime}}
{{Harmonics in equal|25|2|1|intervals=prime|collapsed=1}}
; Intervals
{{Interval table|43ed13/4}}

=== 46ed13/4 ===
* 2.3.5.7.13.19.31 all within 9 cents
* Compressed [[27edo]]
* Much better 3.5.7.19.31 than 27edo
* Much worse 23.29 than 27edo
{{Harmonics in equal|46|13|4|intervals=prime}}
{{Harmonics in equal|27|2|1|intervals=prime|collapsed=1}}
; Intervals
{{Interval table|43ed13/4}}

=== 47ed13/4 ===
* 2.3.5.7.11.13.17.19.23.29.31 all within 18 cents
* Stretched [[28edo]]
* Much better 3.13.17.23.31 than 28edo
* Much worse 2.11.19.29 than 28edo
{{Harmonics in equal|47|13|4|intervals=prime}}
{{Harmonics in equal|28|2|1|intervals=prime|collapsed=1}}
; Intervals
{{Interval table|43ed13/4}}

[[Category:Edonoi]]
[[Category:Lists of scales]]