BudjarnLambeth: {{Editable user page}}

2025-05-18T02:58:19Z

← Older revision		Revision as of 02:58, 18 May 2025
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			{{Editable user page}}

	The '''equal division of 17/5''' ('''ed17/5''') is a [[tuning]] obtained by dividing the [[17/5\|septendecimal major thirteenth (17/5)]] into a number of [[equal]] steps.		The '''equal division of 17/5''' ('''ed17/5''') is a [[tuning]] obtained by dividing the [[17/5\|septendecimal major thirteenth (17/5)]] into a number of [[equal]] steps.

BudjarnLambeth: BudjarnLambeth moved page Ed17/5 to User:BudjarnLambeth/Ed17/5: See#wiki on XA Discord

2025-05-18T01:35:49Z

BudjarnLambeth moved page Ed17/5 to User:BudjarnLambeth/Ed17/5: See#wiki on XA Discord

← Older revision	Revision as of 01:35, 18 May 2025
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BudjarnLambeth: /* Notable ed17/5s */ remove one that’s not as great as it looked on paper

2025-01-13T10:16:31Z

Notable ed17/5s: remove one that’s not as great as it looked on paper

← Older revision		Revision as of 10:16, 13 January 2025
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	== Notable ed17/5s==		== Notable ed17/5s==

	~~=== 21ed17/5 ===~~
	* 2.3.11.13.31 all within 15 cents
	* Stretched [[12edo]]
	* Much better 11.13.23.29.31 than 13edo
	* Much worse 2.3.5.7.17.19 than 13edo
	* The appeal of this tuning is that it has the melodic structure of 12edo but extremely [[xenharmonic]] harmonies forcing the use of 11s and 13s
	~~{{Harmonics in equal\|21\|17\|5\|intervals=prime}}~~
	~~{{Harmonics in equal\|12\|2\|1\|intervals=prime\|collapsed=1}}~~
	~~; Intervals~~
	~~{{Interval table\|21ed17/5}}~~

	=== 22ed17/5 ===		=== 22ed17/5 ===

BudjarnLambeth: Grouping these new edonoi in a single long page because I don’t want to flood new page creations with individual pages for them (this was the same reasoning behind the ed13/4 and ed15/4 pages too). I won’t make a lot of pages like this. Sometimes I just like to explore something odd and document what I find so future explorers can build from where I left off, so that’s what this is. Not anything big or systematic, just sporadic manual exploration.

2025-01-13T10:09:00Z

Grouping these new edonoi in a single long page because I don’t want to flood new page creations with individual pages for them (this was the same reasoning behind the ed13/4 and ed15/4 pages too). I won’t make a lot of pages like this. Sometimes I just like to explore something odd and document what I find so future explorers can build from where I left off, so that’s what this is. Not anything big or systematic, just sporadic manual exploration.

New page

The '''equal division of 17/5''' ('''ed17/5''') is a [[tuning]] obtained by dividing the [[17/5|septendecimal major thirteenth (17/5)]] into a number of [[equal]] steps.

== Properties ==
Division of 17/5 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed17/5 scales have a perceptually important [[Pseudo-octave|false octave]], with various degrees of accuracy.

Equivalence aside, the structural significance of thirteenths like 17/5 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]].

Ed17/5s are in the region where they may experience [[structural beating]] with the interval [[3/1]].

== Notable ed17/5s==

=== 21ed17/5 ===
* 2.3.11.13.31 all within 15 cents
* Stretched [[12edo]]
* Much better 11.13.23.29.31 than 13edo
* Much worse 2.3.5.7.17.19 than 13edo
* The appeal of this tuning is that it has the melodic structure of 12edo but extremely [[xenharmonic]] harmonies forcing the use of 11s and 13s
{{Harmonics in equal|21|17|5|intervals=prime}}
{{Harmonics in equal|12|2|1|intervals=prime|collapsed=1}}
; Intervals
{{Interval table|21ed17/5}}

=== 22ed17/5 ===
* 5.7.11.13.17.19 all within 11 cents
* Stretched [[29ed5]]
* Much better 11.13 than 29ed5
* Much worse 3.31 than 29ed5
{{Harmonics in equal|22|17|5|intervals=prime}}
{{Harmonics in equal|29|5|1|intervals=prime|collapsed=1}}
; Intervals
{{Interval table|22ed17/5}}

=== 28ed17/5 ===
* 2.3.5.11.17.29 all within 14 cents
* Stretched [[16edo]]
* Much better 3.11.17.23.29 than 16edo
* Much worse 2.7.13.19.31 than 16edo
{{Harmonics in equal|28|17|5|intervals=prime}}
{{Harmonics in equal|16|2|1|intervals=prime|collapsed=1}}
; Intervals
{{Interval table|28ed17/5}}

=== 29ed17/5 ===
* 3.5.7.11.13.17.19.29 all within 16 cents
* Compressed [[26edt]] (double Bohlen-Pierce)
* Much better 11.13.19.29 than 26edt
* Much worse 17.23.31 than 26edt
{{Harmonics in equal|29|17|5|intervals=prime}}
{{Harmonics in equal|26|3|1|intervals=prime|collapsed=1}}
; Intervals
{{Interval table|29ed17/5}}

=== 32ed17/5 ===
* 2.3.5.7.11.13.17.19.23.29.31 all within 20 cents
* Compressed [[18edo]]
* Much better 3.5.7.13.17.19.23.29 than 18edo
* Much worse 2 than 18edo
{{Harmonics in equal|32|17|5|intervals=prime}}
{{Harmonics in equal|18|2|1|intervals=prime|collapsed=1}}
; Intervals
{{Interval table|32ed17/5}}

=== 41ed17/5 ===
* 2.3.5.7.11.13.17.19.23.29.31 all within 19 cents
* 2.3.5.7.13.17.23.29.31 all within 12 cents
* Compressed [[23edo]]
* Much better 3.5.7.11.29 than 23edo
* Much worse 2.19 than 23edo
{{Harmonics in equal|41|17|5|intervals=prime}}
{{Harmonics in equal|23|2|1|intervals=prime|collapsed=1}}
; Intervals
{{Interval table|41ed17/5}}

=== 42ed17/5 ===
* 2.3.5.7.11.13.17.19.31 all within 15 cents
* Stretched [[24edo]]
* Much better 7.13 than 24edo
* Much worse 2.3.11.17 than 24edo
* The appeal of this tuning is that it brings 7/1 within 15 cents without pushing any prime below 23/1 outside 15 cents
{{Harmonics in equal|42|17|5|intervals=prime}}
{{Harmonics in equal|24|2|1|intervals=prime|collapsed=1}}
; Intervals
{{Interval table|42ed17/5}}

=== 48ed17/5 ===
* 2.3.5.7.11.17.23.29.31 all within 15 cents
* Compressed [[27edo]]
* Much better 3.5.11.17 than 27edo
* Much worse 2.7.13.19 than 27edo
* The appeal of this tuning is that it brings 11/1 within 15 cents without pushing any prime below 19/1 outside 15 cents
{{Harmonics in equal|48|17|5|intervals=prime}}
{{Harmonics in equal|27|2|1|intervals=prime|collapsed=1}}
; Intervals
{{Interval table|48ed17/5}}

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

User:BudjarnLambeth/Ed17/5 - Revision history

BudjarnLambeth: {{Editable user page}}

BudjarnLambeth: BudjarnLambeth moved page Ed17/5 to User:BudjarnLambeth/Ed17/5: See#wiki on XA Discord

BudjarnLambeth: /* Notable ed17/5s */ remove one that’s not as great as it looked on paper