27edt - Revision history

Rperlner: /* See also */

2025-07-03T19:20:44Z

FloraC: /* Theory */ +subsets and supersets

2025-05-21T14:21:17Z

Theory: +subsets and supersets

← Older revision		Revision as of 14:21, 21 May 2025
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	{{Harmonics in equal\|27\|3\|1\|intervals=integer\|columns=11}}		{{Harmonics in equal\|27\|3\|1\|intervals=integer\|columns=11}}
	{{Harmonics in equal\|27\|3\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 27edt (continued)}}		{{Harmonics in equal\|27\|3\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 27edt (continued)}}

			=== Subsets and supersets ===
			Since 27 factors into primes as 3<sup>3</sup>, 27edt contains [[3edt]] and [[9edt]] as subset edts.

	=== Miscellany ===		=== Miscellany ===

FloraC: /* Theory */ + a second harmonics table

2025-05-21T14:18:27Z

Theory: + a second harmonics table

← Older revision		Revision as of 14:18, 21 May 2025
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	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|27\|3\|1\|columns=11}}		{{Harmonics in equal\|27\|3\|1\|intervals=integer\|columns=11}}
			{{Harmonics in equal\|27\|3\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 27edt (continued)}}

	=== Miscellany ===		=== Miscellany ===
	27 being the third power of 3, and the base interval being 3/1, 27edt is a tuning where the number 3 prevails. This property seems to predestine 27edt as base tuning for {{w\|Klingon}} music since the tradtional Klingon number system is also based on 3. The rather harsh harmonic character of 27edt would suit very well, too<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_86909.html Yahoo! Tuning Group \| ''the evil 27 equal temp scale from outer space'']</ref><ref>[https://web.archive.org/web/20100624113458/https://www.klingon.org/smboard/index.php?topic=1810.0 Klingon Imperial Forums \| ''klingon music theory'']</ref>.		27 being the third power of 3, and the base interval being 3/1, 27edt is a tuning where the number 3 prevails. This property seems to predestine 27edt as base tuning for {{w\|Klingon}} music since the tradtional Klingon number system is also based on 3. The rather harsh harmonic character of 27edt would suit very well, too<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_86909.html Yahoo! Tuning Group \| ''the evil 27 equal temp scale from outer space'']</ref><ref>[https://web.archive.org/web/20100624113458/https://www.klingon.org/smboard/index.php?topic=1810.0 Klingon Imperial Forums \| ''klingon music theory'']</ref>.

	This being said, such a proposal is rather short-sighted from a general cultural perspective, since any kind of living creature would most likely gravitate towards some form of [[low-complexity JI]], and while 27edt will gain appreciation in base-3 cultures at some point, it may not be the first temperament they discover. That would be like aliens assuming dominant tuning in human music is [[100ed10]] (or 1000ed10 or variation thereof) just because we count in base 10.		This being said, such a proposal is rather short-sighted from a general cultural perspective, since any kind of living creature would most likely gravitate towards some form of [[low-complexity JI]], and while 27edt will gain appreciation in base-3 cultures at some point, it may not be the first temperament they discover. That would be like aliens assuming dominant tuning in human music is [[100ed10]] (or 1000ed10 or variation thereof) just because we count in base 10.

	== Intervals ==		== Intervals ==

FloraC: Cleanup

2025-05-21T14:16:00Z

Cleanup

← Older revision		Revision as of 14:16, 21 May 2025
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	{{interwiki		{{interwiki
			\| en = 27edt
	\| de = 27-EDT		\| de = 27-EDT
	~~\| en = 27edt~~
	}}		}}
	{{Infobox ET}}		{{Infobox ET}}
	~~'''27edt''' means '''division of the tritave ([[3/1]]) into 27 equal parts'''.~~		{{ED intro}}

	~~Dividing the interval of 3/1 into 27 equal parts gives a scale with a basic step of 70.4428 [[cent]]s, corresponding~~ to 17.~~035 edo~~, which is nearly identical to one step of [[17edo]] (70.59 cents). Hence it has similar melodic and harmonic properties as 17edo, with the difference that 27 is not a [[prime number]]. In fact, the ~~prime edos that approximate~~ [[~~Pythagorean tuning~~]] ~~commonly become~~ composite edts: e. g. [[19edo]] > [[30edt]], [[29edo]] > [[46edt]] and [[31edo]] > [[49edt]].		== Theory ==
			27edt corresponds to 17.035…edo, which is nearly identical to one step of [[17edo]] (70.59 cents). Hence it has similar melodic and harmonic properties as 17edo, with the difference that 27 is not a [[prime number]]. In fact, the [[prime edo]]s that approximate the 3-limit well often correspond to composite edts: e.g. [[19edo]] → [[30edt]], [[29edo]] → [[46edt]] and [[31edo]] → [[49edt]].

	Compared to 17edo, 27edt approximates the primes 7, 11, and 13 better; it approximates prime 5 equally poorly, but maps ~~5/1~~ to 40 steps rather than 39, corresponding to the 17c [[val]], often considered the better mapping as it equates [[5/4]] and [[6/5]] to major and minor thirds rather than to a neutral third, and 5 has the same sharp tendency as 7 and 11. From a purely tritave-based perspective, it supports [[Minalzidar]] temperament, but otherwise it can be used as a retuning of 17edo with closer-to-just harmonic properties in the no-fives 2.3.7.11.13 subgroup.		Compared to 17edo, 27edt approximates the [[prime interval\|primes]] [[7/1\|7]], [[11/1\|11]], and [[13/1\|13]] better; it approximates prime [[5/1\|5]] equally poorly, but maps it to 40 steps rather than 39 in the [[patent val]], corresponding to the 17c [[val]], often considered the better mapping as it equates [[5/4]] and [[6/5]] to major and minor thirds rather than to a neutral third, and 5 has the same sharp tendency as 7 and 11.

	~~27 being the third power of 3~~, ~~and~~ the ~~base interval being 3/1~~, ~~27edt is~~ a ~~tuning where~~ the ~~number~~ 3 ~~prevails~~. ~~This property seems to predestine 27edt as base tuning for [https://en~~.~~wikipedia~~.~~org/wiki/Klingon Klingon] music (since the tradtional Klingon number system is also based on 3). The rather harsh harmonic character of 27edt would suit very well, too~~.		From a purely tritave-based perspective, it [[support]]s the [[minalzidar]] temperament, but otherwise it can be used as a retuning of 17edo with closer-to-just harmonic properties in the no-fives 2.3.7.11.13 subgroup.

	~~See, e.g., http://launch.dir.groups.yahoo.com/group/tuning/message/86909 and http://www.klingon.org/smboard/index.php?topic~~=~~1810.0.~~		=== Harmonics ===
			{{Harmonics in equal\|27\|3\|1\|columns=11}}

	~~This~~ being ~~said, such a proposal is rather short-sighted from a general cultural perspective, since any kind~~ of ~~living creature would most likely gravitate towards some form of low-complexity JI~~, and ~~while 27edt will gain appreciation in~~ base-3 ~~cultures at some point~~, ~~it may not be~~ the ~~first temperament they discover~~. ~~That would be like aliens assuming dominant~~ tuning ~~in human~~ music is [[~~100ed10~~]~~] (or 1000ed10 or variation thereof) just because we count in base 10~~.		=== Miscellany ===
			27 being the third power of 3, and the base interval being 3/1, 27edt is a tuning where the number 3 prevails. This property seems to predestine 27edt as base tuning for {{w\|Klingon}} music since the tradtional Klingon number system is also based on 3. The rather harsh harmonic character of 27edt would suit very well, too<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_86909.html Yahoo! Tuning Group \| ''the evil 27 equal temp scale from outer space'']</ref><ref>[https://web.archive.org/web/20100624113458/https://www.klingon.org/smboard/index.php?topic=1810.0 Klingon Imperial Forums \| ''klingon music theory'']</ref>.

	~~==Harmonics==~~		This being said, such a proposal is rather short-sighted from a general cultural perspective, since any kind of living creature would most likely gravitate towards some form of [[low-complexity JI]], and while 27edt will gain appreciation in base-3 cultures at some point, it may not be the first temperament they discover. That would be like aliens assuming dominant tuning in human music is [[100ed10]] (or 1000ed10 or variation thereof) just because we count in base 10.
	~~{{Harmonics~~ in ~~equal\|27\|~~3~~\|1\|prec=2\|columns=15}}~~

	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

	[[~~Category:Edt~~]]		== See also ==
	[[~~Category:Nonoctave~~]]		* [[10edf]] – relative edf
			* [[17edo]] – relative edo
			* [[44ed6]] – relative edo

			== Notes ==

Hstraub at 10:45, 18 May 2025

2025-05-18T10:45:56Z

← Older revision		Revision as of 10:45, 18 May 2025
Line 10:		Line 10:
	Compared to 17edo, 27edt approximates the primes 7, 11, and 13 better; it approximates prime 5 equally poorly, but maps 5/1 to 40 steps rather than 39, corresponding to the 17c [[val]], often considered the better mapping as it equates [[5/4]] and [[6/5]] to major and minor thirds rather than to a neutral third, and 5 has the same sharp tendency as 7 and 11. From a purely tritave-based perspective, it supports [[Minalzidar]] temperament, but otherwise it can be used as a retuning of 17edo with closer-to-just harmonic properties in the no-fives 2.3.7.11.13 subgroup.		Compared to 17edo, 27edt approximates the primes 7, 11, and 13 better; it approximates prime 5 equally poorly, but maps 5/1 to 40 steps rather than 39, corresponding to the 17c [[val]], often considered the better mapping as it equates [[5/4]] and [[6/5]] to major and minor thirds rather than to a neutral third, and 5 has the same sharp tendency as 7 and 11. From a purely tritave-based perspective, it supports [[Minalzidar]] temperament, but otherwise it can be used as a retuning of 17edo with closer-to-just harmonic properties in the no-fives 2.3.7.11.13 subgroup.

	27 being the third power of 3, and the base interval being 3/1, 27edt is a tuning where the number 3 prevails. This property seems to predestine 27edt as base tuning for Klingon music (since the tradtional Klingon number system is also based on 3). The rather harsh harmonic character of 27edt would suit very well, too.		27 being the third power of 3, and the base interval being 3/1, 27edt is a tuning where the number 3 prevails. This property seems to predestine 27edt as base tuning for [https://en.wikipedia.org/wiki/Klingon Klingon] music (since the tradtional Klingon number system is also based on 3). The rather harsh harmonic character of 27edt would suit very well, too.

	See, e.g., http://launch.dir.groups.yahoo.com/group/tuning/message/86909 and http://www.klingon.org/smboard/index.php?topic=1810.0.		See, e.g., http://launch.dir.groups.yahoo.com/group/tuning/message/86909 and http://www.klingon.org/smboard/index.php?topic=1810.0.

Hstraub at 10:21, 18 May 2025

2025-05-18T10:21:12Z

← Older revision		Revision as of 10:21, 18 May 2025
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			{{interwiki
			\| de = 27-EDT
			\| en = 27edt
			}}
	{{Infobox ET}}		{{Infobox ET}}
	'''27edt''' means '''division of the tritave ([[3/1]]) into 27 equal parts'''.		'''27edt''' means '''division of the tritave ([[3/1]]) into 27 equal parts'''.

Lériendil at 15:32, 12 January 2025

2025-01-12T15:32:58Z

← Older revision		Revision as of 15:32, 12 January 2025
Line 4:		Line 4:
	Dividing the interval of 3/1 into 27 equal parts gives a scale with a basic step of 70.4428 [[cent]]s, corresponding to 17.035 edo, which is nearly identical to one step of [[17edo]] (70.59 cents). Hence it has similar melodic and harmonic properties as 17edo, with the difference that 27 is not a [[prime number]]. In fact, the prime edos that approximate [[Pythagorean tuning]] commonly become composite edts: e. g. [[19edo]] > [[30edt]], [[29edo]] > [[46edt]] and [[31edo]] > [[49edt]].		Dividing the interval of 3/1 into 27 equal parts gives a scale with a basic step of 70.4428 [[cent]]s, corresponding to 17.035 edo, which is nearly identical to one step of [[17edo]] (70.59 cents). Hence it has similar melodic and harmonic properties as 17edo, with the difference that 27 is not a [[prime number]]. In fact, the prime edos that approximate [[Pythagorean tuning]] commonly become composite edts: e. g. [[19edo]] > [[30edt]], [[29edo]] > [[46edt]] and [[31edo]] > [[49edt]].

	Compared to 17edo, 27edt approximates the primes 7, 11, and 13 better; it approximates prime 5 equally poorly, but maps 5/1 to 40 steps rather than 39, corresponding to the 17c [[val]], often considered the better mapping as it equates [[5/4]] and [[6/5]] to major and minor thirds rather than to a neutral third. From a purely tritave-based perspective, it supports [[Minalzidar]] temperament, but otherwise it can be used as a retuning of 17edo with closer-to-just harmonic properties in the no-fives 2.3.7.11.13 subgroup.		Compared to 17edo, 27edt approximates the primes 7, 11, and 13 better; it approximates prime 5 equally poorly, but maps 5/1 to 40 steps rather than 39, corresponding to the 17c [[val]], often considered the better mapping as it equates [[5/4]] and [[6/5]] to major and minor thirds rather than to a neutral third, and 5 has the same sharp tendency as 7 and 11. From a purely tritave-based perspective, it supports [[Minalzidar]] temperament, but otherwise it can be used as a retuning of 17edo with closer-to-just harmonic properties in the no-fives 2.3.7.11.13 subgroup.

	27 being the third power of 3, and the base interval being 3/1, 27edt is a tuning where the number 3 prevails. This property seems to predestine 27edt as base tuning for Klingon music (since the tradtional Klingon number system is also based on 3). The rather harsh harmonic character of 27edt would suit very well, too.		27 being the third power of 3, and the base interval being 3/1, 27edt is a tuning where the number 3 prevails. This property seems to predestine 27edt as base tuning for Klingon music (since the tradtional Klingon number system is also based on 3). The rather harsh harmonic character of 27edt would suit very well, too.

Lériendil: added comparison w/ 17edo

2025-01-12T15:30:54Z

added comparison w/ 17edo

← Older revision		Revision as of 15:30, 12 January 2025
Line 3:		Line 3:

	Dividing the interval of 3/1 into 27 equal parts gives a scale with a basic step of 70.4428 [[cent]]s, corresponding to 17.035 edo, which is nearly identical to one step of [[17edo]] (70.59 cents). Hence it has similar melodic and harmonic properties as 17edo, with the difference that 27 is not a [[prime number]]. In fact, the prime edos that approximate [[Pythagorean tuning]] commonly become composite edts: e. g. [[19edo]] > [[30edt]], [[29edo]] > [[46edt]] and [[31edo]] > [[49edt]].		Dividing the interval of 3/1 into 27 equal parts gives a scale with a basic step of 70.4428 [[cent]]s, corresponding to 17.035 edo, which is nearly identical to one step of [[17edo]] (70.59 cents). Hence it has similar melodic and harmonic properties as 17edo, with the difference that 27 is not a [[prime number]]. In fact, the prime edos that approximate [[Pythagorean tuning]] commonly become composite edts: e. g. [[19edo]] > [[30edt]], [[29edo]] > [[46edt]] and [[31edo]] > [[49edt]].

			Compared to 17edo, 27edt approximates the primes 7, 11, and 13 better; it approximates prime 5 equally poorly, but maps 5/1 to 40 steps rather than 39, corresponding to the 17c [[val]], often considered the better mapping as it equates [[5/4]] and [[6/5]] to major and minor thirds rather than to a neutral third. From a purely tritave-based perspective, it supports [[Minalzidar]] temperament, but otherwise it can be used as a retuning of 17edo with closer-to-just harmonic properties in the no-fives 2.3.7.11.13 subgroup.

	27 being the third power of 3, and the base interval being 3/1, 27edt is a tuning where the number 3 prevails. This property seems to predestine 27edt as base tuning for Klingon music (since the tradtional Klingon number system is also based on 3). The rather harsh harmonic character of 27edt would suit very well, too.		27 being the third power of 3, and the base interval being 3/1, 27edt is a tuning where the number 3 prevails. This property seems to predestine 27edt as base tuning for Klingon music (since the tradtional Klingon number system is also based on 3). The rather harsh harmonic character of 27edt would suit very well, too.

Lériendil at 10:06, 27 August 2024

2024-08-27T10:06:49Z

← Older revision		Revision as of 10:06, 27 August 2024
Line 11:		Line 11:

	==Harmonics==		==Harmonics==
	{{Harmonics in equal\|30\|3\|1\|prec=2\|columns=15}}		{{Harmonics in equal\|27\|3\|1\|prec=2\|columns=15}}

	== Intervals ==		== Intervals ==

Lériendil at 10:06, 27 August 2024

2024-08-27T10:06:41Z

← Older revision		Revision as of 10:06, 27 August 2024
Line 9:		Line 9:

	This being said, such a proposal is rather short-sighted from a general cultural perspective, since any kind of living creature would most likely gravitate towards some form of low-complexity JI, and while 27edt will gain appreciation in base-3 cultures at some point, it may not be the first temperament they discover. That would be like aliens assuming dominant tuning in human music is [[100ed10]] (or 1000ed10 or variation thereof) just because we count in base 10.		This being said, such a proposal is rather short-sighted from a general cultural perspective, since any kind of living creature would most likely gravitate towards some form of low-complexity JI, and while 27edt will gain appreciation in base-3 cultures at some point, it may not be the first temperament they discover. That would be like aliens assuming dominant tuning in human music is [[100ed10]] (or 1000ed10 or variation thereof) just because we count in base 10.

			==Harmonics==
			{{Harmonics in equal\|30\|3\|1\|prec=2\|columns=15}}

	== Intervals ==		== Intervals ==

← Older revision		Revision as of 19:20, 3 July 2025
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	* [[10edf]] – relative edf		* [[10edf]] – relative edf
	* [[17edo]] – relative edo		* [[17edo]] – relative edo
	* [[44ed6]] – relative ~~edo~~		* [[44ed6]] – relative ed6

	== Notes ==		== Notes ==