User:Lhearne/15edo - Revision history

Fredg999: Text replacement - "Ups and Downs Notation" to "Ups and downs notation"

2025-08-20T01:13:17Z

Text replacement - "Ups and Downs Notation" to "Ups and downs notation"

← Older revision		Revision as of 01:13, 20 August 2025
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	=Notation=		=Notation=
	Because 15edo's best fifth is the same as that of [[5edo]], the circle of fifths fully closes with only five notes, meaning the [[256/243\|Pythagorean limma]] is tempered out. This slightly breaks traditional fifth-based notation, because E and F, as well as B and C, will merge into singular pitches. This also has the effect of making the [[2187/2048\|Pythagorean apotome]] equal to the [[9/8\|Pythagorean whole-tone]], such that the sharp and flat accidentals will indicate raising or lowering by one step of 5edo, or 240 cents. There are two main approaches to dealing with this issue: the use of ups and downs in conjunction with the traditional A through G nominals based on the 5edo circle of fifths, and the use of Porcupine temperament instead of the circle of fifths as a notational basis.		Because 15edo's best fifth is the same as that of [[5edo]], the circle of fifths fully closes with only five notes, meaning the [[256/243\|Pythagorean limma]] is tempered out. This slightly breaks traditional fifth-based notation, because E and F, as well as B and C, will merge into singular pitches. This also has the effect of making the [[2187/2048\|Pythagorean apotome]] equal to the [[9/8\|Pythagorean whole-tone]], such that the sharp and flat accidentals will indicate raising or lowering by one step of 5edo, or 240 cents. There are two main approaches to dealing with this issue: the use of ups and downs in conjunction with the traditional A through G nominals based on the 5edo circle of fifths, and the use of Porcupine temperament instead of the circle of fifths as a notational basis.
	==Ups and ~~Downs Notation~~==		==Ups and downs notation==
	In [[Ups and ~~Downs Notation~~#Summary of EDO notation-.22Pentatonic.22 EDOs\|ups and downs notation]], which is fifth-generated, every 15edo note has at least three names.		In [[Ups and downs notation#Summary of EDO notation-.22Pentatonic.22 EDOs\|ups and downs notation]], which is fifth-generated, every 15edo note has at least three names.
	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
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	0-4-9-13 = D F^ A C^ = D.^m7 = "D dot up minor-seven", or D F^ A B^ = D.^m6 = "D dot up minor-six"		0-4-9-13 = D F^ A C^ = D.^m7 = "D dot up minor-seven", or D F^ A B^ = D.^m6 = "D dot up minor-six"

	For a more complete list, see [[Ups and ~~Downs Notation~~#Chord names in other EDOs\|Ups and ~~Downs Notation~~ - Chord names in other EDOs]].		For a more complete list, see [[Ups and downs notation#Chord names in other EDOs\|Ups and downs notation - Chord names in other EDOs]].
	==Porcupine[7] Notation==		==Porcupine[7] Notation==
	''See the main [[Porcupine Notation\|porcupine notation]] page.''		''See the main [[Porcupine Notation\|porcupine notation]] page.''

	15edo can also be notated using the [[Ups and ~~Downs Notation~~#Natural Generators\|natural generator]], which is not the 9\15 5th but the 2\15 2nd. For 15edo, this is also known as porcupine notation. The 15edo porcupine genchain in both relative and absolute notation:		15edo can also be notated using the [[Ups and downs notation#Natural Generators\|natural generator]], which is not the 9\15 5th but the 2\15 2nd. For 15edo, this is also known as porcupine notation. The 15edo porcupine genchain in both relative and absolute notation:

	...A3 - A4 - A5 - A6 - A7 - A1 - A2 - M3 - M4 - M5 - M6 - P7 - P1 - P2 - m3 - m4 - m5 - m6 - d7 -- d8 - d2 - d3 -- d4 - d5 -- d6...		...A3 - A4 - A5 - A6 - A7 - A1 - A2 - M3 - M4 - M5 - M6 - P7 - P1 - P2 - m3 - m4 - m5 - m6 - d7 -- d8 - d2 - d3 -- d4 - d5 -- d6...

Lhearne: Lhearne moved page User:Gareth.hearne/15edo to User:Lhearne/15edo: moving to my new user page

2022-02-26T17:01:16Z

Lhearne moved page User:Gareth.hearne/15edo to User:Lhearne/15edo: moving to my new user page

← Older revision	Revision as of 17:01, 26 February 2022
(No difference)

Gareth.hearne at 12:52, 24 February 2019

2019-02-24T12:52:51Z

← Older revision		Revision as of 12:52, 24 February 2019
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	inverse of tetrachordal major, "just"/tetrachordal minor - 3123123		inverse of tetrachordal major, "just"/tetrachordal minor - 3123123

	Porcupine bright major ~~epipenta~~ - Porcupine[7] 6\|0 #7 - ~~3222321~~		Porcupine bright major #7 - Porcupine[7] 6\|0 #7 - 3222231

	Porcupine ~~dark~~ major ~~epipenta~~ - Porcupine[7] 6\|0 #7 - ~~3222231~~		Porcupine bright major #6 #7 - Porcupine[7] 6\|0 #7 - 3222321

	Porcupine bright minor ~~epipenta~~ - Porcupine[7] 4\|2 #2 3132222 (mode of ~~dark~~ major ~~epipenta~~)		Porcupine bright minor #2 - Porcupine[7] 4\|2 #2 3132222 (mode of bright major #7)

	Porcupine dark minor ~~epipenta~~ - Porcupine[7] 3\|3 #2 3123222 (inverse of bright major ~~epipenta~~)		Porcupine dark minor #2 - Porcupine[7] 3\|3 #2 3123222 (inverse of bright major #6 #7)

	Porcupine bright harmonic 11th mode - Porcupine[7] 6\|0 b7 3222213		Porcupine bright harmonic 11th mode - Porcupine[7] 6\|0 b7 3222213

Gareth.hearne at 07:27, 9 February 2019

2019-02-09T07:27:05Z

← Older revision		Revision as of 07:27, 9 February 2019
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	inverse of tetrachordal major, "just"/tetrachordal minor - 3123123		inverse of tetrachordal major, "just"/tetrachordal minor - 3123123

	Porcupine ~~harmonic~~ major - Porcupine[7] 6\|0 #7 - ~~3222231~~		Porcupine bright major epipenta - Porcupine[7] 6\|0 #7 - 3222321

	Porcupine ~~melodic~~ major - Porcupine[7] 6\|0 #6 #7 - ~~3222321~~		Porcupine dark major epipenta - Porcupine[7] 6\|0 #7 - 3222231

	Porcupine ~~melodic~~ minor - Porcupine[7] 3\|3 #2 - ~~3123222~~		Porcupine bright minor epipenta - Porcupine[7] 4\|2 #2 3132222 (mode of dark major epipenta)

			Porcupine dark minor epipenta - Porcupine[7] 3\|3 #2 3123222 (inverse of bright major epipenta)

			Porcupine bright harmonic 11th mode - Porcupine[7] 6\|0 b7 3222213

	"just" harmonic minor - 3123141		"just" harmonic minor - 3123141

Gareth.hearne at 04:49, 8 February 2019

2019-02-08T04:49:21Z

← Older revision		Revision as of 04:49, 8 February 2019
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	Porcupine melodic major - Porcupine[7] 6\|0 #6 #7 - 3222321		Porcupine melodic major - Porcupine[7] 6\|0 #6 #7 - 3222321

			Porcupine melodic minor - Porcupine[7] 3\|3 #2 - 3123222

	"just" harmonic minor - 3123141		"just" harmonic minor - 3123141

Gareth.hearne: /* Scales */

2019-02-07T14:20:06Z

Scales

← Older revision		Revision as of 14:20, 7 February 2019
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	<span class="" style="text-align: right; display: block;" data-ve-style="display: block; text-align: right;" data-ve-attributes="{"style":"text-align: right; display: block;"}">[[:de:15edo\|Deutsch]] - [[15平均律\|日本語]]</span>		<span class="" style="text-align: right; display: block;" data-ve-style="display: block; text-align: right;" data-ve-attributes="{"style":"text-align: right; display: block;"}">[[:de:15edo\|Deutsch]] - [[15平均律\|日本語]]</span>
	==Introduction==		==Introduction==
	15 Equal Divisions of the Octave (15edo) is a tuning which divides the octave into 15 equally spaced pitches. It can be thought of as three sets of 5edo connected to each other by intervals of 3edo.[[category:alternative pages]]		15 Equal Divisions of the Octave (15edo) is a tuning which divides the octave into 15 equally spaced pitches. It can be thought of as three sets of 5edo connected to each other by intervals of 3edo.
			[[category:alternative pages]]

	From [http://en.wikipedia.org/wiki/15_equal_temperament Wikipedia]:		From [http://en.wikipedia.org/wiki/15_equal_temperament Wikipedia]:
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	Blackwood[10]: 2121212121 (Blackwood Decatonic)		Blackwood[10]: 2121212121 (Blackwood Decatonic)

			Augmented[12]: 211121112111

	=== Other Scales ===		=== Other Scales ===
	Zarlino/Ptolemy ~~JI Major:~~ 3213231		Zarlino/Ptolemy diatonic, "just" major, Ma grama - 3213231

			inverse of Zarlino/Ptolemy diatonic, natural minor - 3123132

			tetrachordal major, Sa grama - 3213321

			inverse of tetrachordal major, "just"/tetrachordal minor - 3123123

			Porcupine harmonic major - Porcupine[7] 6\|0 #7 - 3222231

			Porcupine melodic major - Porcupine[7] 6\|0 #6 #7 - 3222321

			"just" harmonic minor - 3123141

			"just" harmonic major - 3213141

			"just" melodic minor ascending - 3123231

			"just" double harmonic - 1413141

	=Notation=		=Notation=

PiotrGrochowski at 06:35, 30 September 2018

2018-09-30T06:35:09Z

← Older revision		Revision as of 06:35, 30 September 2018
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	<span class="" style="text-align: right; display: block;" data-ve-style="display: block; text-align: right;" data-ve-attributes="{"style":"text-align: right; display: block;"}">[[:de:15edo\|Deutsch]] - [[15平均律\|日本語]]</span>		<span class="" style="text-align: right; display: block;" data-ve-style="display: block; text-align: right;" data-ve-attributes="{"style":"text-align: right; display: block;"}">[[:de:15edo\|Deutsch]] - [[15平均律\|日本語]]</span>
	==Introduction==		==Introduction==
	15 Equal Divisions of the Octave (15edo) is a tuning which divides the octave into 15 equally spaced pitches. It can be thought of as three sets of 5edo connected to each other by intervals of 3edo.		15 Equal Divisions of the Octave (15edo) is a tuning which divides the octave into 15 equally spaced pitches. It can be thought of as three sets of 5edo connected to each other by intervals of 3edo.[[category:alternative pages]]

	From [http://en.wikipedia.org/wiki/15_equal_temperament Wikipedia]:		From [http://en.wikipedia.org/wiki/15_equal_temperament Wikipedia]:

Keenan Pepper: Keenan Pepper moved page 15edo-b to User:Gareth.hearne/15edo without leaving a redirect: moving all "-a", "-b" etc. pages which have only one contributor to user subpages

2018-09-30T04:12:17Z

Keenan Pepper moved page 15edo-b to User:Gareth.hearne/15edo without leaving a redirect: moving all "-a", "-b" etc. pages which have only one contributor to user subpages

← Older revision	Revision as of 04:12, 30 September 2018
(No difference)

Mike Battaglia: /* 15edo as a Regular Temperament */ forgot 2.3.7.11

2018-09-26T21:54:27Z

15edo as a Regular Temperament: forgot 2.3.7.11

← Older revision		Revision as of 21:54, 26 September 2018
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	\|<15 24 35 52]		\|<15 24 35 52]
	\|14.693746		\|14.693746
			\|-
			\|2.3.7.11
			\|<15 24 42 52]
			\|18.660367
	\|-		\|-
	\|2.5.7.11		\|2.5.7.11
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	\|48.298		\|48.298
	\|}		\|}

	=Rank two temperaments=		=Rank two temperaments=
	[[List of 15et rank two temperaments by badness]]		[[List of 15et rank two temperaments by badness]]

Mike Battaglia: /* Theory */ broken links

2018-09-26T17:18:39Z

Theory: broken links

← Older revision		Revision as of 17:18, 26 September 2018
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	\|}		\|}
	=Theory=		=Theory=
	[http://~~sonic-arts~~.org/~~darreg/dar35.htm~~ The 15-Tone Scale System] by [[Ivor Darreg]] [http://~~www.webcitation~~.org/~~5xZyzKBEW Permalink~~]		[http://www.webcitation.org/5xZyzKBEW The 15-Tone Scale System] by [[Ivor_Darreg\|Ivor Darreg]] (Originally at [http://sonic-arts.org/darreg/dar35.htm], now broken)

	[http://www.inteas.com/Penta01.htm The Pentadecaphonic System]		[https://web.archive.org/web/20110713044141/http://www.inteas.com/Penta01.htm The Pentadecaphonic System] (Originally at [http://www.inteas.com/Penta01.htm], now broken)

			[http://www.webcitation.org/5xeJYBsDg 15-EDO Tutorial] by [[Brent_Carson\|Brent Carson]] (Originally at [http://home.comcast.net/%7Ebrentishere/15noteequaltempermenttutorial.html], now broken)

	~~[http://home.comcast.net/~brentishere/15noteequaltempermenttutorial.html 15-EDO Tutorial] by [[Brent Carson]] [http://www.webcitation.org/5xeJYBsDg Permalink]~~
	=Practical Theory / Books=		=Practical Theory / Books=
	[http://www.swordguitars.com/ Sword, Ronald. "Pendecaphonic Scales for Guitar" IAAA Press, UK-USA. First Ed: June 2009.] - A large repository of all known scales and temperament families in the 15-edo system. 300+ examples /w chord-scale progressions.		[http://www.swordguitars.com/ Sword, Ronald. "Pendecaphonic Scales for Guitar" IAAA Press, UK-USA. First Ed: June 2009.] - A large repository of all known scales and temperament families in the 15-edo system. 300+ examples /w chord-scale progressions.

← Older revision		Revision as of 12:52, 24 February 2019
Line 386:		Line 386:
	inverse of tetrachordal major, "just"/tetrachordal minor - 3123123		inverse of tetrachordal major, "just"/tetrachordal minor - 3123123

	Porcupine bright major ~~epipenta~~ - Porcupine[7] 6\|0 #7 - ~~3222321~~		Porcupine bright major #7 - Porcupine[7] 6\|0 #7 - 3222231

	Porcupine ~~dark~~ major ~~epipenta~~ - Porcupine[7] 6\|0 #7 - ~~3222231~~		Porcupine bright major #6 #7 - Porcupine[7] 6\|0 #7 - 3222321

	Porcupine bright minor ~~epipenta~~ - Porcupine[7] 4\|2 #2 3132222 (mode of ~~dark~~ major ~~epipenta~~)		Porcupine bright minor #2 - Porcupine[7] 4\|2 #2 3132222 (mode of bright major #7)

	Porcupine dark minor ~~epipenta~~ - Porcupine[7] 3\|3 #2 3123222 (inverse of bright major ~~epipenta~~)		Porcupine dark minor #2 - Porcupine[7] 3\|3 #2 3123222 (inverse of bright major #6 #7)

	Porcupine bright harmonic 11th mode - Porcupine[7] 6\|0 b7 3222213		Porcupine bright harmonic 11th mode - Porcupine[7] 6\|0 b7 3222213