User:BudjarnLambeth/Firedance - Revision history

BudjarnLambeth at 03:38, 14 April 2026

2026-04-14T03:38:11Z

← Older revision		Revision as of 03:38, 14 April 2026
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			{{Editable user page\|Don't remove anything (unless it's offensive or factually incorrect), but feel free to add any observations about the scale, subsets, music examples, etc., and feel free to improve the formatting or layout as long as you don't remove information.}}


	[[File:Firedance.png\|thumb\|Firedance scale (circle diagram).]]		[[File:Firedance.png\|thumb\|Firedance scale (circle diagram).]]
	The '''firedance scale''' is a subset of zeta-stretched 15edo described by [[Budjarn Lambeth]] in 2023.		The '''firedance scale''' is a subset of zeta-stretched 15edo described by [[Budjarn Lambeth]] in 2023.

BudjarnLambeth at 03:36, 14 April 2026

2026-04-14T03:36:40Z

← Older revision		Revision as of 03:36, 14 April 2026
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			[[File:Firedance.png\|thumb\|Firedance scale (circle diagram).]]
	The '''firedance scale''' is a subset of zeta-stretched 15edo described by [[Budjarn Lambeth]] in 2023.		The '''firedance scale''' is a subset of zeta-stretched 15edo described by [[Budjarn Lambeth]] in 2023.

BudjarnLambeth at 11:54, 4 February 2026

2026-02-04T11:54:19Z

← Older revision		Revision as of 11:54, 4 February 2026
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! 0 !! 1 !! 2 !! 3 !! 4 !! (5)		! !! 0 !! 1 !! 2 !! 3 !! 4 !! (5)
	\|-		\|-
	! 0		! 0

BudjarnLambeth: BudjarnLambeth moved page Firedance to User:BudjarnLambeth/Firedance

2025-05-07T03:00:31Z

BudjarnLambeth moved page Firedance to User:BudjarnLambeth/Firedance

← Older revision	Revision as of 03:00, 7 May 2025
(No difference)

ArrowHead294 at 13:21, 10 April 2025

2025-04-10T13:21:16Z

← Older revision		Revision as of 13:21, 10 April 2025
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	The '''firedance scale''' is a subset of zeta-stretched 15edo described by [[Budjarn Lambeth]] in 2023.		The '''firedance scale''' is a subset of zeta-stretched 15edo described by [[Budjarn Lambeth]] in 2023.

	Zeta-stretched 15edo (also known as [[47zpi]], the 47th [[zeta peak index]]), is 15edo with octaves compressed according to this process: [[~~The~~ Riemann ~~Zeta Function~~ and ~~Tuning~~#Optimal octave stretch\|Optimal octave stretch]].		Zeta-stretched 15edo (also known as [[47zpi]], the 47th [[zeta peak index]]), is 15edo with octaves compressed according to this process: [[the Riemann zeta function and tuning#Optimal octave stretch\|Optimal octave stretch]].

	You can also stretch 15edo using [[Paul Erlich]]'s [[TOP]] tuning, or using [[TE]] tuning, and get a very similar (but not exactly identical) result. Or even just use plain old pure-octaves [[15edo]]. All are considered acceptable tunings.		You can also stretch 15edo using [[Paul Erlich]]'s [[TOP]] tuning, or using [[TE]] tuning, and get a very similar (but not exactly identical) result. Or even just use plain old pure-octaves [[15edo]]. All are considered acceptable tunings.
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	Attached is [[Scale Workshop]]'s table of interval relationships in the firedance scale:		Attached is [[Scale Workshop]]'s table of interval relationships in the firedance scale:
	{\| class="wikitable"		{\| class="wikitable"
	!		\|-
	! 0 !! 1 !! 2 !! 3 !! 4 !! (5)		! 0 !! 1 !! 2 !! 3 !! 4 !! (5)
	\|-		\|-
Line 58:		Line 58:
	* [https://www.youtube.com/watch?v=eSXomnrP7O8 Improvisation in Zeta-Stretched 15-Tone Equal Temperament (15 EDO)] - [[Budjarn Lambeth]] (2024)		* [https://www.youtube.com/watch?v=eSXomnrP7O8 Improvisation in Zeta-Stretched 15-Tone Equal Temperament (15 EDO)] - [[Budjarn Lambeth]] (2024)

	[[Category:5-tone scales]][[Category:Tempered scales]][[Category:15edo]][[Category:11-limit]][[Category:Pages with Scala files]]		[[Category:5-tone scales]]
			[[Category:Tempered scales]]
			[[Category:15edo]]
			[[Category:11-limit]]
			[[Category:Pages with Scala files]]

ArrowHead294 at 00:38, 28 September 2024

2024-09-28T00:38:23Z

← Older revision		Revision as of 00:38, 28 September 2024
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	\|-		\|-
	! 558.010		! 558.010
	\| 0. \|\| 159.4 \|\| 398.6 \|\| 637.7 \|\| 876.9 \|\| 1195.7		\| 0 \|\| 159.4 \|\| 398.6 \|\| 637.7 \|\| 876.9 \|\| 1195.7
	\|-		\|-
	! 717.441		! 717.441
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	\|}		\|}

	Although it wasn't consciously designed this way, you can see that a lot of ~~warm~~ septimal harmonies occur in the intervals between the intervals. Most notably, all those 717's are decent approximations of [[3/2]], all those 239's are decent approximations of [[8/7]], and all those 956's are decent approximations of [[7/4]].		Although it wasn't consciously designed this way, you can see that a lot of septimal harmonies occur in the intervals between the intervals. Most notably, all those 717's are decent approximations of [[3/2]], all those 239's are decent approximations of [[8/7]], and all those 956's are decent approximations of [[7/4]].

	On top of that, the firedance scale is a very close approximation to this [[primodal]] over-7 scale. A subset of [[56afdo]]:		On top of that, the firedance scale is a very close approximation to this [[primodal]] over-7 scale. A subset of [[56afdo]]:

ArrowHead294: Remove excessive linebreaks, reformat tables

2024-09-24T13:27:11Z

Remove excessive linebreaks, reformat tables

← Older revision		Revision as of 13:27, 24 September 2024
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	The '''firedance scale''' is a subset of zeta-stretched 15edo described by [[Budjarn Lambeth]] in 2023.		The '''firedance scale''' is a subset of zeta-stretched 15edo described by [[Budjarn Lambeth]] in 2023.


	Zeta-stretched 15edo (also known as [[47zpi]], the 47th [[zeta peak index]]), is 15edo with octaves compressed according to this process: [[The Riemann Zeta Function and Tuning#Optimal octave stretch\|Optimal octave stretch]].		Zeta-stretched 15edo (also known as [[47zpi]], the 47th [[zeta peak index]]), is 15edo with octaves compressed according to this process: [[The Riemann Zeta Function and Tuning#Optimal octave stretch\|Optimal octave stretch]].


	You can also stretch 15edo using [[Paul Erlich]]'s [[TOP]] tuning, or using [[TE]] tuning, and get a very similar (but not exactly identical) result. Or even just use plain old pure-octaves [[15edo]]. All are considered acceptable tunings.		You can also stretch 15edo using [[Paul Erlich]]'s [[TOP]] tuning, or using [[TE]] tuning, and get a very similar (but not exactly identical) result. Or even just use plain old pure-octaves [[15edo]]. All are considered acceptable tunings.


	The firedance scale was designed by starting with [[5edo]], and then just tweaking intervals up and down by individual edo-steps of 15edo, by ear, until it sounded good.		The firedance scale was designed by starting with [[5edo]], and then just tweaking intervals up and down by individual edo-steps of 15edo, by ear, until it sounded good.


	Attached is [[Scale Workshop]]'s table of interval relationships in the firedance scale:		Attached is [[Scale Workshop]]'s table of interval relationships in the firedance scale:
	{\| class="wikitable"		{\| class="wikitable"
	!		!
	!0		! 0 !! 1 !! 2 !! 3 !! 4 !! (5)
	!1
	!2
	!3
	!4
	!(5)
	\|-		\|-
	!0.		! 0
	\|0.		\| 0 \|\| 239.147 \|\| 558.010 \|\| 717.441 \|\| 956.588 \|\| 1195.7
	\|239.147
	\|558.010
	\|717.441
	\|956.588
	\|1195.7
	\|-		\|-
	!239.147		! 239.147
	\|0.		\| 0 \|\| 318.9 \|\| 478.3 \|\| 717.4 \|\| 956.6 \|\| 1195.7
	\|318.9
	\|478.3
	\|717.4
	\|956.6
	\|1195.7
	\|-		\|-
	!558.010		! 558.010
	\|0.		\| 0. \|\| 159.4 \|\| 398.6 \|\| 637.7 \|\| 876.9 \|\| 1195.7
	\|159.4
	\|398.6
	\|637.7
	\|876.9
	\|1195.7
	\|-		\|-
	!717.441		! 717.441
	\|0.		\| 0 \|\| 239.1 \|\| 478.3 \|\| 717.4 \|\| 1036.3 \|\| 1195.7
	\|239.1
	\|478.3
	\|717.4
	\|1036.3
	\|1195.7
	\|-		\|-
	!956.588		! 956.588
	\|0.		\| 0 \|\| 239.1 \|\|478.3 \|\| 797.2 \|\| 956.6 \|\| 1195.7
	\|239.1
	\|478.3
	\|797.2
	\|956.6
	\|1195.7
	\|}		\|}

	Although it wasn't consciously designed this way, you can see that a lot of warm septimal harmonies occur in the intervals between the intervals. Most notably, all those 717's are decent approximations of [[3/2]], all those 239's are decent approximations of [[8/7]], and all those 956's are decent approximations of [[7/4]].		Although it wasn't consciously designed this way, you can see that a lot of warm septimal harmonies occur in the intervals between the intervals. Most notably, all those 717's are decent approximations of [[3/2]], all those 239's are decent approximations of [[8/7]], and all those 956's are decent approximations of [[7/4]].


	On top of that, the firedance scale is a very close approximation to this [[primodal]] over-7 scale. A subset of [[56afdo]]:		On top of that, the firedance scale is a very close approximation to this [[primodal]] over-7 scale. A subset of [[56afdo]]:
	*64/56		* 64/56
	*77/56		* 77/56
	*84/56		* 84/56
	*98/56		* 98/56
	*112/56		* 112/56
	56 just being a higher octave of 7 in the [[harmonic series]].		56 just being a higher octave of 7 in the [[harmonic series]].


	So from both a [[regular temperament theory]] point of view and also a primodality point of view, it's quite a nifty little scale with lots of xen harmonies baked into it.		So from both a [[regular temperament theory]] point of view and also a primodality point of view, it's quite a nifty little scale with lots of xen harmonies baked into it.

BudjarnLambeth at 09:19, 24 September 2024

2024-09-24T09:19:02Z

← Older revision		Revision as of 09:19, 24 September 2024
Line 2:		Line 2:


	Zeta-stretched 15edo (also known as [[47zpi]], the 47th [[zeta peak index]]), is 15edo with octaves ~~stretched~~ according to this process: [[The Riemann Zeta Function and Tuning#Optimal octave stretch\|Optimal octave stretch]].		Zeta-stretched 15edo (also known as [[47zpi]], the 47th [[zeta peak index]]), is 15edo with octaves compressed according to this process: [[The Riemann Zeta Function and Tuning#Optimal octave stretch\|Optimal octave stretch]].

BudjarnLambeth: /* Music */

2024-09-24T09:04:33Z

Music

← Older revision		Revision as of 09:04, 24 September 2024
Line 92:		Line 92:

	== Music ==		== Music ==
	* [[https://www.youtube.com/watch?v=eSXomnrP7O8 Improvisation in Zeta-Stretched 15-Tone Equal Temperament (15 EDO)]] - [[Budjarn Lambeth]] (2024)		* [https://www.youtube.com/watch?v=eSXomnrP7O8 Improvisation in Zeta-Stretched 15-Tone Equal Temperament (15 EDO)] - [[Budjarn Lambeth]] (2024)

	[[Category:5-tone scales]][[Category:Tempered scales]][[Category:15edo]][[Category:11-limit]][[Category:Pages with Scala files]]		[[Category:5-tone scales]][[Category:Tempered scales]][[Category:15edo]][[Category:11-limit]][[Category:Pages with Scala files]]

BudjarnLambeth at 09:04, 24 September 2024

2024-09-24T09:04:23Z

← Older revision		Revision as of 09:04, 24 September 2024
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	1195.735000		1195.735000
	</pre>		</pre>

			== Music ==
			* [[https://www.youtube.com/watch?v=eSXomnrP7O8 Improvisation in Zeta-Stretched 15-Tone Equal Temperament (15 EDO)]] - [[Budjarn Lambeth]] (2024)

	[[Category:5-tone scales]][[Category:Tempered scales]][[Category:15edo]][[Category:11-limit]][[Category:Pages with Scala files]]		[[Category:5-tone scales]][[Category:Tempered scales]][[Category:15edo]][[Category:11-limit]][[Category:Pages with Scala files]]