User:Xenllium/Ed9 - Revision history

Fredg999 category edits: Categories

2025-08-01T15:32:52Z

BudjarnLambeth at 03:14, 21 May 2025

2025-05-21T03:14:14Z

← Older revision		Revision as of 03:14, 21 May 2025
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			{{Editable user page}}
	Equal Divisions of the Double Tritave -- frequency ratio [[9/1]], aka "Nonuple" -- are closely related to Equal Divisions of the Tritave -- frequency ratio 3/1, aka "Triple" -- in other words, ED3 or [[Edt\|EDT]] scales. Given any odd-numbered ED3, an ED9 can be generated by taking every other tone of the ED3. For example, given 5ED3 (aka [[5edt]]), two tritaves of which, in cents are:		Equal Divisions of the Double Tritave -- frequency ratio [[9/1]], aka "Nonuple" -- are closely related to Equal Divisions of the Tritave -- frequency ratio 3/1, aka "Triple" -- in other words, ED3 or [[Edt\|EDT]] scales. Given any odd-numbered ED3, an ED9 can be generated by taking every other tone of the ED3. For example, given 5ED3 (aka [[5edt]]), two tritaves of which, in cents are:

BudjarnLambeth: BudjarnLambeth moved page Ed9 to User:Xenllium/Ed9

2025-05-21T03:14:01Z

BudjarnLambeth moved page Ed9 to User:Xenllium/Ed9

← Older revision	Revision as of 03:14, 21 May 2025
(No difference)

BudjarnLambeth: /* Individual pages for ED9s */

2024-10-01T02:39:10Z

Individual pages for ED9s

← Older revision		Revision as of 02:39, 1 October 2024
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	*[[57ed9]]		*[[57ed9]]
	*[[59ed9]]		*[[59ed9]]
			…
	*[[97ed9]]		*[[97ed9]]

	[[Category:Ed9\| ]]		[[Category:Ed9\| ]]
	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]

Contribution: /* Individual pages for ED9s */

2024-05-16T08:45:44Z

Individual pages for ED9s

← Older revision		Revision as of 08:45, 16 May 2024
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	*[[57ed9]]		*[[57ed9]]
	*[[59ed9]]		*[[59ed9]]
			*[[97ed9]]

	[[Category:Ed9\| ]]		[[Category:Ed9\| ]]
	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]

BudjarnLambeth: Changed 9/1 to 9/1

2023-07-06T02:22:34Z

Changed 9/1 to 9/1

← Older revision		Revision as of 02:22, 6 July 2023
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	Equal Divisions of the Double Tritave -- frequency ratio 9/1, aka "Nonuple" -- are closely related to Equal Divisions of the Tritave -- frequency ratio 3/1, aka "Triple" -- in other words, ED3 or [[Edt\|EDT]] scales. Given any odd-numbered ED3, an ED9 can be generated by taking every other tone of the ED3. For example, given 5ED3 (aka [[5edt]]), two tritaves of which, in cents are:		Equal Divisions of the Double Tritave -- frequency ratio [[9/1]], aka "Nonuple" -- are closely related to Equal Divisions of the Tritave -- frequency ratio 3/1, aka "Triple" -- in other words, ED3 or [[Edt\|EDT]] scales. Given any odd-numbered ED3, an ED9 can be generated by taking every other tone of the ED3. For example, given 5ED3 (aka [[5edt]]), two tritaves of which, in cents are:

	0 380 761 1141 1522 1902 2282 2663 3043 3424 3804...		0 380 761 1141 1522 1902 2282 2663 3043 3424 3804...

Xenllium: Created page with "Equal Divisions of the Double Tritave -- frequency ratio 9/1, aka "Nonuple" -- are closely related to Equal Divisions of the Tritave -- frequency ratio 3/1, aka "Triple" -- in..."

2019-03-02T16:47:58Z

Created page with "Equal Divisions of the Double Tritave -- frequency ratio 9/1, aka "Nonuple" -- are closely related to Equal Divisions of the Tritave -- frequency ratio 3/1, aka "Triple" -- in..."

New page

Equal Divisions of the Double Tritave -- frequency ratio 9/1, aka "Nonuple" -- are closely related to Equal Divisions of the Tritave -- frequency ratio 3/1, aka "Triple" -- in other words, ED3 or [[Edt|EDT]] scales. Given any odd-numbered ED3, an ED9 can be generated by taking every other tone of the ED3. For example, given 5ED3 (aka [[5edt]]), two tritaves of which, in cents are:

0 380 761 1141 1522 1902 2282 2663 3043 3424 3804...

...taking every other tone yields:

'''0''' 380 '''761''' 1141 '''1522''' 1902 '''2282''' 2663 '''3043''' 3424 '''3804'''...

'''0 761 1522 2282 3043 3804...'''

The resultant scale we can call 5ED9.

This approach yields more useful scales starting with ED3 systems which are larger, where a composer might decide a single degree is too small to be useful. As one example, consider 53ED3 (aka [[53edt]]), which is well known to be an excellent temperament in the 3.4.5.7.11.13.17.19 subgroup, but whose single degree, approximately 35.9¢, might be "too small" in some context (e.g. guitar frets). Taking every other step of 53ED3 produces [[53ed9|53ED9]], an equal-stepped scale which repeats at 9/1, the double tritave, and has a single step of 71.8¢.

ED9 scales also have the feature that they ascend the pitch continuum twice as fast as ED3 systems. 53 tones of 53ED3 is one tritave, while 53 tones of 53ED9 is two tritaves. Thus, fewer bars would be needed on a metallophone, fewer keys on a keyboard, etc.

See: [[Equal-step tuning|Equal Temperaments]]

=Individual pages for ED9s=
*[[5ed9]]
*[[7ed9]]
*[[9ed9]]
*[[11ed9]]
*[[13ed9]]
*[[15ed9]]
*[[17ed9]]
*[[19ed9]]
*[[21ed9]]
*[[23ed9]]
*[[25ed9]]
*[[27ed9]]
*[[29ed9]]
*[[31ed9]]
*[[33ed9]]
*[[35ed9]]
*[[37ed9]]
*[[39ed9]]
*[[41ed9]]
*[[43ed9]]
*[[45ed9]]
*[[47ed9]]
*[[49ed9]]
*[[51ed9]]
*[[53ed9]]
*[[55ed9]]
*[[57ed9]]
*[[59ed9]]

[[Category:Ed9| ]]
[[Category:Equal-step tuning]]

← Older revision		Revision as of 15:32, 1 August 2025
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	*[[97ed9]]		*[[97ed9]]

	[[Category:Ed9\| ]]		[[Category:Ed9's\| ]] <!-- main article -->
	~~[[Category:Equal~~-~~step tuning]]~~