User talk:BudjarnLambeth/12edo as a 2.3.5.17.19 tuning - Revision history

BudjarnLambeth: BudjarnLambeth moved page User talk:BudjarnLambeth/How I choose a subgroup for an EDO to User talk:BudjarnLambeth/12edo as a 2.3.5.17.19 tuning

2025-04-23T05:10:05Z

BudjarnLambeth moved page User talk:BudjarnLambeth/How I choose a subgroup for an EDO to User talk:BudjarnLambeth/12edo as a 2.3.5.17.19 tuning

← Older revision	Revision as of 05:10, 23 April 2025
(No difference)

BudjarnLambeth: Moved my post to a Discord thread instead at Fredg’s suggestion

2025-01-07T21:58:13Z

Moved my post to a Discord thread instead at Fredg’s suggestion

← Older revision		Revision as of 21:58, 7 January 2025
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	~~''[[User:Dummy index]] posted this on Discord overnight (Sydney time), but I decided to move it here because I would rather discuss it on a talk page:''~~		== Moved post ==
			(I made a post here but moved it to a Discord thread.) --[[User:BudjarnLambeth\|BudjarnLambeth]] ([[User talk:BudjarnLambeth\|talk]]) 21:58, 7 January 2025 (UTC)
	~~“Hello,~~

	~~'''> 16edo: 2 • 5 • 7 • 13 • 27 • 45'''~~

	~~is dual-3. (and 14edo is dual-5 maybe.)~~

	* In the first place, it is too much to have four basis elements within the 5-limit.
	* 27 * 5 / 45 = ~~3 (76 + 37 - 88~~ = 25 steps) is same to nearest approximation of 3rd harmonic. Hence, it is inconsistent between 27 (76 steps) and 3 (25 steps). So we need to differentiate between 3^3 and 27 in some way, to regain regularity.
	* One way, 27 = ~~9+ * 3-~~ = ~~3++ * 3- * 3-~~ (~~76 = 51 + 25 = 26 + 25 + 25). it means 2.5.7.13.27.45+ or 2.3-.3++.5.7.13 subgroup.~~
	* Another way, 27+ = 9+ * 3 = 3+ * 3 * 3 for nearest approximation of 27th harmonic and 27 for 3^3. it means 2.5.7.13.27+.45+ or 2.3.3+.5.7.13 subgroup.”

	''I ~~plan to re-read Index’s~~ post ~~carefully and write a reply~~ here ~~later today (Sydney time). It may be several hours before I can do that due~~ to ~~irl commitments~~.''

	''--[[User:BudjarnLambeth\|BudjarnLambeth]] ([[User talk:BudjarnLambeth\|talk]]) 18:18, 7 January 2025 (UTC)''

BudjarnLambeth: Start talk page as promised on Discord

2025-01-07T18:18:58Z

Start talk page as promised on Discord

New page

''[[User:Dummy index]] posted this on Discord overnight (Sydney time), but I decided to move it here because I would rather discuss it on a talk page:''

“Hello,

'''> 16edo: 2 • 5 • 7 • 13 • 27 • 45'''

is dual-3. (and 14edo is dual-5 maybe.)

* In the first place, it is too much to have four basis elements within the 5-limit.
* 27 * 5 / 45 = 3 (76 + 37 - 88 = 25 steps) is same to nearest approximation of 3rd harmonic. Hence, it is inconsistent between 27 (76 steps) and 3 (25 steps). So we need to differentiate between 3^3 and 27 in some way, to regain regularity.
* One way, 27 = 9+ * 3- = 3++ * 3- * 3- (76 = 51 + 25 = 26 + 25 + 25). it means 2.5.7.13.27.45+ or 2.3-.3++.5.7.13 subgroup.
* Another way, 27+ = 9+ * 3 = 3+ * 3 * 3 for nearest approximation of 27th harmonic and 27 for 3^3. it means 2.5.7.13.27+.45+ or 2.3.3+.5.7.13 subgroup.”

''I plan to re-read Index’s post carefully and write a reply here later today (Sydney time). It may be several hours before I can do that due to irl commitments.''

''--[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 18:18, 7 January 2025 (UTC)''