729edt - Revision history

FloraC: Adopt template: ED intro

2024-04-27T10:03:29Z

Adopt template: ED intro

← Older revision		Revision as of 10:03, 27 April 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~729 equal divisions of the tritave, 729edt, is the tuning system that divides the [[3/1]] interval into steps of 2.60899 cents each.~~		{{ED intro}}

	729edt is closely related to [[460edo]], with the difference of 3/1 instead of 2/1 being just. The mappings match through the 23-limit, where they temper out exactly the same commas. Overall, 729edt approximates harmonics 2, 3, 5, 13, and 17 exceptionally well, while 460edo only has this good of an error on the 19th harmonic.		729edt is closely related to [[460edo]], with the difference of 3/1 instead of 2/1 being just. The mappings match through the 23-limit, where they temper out exactly the same commas. Overall, 729edt approximates harmonics 2, 3, 5, 13, and 17 exceptionally well, while 460edo only has this good of an error on the 19th harmonic.

FloraC: Corrections (same consistency limit as 460edo and same temperament as 460et in the 23-limit)

2023-07-20T05:29:39Z

Corrections (same consistency limit as 460edo and same temperament as 460et in the 23-limit)

← Older revision		Revision as of 05:29, 20 July 2023
Line 2:		Line 2:
	729 equal divisions of the tritave, 729edt, is the tuning system that divides the [[3/1]] interval into steps of 2.60899 cents each.		729 equal divisions of the tritave, 729edt, is the tuning system that divides the [[3/1]] interval into steps of 2.60899 cents each.

	729edt is closely related to [[460edo]], with the difference of 3/1 instead of 2/1 being just~~, and it actually beats it slightly in consistency limit, being consistent in~~ the 22-~~integer~~ limit, ~~while 460edo is consistent only to 21-odd-limit~~. Overall, 729edt ~~performs exceptionally in~~ 2.3.5.13.17 ~~subgroup~~, while 460edo only has this good of an error on the 19th harmonic.		729edt is closely related to [[460edo]], with the difference of 3/1 instead of 2/1 being just. The mappings match through the 23-limit, where they temper out exactly the same commas. Overall, 729edt approximates harmonics 2, 3, 5, 13, and 17 exceptionally well, while 460edo only has this good of an error on the 19th harmonic.

	729edt tempers out the {{monzo\|-81 28 -54}} comma which sets 27 intervals of [[25/24]] equal to the tritave.		729edt tempers out the {{monzo\|-81 28 -54}} comma which sets 27 intervals of [[25/24]] equal to the tritave.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{~~harmonics~~ in equal\|729\|3~~\|columns=10~~\|intervals=prime}}		{{Harmonics in equal\|729\|3\|intervals=prime}}

Eliora: Created page with "{{Infobox ET}} 729 equal divisions of the tritave, 729edt, is the tuning system that divides the 3/1 interval into steps of 2.60899 cents each. 729edt is closely related..."

2023-07-20T00:39:24Z

Created page with "{{Infobox ET}} 729 equal divisions of the tritave, 729edt, is the tuning system that divides the 3/1 interval into steps of 2.60899 cents each. 729edt is closely related..."

New page

{{Infobox ET}}
729 equal divisions of the tritave, 729edt, is the tuning system that divides the [[3/1]] interval into steps of 2.60899 cents each.

729edt is closely related to [[460edo]], with the difference of 3/1 instead of 2/1 being just, and it actually beats it slightly in consistency limit, being consistent in the 22-integer limit, while 460edo is consistent only to 21-odd-limit. Overall, 729edt performs exceptionally in 2.3.5.13.17 subgroup, while 460edo only has this good of an error on the 19th harmonic.

729edt tempers out the {{monzo|-81 28 -54}} comma which sets 27 intervals of [[25/24]] equal to the tritave.
=== Prime harmonics ===
{{harmonics in equal|729|3|columns=10|intervals=prime}}