789edo - Revision history

Lériendil at 02:31, 2 April 2025

2025-04-02T02:31:36Z

← Older revision		Revision as of 02:31, 2 April 2025
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	789edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[5902edo]]; notably, it is the denominator of logarithmic [[semiconvergent]]s to both [[5/4]] and [[7/5]], and remarkably tempers out the [[Don Page comma]] between the intervals of [[128/125]] and [[50/49]], mapping each to 27 and 23 steps respectively, and additionally tempers out 281484423828125/281474976710656 ([-48 0 11 8⟩), supporting exodia, the subgroup restriction of mohajira. It also has a very accurate representation of the 17th harmonic (due to tempering out S49/S50 = [[2000033/2000000]], equating [[17/16]] to three [[50/49]] intervals) and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.		789edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[5902edo]]; notably, it is the denominator of logarithmic [[semiconvergent]]s to both [[5/4]] and [[7/5]], and remarkably tempers out the [[Don Page comma]] between the intervals of [[128/125]] and [[50/49]], mapping each to 27 and 23 steps respectively, and additionally tempers out 281484423828125/281474976710656 ([-48 0 11 8⟩), supporting exodia, the subgroup restriction of mohajira. It also has a very accurate representation of the 17th harmonic (due to tempering out S49/S50 = [[2000033/2000000]], equating [[17/16]] to three [[50/49]] intervals) and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.

	It is also the most accurate edo below 10000 to approximate [[quarter-comma meantone]], with ~~its~~ approximation of {{monzo\| 0 0 1/4 }} ~~with~~ a relative error of only 0.06%.		It is also the most accurate edo below 10000 to approximate [[quarter-comma meantone]], with an approximation of {{monzo\| 0 0 1/4 }} by 458\789 with a relative error of only 0.03%.

	[[1578edo]], which doubles it, provides good corrections for the 3rd and 11th harmonics, making for a very strong [[11-limit]] and higher-limit system.		[[1578edo]], which doubles it, provides good corrections for the 3rd and 11th harmonics, making for a very strong [[11-limit]] and higher-limit system.

Lériendil: 1578edo's quarter-comma meantone actually comes from 789

2025-04-02T02:31:00Z

1578edo's quarter-comma meantone actually comes from 789

← Older revision		Revision as of 02:31, 2 April 2025
Line 3:		Line 3:

	789edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[5902edo]]; notably, it is the denominator of logarithmic [[semiconvergent]]s to both [[5/4]] and [[7/5]], and remarkably tempers out the [[Don Page comma]] between the intervals of [[128/125]] and [[50/49]], mapping each to 27 and 23 steps respectively, and additionally tempers out 281484423828125/281474976710656 ([-48 0 11 8⟩), supporting exodia, the subgroup restriction of mohajira. It also has a very accurate representation of the 17th harmonic (due to tempering out S49/S50 = [[2000033/2000000]], equating [[17/16]] to three [[50/49]] intervals) and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.		789edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[5902edo]]; notably, it is the denominator of logarithmic [[semiconvergent]]s to both [[5/4]] and [[7/5]], and remarkably tempers out the [[Don Page comma]] between the intervals of [[128/125]] and [[50/49]], mapping each to 27 and 23 steps respectively, and additionally tempers out 281484423828125/281474976710656 ([-48 0 11 8⟩), supporting exodia, the subgroup restriction of mohajira. It also has a very accurate representation of the 17th harmonic (due to tempering out S49/S50 = [[2000033/2000000]], equating [[17/16]] to three [[50/49]] intervals) and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.

			It is also the most accurate edo below 10000 to approximate [[quarter-comma meantone]], with its approximation of {{monzo\| 0 0 1/4 }} with a relative error of only 0.06%.

	[[1578edo]], which doubles it, provides good corrections for the 3rd and 11th harmonics, making for a very strong [[11-limit]] and higher-limit system.		[[1578edo]], which doubles it, provides good corrections for the 3rd and 11th harmonics, making for a very strong [[11-limit]] and higher-limit system.

Francium: changed EDO intro to ED intro

2025-02-21T05:54:57Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:54, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|789~~}}		{{ED intro}}

	789edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[5902edo]]; notably, it is the denominator of logarithmic [[semiconvergent]]s to both [[5/4]] and [[7/5]], and remarkably tempers out the [[Don Page comma]] between the intervals of [[128/125]] and [[50/49]], mapping each to 27 and 23 steps respectively, and additionally tempers out 281484423828125/281474976710656 ([-48 0 11 8⟩), supporting exodia, the subgroup restriction of mohajira. It also has a very accurate representation of the 17th harmonic (due to tempering out S49/S50 = [[2000033/2000000]], equating [[17/16]] to three [[50/49]] intervals) and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.		789edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[5902edo]]; notably, it is the denominator of logarithmic [[semiconvergent]]s to both [[5/4]] and [[7/5]], and remarkably tempers out the [[Don Page comma]] between the intervals of [[128/125]] and [[50/49]], mapping each to 27 and 23 steps respectively, and additionally tempers out 281484423828125/281474976710656 ([-48 0 11 8⟩), supporting exodia, the subgroup restriction of mohajira. It also has a very accurate representation of the 17th harmonic (due to tempering out S49/S50 = [[2000033/2000000]], equating [[17/16]] to three [[50/49]] intervals) and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.

Lériendil at 21:10, 11 November 2024

2024-11-11T21:10:06Z

← Older revision		Revision as of 21:10, 11 November 2024
Line 2:		Line 2:
	{{EDO intro\|789}}		{{EDO intro\|789}}

	789edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[5902edo]]; notably, it is the denominator of logarithmic [[semiconvergent]]s to both [[5/4]] and [[7/5]]. It also has a very accurate representation of the 17th harmonic (due to tempering out S49/S50 = [[2000033/2000000]], equating [[17/16]] to three [[50/49]] intervals) and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.		789edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[5902edo]]; notably, it is the denominator of logarithmic [[semiconvergent]]s to both [[5/4]] and [[7/5]], and remarkably tempers out the [[Don Page comma]] between the intervals of [[128/125]] and [[50/49]], mapping each to 27 and 23 steps respectively, and additionally tempers out 281484423828125/281474976710656 ([-48 0 11 8⟩), supporting exodia, the subgroup restriction of mohajira. It also has a very accurate representation of the 17th harmonic (due to tempering out S49/S50 = [[2000033/2000000]], equating [[17/16]] to three [[50/49]] intervals) and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.

	[[1578edo]], which doubles it, provides good corrections for the 3rd and 11th harmonics, making for a very strong [[11-limit]] and higher-limit system.		[[1578edo]], which doubles it, provides good corrections for the 3rd and 11th harmonics, making for a very strong [[11-limit]] and higher-limit system.
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	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|789}}		{{Harmonics in equal\|789}}

	~~{{stub}}~~

Lériendil at 05:25, 24 October 2024

2024-10-24T05:25:22Z

← Older revision		Revision as of 05:25, 24 October 2024
Line 2:		Line 2:
	{{EDO intro\|789}}		{{EDO intro\|789}}

	789edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[5902edo]]; notably, it is the denominator of logarithmic [[semiconvergent]]s to both [[5/4]] and [[7/5]]. It also has a very accurate representation of the 17th harmonic (due to tempering S49/S50 = [[2000033/2000000]], equating [[17/16]] to three [[50/49]] intervals) and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.		789edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[5902edo]]; notably, it is the denominator of logarithmic [[semiconvergent]]s to both [[5/4]] and [[7/5]]. It also has a very accurate representation of the 17th harmonic (due to tempering out S49/S50 = [[2000033/2000000]], equating [[17/16]] to three [[50/49]] intervals) and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.

	[[1578edo]], which doubles it, provides good corrections for the 3rd and 11th harmonics, making for a very strong [[11-limit]] and higher-limit system.		[[1578edo]], which doubles it, provides good corrections for the 3rd and 11th harmonics, making for a very strong [[11-limit]] and higher-limit system.

Lériendil: 3945 is just 5*789, whoops

2024-10-24T05:01:50Z

3945 is just 5*789, whoops

← Older revision		Revision as of 05:01, 24 October 2024
Line 2:		Line 2:
	{{EDO intro\|789}}		{{EDO intro\|789}}

	789edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[~~3945edo~~]]; notably, it is the denominator of logarithmic [[semiconvergent]]s to both [[5/4]] and [[7/5]]. It also has a very accurate representation of the 17th harmonic (due to tempering S49/S50 = [[2000033/2000000]], equating [[17/16]] to three [[50/49]] intervals) and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.		789edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[5902edo]]; notably, it is the denominator of logarithmic [[semiconvergent]]s to both [[5/4]] and [[7/5]]. It also has a very accurate representation of the 17th harmonic (due to tempering S49/S50 = [[2000033/2000000]], equating [[17/16]] to three [[50/49]] intervals) and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.

	[[1578edo]], which doubles it, provides good corrections for the 3rd and 11th harmonics, making for a very strong [[11-limit]] and higher-limit system.		[[1578edo]], which doubles it, provides good corrections for the 3rd and 11th harmonics, making for a very strong [[11-limit]] and higher-limit system.

Lériendil at 21:59, 20 October 2024

2024-10-20T21:59:32Z

← Older revision		Revision as of 21:59, 20 October 2024
Line 2:		Line 2:
	{{EDO intro\|789}}		{{EDO intro\|789}}

	789edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[3945edo]]; notably, it is the denominator of [[semiconvergent]]s to both [[5/4]] and [[7/5]]. It also has a very accurate representation of the 17th harmonic (due to tempering S49/S50 = [[2000033/2000000]], equating [[17/16]] to three [[50/49]] intervals) and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.		789edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[3945edo]]; notably, it is the denominator of logarithmic [[semiconvergent]]s to both [[5/4]] and [[7/5]]. It also has a very accurate representation of the 17th harmonic (due to tempering S49/S50 = [[2000033/2000000]], equating [[17/16]] to three [[50/49]] intervals) and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.

	[[1578edo]], which doubles it, provides good corrections for the 3rd and 11th harmonics, making for a very strong [[11-limit]] and higher-limit system.		[[1578edo]], which doubles it, provides good corrections for the 3rd and 11th harmonics, making for a very strong [[11-limit]] and higher-limit system.

Lériendil at 21:58, 20 October 2024

2024-10-20T21:58:36Z

← Older revision		Revision as of 21:58, 20 October 2024
Line 2:		Line 2:
	{{EDO intro\|789}}		{{EDO intro\|789}}

	789edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[3945edo]]. It also has a very accurate representation of the 17th harmonic (due to tempering S49/S50 = [[2000033/2000000]], equating [[17/16]] to three [[50/49]] intervals) and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.		789edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[3945edo]]; notably, it is the denominator of [[semiconvergent]]s to both [[5/4]] and [[7/5]]. It also has a very accurate representation of the 17th harmonic (due to tempering S49/S50 = [[2000033/2000000]], equating [[17/16]] to three [[50/49]] intervals) and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.

	[[1578edo]], which doubles it, provides good corrections for the 3rd and 11th harmonics, making for a very strong [[11-limit]] and higher-limit system.		[[1578edo]], which doubles it, provides good corrections for the 3rd and 11th harmonics, making for a very strong [[11-limit]] and higher-limit system.

Lériendil: fixed s-expression

2024-10-20T21:45:49Z

fixed s-expression

← Older revision		Revision as of 21:45, 20 October 2024
Line 2:		Line 2:
	{{EDO intro\|789}}		{{EDO intro\|789}}

	789edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[3945edo]]. It also has a very accurate representation of the 17th harmonic (due to tempering S49/~~S51~~ = [[2000033/2000000]], equating [[17/16]] to three [[50/49]] intervals) and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.		789edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[3945edo]]. It also has a very accurate representation of the 17th harmonic (due to tempering S49/S50 = [[2000033/2000000]], equating [[17/16]] to three [[50/49]] intervals) and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.

	[[1578edo]], which doubles it, provides good corrections for the 3rd and 11th harmonics, making for a very strong [[11-limit]] and higher-limit system.		[[1578edo]], which doubles it, provides good corrections for the 3rd and 11th harmonics, making for a very strong [[11-limit]] and higher-limit system.

Lériendil: clevelandisma mention

2024-10-20T21:01:35Z

clevelandisma mention

← Older revision		Revision as of 21:01, 20 October 2024
Line 2:		Line 2:
	{{EDO intro\|789}}		{{EDO intro\|789}}

	789edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[3945edo]]. It also has a very accurate representation of the 17th harmonic and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.		789edo is notable for an extremely good approximation of the [[2.5.7 subgroup]], unbeaten until [[3945edo]]. It also has a very accurate representation of the 17th harmonic (due to tempering S49/S51 = [[2000033/2000000]], equating [[17/16]] to three [[50/49]] intervals) and has a good 9th and 23rd harmonic as well; there is a common flat tendency allowing consistency to high distance in the 2.9.5.7.33.17.23 subgroup.

	[[1578edo]], which doubles it, provides good corrections for the 3rd and 11th harmonics, making for a very strong [[11-limit]] and higher-limit system.		[[1578edo]], which doubles it, provides good corrections for the 3rd and 11th harmonics, making for a very strong [[11-limit]] and higher-limit system.