97ed9 - Revision history

FloraC: Cleanup +1

2025-05-23T12:50:19Z

Cleanup +1

← Older revision		Revision as of 12:50, 23 May 2025
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	97ed9 corresponds to 30.6001…edo. Each step of 97ed9 corresponds closely to five steps of [[153edo]].		97ed9 corresponds to 30.6001…edo. Each step of 97ed9 corresponds closely to five steps of [[153edo]].

	97ed9 features a well-balanced [[harmonic series segment]] from 4 to 9 and another from 39 to 50. It performs well across all [[prime harmonics]] from 5 to 19, with the exception of 13, which is slightly flat.		97ed9 features a well-balanced [[harmonic series segment]] from 4 to 9 and another from 39 to 50 (see table below). It performs well across all [[prime harmonics]] from 5 to 19, with the exception of 13, which is slightly flat.

	97ed9 sets a height record on the [[The Riemann zeta function and tuning\|Riemann zeta function]] with [[The Riemann zeta function and tuning #Removing primes\|primes 2 and 3 removed]], approximating 30.59745…edo. This record remains unbeaten until approximately 41.3478…edo.		97ed9 sets a height record on the [[The Riemann zeta function and tuning\|Riemann zeta function]] with [[The Riemann zeta function and tuning #Removing primes\|primes 2 and 3 removed]], approximating 30.59745…edo. This record remains unbeaten until approximately 41.3478…edo.
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	Additionally, 97ed9 is close to [[125zpi]] (see [[Zeta peak index]]).		Additionally, 97ed9 is close to [[125zpi]] (see [[Zeta peak index]]).

	=== ~~Harmonic series ===~~		=== Harmonics ===
			{{Harmonics in equal\|97\|9\|1\|intervals=integer\|columns=11}}
	~~=== 2 to 19~~ ===		{{Harmonics in equal\|97\|9\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 97ed9 (continued)}}
	{{Harmonics in equal\|97\|9\|1\|columns=9}}		{{Harmonics in equal\|97\|9\|1\|intervals=integer\|columns=12\|start=38\|collapsed=true\|title=Approximation of harmonics in 97ed9 (39–50)}}
	{{Harmonics in equal\|97\|9\|1\|columns=9\|title=(~~contd.~~)~~\|start=10~~}}

	~~=== 36 to 53 ===~~
	{{Harmonics in equal\|97\|9\|1\|~~columns~~=9\|~~collapsed~~=1\|start=~~35}}~~
	~~{{Harmonics in equal~~\|~~97\|9\|1\|columns~~=9\|title=(~~contd.~~)~~\|collapsed=1\|start=44~~}}

	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

FloraC: Cleanup

2025-05-23T12:45:46Z

Cleanup

← Older revision		Revision as of 12:45, 23 May 2025
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''97ed9''' is an [[Equal-step tuning\|equal-step]] [[tuning system]] created by dividing the interval of [[9/1]] into 97 equal parts.~~		{{ED intro}}

	~~This system can be approximated as~~ 30.~~6001 [[EDO]], meaning each~~ step of 97ed9 corresponds closely to five steps of [[153edo]].		== Theory ==
			97ed9 corresponds to 30.6001…edo. Each step of 97ed9 corresponds closely to five steps of [[153edo]].

	~~97ed9 is a non-[[octave]], non-[[tritave]] scale.~~

	~~== Theory ==~~
	97ed9 features a well-balanced [[harmonic series segment]] from 4 to 9 and another from 39 to 50. It performs well across all [[prime harmonics]] from 5 to 19, with the exception of 13, which is slightly flat.		97ed9 features a well-balanced [[harmonic series segment]] from 4 to 9 and another from 39 to 50. It performs well across all [[prime harmonics]] from 5 to 19, with the exception of 13, which is slightly flat.

	97ed9 sets a height record on the [[The Riemann zeta function and tuning\|Riemann zeta function]] with [[The Riemann zeta function and tuning#Removing primes\|primes 2 and 3 removed]], approximating 30.~~59745 EDO~~. This record remains unbeaten until approximately 41.~~3478 EDO~~.		97ed9 sets a height record on the [[The Riemann zeta function and tuning\|Riemann zeta function]] with [[The Riemann zeta function and tuning #Removing primes\|primes 2 and 3 removed]], approximating 30.59745…edo. This record remains unbeaten until approximately 41.3478…edo.

	Additionally, 97ed9 is close to [[125zpi]] (see [[Zeta peak index]]).		Additionally, 97ed9 is close to [[125zpi]] (see [[Zeta peak index]]).

	== Harmonic series ==		=== Harmonic series ===

	=== 2 to 19 ===		=== 2 to 19 ===
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	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}


	~~{{todo\|expand}}~~
	~~[[Category:Ed9]][[Category:Equal-step tuning]]~~

BudjarnLambeth: Add infobox ET, tweak wording, tweak tables

2024-12-23T01:18:52Z

Add infobox ET, tweak wording, tweak tables

← Older revision		Revision as of 01:18, 23 December 2024
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	~~== Theory ==~~		{{Infobox ET}}
			'''97ed9''' is an [[Equal-step tuning\|equal-step]] [[tuning system]] created by dividing the interval of [[9/1]] into 97 equal parts.

	~~97ed9 is an~~ [[~~Equal-step tuning\|equal-step~~]] ~~[[tuning system]] created by dividing the interval~~ of [[~~9/1~~]] ~~into 97 equal parts~~.		This system can be approximated as 30.6001 [[EDO]], meaning each step of 97ed9 corresponds closely to five steps of [[153edo]].

	~~This system can be approximated as 30.6001~~ [[~~EDO~~]], ~~meaning each step of 97ed9 corresponds closely to five steps of~~ [[~~153edo~~]].		97ed9 is a non-[[octave]], non-[[tritave]] scale.

	~~This non-octave, non-tritave scale~~ features a well-balanced [[harmonic series segment]] from 4 to 9 and another from 39 to 50. It performs well across all [[prime harmonics]] from 5 to 19, with the exception of 13, which is slightly flat.		== Theory ==
			97ed9 features a well-balanced [[harmonic series segment]] from 4 to 9 and another from 39 to 50. It performs well across all [[prime harmonics]] from 5 to 19, with the exception of 13, which is slightly flat.

	97ed9 sets a height record on the [[The Riemann zeta function and tuning\|Riemann zeta function]] with [[The Riemann zeta function and tuning#Removing primes\|primes 2 and 3 removed]], approximating 30.59745 EDO. This record remains unbeaten until approximately 41.3478 EDO.		97ed9 sets a height record on the [[The Riemann zeta function and tuning\|Riemann zeta function]] with [[The Riemann zeta function and tuning#Removing primes\|primes 2 and 3 removed]], approximating 30.59745 EDO. This record remains unbeaten until approximately 41.3478 EDO.
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	== Harmonic series ==		== Harmonic series ==

	=== 2 to 15 ===		=== 2 to 19 ===
	{{Harmonics in equal\|97\|9\|1\|columns=7}}		{{Harmonics in equal\|97\|9\|1\|columns=9}}
	{{Harmonics in equal\|97\|9\|1\|columns=7\|title=(contd.)\|start=8}}		{{Harmonics in equal\|97\|9\|1\|columns=9\|title=(contd.)\|start=10}}

	=== 38 to 52 ===		=== 36 to 53 ===
	{{Harmonics in equal\|97\|9\|1\|columns=7\|collapsed=1\|start=37}}		{{Harmonics in equal\|97\|9\|1\|columns=9\|collapsed=1\|start=35}}
	{{Harmonics in equal\|97\|9\|1\|columns=7\|title=(contd.)\|collapsed=1\|start=45}}		{{Harmonics in equal\|97\|9\|1\|columns=9\|title=(contd.)\|collapsed=1\|start=44}}

	== Intervals ==		== Intervals ==

BudjarnLambeth: Intervals

2024-12-23T01:01:48Z

Intervals

← Older revision		Revision as of 01:01, 23 December 2024
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	{{Harmonics in equal\|97\|9\|1\|columns=7\|collapsed=1\|start=37}}		{{Harmonics in equal\|97\|9\|1\|columns=7\|collapsed=1\|start=37}}
	{{Harmonics in equal\|97\|9\|1\|columns=7\|title=(contd.)\|collapsed=1\|start=45}}		{{Harmonics in equal\|97\|9\|1\|columns=7\|title=(contd.)\|collapsed=1\|start=45}}

			== Intervals ==
			{{Interval table}}


	{{todo\|expand}}		{{todo\|expand}}
	[[Category:Ed9]][[Category:Equal-step tuning]]		[[Category:Ed9]][[Category:Equal-step tuning]]

BudjarnLambeth: Tidy up tables

2024-12-23T01:00:55Z

Tidy up tables

← Older revision		Revision as of 01:00, 23 December 2024
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	97ed9 sets a height record on the [[The Riemann zeta function and tuning\|Riemann zeta function]] with [[The Riemann zeta function and tuning#Removing primes\|primes 2 and 3 removed]], approximating 30.59745 EDO. This record remains unbeaten until approximately 41.3478 EDO.		97ed9 sets a height record on the [[The Riemann zeta function and tuning\|Riemann zeta function]] with [[The Riemann zeta function and tuning#Removing primes\|primes 2 and 3 removed]], approximating 30.59745 EDO. This record remains unbeaten until approximately 41.3478 EDO.

	Additionally, 97ed9 is close to [[125zpi]].		Additionally, 97ed9 is close to [[125zpi]] (see [[Zeta peak index]]).

	== Harmonic series ==		== Harmonic series ==

	~~{{Harmonics in equal\|97\|9\|1\|prec~~=~~1\|columns~~=15}}		=== 2 to 15 ===
	{{Harmonics in equal\|97\|9\|~~1\|prec=~~1\|columns=~~16\|start=16~~}}		{{Harmonics in equal\|97\|9\|1\|columns=7}}
	{{Harmonics in equal\|97\|9\|1\|~~prec~~=1\|~~columns~~=18\|start=32}}		{{Harmonics in equal\|97\|9\|1\|columns=7\|title=(contd.)\|start=8}}

			=== 38 to 52 ===
			{{Harmonics in equal\|97\|9\|1\|columns=7\|collapsed=1\|start=37}}
			{{Harmonics in equal\|97\|9\|1\|columns=7\|title=(contd.)\|collapsed=1\|start=45}}


			{{todo\|expand}}
	[[Category:Ed9]][[Category:Equal-step tuning]]		[[Category:Ed9]][[Category:Equal-step tuning]]

BudjarnLambeth at 11:28, 1 October 2024

2024-10-01T11:28:08Z

← Older revision		Revision as of 11:28, 1 October 2024
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	{{Harmonics in equal\|97\|9\|1\|prec=1\|columns=18\|start=32}}		{{Harmonics in equal\|97\|9\|1\|prec=1\|columns=18\|start=32}}

	[[Category:Ed9]][[Category:Equal-step ~~tunings~~]]		[[Category:Ed9]][[Category:Equal-step tuning]]

BudjarnLambeth: Categorised uncategorised page

2024-09-11T03:11:06Z

Categorised uncategorised page

← Older revision		Revision as of 03:11, 11 September 2024
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	{{Harmonics in equal\|97\|9\|1\|prec=1\|columns=16\|start=16}}		{{Harmonics in equal\|97\|9\|1\|prec=1\|columns=16\|start=16}}
	{{Harmonics in equal\|97\|9\|1\|prec=1\|columns=18\|start=32}}		{{Harmonics in equal\|97\|9\|1\|prec=1\|columns=18\|start=32}}

			[[Category:Ed9]][[Category:Equal-step tunings]]

Contribution at 18:39, 16 May 2024

2024-05-16T18:39:17Z

← Older revision		Revision as of 18:39, 16 May 2024
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	This system can be approximated as 30.6001 [[EDO]], meaning each step of 97ed9 corresponds closely to five steps of [[153edo]].		This system can be approximated as 30.6001 [[EDO]], meaning each step of 97ed9 corresponds closely to five steps of [[153edo]].

	This non-octave, non-tritave scale features a well-balanced harmonic series segment from 4 to 9 and another from 39 to 50. It performs well across all prime harmonics from 5 to 19, with the exception of 13, which is slightly flat.		This non-octave, non-tritave scale features a well-balanced [[harmonic series segment]] from 4 to 9 and another from 39 to 50. It performs well across all [[prime harmonics]] from 5 to 19, with the exception of 13, which is slightly flat.

	97ed9 sets a height record on the [[The Riemann zeta function and tuning\|Riemann zeta function]] with [[The Riemann zeta function and tuning#Removing primes\|primes 2 and 3 removed]], approximating 30.59745 EDO. This record remains unbeaten until approximately 41.3478 EDO.		97ed9 sets a height record on the [[The Riemann zeta function and tuning\|Riemann zeta function]] with [[The Riemann zeta function and tuning#Removing primes\|primes 2 and 3 removed]], approximating 30.59745 EDO. This record remains unbeaten until approximately 41.3478 EDO.

Contribution at 10:07, 16 May 2024

2024-05-16T10:07:12Z

← Older revision		Revision as of 10:07, 16 May 2024
Line 7:		Line 7:
	This non-octave, non-tritave scale features a well-balanced harmonic series segment from 4 to 9 and another from 39 to 50. It performs well across all prime harmonics from 5 to 19, with the exception of 13, which is slightly flat.		This non-octave, non-tritave scale features a well-balanced harmonic series segment from 4 to 9 and another from 39 to 50. It performs well across all prime harmonics from 5 to 19, with the exception of 13, which is slightly flat.

	97ed9 sets a height record on the Riemann zeta function with primes 2 and 3 removed, approximating 30.59745 EDO. This record remains unbeaten until approximately 41.3478 EDO.		97ed9 sets a height record on the [[The Riemann zeta function and tuning\|Riemann zeta function]] with [[The Riemann zeta function and tuning#Removing primes\|primes 2 and 3 removed]], approximating 30.59745 EDO. This record remains unbeaten until approximately 41.3478 EDO.

	Additionally, 97ed9 is close to [[125zpi]].		Additionally, 97ed9 is close to [[125zpi]].

Contribution at 10:05, 16 May 2024

2024-05-16T10:05:18Z

← Older revision		Revision as of 10:05, 16 May 2024
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	97ed9 sets a height record on the Riemann zeta function with primes 2 and 3 removed, approximating 30.59745 EDO. This record remains unbeaten until approximately 41.3478 EDO.		97ed9 sets a height record on the Riemann zeta function with primes 2 and 3 removed, approximating 30.59745 EDO. This record remains unbeaten until approximately 41.3478 EDO.

	Additionally, 97ed9 is close to 125zpi.		Additionally, 97ed9 is close to [[125zpi]].

	== Harmonic series ==		== Harmonic series ==