153edt - Revision history

BudjarnLambeth: /* Harmonics */ copied format from 209edt

2024-10-05T12:10:59Z

Harmonics: copied format from 209edt

← Older revision		Revision as of 12:10, 5 October 2024
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	== Harmonics ==		== Harmonics ==
			{{Harmonics in equal\|153\|3\|1\|intervals = prime\|columns = 9}}
	{{Harmonics in equal\|153\|3\|1}}		{{Harmonics in equal\|153\|3\|1\|start = 12\|collapsed = 1\|intervals = odd}}
	{{Harmonics in equal\|153\|3\|1\|intervals=~~prime~~}}

Lériendil: also makes more sense here to show primes

2024-10-05T11:40:20Z

also makes more sense here to show primes

← Older revision		Revision as of 11:40, 5 October 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~{{ED intro}}~~

	153edt is notable for being the denominator of a convergent to log<sub>3</sub>(7/3), after [[9edt]], [[13edt]] and [[35edt]], and the last before [[3401edt]], and therefore has an extremely accurate approximation to [[7/3]], a mere 0.0036 cents flat. In fact, 153edt demonstrates 11-strong 7-3 [[telicity]], due to the next term in the continued fraction expansion being large (note how much larger 3401 is than 153), although 3401edt in fact surpasses it, demonstrating 16-strong 7-3 telicity.		153edt is notable for being the denominator of a convergent to log<sub>3</sub>(7/3), after [[9edt]], [[13edt]] and [[35edt]], and the last before [[3401edt]], and therefore has an extremely accurate approximation to [[7/3]], a mere 0.0036 cents flat. In fact, 153edt demonstrates 11-strong 7-3 [[telicity]], due to the next term in the continued fraction expansion being large (note how much larger 3401 is than 153), although 3401edt in fact surpasses it, demonstrating 16-strong 7-3 telicity.
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	== Harmonics ==		== Harmonics ==
	{{Harmonics in equal
	\| ~~steps =~~ 153		{{Harmonics in equal\|153\|3\|1}}
	\| ~~num =~~ 3		{{Harmonics in equal\|153\|3\|1\|intervals=prime}}
	\| ~~denom =~~ 1
	}}
	{{Harmonics in equal
	\| ~~steps =~~ 153
	\| ~~num =~~ 3
	\| ~~denom =~~ 1
	\| ~~start~~ = 12
	~~\| collapsed = 1~~
	}}

BudjarnLambeth at 10:18, 5 October 2024

2024-10-05T10:18:09Z

← Older revision		Revision as of 10:18, 5 October 2024
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	However, 153edt's approximation of [[2/1]] is close to maximally bad, meaning that it is as far from an octave-equivalent tuning that an [[EDT]] of this size can be (though by this point, it is only 6 or so cents off).		However, 153edt's approximation of [[2/1]] is close to maximally bad, meaning that it is as far from an octave-equivalent tuning that an [[EDT]] of this size can be (though by this point, it is only 6 or so cents off).

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

	== Harmonics ==		== Harmonics ==

BudjarnLambeth: Intro inter harm

2024-10-05T09:04:35Z

Intro inter harm

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{Harmonics in equal|153|3|1|intervals=prime}}
+{{ED intro}}
 edt is notable for being the denominator of a convergent to log<sub>3</sub>(7/3), after [[9edt]], [[13edt]] and [[35edt]], and the last before [[3401edt]], and therefore has an extremely accurate approximation to [[7/3]], a mere 0.0036 cents flat. In fact, 153edt demonstrates 11-strong 7-3 [[telicity]], due to the next term in the continued fraction expansion being large (note how much larger 3401 is than 153), although 3401edt in fact surpasses it, demonstrating 16-strong 7-3 telicity.
@@ Line 7: / Line 7: @@
 However, 153edt's approximation of [[2/1]] is close to maximally bad, meaning that it is as far from an octave-equivalent tuning that an [[EDT]] of this size can be (though by this point, it is only 6 or so cents off).

Lériendil at 10:07, 27 August 2024

2024-08-27T10:07:13Z

← Older revision		Revision as of 10:07, 27 August 2024
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	~~{{Stub}}~~
	{{Infobox ET}}		{{Infobox ET}}
	{{Harmonics in equal\|153\|3\|1\|intervals=prime}}		{{Harmonics in equal\|153\|3\|1\|intervals=prime}}

Lériendil at 11:25, 26 August 2024

2024-08-26T11:25:49Z

← Older revision		Revision as of 11:25, 26 August 2024
Line 3:		Line 3:
	{{Harmonics in equal\|153\|3\|1\|intervals=prime}}		{{Harmonics in equal\|153\|3\|1\|intervals=prime}}

	153edt is notable for being the denominator of a convergent to log<sub>3</sub>(7/3), after [[9edt]], [[13edt]] and [[35edt]], and the last before [[3401edt]], and therefore has an extremely accurate approximation to [[7/3]]. In fact, 153edt demonstrates 11-strong 7-3 [[telicity]], due to the next term in the continued fraction expansion being large (note how much larger 3401 is than 153), although 3401edt in fact surpasses it, demonstrating 16-strong 7-3 telicity.		153edt is notable for being the denominator of a convergent to log<sub>3</sub>(7/3), after [[9edt]], [[13edt]] and [[35edt]], and the last before [[3401edt]], and therefore has an extremely accurate approximation to [[7/3]], a mere 0.0036 cents flat. In fact, 153edt demonstrates 11-strong 7-3 [[telicity]], due to the next term in the continued fraction expansion being large (note how much larger 3401 is than 153), although 3401edt in fact surpasses it, demonstrating 16-strong 7-3 telicity.

	In the no-twos [[7-limit]], 153edt supports [[canopus]] temperament, which gives it a rather accurate approximation of the 5th harmonic; and it additionally is accurate in the [[11-limit]], tempering out the comma [[387420489/386683451]] in the 3.7.11 subgroup. Harmonics 19 and 29 are also notably good.		In the no-twos [[7-limit]], 153edt supports [[canopus]] temperament, which gives it a rather accurate approximation of the 5th harmonic; and it additionally is accurate in the [[11-limit]], tempering out the comma [[387420489/386683451]] in the 3.7.11 subgroup. Harmonics 19 and 29 are also notably good.

	However, 153edt's approximation of [[2/1]] is close to maximally bad, meaning that it is as far from an octave-equivalent tuning that an [[EDT]] of this size can be (though by this point, it is only 6 or so cents off).		However, 153edt's approximation of [[2/1]] is close to maximally bad, meaning that it is as far from an octave-equivalent tuning that an [[EDT]] of this size can be (though by this point, it is only 6 or so cents off).

Lériendil at 11:25, 26 August 2024

2024-08-26T11:25:23Z

← Older revision		Revision as of 11:25, 26 August 2024
Line 6:		Line 6:

	In the no-twos [[7-limit]], 153edt supports [[canopus]] temperament, which gives it a rather accurate approximation of the 5th harmonic; and it additionally is accurate in the [[11-limit]], tempering out the comma [[387420489/386683451]] in the 3.7.11 subgroup. Harmonics 19 and 29 are also notably good.		In the no-twos [[7-limit]], 153edt supports [[canopus]] temperament, which gives it a rather accurate approximation of the 5th harmonic; and it additionally is accurate in the [[11-limit]], tempering out the comma [[387420489/386683451]] in the 3.7.11 subgroup. Harmonics 19 and 29 are also notably good.

			However, 153edt's approximation of [[2/1]] is close to maximally bad, meaning that it is as far from an octave-equivalent tuning that an [[EDT]] of this size can be (though by this point, it is only 6 or so cents off).

Lériendil at 11:24, 26 August 2024

2024-08-26T11:24:10Z

← Older revision		Revision as of 11:24, 26 August 2024
Line 5:		Line 5:
	153edt is notable for being the denominator of a convergent to log<sub>3</sub>(7/3), after [[9edt]], [[13edt]] and [[35edt]], and the last before [[3401edt]], and therefore has an extremely accurate approximation to [[7/3]]. In fact, 153edt demonstrates 11-strong 7-3 [[telicity]], due to the next term in the continued fraction expansion being large (note how much larger 3401 is than 153), although 3401edt in fact surpasses it, demonstrating 16-strong 7-3 telicity.		153edt is notable for being the denominator of a convergent to log<sub>3</sub>(7/3), after [[9edt]], [[13edt]] and [[35edt]], and the last before [[3401edt]], and therefore has an extremely accurate approximation to [[7/3]]. In fact, 153edt demonstrates 11-strong 7-3 [[telicity]], due to the next term in the continued fraction expansion being large (note how much larger 3401 is than 153), although 3401edt in fact surpasses it, demonstrating 16-strong 7-3 telicity.

	In the no-twos [[7-limit]], 153edt supports [[canopus]] temperament, which gives it a rather accurate approximation of the 5th harmonic; and it additionally is accurate in the [[11-limit]], tempering out the comma [[387420489/386683451]] in the 3.7.11 subgroup.		In the no-twos [[7-limit]], 153edt supports [[canopus]] temperament, which gives it a rather accurate approximation of the 5th harmonic; and it additionally is accurate in the [[11-limit]], tempering out the comma [[387420489/386683451]] in the 3.7.11 subgroup. Harmonics 19 and 29 are also notably good.

Lériendil at 11:23, 26 August 2024

2024-08-26T11:23:47Z

← Older revision		Revision as of 11:23, 26 August 2024
Line 3:		Line 3:
	{{Harmonics in equal\|153\|3\|1\|intervals=prime}}		{{Harmonics in equal\|153\|3\|1\|intervals=prime}}

	~~Note~~ the ~~incredibly~~ accurate ~~representation~~ of the ~~7th~~ harmonic.		153edt is notable for being the denominator of a convergent to log<sub>3</sub>(7/3), after [[9edt]], [[13edt]] and [[35edt]], and the last before [[3401edt]], and therefore has an extremely accurate approximation to [[7/3]]. In fact, 153edt demonstrates 11-strong 7-3 [[telicity]], due to the next term in the continued fraction expansion being large (note how much larger 3401 is than 153), although 3401edt in fact surpasses it, demonstrating 16-strong 7-3 telicity.

			In the no-twos [[7-limit]], 153edt supports [[canopus]] temperament, which gives it a rather accurate approximation of the 5th harmonic; and it additionally is accurate in the [[11-limit]], tempering out the comma [[387420489/386683451]] in the 3.7.11 subgroup.

Lériendil at 03:08, 19 July 2024

2024-07-19T03:08:50Z

← Older revision		Revision as of 03:08, 19 July 2024
Line 1:		Line 1:
	{{Stub}}		{{Stub}}
	{{Infobox ET}}		{{Infobox ET}}
			{{Harmonics in equal\|153\|3\|1\|intervals=prime}}

			Note the incredibly accurate representation of the 7th harmonic.