59edf - Revision history

BudjarnLambeth at 22:29, 17 October 2025

2025-10-17T22:29:24Z

← Older revision		Revision as of 22:29, 17 October 2025
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	=== Harmonics ===		=== Harmonics ===
			59edf approximates all no-19s [[29-limit]] primes with less than 30% relative error.
	{{Harmonics in equal\|59\|3\|2\|intervals=integer\|columns=11}}		{{Harmonics in equal\|59\|3\|2\|intervals=integer\|columns=11}}
	{{Harmonics in equal\|59\|3\|2\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 58edf (continued)}}		{{Harmonics in equal\|59\|3\|2\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 58edf (continued)}}

BudjarnLambeth at 22:26, 17 October 2025

2025-10-17T22:26:48Z

← Older revision		Revision as of 22:26, 17 October 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	59edf corresponds is [[101edo]] but with the [[3/2\|perfect fifth]] rather than the [[2/1\|octave]] being just. The octave is [[stretched and compressed tuning\|stretched]] by about 1.65 [[cents]]. 58edf is [[consistent]] to the [[integer limit\|7-integer-limit]]. In comparison, 101edo is only consistent up to the 3-integer-limit.		59edf corresponds is [[101edo]] but with the [[3/2\|perfect fifth]] rather than the [[2/1\|octave]] being just. The octave is [[stretched and compressed tuning\|stretched]] by about 1.65 [[cents]]. 58edf is [[consistent]] to the [[integer limit\|7-integer-limit]]. In comparison, 101edo is only consistent up to the 3-integer-limit.

	Where each of 101edo's [[prime]]s 5, 7 and 11 have two about equally good mappings with 40-60% [[relative error]], 59edf instead has one mapping for each with 5-30% relative error, at the cost of only minimal damage to the 2 and 3.		Where each of 101edo's [[prime]]s 5, 7 and 11 have two about equally good mappings with 40-60% [[relative error]], 59edf instead has one mapping for each with 5-30% relative error, at the cost of only minimal damage to the 2 and 3.

			59edf is very close to [[zpi\|581zpi]], the biggest of the [[Zeta]] peaks near 101edo.

	=== Harmonics ===		=== Harmonics ===

BudjarnLambeth: Every EDF up to 60 except this one had a page, so I made this one such that someone can travel between any smaller EDF and 60edf just using the info boxes; ended up discovering this is actually a pretty based stretched tuning of 101edo along the way

2025-10-17T22:23:29Z

Every EDF up to 60 except this one had a page, so I made this one such that someone can travel between any smaller EDF and 60edf just using the info boxes; ended up discovering this is actually a pretty based stretched tuning of 101edo along the way

New page

{{Infobox ET}}
{{ED intro}}

== Theory ==
59edf corresponds is [[101edo]] but with the [[3/2|perfect fifth]] rather than the [[2/1|octave]] being just. The octave is [[stretched and compressed tuning|stretched]] by about 1.65 [[cents]]. 58edf is [[consistent]] to the [[integer limit|7-integer-limit]]. In comparison, 101edo is only consistent up to the 3-integer-limit.

Where each of 101edo's [[prime]]s 5, 7 and 11 have two about equally good mappings with 40-60% [[relative error]], 59edf instead has one mapping for each with 5-30% relative error, at the cost of only minimal damage to the 2 and 3.

=== Harmonics ===
{{Harmonics in equal|59|3|2|intervals=integer|columns=11}}
{{Harmonics in equal|59|3|2|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 58edf (continued)}}

=== Subsets and supersets ===
59 is a prime number, so 59edf has no subset edfs. Its smallest supersets are [[118edf]] and [[177edf]].

== Intervals ==
{{Interval table}}

== See also ==
* [[101edo]] – relative edo
* [[160edt]] – relative edt
* [[261ed6]] – relative ed6

{{stub}}