65edt - Revision history

FloraC: /* Theory */ prime 3

2025-06-20T13:08:56Z

Theory: prime 3

← Older revision		Revision as of 13:08, 20 June 2025
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	== Theory ==		== Theory ==
	65edt is almost identical to [[41edo]], but with the perfect twelfth rather than the [[2/1\|octave]] being just. The octave is about 0.305 cents compressed. Like 41edo, 65edt is [[consistent]] to the [[integer limit\|16-integer-limit]], and in comparison, it improves the intonation of primes [[11/1\|11]], [[13/1\|13]], and [[17/1\|17]] at the expense of less accurate ~~tunings~~ of 2, [[5/1\|5]], [[7/1\|7]], and [[19/1\|19]], commending itself as a suitable tuning for [[13-limit\|13-]] and [[17-limit]]-focused harmonies.		65edt is almost identical to [[41edo]], but with the perfect twelfth rather than the [[2/1\|octave]] being just. The octave is about 0.305 cents compressed. Like 41edo, 65edt is [[consistent]] to the [[integer limit\|16-integer-limit]], and in comparison, it improves the intonation of primes 3, [[11/1\|11]], [[13/1\|13]], and [[17/1\|17]] at the expense of less accurate intonations of 2, [[5/1\|5]], [[7/1\|7]], and [[19/1\|19]], commending itself as a suitable tuning for [[13-limit\|13-]] and [[17-limit]]-focused harmonies.

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

2025-06-20T13:05:43Z

Theory: expand

← Older revision		Revision as of 13:05, 20 June 2025
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	== Theory ==		== Theory ==
	65edt is almost identical to [[41edo]], but with the ~~3/1~~ rather than the [[2/1]] being just. The octave is about 0.~~3053~~ cents compressed. Like 41edo, 65edt is [[consistent]] to the [[integer limit\|16-integer-limit]].		65edt is almost identical to [[41edo]], but with the perfect twelfth rather than the [[2/1\|octave]] being just. The octave is about 0.305 cents compressed. Like 41edo, 65edt is [[consistent]] to the [[integer limit\|16-integer-limit]], and in comparison, it improves the intonation of primes [[11/1\|11]], [[13/1\|13]], and [[17/1\|17]] at the expense of less accurate tunings of 2, [[5/1\|5]], [[7/1\|7]], and [[19/1\|19]], commending itself as a suitable tuning for [[13-limit\|13-]] and [[17-limit]]-focused harmonies.

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

2025-06-19T12:50:30Z

← Older revision		Revision as of 12:50, 19 June 2025
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	* [[95ed5]] – relative ed5		* [[95ed5]] – relative ed5
	* [[106ed6]] – relative ed6		* [[106ed6]] – relative ed6
			* [[147ed12]] – relative ed12
			* [[361ed448]] – close to the zeta-optimized tuning for 41edo

			[[Category:41edo]]

2025-03-20T17:35:53Z

Intervals: correction

2025-03-20T17:19:38Z

Intervals: +some ratios

2025-03-20T16:27:44Z

Theory: +subsets and supersets

← Older revision		Revision as of 16:27, 20 March 2025
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	{{Harmonics in equal\|65\|3\|1\|intervals=integer}}		{{Harmonics in equal\|65\|3\|1\|intervals=integer}}
	{{Harmonics in equal\|65\|3\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|Approximation of harmonics in 65edt (continued)}}		{{Harmonics in equal\|65\|3\|1\|intervals=integer\|columns=12\|start=12\|collapsed=true\|Approximation of harmonics in 65edt (continued)}}

			=== Subsets and supersets ===
			Since 65 factors into primes as {{nowrap\| 5 × 13 }}, 65edt contains [[5edt]] and [[13edt]] as subset edts.

	== Intervals ==		== Intervals ==

2025-03-20T16:26:42Z

+see also

2025-03-20T16:24:42Z

Cleanup

2024-10-06T07:26:21Z

Headings and stuff

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 '''[[Edt|Division of the third harmonic]] into 65 equal parts''' (65EDT) is almost identical to [[41edo|41 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.3053 cents compressed and the step size is about 29.2608 cents. It is consistent to the [[15-odd-limit|16-integer-limit]].
-==Harmonics==
+==Intervals==
 {| class="wikitable"
 |-
@@ Line 407: / Line 405: @@
 | | [[3/2|just perfect fifth]] plus an octave
 |}
 [[Category:Edt]]
 [[Category:Edonoi]]

2024-05-17T12:20:30Z

← Older revision		Revision as of 12:20, 17 May 2024
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	{{Infobox ET}}		{{Infobox ET}}
	'''[[Edt\|Division of the third harmonic]] into 65 equal parts''' (65EDT) is almost identical to [[41edo\|41 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.3053 cents compressed and the step size is about 29.2608 cents. It is consistent to the [[15-odd-limit\|16-integer-limit]].		'''[[Edt\|Division of the third harmonic]] into 65 equal parts''' (65EDT) is almost identical to [[41edo\|41 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 0.3053 cents compressed and the step size is about 29.2608 cents. It is consistent to the [[15-odd-limit\|16-integer-limit]].

			==Harmonics==
			{{Harmonics in equal\|65\|3\|1\|prec=2\|columns=15}}

	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! \| ~~degree~~		! \| Degree
	! \| ~~cents~~ value		! \| Cent value
	!~~hekts~~		! Hekts
	! \| ~~corresponding~~ <br>JI intervals		! \| Corresponding<br>JI intervals
	! \| ~~comments~~		! \| Comments
	\|-		\|-
	! colspan="3" \| 0		! colspan="3" \| 0