10edf - Revision history

FloraC: Text replacement - "octave" to "octave"

2026-07-14T14:15:27Z

Text replacement - "octave" to "octave"

← Older revision		Revision as of 14:15, 14 July 2026
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	== Theory ==		== Theory ==
	10edf is related to [[17edo]], but with the [[3/2\|perfect fifth]] rather than the [[~~2/1\|~~octave]] being just. The octave is compressed by about 6.68{{c}}, a small but significant deviation. 10edf is [[consistent]] to the [[integer limit\|7-integer-limit]], but not to the 8-integer-limit. In comparison, 17edo is only consistent up to the 4-integer-limit. This makes 10edf a suitable tuning perhaps in the [[5-limit]], but overcompressed in any other limits, as well as the no-5 13-limit, where 17edo is best at.		10edf is related to [[17edo]], but with the [[3/2\|perfect fifth]] rather than the [[octave]] being just. The octave is compressed by about 6.68{{c}}, a small but significant deviation. 10edf is [[consistent]] to the [[integer limit\|7-integer-limit]], but not to the 8-integer-limit. In comparison, 17edo is only consistent up to the 4-integer-limit. This makes 10edf a suitable tuning perhaps in the [[5-limit]], but overcompressed in any other limits, as well as the no-5 13-limit, where 17edo is best at.

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

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''9ed(3/2) + 10ed(3/2) + 11ed(3/2) locked at 6:8:11 improv'' (2026)

2026-07-08T06:03:21Z

Music: Add Bryan Deister's ''9ed(3/2) + 10ed(3/2) + 11ed(3/2) locked at 6:8:11 improv'' (2026)

← Older revision		Revision as of 06:03, 8 July 2026
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	== Music ==		== Music ==
			=== 21st century ===
	; [[Peter Kosmorsky]]		; [[Peter Kosmorsky]]
	* [https://www.archive.org/details/10Edf ''10 edf''] (archived 2011)		* [https://www.archive.org/details/10Edf ''10 edf''] (archived 2011)

			; [[Bryan Deister]]
			* [https://www.youtube.com/shorts/U-XewMZiBC0 ''9ed(3/2) + 10ed(3/2) + 11ed(3/2) locked at 6:8:11 improv''] (2026, polymicrotonal, playing in 3 tuning systems simultaneously)

	== See also ==		== See also ==

ArrowHead294 at 15:29, 19 June 2025

2025-06-19T15:29:56Z

← Older revision		Revision as of 15:29, 19 June 2025
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	== Theory ==		== Theory ==
	10edf is related to [[17edo]], but with the [[3/2\|perfect fifth]] rather than the [[2/1\|octave]] being just. The octave is about 6.68 ~~cents compressed~~. 10edf is [[consistent]] to the [[integer limit\|7-integer-limit]], but not to the 8-integer-limit. In comparison, 17edo is only consistent up to the 4-integer-limit. This makes 10edf a suitable tuning perhaps in the [[5-limit]], but overcompressed in any other limits, as well as the no-5 13-limit, where 17edo is best at.		10edf is related to [[17edo]], but with the [[3/2\|perfect fifth]] rather than the [[2/1\|octave]] being just. The octave is compressed by about 6.68{{c}}, a small but significant deviation. 10edf is [[consistent]] to the [[integer limit\|7-integer-limit]], but not to the 8-integer-limit. In comparison, 17edo is only consistent up to the 4-integer-limit. This makes 10edf a suitable tuning perhaps in the [[5-limit]], but overcompressed in any other limits, as well as the no-5 13-limit, where 17edo is best at.

	=== Harmonics ===		=== Harmonics ===
Line 14:		Line 14:
	== Intervals ==		== Intervals ==
	{\| class="wikitable center-all right-2"		{\| class="wikitable center-all right-2"
			\|-
	! #		! #
	! Cents		! Cents

FloraC: /* Theory */ + an evaluation on the amount of octave compression

2025-05-21T14:37:09Z

Theory: + an evaluation on the amount of octave compression

← Older revision		Revision as of 14:37, 21 May 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	10edf is related to [[17edo]], but with the [[3/2\|perfect fifth]] rather than the [[2/1\|octave]] being just. The octave is about 6.68 cents compressed. 10edf is [[consistent]] to the [[integer limit\|7-integer-limit]], but not to the 8-integer-limit. In comparison, 17edo is only consistent up to the 4-integer-limit.		10edf is related to [[17edo]], but with the [[3/2\|perfect fifth]] rather than the [[2/1\|octave]] being just. The octave is about 6.68 cents compressed. 10edf is [[consistent]] to the [[integer limit\|7-integer-limit]], but not to the 8-integer-limit. In comparison, 17edo is only consistent up to the 4-integer-limit. This makes 10edf a suitable tuning perhaps in the [[5-limit]], but overcompressed in any other limits, as well as the no-5 13-limit, where 17edo is best at.

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

FloraC: /* Theory */ +subsets and supersets

2025-05-21T14:32:19Z

Theory: +subsets and supersets

← Older revision		Revision as of 14:32, 21 May 2025
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	{{Harmonics in equal\|10\|3\|2\|intervals=integer\|columns=11}}		{{Harmonics in equal\|10\|3\|2\|intervals=integer\|columns=11}}
	{{Harmonics in equal\|10\|3\|2\|intervals=integer\|columns=12\|start=12\|collapsed=true\|Approximation of harmonics in 10edf (continued)}}		{{Harmonics in equal\|10\|3\|2\|intervals=integer\|columns=12\|start=12\|collapsed=true\|Approximation of harmonics in 10edf (continued)}}

			=== Subsets and supersets ===
			Since 10 factors into primes as {{nowrap\| 2 × 5 }}, 10edf contains [[2edf]] and [[5edf]] as subset edfs.

	== Intervals ==		== Intervals ==

FloraC: Cleanup (2/2)

2025-05-21T14:30:50Z

Cleanup (2/2)

← Older revision		Revision as of 14:30, 21 May 2025
Line 9:		Line 9:
	{{Harmonics in equal\|10\|3\|2\|intervals=integer\|columns=12\|start=12\|collapsed=true\|Approximation of harmonics in 10edf (continued)}}		{{Harmonics in equal\|10\|3\|2\|intervals=integer\|columns=12\|start=12\|collapsed=true\|Approximation of harmonics in 10edf (continued)}}

	==Intervals==		== Intervals ==
	{\| class="wikitable"		{\| class="wikitable center-all right-2"
	!~~degree~~		! #
	!		! Cents
	![[1L 3s (fifth-equivalent)\|Neptunian]] notation using 8\10edf		! [[1L 3s (fifth-equivalent)\|Neptunian]] notation<br>using 8\10edf
	![[Ed9/4\|Neapolitan]] notation using 3/10edf		! [[Ed9/4\|Neapolitan]] notation<br>using 3/10edf
	\|-		\|-
	~~! colspan="2"~~ \|0		\| 0
	\|C		\| 0.0
	\|F		\| C
			\| F
	\|-		\|-
	\| 1		\| 1
	\|70.~~1955~~		\| 70.2
	\|^C, vDb		\| ^C, vDb
	\|F^, Gb		\| F^, Gb
	\|-		\|-
	\|2		\| 2
	\|140.~~391~~		\| 140.4
	\|C#, Db		\| C#, Db
	\|F#, Gd		\| F#, Gd
	\|-		\|-
	\|3		\| 3
	\|210.~~5865~~		\| 210.6
	\|vD		\| vD
	\|G		\| G
	\|-		\|-
	\|4		\| 4
	\|280.~~782~~		\| 280.8
	\|D		\| D
	\|G^, Ab		\| G^, Ab
	\|-		\|-
	\|5		\| 5
	\|~~350~~.~~9775~~		\| 351.0
	\|^D, vE		\| ^D, vE
	\|G#, Ad		\| G#, Ad
	\|-		\|-
	\|6		\| 6
	\|421.~~173~~		\| 421.2
	\|E		\| E
	\|A		\| A
	\|-		\|-
	\|7		\| 7
	\|491.~~3685~~		\| 491.4
	\|^E, vF		\| ^E, vF
	\|A^, Hb		\| A^, Hb
	\|-		\|-
	\| 8		\| 8
	\|561.~~564~~		\| 561.6
	\|F		\| F
	\|A#, Hd		\| A#, Hd
	\|-		\|-
	\|9		\| 9
	\|631.~~7595~~		\| 631.8
	\|^F, vC		\| ^F, vC
	\|H		\| H
	\|-		\|-
	\|10		\| 10
	\|~~701~~.~~955~~		\| 702.0
	\|C		\| C
	\|B		\| B
	\|-		\|-
	\|11		\| 11
	\|772.~~1505~~		\| 772.2
	\|^C, vDb		\| ^C, vDb
	\|B^, Cb		\| B^, Cb
	\|-		\|-
	\|12		\| 12
	\|842.~~346~~		\| 842.3
	\|C#, Db		\| C#, Db
	\|B#, Cd		\| B#, Cd
	\|-		\|-
	\|13		\| 13
	\|912.~~5415~~		\| 912.5
	\|vD		\| vD
	\|C		\| C
	\|-		\|-
	\|14		\| 14
	\|982.~~737~~		\| 982.7
	\|D		\| D
	\|C^, Db		\| C^, Db
	\|-		\|-
	\|15		\| 15
	\|1052.~~9325~~		\| 1052.9
	\|^D, vE		\| ^D, vE
	\|C#, Dd		\| C#, Dd
	\|-		\|-
	\|16		\| 16
	\|1123.~~128~~		\| 1123.1
	\|E		\| E
	\|D		\| D
	\|-		\|-
	\|17		\| 17
	\|1193.~~3235~~		\| 1193.3
	\|^E, vF		\| ^E, vF
	\|D^, Eb		\| D^, Eb
	\|-		\|-
	\|18		\| 18
	\|1263.~~519~~		\| 1263.5
	\|F		\| F
	\|D#, Eb		\| D#, Eb
	\|-		\|-
	\|19		\| 19
	\|1333.~~7145~~		\| 1333.7
	\|^F, vC		\| ^F, vC
	\|E		\| E
	\|-		\|-
	\|20		\| 20
	\|1403.91		\| 1403.9
	\|C		\| C
	\|F		\| F
	\|}		\|}

FloraC: Cleanup (1/)

2025-05-21T14:26:52Z

Cleanup (1/)

← Older revision		Revision as of 14:26, 21 May 2025
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	{{Infobox ET}}		{{Infobox ET}}
	'''[[EDF\|Division of the just perfect fifth]] into 10 equal parts''' (10EDF) is related to [[17edo\|17 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 6.6765 cents compressed and the step size is about 70.1955 cents. It is consistent to the [[7-odd-limit\|7-integer-limit]], but not to the 8-integer-limit. In comparison, 17edo is only consistent up to the [[3-odd-limit\|4-integer-limit]].		{{ED intro}}

	~~Lookalikes:~~ [[17edo]], [[~~27edt~~]]		== Theory ==
	{{~~todo~~\|~~improve synopsis~~\|~~text~~=~~Make it longer, describe more about the tuning.~~}}		10edf is related to [[17edo]], but with the [[3/2\|perfect fifth]] rather than the [[2/1\|octave]] being just. The octave is about 6.68 cents compressed. 10edf is [[consistent]] to the [[integer limit\|7-integer-limit]], but not to the 8-integer-limit. In comparison, 17edo is only consistent up to the 4-integer-limit.

			=== Harmonics ===
			{{Harmonics in equal\|10\|3\|2\|intervals=integer\|columns=11}}
			{{Harmonics in equal\|10\|3\|2\|intervals=integer\|columns=12\|start=12\|collapsed=true\|Approximation of harmonics in 10edf (continued)}}

	==Intervals==		==Intervals==
Line 117:		Line 121:
	\|}		\|}

	== ~~Harmonics~~ ==		== Music ==
	~~{{Harmonics in equal~~		; [[Peter Kosmorsky]]
	~~\| steps = 10~~		* [https://www.archive.org/details/10Edf ''10 edf''] (archived 2011)
	~~\| num = 3~~
	~~\| denom = 2~~
	}}
	~~{{Harmonics in equal~~
	~~\| steps =~~ 10
	~~\| num = 3~~
	~~\| denom = 2~~
	~~\| start = 12~~
	~~\| collapsed = 1~~
	}}

	==~~Music~~==		== See also ==
	*~~http://www.archive.org/details/10Edf by~~ [[~~Peter Kosmorsky~~]]		* [[17edo]] – relative edo
			* [[27edt]] – relative edt
			* [[44ed6]] – relative ed6

	~~[[Category:Edf]]~~
	[[Category:Listen]]		[[Category:Listen]]

	~~[[Category:todo:expand]]~~
	~~[[Category:todo:improve synopsis]]~~

BudjarnLambeth: {{todo|improve synopsis|text=Make it longer, describe more about the tuning.}}

2024-12-19T08:58:19Z

{{todo|improve synopsis|text=Make it longer, describe more about the tuning.}}

← Older revision		Revision as of 08:58, 19 December 2024
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	Lookalikes: [[17edo]], [[27edt]]		Lookalikes: [[17edo]], [[27edt]]
			{{todo\|improve synopsis\|text=Make it longer, describe more about the tuning.}}

	==Intervals==		==Intervals==

BudjarnLambeth: Harmonics

2024-10-02T10:08:08Z

Harmonics

@@ Line 115: / Line 115: @@
 |F
 |}
 ==Music==

FloraC: -irrelevant shit

2024-05-07T13:20:19Z

-irrelevant shit

Show changes