10edf - Revision history

ArrowHead294 at 15:29, 19 June 2025

2025-06-19T15:29:56Z

← Older revision		Revision as of 15:29, 19 June 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. 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 ===
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	== 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
Line 8:		Line 8:
	{{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==
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	\|}		\|}

	== ~~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
Line 3:		Line 3:

	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

CompactStar at 03:41, 5 April 2023

2023-04-05T03:41:41Z

← Older revision		Revision as of 03:41, 5 April 2023
Line 116:		Line 116:
	\|}		\|}
	==Scale tree==		==Scale tree==
	If 4\7 (four degrees of 7EDO) is at one extreme and 3\5 (three degrees of 5EDO) is at the other, all other possible 5L 2s scales exist in a continuum between them. You can chop this continuum up by taking [[Mediant\|"freshman sums"]] of the two edges - adding together the numerators, then adding together the denominators (i.e. adding them together as if you would be adding the complex numbers analogous real and imaginary parts). Thus, between 4\7 and 3\5 you have (4+3)\(7+5) = 7\12, seven degrees of 12EDO.		EDF scales can be approximated in [[EDO]]s by subdividing diatonic fifths. If 4\7 (four degrees of 7EDO) is at one extreme and 3\5 (three degrees of 5EDO) is at the other, all other possible 5L 2s scales exist in a continuum between them. You can chop this continuum up by taking [[Mediant\|"freshman sums"]] of the two edges - adding together the numerators, then adding together the denominators (i.e. adding them together as if you would be adding the complex numbers analogous real and imaginary parts). Thus, between 4\7 and 3\5 you have (4+3)\(7+5) = 7\12, seven degrees of 12EDO.

	If we carry this freshman-summing out a little further, new, larger [[EDO]]s pop up in our continuum.		If we carry this freshman-summing out a little further, new, larger [[EDO]]s pop up in our continuum.

Moremajorthanmajor at 18:11, 22 March 2023

2023-03-22T18:11:51Z

← Older revision		Revision as of 18:11, 22 March 2023
Line 9:		Line 9:
	!		!
	![[1L 3s (fifth-equivalent)\|Neptunian]] notation using 8\10edf		![[1L 3s (fifth-equivalent)\|Neptunian]] notation using 8\10edf
			![[Ed9/4\|Neapolitan]] notation using 3/10edf
	\|-		\|-
	! colspan="2" \|0		! colspan="2" \|0
	\|C		\|C
			\|F
	\|-		\|-
	\| 1		\| 1
	\|70.1955		\|70.1955
	\|^C, vDb		\|^C, vDb
			\|F^, Gb
	\|-		\|-
	\|2		\|2
	\|140.391		\|140.391
	\|C#, Db		\|C#, Db
			\|F#, Gd
	\|-		\|-
	\|3		\|3
	\|210.5865		\|210.5865
	\|vD		\|vD
			\|G
	\|-		\|-
	\|4		\|4
	\|280.782		\|280.782
	\|D		\|D
			\|G^, Ab
	\|-		\|-
	\|5		\|5
	\|350.9775		\|350.9775
	\|^D, vE		\|^D, vE
			\|G#, Ad
	\|-		\|-
	\|6		\|6
	\|421.173		\|421.173
	\|E		\|E
			\|A
	\|-		\|-
	\|7		\|7
	\|491.3685		\|491.3685
	\|^E, vF		\|^E, vF
			\|A^, Hb
	\|-		\|-
	\| 8		\| 8
	\|561.564		\|561.564
	\|F		\|F
			\|A#, Hd
	\|-		\|-
	\|9		\|9
	\|631.7595		\|631.7595
	\|^F, vC		\|^F, vC
			\|H
	\|-		\|-
	\|10		\|10
	\|701.955		\|701.955
	\|C		\|C
			\|B
	\|-		\|-
	\|11		\|11
	\|772.1505		\|772.1505
	\|^C, vDb		\|^C, vDb
			\|B^, Cb
	\|-		\|-
	\|12		\|12
	\|842.346		\|842.346
	\|C#, Db		\|C#, Db
			\|B#, Cd
	\|-		\|-
	\|13		\|13
	\|912.5415		\|912.5415
	\|vD		\|vD
			\|C
	\|-		\|-
	\|14		\|14
	\|982.737		\|982.737
	\|D		\|D
			\|C^, Db
	\|-		\|-
	\|15		\|15
	\|1052.9325		\|1052.9325
	\|^D, vE		\|^D, vE
			\|C#, Dd
	\|-		\|-
	\|16		\|16
	\|1123.128		\|1123.128
	\|E		\|E
			\|D
	\|-		\|-
	\|17		\|17
	\|1193.3235		\|1193.3235
	\|^E, vF		\|^E, vF
			\|D^, Eb
	\|-		\|-
	\|18		\|18
	\|1263.519		\|1263.519
	\|F		\|F
			\|D#, Eb
	\|-		\|-
	\|19		\|19
	\|1333.7145		\|1333.7145
	\|^F, vC		\|^F, vC
			\|E
	\|-		\|-
	\|20		\|20
	\|1403.91		\|1403.91
	\|C		\|C
			\|F
	\|}		\|}
	==Scale tree==		==Scale tree==
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	\| \|\| \|\| \|\| \|\| \|\| \|\|38\65\|\|70.1539\|\|		\| \|\| \|\| \|\| \|\| \|\| \|\|38\65\|\|70.1539\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\|31\53\|\| \|\|70.1887\|\|The ~~generator~~ closest to a just [[3/2]] for EDOs less than 200		\| \|\| \|\| \|\| \|\| \|\|31\53\|\| \|\|70.1887\|\|The fifth closest to a just [[3/2]] for EDOs less than 200
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| \|\|55\94\|\|70.2128\|\|[[Garibaldi]] / [[Cassandra]]		\| \|\| \|\| \|\| \|\| \|\| \|\|55\94\|\|70.2128\|\|[[Garibaldi]] / [[Cassandra]]