User:PiotrGrochowski/Extra-Diatonic Intervals - Revision history

PiotrGrochowski at 09:55, 7 October 2018

2018-10-07T09:55:52Z

← Older revision		Revision as of 09:55, 7 October 2018
Line 1:		Line 1:
	[[Extra-Diatonic Intervals]] tries to base on 72edo and tries to take into account that superpyth minor seconds can reach 70 cents, although in meantone it's actually an augmented unison. However, superpyth is not suited for a diatonic scale, we can exclude it out of my version and base it on some meantone tuning like [[43edo]], [[74edo]] or [[105edo]]~~. To convert an interval to a name, select the closest 43edo interval, round down if halfway. I might do another one based on [[50edo]] and meanpop too..~~.		[[Extra-Diatonic Intervals]] tries to base on 72edo and tries to take into account that superpyth minor seconds can reach 70 cents, although in meantone it's actually an augmented unison. However, superpyth is not suited for a diatonic scale, we can exclude it out of my version and base it on some meantone tuning like [[43edo]], [[74edo]] or [[105edo]].

	[[13-limit]] ratios are based on [[grosstone]] and are 69–integer–limit. They are valid to the amount of fifths, and need not necessarily convert to the same interval.		[[13-limit]] ratios are based on [[grosstone]] and are 69–integer–limit. They are valid to the amount of fifths, and need not necessarily convert to the same interval.

	The base intervals come from the circle of fifths from -7 to 7 fifths: diminished octave, diminished fifth, minor second, minor sixth, minor third, minor seventh, fourth, unison, fifth, major second, major sixth, major third, major seventh, augmented fourth ~~a d~~ augmented unison. This is unlike Igliashon's [[Extra-Diatonic Intervals]], which only uses -5 to +5 fifths. The reasoning for the expanded range is that a chromatic scale is made of 6 augmented fourths and 6 diminished fifths, as well as 7 minor seconds and 5 augmented unisons. In the other hand, the diminished fourth at -8 fifths is considered a wolf major third in [[5-limit]], and a septimal major third in [[7-limit]], so this system names it a high major third instead.		The base intervals come from the circle of fifths from -7 to 7 fifths: diminished octave, diminished fifth, minor second, minor sixth, minor third, minor seventh, fourth, unison, fifth, major second, major sixth, major third, major seventh, augmented fourth and augmented unison. This is unlike Igliashon's [[Extra-Diatonic Intervals]], which only uses -5 to +5 fifths. The reasoning for the expanded range is that a chromatic scale is made of 6 augmented fourths and 6 diminished fifths, as well as 7 minor seconds and 5 augmented unisons. In the other hand, the diminished fourth at -8 fifths is considered a wolf major third in [[5-limit]], and a septimal major third in [[7-limit]], so this system names it a high major third instead.

	This project can be used for converting intervals of an entire edo to interval names in this system: https://scratch.mit.edu/projects/250811968/		'''To convert an interval to a name, select the closest 43edo interval, round down if halfway.''' This project can be used for converting intervals of an entire edo to interval names in this system: https://scratch.mit.edu/projects/250811968/

			Like Igliashon's [[Extra-Diatonic Intervals]], this is based on size, not the harmonic function. For example 2 steps in 26edo (92.308 cents) is named augmented unison, although it is not one in its meantone system.

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PiotrGrochowski at 07:12, 7 October 2018

2018-10-07T07:12:10Z

← Older revision		Revision as of 07:12, 7 October 2018
Line 5:		Line 5:
	The base intervals come from the circle of fifths from -7 to 7 fifths: diminished octave, diminished fifth, minor second, minor sixth, minor third, minor seventh, fourth, unison, fifth, major second, major sixth, major third, major seventh, augmented fourth a d augmented unison. This is unlike Igliashon's [[Extra-Diatonic Intervals]], which only uses -5 to +5 fifths. The reasoning for the expanded range is that a chromatic scale is made of 6 augmented fourths and 6 diminished fifths, as well as 7 minor seconds and 5 augmented unisons. In the other hand, the diminished fourth at -8 fifths is considered a wolf major third in [[5-limit]], and a septimal major third in [[7-limit]], so this system names it a high major third instead.		The base intervals come from the circle of fifths from -7 to 7 fifths: diminished octave, diminished fifth, minor second, minor sixth, minor third, minor seventh, fourth, unison, fifth, major second, major sixth, major third, major seventh, augmented fourth a d augmented unison. This is unlike Igliashon's [[Extra-Diatonic Intervals]], which only uses -5 to +5 fifths. The reasoning for the expanded range is that a chromatic scale is made of 6 augmented fourths and 6 diminished fifths, as well as 7 minor seconds and 5 augmented unisons. In the other hand, the diminished fourth at -8 fifths is considered a wolf major third in [[5-limit]], and a septimal major third in [[7-limit]], so this system names it a high major third instead.

	This project can be used for converting intervals of an entire edo to interval names ~~given here~~: https://scratch.mit.edu/projects/250811968/		This project can be used for converting intervals of an entire edo to interval names in this system: https://scratch.mit.edu/projects/250811968/

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PiotrGrochowski at 07:11, 7 October 2018

2018-10-07T07:11:57Z

← Older revision		Revision as of 07:11, 7 October 2018
Line 4:		Line 4:

	The base intervals come from the circle of fifths from -7 to 7 fifths: diminished octave, diminished fifth, minor second, minor sixth, minor third, minor seventh, fourth, unison, fifth, major second, major sixth, major third, major seventh, augmented fourth a d augmented unison. This is unlike Igliashon's [[Extra-Diatonic Intervals]], which only uses -5 to +5 fifths. The reasoning for the expanded range is that a chromatic scale is made of 6 augmented fourths and 6 diminished fifths, as well as 7 minor seconds and 5 augmented unisons. In the other hand, the diminished fourth at -8 fifths is considered a wolf major third in [[5-limit]], and a septimal major third in [[7-limit]], so this system names it a high major third instead.		The base intervals come from the circle of fifths from -7 to 7 fifths: diminished octave, diminished fifth, minor second, minor sixth, minor third, minor seventh, fourth, unison, fifth, major second, major sixth, major third, major seventh, augmented fourth a d augmented unison. This is unlike Igliashon's [[Extra-Diatonic Intervals]], which only uses -5 to +5 fifths. The reasoning for the expanded range is that a chromatic scale is made of 6 augmented fourths and 6 diminished fifths, as well as 7 minor seconds and 5 augmented unisons. In the other hand, the diminished fourth at -8 fifths is considered a wolf major third in [[5-limit]], and a septimal major third in [[7-limit]], so this system names it a high major third instead.

			This project can be used for converting intervals of an entire edo to interval names given here: https://scratch.mit.edu/projects/250811968/

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PiotrGrochowski: import a revision from the time machine: :dev:User:PiotrGrochowski/Extra-Diatonic Intervals

2018-10-04T14:48:41Z

import a revision from the time machine: dev:User:PiotrGrochowski/Extra-Diatonic Intervals

Show changes

PiotrGrochowski: complete up to fourth, add info about fractions and make "comma unison" consistent by renaming it to "high unison"

2018-10-01T18:00:46Z

complete up to fourth, add info about fractions and make "comma unison" consistent by renaming it to "high unison"

@@ Line 1: / Line 1: @@
-[[Extra-Diatonic Intervals]] tries to base on 72edo and tries to take into account that superpyth minor seconds can reach 70 cents, although in meantone it's actually an augmented unison. However, superpyth is not suited for a diatonic scale, we can exclude it out of my version and base it on some meantone tuning like [[43edo]], [[74edo]] or [[105edo]]. To convert an interval to a name, select the closest 43edo interval. 13–limit ratios are based on [[grosstone]]. I might do another one based on [[50edo]] and meanpop too...
+[[Extra-Diatonic Intervals]] tries to base on 72edo and tries to take into account that superpyth minor seconds can reach 70 cents, although in meantone it's actually an augmented unison. However, superpyth is not suited for a diatonic scale, we can exclude it out of my version and base it on some meantone tuning like [[43edo]], [[74edo]] or [[105edo]]. To convert an interval to a name, select the closest 43edo interval. 13–limit ratios are based on [[grosstone]] and do not have numbers 70 or more. I might do another one based on [[50edo]] and meanpop too...
 {| class="wikitable"
@@ Line 19: / Line 19: @@
 |1/1
 |-
-|comma unison
+|high unison
 |1
 |1
@@ Line 117: / Line 117: @@
 |high neutral third
 |9
+|13
 |}

PiotrGrochowski: ditch the 105edo column, it produces an uneven 3–1 step scale that may be inconsistent

2018-10-01T17:36:22Z

ditch the 105edo column, it produces an uneven 3–1 step scale that may be inconsistent

← Older revision		Revision as of 17:36, 1 October 2018
Line 7:		Line 7:
	\|43edo steps		\|43edo steps
	\|74edo steps		\|74edo steps
	~~\|105edo steps~~
	\|43edo cents		\|43edo cents
	\|fifths		\|fifths
Line 13:		Line 12:
	\|-		\|-
	\|unison		\|unison
	\|0
	\|0		\|0
	\|0		\|0
Line 25:		Line 23:
	\|1		\|1
	\|2		\|2
	\|3
	\|27.907		\|27.907
	\| -12		\| -12
Line 34:		Line 31:
	\|2		\|2
	\|3		\|3
	\|4
	\|55.814		\|55.814
	\| +19		\| +19
Line 43:		Line 39:
	\|3		\|3
	\|5		\|5
	\|7
	\|83.721		\|83.721
	\| +7		\| +7
Line 52:		Line 47:
	\|4		\|4
	\|7		\|7
	~~\|10~~
	\|111.628		\|111.628
	\| -5		\| -5
Line 61:		Line 55:
	\|5		\|5
	\|9		\|9
	~~\|13~~
	\|139.535		\|139.535
	\| -17		\| -17
Line 70:		Line 63:
	\|6		\|6
	\|10		\|10
	~~\|14~~
	\|167.442		\|167.442
	\| +14		\| +14
Line 79:		Line 71:
	\|7		\|7
	\|12		\|12
	~~\|17~~
	\|195.349		\|195.349
	\| +2		\| +2
Line 88:		Line 79:
	\|8		\|8
	\|14		\|14
	~~\|20~~
	\|223.256		\|223.256
	\| -10		\| -10
Line 97:		Line 87:
	\|9		\|9
	\|15		\|15
	~~\|21~~
	\|251.163		\|251.163
	\| +21		\| +21
Line 106:		Line 95:
	\|10		\|10
	\|17		\|17
	~~\|24~~
	\|279.070		\|279.070
	\| +9		\| +9
Line 115:		Line 103:
	\|11		\|11
	\|19		\|19
	~~\|27~~
	\|306.977		\|306.977
	\| -3		\| -3
Line 124:		Line 111:
	\|12		\|12
	\|21		\|21
	~~\|30~~
	\|334.884		\|334.884
	\| -15		\| -15
	\|27/22, 39/32, 40/33, 60/49, 65/54		\|27/22, 39/32, 40/33, 60/49, 65/54
			\|-
			\|high neutral third
			\|9
			\|
	\|}		\|}

PiotrGrochowski at 17:18, 1 October 2018

2018-10-01T17:18:58Z

← Older revision		Revision as of 17:18, 1 October 2018
Line 1:		Line 1:
	[[Extra-Diatonic Intervals]] tries to base on 72edo and tries to take into account that superpyth minor seconds can reach 70 cents, although in meantone it's actually an augmented unison. However, superpyth is not suited for a diatonic scale, we can exclude it out of my version and base it on some meantone tuning like [[43edo]], [[74edo]] or [[105edo]]. To convert an interval to a name, select the closest 43edo interval. 13–limit ratios are based on [[grosstone]]. I might do another one based on [[50edo]] and meanpop ~~instead~~...		[[Extra-Diatonic Intervals]] tries to base on 72edo and tries to take into account that superpyth minor seconds can reach 70 cents, although in meantone it's actually an augmented unison. However, superpyth is not suited for a diatonic scale, we can exclude it out of my version and base it on some meantone tuning like [[43edo]], [[74edo]] or [[105edo]]. To convert an interval to a name, select the closest 43edo interval. 13–limit ratios are based on [[grosstone]]. I might do another one based on [[50edo]] and meanpop too...

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PiotrGrochowski: continuing making intervals

2018-10-01T17:17:08Z

continuing making intervals

@@ Line 57: / Line 57: @@
 |15/14, 16/15, 27/25, 35/33
 |-
-|lesser neutral second
+|low neutral second
 |4
 |5
@@ Line 66: / Line 66: @@
 |12/11, 13/12, 54/49
 |-
-|greater neutral second
+|high neutral second
 |4
 |6
@@ Line 101: / Line 101: @@
 | +21
 |15/13, 55/48
 |}

PiotrGrochowski at 16:59, 1 October 2018

2018-10-01T16:59:12Z

← Older revision		Revision as of 16:59, 1 October 2018
Line 93:		Line 93:
	\|8/7		\|8/7
	\|-		\|-
	\|~~uh,~~		\|second–third
	\|		\|6
	\|9		\|9
	\|		\|15
	\|		\|21
	\|251.163		\|251.163
	\|		\| +21
	\|		\|15/13, 55/48
	\|}		\|}

PiotrGrochowski at 16:42, 1 October 2018

2018-10-01T16:42:17Z

@@ Line 83: / Line 83: @@
 | +2
 |9/8, 10/9, 28/25, 49/44, 55/49
 |}