Warped diatonic - Revision history

Eliora: fix pagename mid-page

2025-08-12T04:14:52Z

fix pagename mid-page

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	= Example: Godzilla[9] =		== Example: Godzilla[9] ==
	Godzilla[9] in [[19edo\|19edo]] has steps of {{nowrap\|3 3 1 3 1 3 1 3 1}}. That corresponds to LLsLsLsLs where L is 189.5 cents and s is 63.2 cents. These step sizes are well within the range where they are "recognized" as diatonic scale steps. If you play 0 3 6 7 10 in 19edo (with no drone or harmony, just the melody) it will sound like "do re mi fa sol", leading you to believe that "sol" is a 3/2 interval above "do", but in fact it's not—it's closer to 10/7. The "real" 3/2 is another small step above that, in the melodic position of a flatted "la".		Godzilla[9] in [[19edo\|19edo]] has steps of {{nowrap\|3 3 1 3 1 3 1 3 1}}. That corresponds to LLsLsLsLs where L is 189.5 cents and s is 63.2 cents. These step sizes are well within the range where they are "recognized" as diatonic scale steps. If you play 0 3 6 7 10 in 19edo (with no drone or harmony, just the melody) it will sound like "do re mi fa sol", leading you to believe that "sol" is a 3/2 interval above "do", but in fact it's not—it's closer to 10/7. The "real" 3/2 is another small step above that, in the melodic position of a flatted "la".

ArrowHead294 at 22:03, 22 September 2024

2024-09-22T22:03:08Z

← Older revision		Revision as of 22:03, 22 September 2024
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	A '''warped diatonic scale''' is a scale (excluding the diatonic scale itself) that contains relatively long substrings of the [[~~5L_2s\|~~5L 2s]] diatonic scale ("LLsLLLsLLsLLLs...") in its sequence of large and small steps, and such that the sizes of those steps are similar to those of the diatonic scale (namely, in the ballpark of 200 and 100 cents).		A '''warped diatonic scale''' is a scale (excluding the diatonic scale itself) that contains relatively long substrings of the [[5L 2s]] diatonic scale ("LLsLLLsLLsLLLs...") in its sequence of large and small steps, and such that the sizes of those steps are similar to those of the diatonic scale (namely, in the ballpark of 200 and 100 cents).

	Such scales may mislead a diatonic-conditioned listener into assigning the intervals to diatonic scale categories, but the categorization will be violated when either (1) the part of the scale that doesn't agree with 5L2s is reached, or (2) the harmonic nature of the intervals is drastically different than what's expected from the diatonic scale.		Such scales may mislead a diatonic-conditioned listener into assigning the intervals to diatonic scale categories, but the categorization will be violated when either (1) the part of the scale that doesn't agree with 5L2s is reached, or (2) the harmonic nature of the intervals is drastically different than what's expected from the diatonic scale.
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	\|-		\|-
	\| 8		\| 8
	\| [[~~3L_2s\|~~3L 2s]]		\| [[3L 2s]]
	\| Sensi, Squares, Petrtri, A-Team, Father		\| Sensi, Squares, Petrtri, A-Team, Father
	\| LsLLsL		\| LsLLsL
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	\|-		\|-
	\| 9		\| 9
	\| [[~~4L_1s\|~~4L 1s]]		\| [[4L 1s]]
	\| Bug, superpelog		\| Bug, superpelog
	\| LLLsLL, LLsLLL		\| LLLsLL, LLsLLL
Line 63:		Line 63:
	\|-		\|-
	\| 10		\| 10
	\| [[~~4L_2s\|~~4L 2s]]		\| [[4L 2s]]
	\| Decimal, lemba		\| Decimal, lemba
	\| LLsLLsLL		\| LLsLLsLL
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	\|-		\|-
	\| 11		\| 11
	\| [[~~4L_3s\|~~4L 3s]]		\| [[4L 3s]]
	\| Orgone, keemun, sixix		\| Orgone, keemun, sixix
	\| LsLLsL		\| LsLLsL
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	\|-		\|-
	\| 11		\| 11
	\| [[~~5L_1s\|~~5L 1s]]		\| [[5L 1s]]
	\| Machine, gorgo		\| Machine, gorgo
	\| LLLsLL, LLsLLL		\| LLLsLL, LLsLLL
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	\|-		\|-
	\| '''12'''		\| '''12'''
	\| '''[[~~5L_2s\|~~5L 2s]]'''		\| '''[[5L 2s]]'''
	\| '''Ordinary diatonic'''		\| '''Ordinary diatonic'''
	\| (infinitely long)		\| (infinitely long)
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	\|-		\|-
	\| 13		\| 13
	\| [[~~5L_3s\|~~5L 3s]]		\| [[5L 3s]]
	\| Father, A-Team, Petrtri		\| Father, A-Team, Petrtri
	\| LsLLsLL, LLsLLsL		\| LsLLsLL, LLsLLsL
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	\|-		\|-
	\| 13		\| 13
	\| [[~~6L_1s\|~~6L 1s]]		\| [[6L 1s]]
	\| Glacial, leantone, tetracot		\| Glacial, leantone, tetracot
	\| LLLsLL, LLsLLL		\| LLLsLL, LLsLLL
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	\|-		\|-
	\| 14		\| 14
	\| [[~~5L_4s\|~~5L 4s]]		\| [[5L 4s]]
	\| Superpelog, godzilla		\| Superpelog, godzilla
	\| LsLLsL		\| LsLLsL
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	\|-		\|-
	\| 14		\| 14
	\| [[~~6L_2s\|~~6L 2s]]		\| [[6L 2s]]
	\| Hedgehog		\| Hedgehog
	\| LLsLLLsLL		\| LLsLLLsLL
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	\|-		\|-
	\| 15		\| 15
	\| [[~~6L_3s\|~~6L 3s]]		\| [[6L 3s]]
	\| Triforce		\| Triforce
	\| LLsLLsLL		\| LLsLLsLL
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	\|-		\|-
	\| 15		\| 15
	\| [[~~7L_1s\|~~7L 1s]]		\| [[7L 1s]]
	\| Porcupine		\| Porcupine
	\| LLLsLL, LLsLLL		\| LLLsLL, LLsLLL
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	\|-		\|-
	\| 16		\| 16
	\| [[~~6L_4s\|~~6L 4s]]		\| [[6L 4s]]
	\| Lemba, antikythera		\| Lemba, antikythera
	\| LsLLsL		\| LsLLsL
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	\|-		\|-
	\| 16		\| 16
	\| [[~~7L_2s\|~~7L 2s]]		\| [[7L 2s]]
	\| Mavila		\| Mavila
	\| LLsLLLsLL		\| LLsLLLsLL
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	=== Warped antidiatonic ===		=== Warped antidiatonic ===
	The scales at the top and bottom of this table are questionable as "warped antidiatonics", but the ones near 2x+y=9 are good examples.		The scales at the top and bottom of this table are questionable as "warped antidiatonics", but the ones near {{nowrap\|2''x'' + ''y'' {{=}} 9}} are good examples.
	{\| class="wikitable"		{\| class="wikitable"
	! {{nowrap\|2''x'' + ''y''}}		! {{nowrap\|2''x'' + ''y''}}

ArrowHead294: Formatting

2024-09-22T22:00:54Z

Formatting

Show changes

CompactStar at 19:03, 4 March 2024

2024-03-04T19:03:16Z

← Older revision		Revision as of 19:03, 4 March 2024
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	! \| 2x+y		! \| 2x+y
	! \| Formula		! \| Formula
	! \| Temperaments~~/names~~		! \| Temperaments
	! \| 5L2s substrings		! \| 5L2s substrings
	! \| Comments		! \| Comments

Dummy index: +category

2023-07-08T04:01:12Z

+category

← Older revision		Revision as of 04:01, 8 July 2023
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	<ul><li>2L+s, which is expected to be 4/3, is really more like 9/7.</li><li>2L+2s, which is expected to be a "dissonant tritone" like 10/7, is actually the "real" 4/3. In "ti do re mi fa", the ti-fa interval is a tempered 4/3.</li><li>3L+s, which is expected to be 3/2, is really more like 10/7.</li><li>3L+2s, which is expected to be an 8/5, is actually the "real" 3/2. In the "minor" scale "la ti do re mi fa", it's the "fa" rather than the "mi" that forms a 3/2 with the root "la".</li><li>4L+2s, which is expected to be a "minor seventh" (16/9~9/5), is actually 5/3. So in the "natural minor" scale "la ti do re mi fa sol", the outer la-sol interval is the easily recognizable consonance 5/3, but that's the "wrong" consonance for a diatonically-conditioned listener.</li><li>L+2s, which is not found in the ordinary diatonic scale but is familiar from the melodic and harmonic minor scales, is expected to be something close to a "major third" (in 12edo it's 400 cents, in meantone it's a tempered 9/7). In godzilla[9] it's the just minor third 6/5.</li><li>Finally, although there are 7 or even 8 consecutive notes of the scale that sound melodically familiar, the way the scale closes at the 2/1 is very unexpected and jarring for a diatonically-conditioned listener. When you get to 5L+3s that sounds melodically like it ought to be at least an "octave", probably something larger like an "augmented octave". But the real 2/1 is actually one small step beyond that, at 5L+4s.</li></ul> [[Category:todo:link]]		<ul><li>2L+s, which is expected to be 4/3, is really more like 9/7.</li><li>2L+2s, which is expected to be a "dissonant tritone" like 10/7, is actually the "real" 4/3. In "ti do re mi fa", the ti-fa interval is a tempered 4/3.</li><li>3L+s, which is expected to be 3/2, is really more like 10/7.</li><li>3L+2s, which is expected to be an 8/5, is actually the "real" 3/2. In the "minor" scale "la ti do re mi fa", it's the "fa" rather than the "mi" that forms a 3/2 with the root "la".</li><li>4L+2s, which is expected to be a "minor seventh" (16/9~9/5), is actually 5/3. So in the "natural minor" scale "la ti do re mi fa sol", the outer la-sol interval is the easily recognizable consonance 5/3, but that's the "wrong" consonance for a diatonically-conditioned listener.</li><li>L+2s, which is not found in the ordinary diatonic scale but is familiar from the melodic and harmonic minor scales, is expected to be something close to a "major third" (in 12edo it's 400 cents, in meantone it's a tempered 9/7). In godzilla[9] it's the just minor third 6/5.</li><li>Finally, although there are 7 or even 8 consecutive notes of the scale that sound melodically familiar, the way the scale closes at the 2/1 is very unexpected and jarring for a diatonically-conditioned listener. When you get to 5L+3s that sounds melodically like it ought to be at least an "octave", probably something larger like an "augmented octave". But the real 2/1 is actually one small step beyond that, at 5L+4s.</li></ul> [[Category:todo:link]]
	[[Category:Lists of scales]]		[[Category:Lists of scales]]
			[[Category:Diatonic]]

BudjarnLambeth: Added to category “lists of scales”

2023-04-15T05:43:06Z

Added to category “lists of scales”

← Older revision		Revision as of 05:43, 15 April 2023
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	<ul><li>2L+s, which is expected to be 4/3, is really more like 9/7.</li><li>2L+2s, which is expected to be a "dissonant tritone" like 10/7, is actually the "real" 4/3. In "ti do re mi fa", the ti-fa interval is a tempered 4/3.</li><li>3L+s, which is expected to be 3/2, is really more like 10/7.</li><li>3L+2s, which is expected to be an 8/5, is actually the "real" 3/2. In the "minor" scale "la ti do re mi fa", it's the "fa" rather than the "mi" that forms a 3/2 with the root "la".</li><li>4L+2s, which is expected to be a "minor seventh" (16/9~9/5), is actually 5/3. So in the "natural minor" scale "la ti do re mi fa sol", the outer la-sol interval is the easily recognizable consonance 5/3, but that's the "wrong" consonance for a diatonically-conditioned listener.</li><li>L+2s, which is not found in the ordinary diatonic scale but is familiar from the melodic and harmonic minor scales, is expected to be something close to a "major third" (in 12edo it's 400 cents, in meantone it's a tempered 9/7). In godzilla[9] it's the just minor third 6/5.</li><li>Finally, although there are 7 or even 8 consecutive notes of the scale that sound melodically familiar, the way the scale closes at the 2/1 is very unexpected and jarring for a diatonically-conditioned listener. When you get to 5L+3s that sounds melodically like it ought to be at least an "octave", probably something larger like an "augmented octave". But the real 2/1 is actually one small step beyond that, at 5L+4s.</li></ul> [[Category:todo:link]]		<ul><li>2L+s, which is expected to be 4/3, is really more like 9/7.</li><li>2L+2s, which is expected to be a "dissonant tritone" like 10/7, is actually the "real" 4/3. In "ti do re mi fa", the ti-fa interval is a tempered 4/3.</li><li>3L+s, which is expected to be 3/2, is really more like 10/7.</li><li>3L+2s, which is expected to be an 8/5, is actually the "real" 3/2. In the "minor" scale "la ti do re mi fa", it's the "fa" rather than the "mi" that forms a 3/2 with the root "la".</li><li>4L+2s, which is expected to be a "minor seventh" (16/9~9/5), is actually 5/3. So in the "natural minor" scale "la ti do re mi fa sol", the outer la-sol interval is the easily recognizable consonance 5/3, but that's the "wrong" consonance for a diatonically-conditioned listener.</li><li>L+2s, which is not found in the ordinary diatonic scale but is familiar from the melodic and harmonic minor scales, is expected to be something close to a "major third" (in 12edo it's 400 cents, in meantone it's a tempered 9/7). In godzilla[9] it's the just minor third 6/5.</li><li>Finally, although there are 7 or even 8 consecutive notes of the scale that sound melodically familiar, the way the scale closes at the 2/1 is very unexpected and jarring for a diatonically-conditioned listener. When you get to 5L+3s that sounds melodically like it ought to be at least an "octave", probably something larger like an "augmented octave". But the real 2/1 is actually one small step beyond that, at 5L+4s.</li></ul> [[Category:todo:link]]
			[[Category:Lists of scales]]

Moremajorthanmajor at 22:00, 5 April 2023

2023-04-05T22:00:09Z

@@ Line 14: / Line 14: @@
 ! | 5L2s substrings
 ! | Comments
 |-
 | | 8
@@ Line 110: / Line 140: @@
 | | LLsLLLsLL
 | |
 |-
 | | 20
-| | [[9L 2s]]
+| |[[9L 2s]]
 | | Casablanca
-| |
+| | LLLsLL, LLsLLL
 | |
 |}

CompactStar at 07:57, 4 April 2023

2023-04-04T07:57:16Z

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	\| \| Casablanca		\| \| Casablanca
	\| \|		\| \|
	~~\| \|~~
	\| \|		\| \|
	\|}		\|}

CompactStar at 07:57, 4 April 2023

2023-04-04T07:57:03Z

← Older revision		Revision as of 07:57, 4 April 2023
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	\| \| LLsLLLsLL		\| \| LLsLLLsLL
	\| \|		\| \|
	\| -		\|-
	\| \| 20		\| \| 20
	\| \| [[9L 2s]]		\| \| [[9L 2s]]

CompactStar at 07:56, 4 April 2023

2023-04-04T07:56:52Z

← Older revision		Revision as of 07:56, 4 April 2023
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	\| \| Mavila		\| \| Mavila
	\| \| LLsLLLsLL		\| \| LLsLLLsLL
	\| \|		\| \|
	\| -		\| -
	\| \| 20		\| \| 20
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	\| \| Casablanca		\| \| Casablanca
	\| \|		\| \|
			\| \|
	\| \|		\| \|
	\|}		\|}