User:Hkm - Revision history

Hkm: Blanked the page

2026-02-13T02:35:19Z

Blanked the page

← Older revision		Revision as of 02:35, 13 February 2026
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	The following equivalence forms a definition of the opposites "intervallically otonal" and "intervallically utonal." If any one of the following statements is true, then they are all true; if any one is false, they are all false.

	~~# JI interval c between notes A and B, where A is below B, is intervallically otonal~~
	~~# A is intervallically utonal to B~~
	~~# B is intervallically otonal to A~~
	~~# c tends to have higher prime factors in the numerator and more prime factors in the denominator~~

	If the JI interpretations of a cent value (from which that cent value draws its perceptual properties) tend to be otonal, then the cent value is called "roughly otonal." Even JI ratios that are "intervallically utonal" can be "roughly otonal": 32/25, which is quite close to 7/6 and is perceived as a tempered version of such, is an example. Simpler intervals tend to have more prominent effects and larger capture regions for rough otonality.

	HKM finds that the perceptual root of a chord is the interval which tends to be the most roughly utonal and consonant to the other notes of the chord, and the perceptual tonic of a progression is (usually) determinable the same way. The strength of a resolution tends to approximate the strength of the root of the last chord as a perceptual tonic of the chord of the resolution and those chords preceding it.

Hkm at 19:48, 26 January 2026

2026-01-26T19:48:24Z

← Older revision		Revision as of 19:48, 26 January 2026
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	If the JI interpretations of a cent value (from which that cent value draws its perceptual properties) tend to be otonal, then the cent value is called "roughly otonal." Even JI ratios that are "intervallically utonal" can be "roughly otonal": 32/25, which is quite close to 7/6 and is perceived as a tempered version of such, is an example. Simpler intervals tend to have more prominent effects and larger capture regions for rough otonality.		If the JI interpretations of a cent value (from which that cent value draws its perceptual properties) tend to be otonal, then the cent value is called "roughly otonal." Even JI ratios that are "intervallically utonal" can be "roughly otonal": 32/25, which is quite close to 7/6 and is perceived as a tempered version of such, is an example. Simpler intervals tend to have more prominent effects and larger capture regions for rough otonality.

	HKM finds that the perceptual root of a chord is the interval which tends to be the most roughly utonal and consonant to the other notes of the chord, and the perceptual tonic of a progression is (usually) determinable the same way. The strength of a resolution tends to approximate the ~~strengths~~ of ~~notes~~ of the last chord as perceptual ~~tonics~~ of the chord of the resolution and those chords preceding it.		HKM finds that the perceptual root of a chord is the interval which tends to be the most roughly utonal and consonant to the other notes of the chord, and the perceptual tonic of a progression is (usually) determinable the same way. The strength of a resolution tends to approximate the strength of the root of the last chord as a perceptual tonic of the chord of the resolution and those chords preceding it.

Hkm at 19:10, 26 January 2026

2026-01-26T19:10:59Z

← Older revision		Revision as of 19:10, 26 January 2026
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	The following equivalence forms a definition of the opposites "intervallically otonal" and "intervallically utonal":		The following equivalence forms a definition of the opposites "intervallically otonal" and "intervallically utonal." If any one of the following statements is true, then they are all true; if any one is false, they are all false.

	# JI interval c between notes A and B, where A is below B, is intervallically otonal		# JI interval c between notes A and B, where A is below B, is intervallically otonal

Hkm at 18:34, 26 January 2026

2026-01-26T18:34:52Z

← Older revision		Revision as of 18:34, 26 January 2026
Line 8:		Line 8:
	If the JI interpretations of a cent value (from which that cent value draws its perceptual properties) tend to be otonal, then the cent value is called "roughly otonal." Even JI ratios that are "intervallically utonal" can be "roughly otonal": 32/25, which is quite close to 7/6 and is perceived as a tempered version of such, is an example. Simpler intervals tend to have more prominent effects and larger capture regions for rough otonality.		If the JI interpretations of a cent value (from which that cent value draws its perceptual properties) tend to be otonal, then the cent value is called "roughly otonal." Even JI ratios that are "intervallically utonal" can be "roughly otonal": 32/25, which is quite close to 7/6 and is perceived as a tempered version of such, is an example. Simpler intervals tend to have more prominent effects and larger capture regions for rough otonality.

	HKM finds that the perceptual root of a chord is the interval which tends to be the most roughly utonal and consonant to the other notes of the chord, and the perceptual tonic of a progression is (~~somewhat~~) determinable the same way. The strength of a resolution tends to approximate the strengths of notes of the last chord as perceptual tonics of the chord of the resolution and those chords preceding it.		HKM finds that the perceptual root of a chord is the interval which tends to be the most roughly utonal and consonant to the other notes of the chord, and the perceptual tonic of a progression is (usually) determinable the same way. The strength of a resolution tends to approximate the strengths of notes of the last chord as perceptual tonics of the chord of the resolution and those chords preceding it.

Hkm at 00:10, 26 January 2026

2026-01-26T00:10:39Z

← Older revision		Revision as of 00:10, 26 January 2026
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	The following ~~equivalency of statements form~~ a definition of the opposites "intervallically otonal" and "intervallically utonal":		The following equivalence forms a definition of the opposites "intervallically otonal" and "intervallically utonal":

	# JI interval c between notes A and B, where A is below B, is intervallically otonal		# JI interval c between notes A and B, where A is below B, is intervallically otonal

Hkm at 23:12, 25 January 2026

2026-01-25T23:12:01Z

← Older revision		Revision as of 23:12, 25 January 2026
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	The following ~~equivalent~~ statements form a definition of the opposites "intervallically otonal" and "intervallically utonal":		The following equivalency of statements form a definition of the opposites "intervallically otonal" and "intervallically utonal":

	# JI interval c between notes A and B, where A is below B, is intervallically otonal		# JI interval c between notes A and B, where A is below B, is intervallically otonal

Hkm at 06:08, 24 January 2026

2026-01-24T06:08:42Z

← Older revision		Revision as of 06:08, 24 January 2026
Line 1:		Line 1:
	The following equivalent statements form a definition of the opposites "intervallically otonal" and "intervallically utonal":		The following equivalent statements form a definition of the opposites "intervallically otonal" and "intervallically utonal":

	# JI interval c between notes A and B, where A is below B, is intervallically otonal - A is intervallically utonal to B - B is intervallically otonal to A - c tends to have higher prime factors in the numerator and more prime factors in the denominator		# JI interval c between notes A and B, where A is below B, is intervallically otonal
			# A is intervallically utonal to B
			# B is intervallically otonal to A
			# c tends to have higher prime factors in the numerator and more prime factors in the denominator

	If the JI interpretations of a cent value (from which that cent value draws its perceptual properties) tend to be otonal, then the cent value is called "roughly otonal." Even JI ratios that are "intervallically utonal" can be "roughly otonal": 32/25, which is quite close to 7/6 and is perceived as a tempered version of such, is an example. Simpler intervals tend to have more prominent effects and larger capture regions for rough otonality.		If the JI interpretations of a cent value (from which that cent value draws its perceptual properties) tend to be otonal, then the cent value is called "roughly otonal." Even JI ratios that are "intervallically utonal" can be "roughly otonal": 32/25, which is quite close to 7/6 and is perceived as a tempered version of such, is an example. Simpler intervals tend to have more prominent effects and larger capture regions for rough otonality.

	HKM finds that the perceptual root of a chord is the interval which tends to be the most roughly utonal and consonant to the other notes of the chord, and the perceptual tonic of a progression is (somewhat) determinable the same way. The strength of a resolution tends to approximate the strengths of notes of the last chord as perceptual tonics of the chord of the resolution and those chords preceding it.		HKM finds that the perceptual root of a chord is the interval which tends to be the most roughly utonal and consonant to the other notes of the chord, and the perceptual tonic of a progression is (somewhat) determinable the same way. The strength of a resolution tends to approximate the strengths of notes of the last chord as perceptual tonics of the chord of the resolution and those chords preceding it.

Hkm at 06:08, 24 January 2026

2026-01-24T06:08:17Z

← Older revision		Revision as of 06:08, 24 January 2026
Line 1:		Line 1:
	The following equivalent statements form a definition of the opposites "~~intervalically~~ otonal" and "~~intervalically~~ utonal":		The following equivalent statements form a definition of the opposites "intervallically otonal" and "intervallically utonal":
	~~- JI interval c between notes A and B, where A is below B, is intervalically otonal~~
	~~- A is intervalically utonal to B~~
	~~- B is intervalically otonal to A~~
	~~- c tends to have higher prime factors in the numerator and more prime factors in the denominator~~

	If the JI interpretations of a cent value (from which that cent value draws its perceptual properties) tend to be otonal, then the cent value is called "roughly otonal." Even JI ratios that are "~~intervalically~~ utonal" can be "roughly otonal": 32/25, which is quite close to 7/6 and is perceived as a tempered version of such, is an example. Simpler intervals tend to have more prominent effects and larger capture regions for rough otonality.		# JI interval c between notes A and B, where A is below B, is intervallically otonal - A is intervallically utonal to B - B is intervallically otonal to A - c tends to have higher prime factors in the numerator and more prime factors in the denominator

			If the JI interpretations of a cent value (from which that cent value draws its perceptual properties) tend to be otonal, then the cent value is called "roughly otonal." Even JI ratios that are "intervallically utonal" can be "roughly otonal": 32/25, which is quite close to 7/6 and is perceived as a tempered version of such, is an example. Simpler intervals tend to have more prominent effects and larger capture regions for rough otonality.

	HKM finds that the perceptual root of a chord is the interval which tends to be the most roughly utonal and consonant to the other notes of the chord, and the perceptual tonic of a progression is (somewhat) determinable the same way. The strength of a resolution tends to approximate the strengths of notes of the last chord as perceptual tonics of the chord of the resolution and those chords preceding it.		HKM finds that the perceptual root of a chord is the interval which tends to be the most roughly utonal and consonant to the other notes of the chord, and the perceptual tonic of a progression is (somewhat) determinable the same way. The strength of a resolution tends to approximate the strengths of notes of the last chord as perceptual tonics of the chord of the resolution and those chords preceding it.

Hkm: Created page with "The following equivalent statements form a definition of the opposites "intervalically otonal" and "intervalically utonal": - JI interval c between notes A and B, where A is below B, is intervalically otonal - A is intervalically utonal to B - B is intervalically otonal to A - c tends to have higher prime factors in the numerator and more prime factors in the denominator If the JI interpretations of a cent value (from which that cent value draws its perceptual propertie..."

2026-01-24T06:03:29Z

Created page with "The following equivalent statements form a definition of the opposites "intervalically otonal" and "intervalically utonal": - JI interval c between notes A and B, where A is below B, is intervalically otonal - A is intervalically utonal to B - B is intervalically otonal to A - c tends to have higher prime factors in the numerator and more prime factors in the denominator If the JI interpretations of a cent value (from which that cent value draws its perceptual propertie..."

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The following equivalent statements form a definition of the opposites "intervalically otonal" and "intervalically utonal":
- JI interval c between notes A and B, where A is below B, is intervalically otonal
- A is intervalically utonal to B
- B is intervalically otonal to A
- c tends to have higher prime factors in the numerator and more prime factors in the denominator

If the JI interpretations of a cent value (from which that cent value draws its perceptual properties) tend to be otonal, then the cent value is called "roughly otonal." Even JI ratios that are "intervalically utonal" can be "roughly otonal": 32/25, which is quite close to 7/6 and is perceived as a tempered version of such, is an example. Simpler intervals tend to have more prominent effects and larger capture regions for rough otonality.

HKM finds that the perceptual root of a chord is the interval which tends to be the most roughly utonal and consonant to the other notes of the chord, and the perceptual tonic of a progression is (somewhat) determinable the same way. The strength of a resolution tends to approximate the strengths of notes of the last chord as perceptual tonics of the chord of the resolution and those chords preceding it.