User:CritDeathX/Sam's Idea Of Consonance - Revision history

CritDeathX: /* Singular Chords */

2020-09-12T00:56:18Z

Singular Chords

← Older revision		Revision as of 00:56, 12 September 2020
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	=== Singular Chords ===		=== Singular Chords ===
	When it comes to just one chord, though, it'd be best to rely on which note most of the linear tones are found. For example, 9:11:13 in the last headliner had most of its linear tones occur on 9, so since 3 linear tones appeared on 9, we can say that the harmonal limit is 3.		When it comes to just one chord, though, it'd be best to rely on which note most of the linear tones are found. For example, 9:11:13 in the last headliner had most of its linear tones occur on 9, so since 3 linear tones appeared on 9, we can say that the harmonal limit for this chord is 3.

CritDeathX at 00:52, 12 September 2020

2020-09-12T00:52:27Z

← Older revision		Revision as of 00:52, 12 September 2020
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	Okay, so a while back, I had developed this method of finding how consonant a chord was. The basic idea was to find how many combination/difference tones lined up with a chord.		Okay, so a while back, I had developed this method of finding how consonant a chord was. The basic idea was to find how many combination/difference tones lined up with a chord.

			== Linear Tones ==

			=== Formula ===
	In order to find what tones line up with the chord, the resulting tone must either be		In order to find what tones line up with the chord, the resulting tone must either be
	# The number up/down whatever octaves [h*(2^x)]. (''e.g., 1/4, 3/6, 26/13'')		# The number up/down whatever octaves [h*(2^x)]. (''e.g., 1/4, 3/6, 26/13'')
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	Thus, by these rules, it cannot line up if it results in any other harmonic/interval.		Thus, by these rules, it cannot line up if it results in any other harmonic/interval.

	== ~~Linear Tones~~ ==		=== Demonstration ===
	I'll show an example of what I mean using 4:5:6.		I'll show an example of what I mean using 4:5:6.

CritDeathX: /* Harmonal Limits */

2020-09-12T00:50:12Z

Harmonal Limits

← Older revision		Revision as of 00:50, 12 September 2020
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	This is a term that I'm coining to describe certain patterns or outliers within a series of chords or a scale(s) based off of their linear tones.		This is a term that I'm coining to describe certain patterns or outliers within a series of chords or a scale(s) based off of their linear tones.

	~~For example, here~~'s [[:File:Erv Wilson's Fibonnaci Progression.png\|an example progression using a Fibonnaci sequence from Erv Wilson's letter to McLaren]]. We can look at the linear tones of these chords and see whether we can notice anything interesting:		=== Chord Progressions ===
			Here's [[:File:Erv Wilson's Fibonnaci Progression.png\|an example progression using a Fibonnaci sequence from Erv Wilson's letter to McLaren]]. We can look at the linear tones of these chords and see whether we can notice anything interesting:
	{\| class="wikitable"		{\| class="wikitable"
	!1st chord		!1st chord
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	\|}		\|}
	Although its hard to figure out how to represent harmonal limits, I think the best way to do it is to have ([lowest number of unique notes in a chord]-[highest]) on the denominator and have ([lowest linear tone]-[highest]) on the denominator. In this case, it would look like (8-10)/(3-4), which if we were to translate this into a proper number it would equal 2.		Although its hard to figure out how to represent harmonal limits, I think the best way to do it is to have ([lowest number of unique notes in a chord]-[highest]) on the denominator and have ([lowest linear tone]-[highest]) on the denominator. In this case, it would look like (8-10)/(3-4), which if we were to translate this into a proper number it would equal 2.

			=== Singular Chords ===
			When it comes to just one chord, though, it'd be best to rely on which note most of the linear tones are found. For example, 9:11:13 in the last headliner had most of its linear tones occur on 9, so since 3 linear tones appeared on 9, we can say that the harmonal limit is 3.

CritDeathX: /* Demonstration */

2020-09-11T22:37:41Z

Demonstration

← Older revision		Revision as of 22:37, 11 September 2020
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	Thus, by these rules, it cannot line up if it results in any other harmonic/interval.		Thus, by these rules, it cannot line up if it results in any other harmonic/interval.

	== ~~Demonstration~~ ==		== Linear Tones ==
	I'll show an example of what I mean using 4:5:6.		I'll show an example of what I mean using 4:5:6.

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	''etc...''		''etc...''

	An interesting thing to note is that after the 5-note chord, the amount of times that the tones line up rises linearly by 2x.		An interesting thing to note is that after the 5-note chord, the amount of times that the linear tones line up rises linearly by 2x.

	To show an example of this method with the added reference, I'll show how 9:11:13 works here.		To show an example of this method with the added reference, I'll show how 9:11:13 works here.
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	== Harmonal Limits ==		== Harmonal Limits ==
	This is a term that I'm coining to describe certain patterns or outliers within a series of chords or a scale(s) based off of their ~~combination/difference~~ tones.		This is a term that I'm coining to describe certain patterns or outliers within a series of chords or a scale(s) based off of their linear tones.

	For example, here's [[:File:Erv Wilson's Fibonnaci Progression.png\|an example progression using a Fibonnaci sequence from Erv Wilson's letter to McLaren]]. We can look at the tones of these chords and see whether we can notice anything interesting:		For example, here's [[:File:Erv Wilson's Fibonnaci Progression.png\|an example progression using a Fibonnaci sequence from Erv Wilson's letter to McLaren]]. We can look at the linear tones of these chords and see whether we can notice anything interesting:
	{\| class="wikitable"		{\| class="wikitable"
	!1st chord		!1st chord

CritDeathX: /* Harmonal Limits */

2020-09-11T22:35:31Z

Harmonal Limits

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	\|-		\|-
	\|8		\|8
	\|		\|8
	\|9		\|9
	\|8		\|8

CritDeathX: /* Harmonal Limits */

2020-09-11T22:33:15Z

Harmonal Limits

@@ Line 71: / Line 71: @@
 We then compare it to the 3-note reference point, 4:5:6. 4:5:6's tones line up 4 times, and 9:11:13's tones line up 4 times as well. By this conclusion, 9:11:13 should be as consonant as 4:5:6. (''its also proportional like 4:5:6, so take that as you will'')
 == Harmonal Limits ==
-This is a term that I'm coining to describe certain patterns within a series of chords or a scale(s) based off of their combination/difference tones. For example, here's an example progression from Erv Wilson's letter to McLaren.
+This is a term that I'm coining to describe certain patterns or outliers within a series of chords or a scale(s) based off of their combination/difference tones.

CritDeathX: Currently working on it

2020-09-11T21:33:00Z

Currently working on it

← Older revision		Revision as of 21:33, 11 September 2020
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	Okay, so a while back, I had developed this method of finding how consonant a chord was. The basic idea was to find how many combination/difference tones lined up with a chord~~. I may add something to have it work with [[harmonic series]] scales as well~~.		Okay, so a while back, I had developed this method of finding how consonant a chord was. The basic idea was to find how many combination/difference tones lined up with a chord.

	In order to find what tones line up with the chord, the resulting tone must either be		In order to find what tones line up with the chord, the resulting tone must either be
Line 7:		Line 7:
	Thus, by these rules, it cannot line up if it results in any other harmonic/interval.		Thus, by these rules, it cannot line up if it results in any other harmonic/interval.

			== Demonstration ==
	I'll show an example of what I mean using 4:5:6.		I'll show an example of what I mean using 4:5:6.

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	We then compare it to the 3-note reference point, 4:5:6. 4:5:6's tones line up 4 times, and 9:11:13's tones line up 4 times as well. By this conclusion, 9:11:13 should be as consonant as 4:5:6. (''its also proportional like 4:5:6, so take that as you will'')		We then compare it to the 3-note reference point, 4:5:6. 4:5:6's tones line up 4 times, and 9:11:13's tones line up 4 times as well. By this conclusion, 9:11:13 should be as consonant as 4:5:6. (''its also proportional like 4:5:6, so take that as you will'')

	~~Like~~ I ~~said at the beginning~~, I'~~ll see if I can make it also work with scales built~~ from ~~the harmonic series~~.		== Harmonal Limits ==
			This is a term that I'm coining to describe certain patterns within a series of chords or a scale(s) based off of their combination/difference tones. For example, here's an example progression from Erv Wilson's letter to McLaren.

CritDeathX at 19:26, 10 July 2020

2020-07-10T19:26:45Z

← Older revision		Revision as of 19:26, 10 July 2020
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	Okay, so a while back, I had developed this method of finding how consonant a chord was. The basic idea was to find how many combination/difference tones lined up with a chord. I may add something to have it work with harmonic series scales as well.		Okay, so a while back, I had developed this method of finding how consonant a chord was. The basic idea was to find how many combination/difference tones lined up with a chord. I may add something to have it work with [[harmonic series]] scales as well.

	In order to find what tones line up with the chord, the resulting tone must either be		In order to find what tones line up with the chord, the resulting tone must either be

CritDeathX at 18:59, 10 July 2020

2020-07-10T18:59:56Z

← Older revision		Revision as of 18:59, 10 July 2020
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	In order to find what tones line up with the chord, the resulting tone must either be		In order to find what tones line up with the chord, the resulting tone must either be
	# The number up/down whatever octaves [h*(2^x]. (''e.g., 1/4, 3/6, 26/13'')		# The number up/down whatever octaves [h*(2^x)]. (''e.g., 1/4, 3/6, 26/13'')
	# A power of 2. (''e.g., 2/6, 8/9, 16/7'')		# A power of 2. (''e.g., 2/6, 8/9, 16/7'')
	# Another note/interval within the chord. (''e.g., in the case of 4:5:6 [which will be demonstrated soon], 10/4'')		# Another note/interval within the chord. (''e.g., in the case of 4:5:6 [which will be demonstrated soon], 10/4'')

CritDeathX at 18:50, 10 July 2020

2020-07-10T18:50:13Z

← Older revision		Revision as of 18:50, 10 July 2020
Line 2:		Line 2:

	In order to find what tones line up with the chord, the resulting tone must either be		In order to find what tones line up with the chord, the resulting tone must either be
	1. The number up/down whatever octaves [h*(2^x]. (''e.g., 1/4, 3/6, 26/13'')		# The number up/down whatever octaves [h*(2^x]. (''e.g., 1/4, 3/6, 26/13'')
	2. A power of 2. (''e.g., 2/6, 8/9, 16/7'')		# A power of 2. (''e.g., 2/6, 8/9, 16/7'')
	3. Another note/interval within the chord. (''e.g., in the case of 4:5:6 [which will be demonstrated soon], 10/4'')		# Another note/interval within the chord. (''e.g., in the case of 4:5:6 [which will be demonstrated soon], 10/4'')
	Thus, by these rules, it cannot line up if it results in any other harmonic/interval.		Thus, by these rules, it cannot line up if it results in any other harmonic/interval.

	I'll show an example of what I mean using 4:5:6.		I'll show an example of what I mean using 4:5:6.

	''5-4 = 1		''5-4 = 1; 1/4 = lines up with 4''
	1/4 = lines up with 4

	6-4 = 2		''6-4 = 2; 2/4 = lines up with 4''
	2/4 = lines up with 4

	6-5 = 1		''6-5 = 1; 1/5 = lines up with 5''
	1/5 = lines up with 5

	5+4 = 9		''5+4 = 9; 9/4 = doesn't line up''
	9/4 = doesn't line up

	6+4 = 10		''6+4 = 10; 10/4 = lines up with 4:5''
	10/4 = lines up with 4:5

	6+5 = 11		''6+5 = 11; 11/5 = doesn't line up''
	11/5 = doesn't line up''

	As you can see, 4 of these tones line up with the base chord. To add a further reference for consonance, I suggest comparing how many tones line up with a chord compared to a unique x-note chord built off of 4. So for 3 notes, its 4:5:6, 4 notes is 4:5:6:7, 5 notes is 4:5:6:7:9, etc. Here's a list of how many tones line up with a(n) x-note /4 chord:		As you can see, 4 of these tones line up with the base chord. To add a further reference for consonance, I suggest comparing how many tones line up with a chord compared to a unique x-note chord built off of 4. So for 3 notes, its 4:5:6, 4 notes is 4:5:6:7, 5 notes is 4:5:6:7:9, etc. Here's a list of how many tones line up with a(n) x-note /4 chord:

	4:5:6 = 4		''4:5:6 = 4''
	4:5:6:7 = 8
	4:5:6:7:9 = 15		''4:5:6:7 = 8''
	4:5:6:7:9:11 = 25
	4:5:6:7:9:11:13 = 37		''4:5:6:7:9 = 15''
	4:5:6:7:9:11:13:15 = 51
	4:5:6:7:9:11:13:15:17 = 67		''4:5:6:7:9:11 = 25''
	4:5:6:7:9:11:13:15:17:19 = 85
	4:5:6:7:9:11:13:15:17:19:21 = 105		''4:5:6:7:9:11:13 = 37''
	...:23 = 127
	...:25 = 151		''4:5:6:7:9:11:13:15 = 51''
	...:27 = 177
	...:29 = 205		''4:5:6:7:9:11:13:15:17 = 67''
	...:31 = 235
	etc...		''4:5:6:7:9:11:13:15:17:19 = 85''

			''4:5:6:7:9:11:13:15:17:19:21 = 105''

			''...:23 = 127''

			''...:25 = 151''

			''...:27 = 177''

			''...:29 = 205''

			''...:31 = 235''

			''etc...''

	An interesting thing to note is that after the 5-note chord, the amount of times that the tones line up rises linearly by 2x.		An interesting thing to note is that after the 5-note chord, the amount of times that the tones line up rises linearly by 2x.
Line 49:		Line 57:
	To show an example of this method with the added reference, I'll show how 9:11:13 works here.		To show an example of this method with the added reference, I'll show how 9:11:13 works here.

	''11-9 = 2		''11-9 = 2; 2/9 = lines up with 9''
	2/9 = lines up with 9

	13-9 = 4		''13-9 = 4; 4/9 = lines up with 9''
	4/9 = lines up with 9

	13-11 = 2		''13-11 = 2; 2/11 = lines up with 11''
	2/11 = lines up with 11

	11+9 = 20		''11+9 = 20; 20/9 = doesn't line up''
	20/9 = doesn't line up

	13+9 = 22		''13+9 = 22; 22/9 = lines up with 9:11''
	22/9 = lines up with 9:11

	13+11 = 24		''13+11 = 24; 24/11 = doesn't line up''
	24/11 = doesn't line up''

	We then compare it to the 3-note reference point, 4:5:6. 4:5:6's tones line up 4 times, and 9:11:13's tones line up 4 times as well. By this conclusion, 9:11:13 should be as consonant as 4:5:6. (its also proportional like 4:5:6, so take that as you will)		We then compare it to the 3-note reference point, 4:5:6. 4:5:6's tones line up 4 times, and 9:11:13's tones line up 4 times as well. By this conclusion, 9:11:13 should be as consonant as 4:5:6. (''its also proportional like 4:5:6, so take that as you will'')

	Like I said at the beginning, I'll see if I can make it work with scales built from the harmonic series~~, as well~~.		Like I said at the beginning, I'll see if I can make it also work with scales built from the harmonic series.