User:CritDeathX/Sam's Idea Of Consonance: Difference between revisions

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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.

== Linear Tones ==

=== Formula ===

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'')

Line 7:

Line 10:

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.

Line 53:

Line 57:

''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.

Line 71:

Line 75:

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~~.

I should note that they may not ''sound'' consonant on first listen, but if you were to hear it for a long enough time, you'd notice how ''weirdly'' consonant they are. I think this might be a useful method for finding alien harmonies without sacrificing the idea of consonance entirely.

== 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 linear tones.

=== 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"

!1st chord

!2

!3

!4

!5

!6

!7

!8

|-

|8

|9

|8

|10

|}

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 for this chord is 3.

@@ Line 1: / Line 1: @@
-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.
+== Linear Tones ==
+=== Formula ===
 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'')
@@ Line 7: / Line 10: @@
 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.
@@ Line 53: / Line 57: @@
 ''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.
@@ Line 71: / Line 75: @@
 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.
+I should note that they may not ''sound'' consonant on first listen, but if you were to hear it for a long enough time, you'd notice how ''weirdly'' consonant they are. I think this might be a useful method for finding alien harmonies without sacrificing the idea of consonance entirely.
+== 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 linear tones.
+=== 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"
+!1st chord
+!2
+!3
+!4
+!5
+!6
+!7
+!8
+|-
+|8
+|8
+|9
+|8
+|8
+|8
+|8
+|10
+|}
+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 for this chord is 3.