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 | 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 | ||
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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 == | |||
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'') | ||
== 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. | |||
Revision as of 21:33, 11 September 2020
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
- 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)
- 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.
Demonstration
I'll show an example of what I mean using 4:5:6.
5-4 = 1; 1/4 = lines up with 4
6-4 = 2; 2/4 = lines up with 4
6-5 = 1; 1/5 = lines up with 5
5+4 = 9; 9/4 = doesn't line up
6+4 = 10; 10/4 = lines up with 4:5
6+5 = 11; 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:
4:5:6 = 4
4:5:6:7 = 8
4:5:6:7:9 = 15
4:5:6:7:9:11 = 25
4:5:6:7:9:11:13 = 37
4:5:6:7:9:11:13:15 = 51
4:5:6:7:9:11:13:15:17 = 67
4:5:6:7:9:11:13:15:17:19 = 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.
To show an example of this method with the added reference, I'll show how 9:11:13 works here.
11-9 = 2; 2/9 = lines up with 9
13-9 = 4; 4/9 = lines up with 9
13-11 = 2; 2/11 = lines up with 11
11+9 = 20; 20/9 = doesn't line up
13+9 = 22; 22/9 = lines up with 9:11
13+11 = 24; 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)
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.