User:CritDeathX/Sam's Idea Of Consonance

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 1. 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) 3. 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.

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)

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