User:CritDeathX/Sam's Idea Of Consonance: Difference between revisions
CritDeathX (talk | contribs) Created page with "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..." |
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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'') | |||
# 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. | 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. | ||
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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 | Like I said at the beginning, I'll see if I can make it also work with scales built from the harmonic series. | ||