I've been thinking of ways to harmonize melodies. One of my ways is to not think in terms of the seven diatonic chords, but to just think of in terms of "odd chords" and "even chords".

Let's say we take the C major scale in two octaves:
C D E F G A B C D  E   F  G  A   B  C
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

So we have two types of chords, where their notes can be:
Even: 2 4 6 8 10 12 14 16
Odd:  1 3 5 7 9 11 13 15

Where to generate a chord you'd pick a subset of three or more notes. So example of even chords would be: [2,4,6] [4,6,8] [8,12,16] And example of odd chords would be: [1,3,5] [3,5,7] [5,11,15].

So to harmonize a melody, if the melody note falls on an even number, harmonize it with an even chord, and if the melody note is odd, harmonize it with an odd chord.

For example in the melody of Mary had a little lamb: [3] 2 1 2 3 3 3 [2] 2 2 3 3 3 ...
I harmonize the [3] (an odd note) with [1,3,5] (an odd chord)
I harmonize the [2] (an even note) with [2,4,6] (an even chord)

This Odd/Even idea is also compatible with the idea that people often substitute the ii,IV,vi with eachother. And the iii,V,vii with each other.

But I was wondering if others think this holds any truth or maybe there is an actual name for this in music theory?

Note: after writing this I came across a cool concept. If you take the odd scale degrees on a piano: 1,3,5,7,9,11,13,15. and have the left hand in charge of the first four notes (1,3,5,7), and the right hand in charge of the last four notes (9,11,13,15). then without moving your fingers you can get to all the diatonic chords in the scale. For example: I would be [1,3,5] and ii would be (using right hand): [9,11,13] .. iii would be [3,5,7] and so forth.

closed as unclear what you're asking by David Bowling, Tim, Richard, MattPutnam, guidot Nov 6 '18 at 21:55

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    The more I read this the less I feel like I understand what you are asking about especially after the edits. You seem to be trying to jam up a bunch of concepts into numbering the scale degrees then talking about several observations that are typical theory that don't involve any "even or odd" observations. I also have no clue what "truer" is supposed to mean. – Dom Oct 29 '18 at 1:33
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    Sounds like you're trying to re-invent the wheel, which goes round happily enough already. Almost like painting by numbers? – Tim Oct 29 '18 at 7:44
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    @foreyez again this is not new information and like Tim said this is reinventing the wheel. The Note is an even bigger showing of this. You just have your fingers spread out in 3rds and of course that covers every note in the scale. There's a reason that a 13th chord is the highest extension as at the 15th you are back at the root. – Dom Oct 29 '18 at 14:24

You've actually noticed a basic music theory concept where chords are built in thirds, or in a more fancy terminology we use Tertian harmony. This means that you skip a note in the scale when constructing most typical chords. Because of this chord a 3rd or 5th above or below a note will share notes when constructed with the same scale hence their relationship in common practice harmony.

This explains most of what is in your post, however, don't associate this with consonance. B, D, F is 7, 9, and 11 and it's a diminished triad that most would consider dissonant.

I would strongly advise against using the terminology even/odd since when using scale degrees each octave this will change. I would also advise against listing scale degrees in sets like that since it clashes with set theory which does not use scale degrees at all, but just semitones so looking at [1, 3, 5], I don't see a major chord, but a set of notes each two semitones apart.

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