Q: chords, mathematicaly?

[antto]

no, i'm not randomizing existing melodies into different chords or something..

what i'm doing is so very simple:
i'm generating a pattern of few numbers

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0 2 0 0 3 2 1 1 3 2 0 1

now this doesn't mean nothing yet
then (my idea was) i read some "chord" information from my file
(major 0 4 7)
and i replace the numbers whith these

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0 2 0 0 3 2 1 1 3 2 0 1
0 7 0 0 ? 7 4 4 ? 7 0 4

in this case, i had 0 1 2 and 3, so the "3" will be replaced by a 12 actually (which is an upper-root) blah this doesn't really matter, it's just a rude example

the numbers that i will generate will be with values from 0 to 12 or something, so there will be plenty room
these numbers are actually "indexes"
my result will be added to the root note, so 0+root_note = root_note

i hope you understand now..

[Musicologo]

Antto, for each Major chord you have inversions.

C-E-G it's the same thing as E-G-C or G-C-E. It's all the same Major Chord.

That's why 0,4,7 is equal to 0,3,8 and 0,5,9.

You can think of it mathematically as permutations inside the same set.

So Major Chord = x,x+4,x+7; x,x+3,x+8; x,x+5,x+9

Minor Chord= x,x+3,x+7; x,x+4,x+9; x,x+5,x+8

Dimineshed 7th chord= x,x+3,x+6,x+9 (all other permutations are equal)

Augmented chord= x,x+4,x+8 (all other permutations are equal)

Seventh Chord= x,x+4,x+7,x+10; x,x+3,x+6,x+8; x,x+3,x+5,x+9; x,x+2,x+6,x+9

Minor Seventh Chord= x,x+3,x+7,x+10; x,x+4,x+7,x+9; x,x+3,x+5,x+8; x,x+2,x+5,x+9

Seventh Major Chord= x,x+4,x+7,x+11; x,x+3,x+7,x+8; x,x+4,x+5,x+9; x,x+1,x+5,x+8

etc...

[antto]

Antto, for each Major chord you have inversions.

C-E-G it's the same thing as E-G-C or G-C-E. It's all the same Major Chord.

That's why 0,4,7 is equal to 0,3,8 and 0,5,9.

so, with (0,5,9) you mean the G-C-E case?!
can't i go by with only the 0,4,7 case?!
my algorithm doesn't need to be aware of what the root note is, that would also be too complicated..

You can think of it mathematically as permutations inside the same set.

So Major Chord = x,x+4,x+7; x,x+3,x+8; x,x+5,x+9

Minor Chord= x,x+3,x+7; x,x+4,x+9; x,x+5,x+8

Dimineshed 7th chord= x,x+3,x+6,x+9 (all other permutations are equal)

Augmented chord= x,x+4,x+8 (all other permutations are equal)

Seventh Chord= x,x+4,x+7,x+10; x,x+3,x+6,x+8; x,x+3,x+5,x+9; x,x+2,x+6,x+9

Minor Seventh Chord= x,x+3,x+7,x+10; x,x+4,x+7,x+9; x,x+3,x+5,x+8; x,x+2,x+5,x+9

Seventh Major Chord= x,x+4,x+7,x+11; x,x+3,x+7,x+8; x,x+4,x+5,x+9; x,x+1,x+5,x+8

etc...

"permutations" is one word that scares me
thanks for the info, you could just write "0" instead of "x" .. would be easier for you..

7thMaj: <caugh>
if i hold C and E (x, x+4) that's a 7thMajor chord!?

oh, ok, i just opened up that arpegiator synth thing, and checked what it does when i select that chord (i suppose i'm looking at the same chord, it's written as Maj7)
i press C, it plays C, E, G, B
that's 0,5,7,11

hm..
this is going nowhere, or it's too hard for me to understand

[Musicologo]

It's simple you're just not reading what I wrote.
You can take out X and put 0 in place if you want, of if it's easier for you.

And no, you can't just go with 0,4,7. if you want ALL major chords, then you also need 0,3,8 and 0,5,9.

C-E it's not a maj7th chord I don't know where you read that.

I wrote 0,4,7,11. That's C-E-G-B.
You tell it's 0,5,7,11 it's not. E is 4 not 5.

Just replace all x for 0 and you have your formulas. And you can believe they're right.

About permutations it's easy to understand. If a chord has 3 notes it can begin in any of them. so you'll have 3 formulas for each 3 note chord. And you'll have 4 formulas for each 4 note chord.

Altough the chord is the same it doesn't sound the same to have C-E-G or E-G-C or G-C-E, because the intervals between the notes are not the same.

on C-E-G you have a 4 interval between the lowest notes, in E-G-C you have 3 interval. The ear can notice that difference.

[antto]

oh, i understand now
so, for a chord of 3 notes (say a major chord) there is a "case" for each of the 3 notes, and the intervals are different, altho, it's still the same chord

now how the hell do i implement this
..when all i'm generating are random numbers

C-E-G ... then E-G-C
with my earlier understanding (0,4,7) if my root_note was E my result would be quite different than E-G-C (which would require a 0,3,8 )

i don't understand, must the root note be taken into account?!
is it wrong to just add 0,4,7 to any note and say that it's a major chord?
what if it's C# (oh don't tell me there is a special case for this too, grrr)

[Musicologo]

Antto you're not thinking clear.

your 0,4,7 will ALWAYS make major chords it doesn't matter the root.

BUT

0,3,8 will ALWAYS make ALSO major chords it doesn't matter the root.

AND

0,5,9 will ALWAYS make ALSO major chords it doesn't matter the root.

You ask C#.

if you apply 0,4,7 to C# you'll have C#-E#-G#, which is C# major.
BUT if you apply 0,3,8 you'll have C#-E-A which is also a major chord - in this case is A major in first inverson, and it will sound different from A-C#-E (the root position).
If you apply 0,5,9 you'll have C#-F#-A#, which is also a major chord - in this case is F# major in first inverson, which will also sound different from F#-A#-C#, the root position.

You have 12 different notes - C,C#,D,D#,E,F,F#,G,G#,A,A#,B

So you'll have 12 * 3 = 36 different chords.

12 Major chords in root position, 12 major chords in first inversion and 12 major chords in second inversion.