[PD] chord libraries?

[William Huston]

Thanks Matt!

Yeah, I'm pretty good with the mathematics of permutations and
combinations...

My goal is to be able to generate (and hopefully identify, given a list of
MIDI notes) any given chord/inversion. Which somewhat restricts these to
"musical" chords.

I think a cluster, a tetrachord of all minor 2nds is not terribly useful
and probably doesn't have a name. Yes it is good to characterize it for
completeness :)

My main purpose now is to build an instrument which allows me to traverse a
"chord map", which generally follows how most songs are structured. With an
easy way to change the tonic, make inversions, and maybe throw in some
substitutions.

I have a 4x4 drum pad controller, which I want to use to play a drone
chord, and move through a map, while I play a lead with my right hand.

I really like what this guy has done (but there are many maps like this):

http://mugglinworks.com/chordmaps/genmap.htm


On Tuesday, November 3, 2015, Matt Barber <brbrofsvl at gmail.com> wrote:
> I just remembered this Julian Hook article on Music Theory Online, if you
want to find out more about how to find the number of chords of a given
size:
> http://www.mtosmt.org/issues/mto.07.13.4/mto.07.13.4.hook.html
>
> On Mon, Nov 2, 2015 at 3:00 PM, William Huston <williamahuston at gmail.com>
wrote:
>>
>> Matt suggested I forward this side discussion (and attachment) to the
list.
>>
>> N.B., Matt is referring by number to the list of 55 intervals I
identified in my original, quoted below. However, it was an HTML list, and
the numbering got munched during quoting. Sorry if that makes this slightly
unclear.  --BH
>>
>>
>> ---------- Forwarded message ----------
>> From: Matt Barber <brbrofsvl at gmail.com>
>> Date: Monday, November 2, 2015
>> Subject: chord libraries?
>> To: William Huston <williamahuston at gmail.com>
>>
>>
>> We also eliminate transpositions, so in this case 55 is the same chord
as 1, 18 and 12 are the same, and so forth. If we eliminate all
transpositions and inversions, we end up with 12 trichords:
>> 012*
>> 013
>> 014
>> 015
>> 016
>> 024*
>> 025
>> 026
>> 027*
>> 036*
>> 037
>> 048*
>> I marked the 5 that are self-inversional with a star. They're all
"musical," but again it depends on the type of music you're looking at. All
19 trichords (eliminating transpositions and respacing) have been in use as
simultaneities since the late 1800s, but some more than others. 012 didn't
get a huge foothold until the first decade or two of the 20th century.
>> See the attached; it does eliminate inversions, but it wouldn't be that
hard to make that a user preference. [list-setclass] outputs the normal
form as I described above, and the interval-vector one outputs a catalog of
the chromatic intervals contained in the chord (eliminating unisons,
octaves and inversions). In mod 12 there are 6 chromatic intervals,
counting minor seconds and major sevenths as the same -- the output just
gives you the number of each interval in the chord from 1 to 6 (or whatever
if you choose a different modulus).
>> Matt
>> PS -- if you like, you can bump this response up to the list.
>> On Mon, Nov 2, 2015 at 12:28 PM, William Huston <williamahuston at gmail.com>
wrote:
>> >
>> > Thanks Matt. Yes interested.
>> >
>> > FTR, if we do not eliminate inversions, I count 55 3-tone chords in
12TET:
>> >
>> > 111000000000
>> > 110100000000
>> > 110010000000
>> > 110001000000
>> > 110000100000
>> > 110000010000
>> > 110000001000
>> > 110000000100
>> > 110000000010
>> > 110000000001
>> > 101100000000
>> > 101010000000
>> > 101001000000
>> > 101000100000
>> > 101000010000
>> > 101000001000
>> > 101000000100
>> > 101000000010
>> > 101000000001
>> > 100110000000
>> > 100101000000
>> > 100100100000
>> > 100100010000
>> > 100100001000
>> > 100100000100
>> > 100100000010
>> > 100100000001
>> > 100011000000
>> > 100010100000
>> > 100010010000
>> > 100010001000
>> > 100010000100
>> > 100010000010
>> > 100010000001
>> > 100001100000
>> > 100001010000
>> > 100001001000
>> > 100001000100
>> > 100001000010
>> > 100001000001
>> > 100000110000
>> > 100000101000
>> > 100000100100
>> > 100000100010
>> > 100000100001
>> > 100000011000
>> > 100000010100
>> > 100000010010
>> > 100000010001
>> > 100000001100
>> > 100000001010
>> > 100000001001
>> > 100000000110
>> > 100000000101
>> > 100000000011
>> >
>> > But roughly 2/3's are inversions, so if we exclude inversions as being
the same chord, then yes we get 55*.3333 =~ 19. I'm guessing at least one
of these is an inversion of itself which is why 55 is not evenly divisible
by 3.
>> >
>> > Anyway, I'm not sure how many of these are really musical. I would
think of those 19, only about 8-10 are commonly used.
>> >
>> > Thanks, interested in whatever you have :)
>> >
>> > BH
>> >
>>
>>
>>
>>
>>
>> --
>> --
>> May you, and all beings
>> be happy and free from suffering :)
>> -- ancient Buddhist Prayer (Metta)
>>
>>
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>

-- 
--
May you, and all beings
be happy and free from suffering :)
-- ancient Buddhist Prayer (Metta)
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