[PD] chord libraries?

Tue Nov 3 20:09:42 CET 2015

I read in a book about Varese that the (0,1,2,3) tetrachord (all minor
seconds) recurs throughout his work.  So yeah, I'd consider it worthy :)

M

On Tue, Nov 03, 2015 at 01:59:59PM -0500, William Huston wrote:
> 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)
> >>
> >>
> >> _______________________________________________
> >> Pd-list at lists.iem.at mailing list
> >> UNSUBSCRIBE and account-management ->
> http://lists.puredata.info/listinfo/pd-list
> >>
> >
> >
> 
> -- 
> --
> May you, and all beings
> be happy and free from suffering :)
> -- ancient Buddhist Prayer (Metta)

> _______________________________________________
> Pd-list at lists.iem.at mailing list
> UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list