[PD] Fwd: chord libraries?

[Matt Barber]

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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