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 <williamahus...@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 <brbrof...@gmail.com> > Date: Monday, November 2, 2015 > Subject: chord libraries? > To: William Huston <williamahus...@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 <williamahus...@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@lists.iem.at mailing list > UNSUBSCRIBE and account-management -> > http://lists.puredata.info/listinfo/pd-list > >
_______________________________________________ Pd-list@lists.iem.at mailing list UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list