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):
On Tuesday, November 3, 2015, Matt Barber <brbrofsvl@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@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@gmail.com> >> Date: Monday, November 2, 2015 >> Subject: chord libraries? >> To: William Huston <williamahuston@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@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 >> > >
--
--
May you, and all beings
be happy and free from suffering :)
-- ancient Buddhist Prayer (Metta)