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 <[email protected]> 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 <[email protected]> > 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 <[email protected]> > >> Date: Monday, November 2, 2015 > >> Subject: chord libraries? > >> To: William Huston <[email protected]> > >> > >> > >> 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 <[email protected]> > 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) > >> > >> > >> _______________________________________________ > >> [email protected] 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) > _______________________________________________ > [email protected] mailing list > UNSUBSCRIBE and account-management -> > http://lists.puredata.info/listinfo/pd-list _______________________________________________ [email protected] mailing list UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list
