http://xenharmonic.wikispaces.com/Chords
On Tue, Nov 3, 2015 at 3:38 PM, Matt Barber <[email protected]> wrote: > I hate to be a pedant/ass about this, but it's important to indicate the > scope of application. Most music (I'm not sure about "most songs") doesn't > use chords at all – chords are mostly a Western phenomenon (with some > important exceptions, e.g. Central Africa). > > All 29 tetrachord types can be found in: > > Western classical music of the last 100 years (at least) > Jazz > > And if you count melodic structures as well: > South Indian (Carnatic) ragas > Western classical music of the last 300 years (at least) > Prog Rock > > etc. > > That cluster is sometimes called the chromatic tetrachord, 0123, 4-1, the > B-A-C-H tetrachord, or something like "the four-note chromatic cluster." It > functions in lots of music, but probably not the kind modeled by the map > you linked to. > > If you're looking for chord maps, do you know about Tonnetze? > > https://en.wikipedia.org/wiki/Tonnetz > > It says almost nothing about syntax -- the map you linked to is a syntax > graph -- but it does systemize some tonal relations. > > On Tue, Nov 3, 2015 at 1:59 PM, William Huston <[email protected]> > 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 > >
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