No worries, Matt!! One thing I love about this community is, that while there is complete love for newbies--
(e.g. my first (and ugliest!) snare patch I posted to the Facebook group got like 30 likes!!)
-- I feel there is also a gentle demand (and sometimes not so gentle) for intellectual rigor, scientific investigation, completeness in the solution. A kind of technical aesthetic. I really appreciate that.
So I do appreciate all of these comments --
Miller your comment about Varese made me laugh... when I dreamed up that ugly tetrachord of all minor seconds, I immediately thought of Frank Zappa and the "Zappa Cluster". I think he studied with Varese....
But I am caught between dealing with a broad robust complete solution, and also something I can reasonable a) get my head around, and b) deal with using my existing controllers.
I just want to play around with some chord maps, like Stephen Mugglin's. And just see where that goes. I have an existing pad controller, and I think I can map a subset of it. Pick a chord with my left had on the pad controller, and pick a tonic with the keyboard on the right. I want to build a sophisticated Autoharp with PD :)
I will keep in mind general applicability, and completeness, which I hear from your comments.
However-- any instrument or song made with it, or the scale mode it uses... is a limited subset of possibilities. Like Iambic Pentameter. Or Haiku.
It's an artificially imposed limitation on the field of all possibilities.
It's not all possible chords --whatever that means! e.g. combinations of notes made of tone timbres composed of sinusoids with certain mathematical relationships between partials... but it is a
subset of these.
And while yes I appreciate the links to the microtonal stuff, I just cannot deal with that now! Ha ha. I love listening to it-- like
this guy...solution.
Many thanks for the link to Tonnetz!
On Tuesday, November 3, 2015, Matt Barber <
brbrofsvl@gmail.com> 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 <
williamahuston@gmail.com> 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 <
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)
>> >>
>> >>
>> >> ______________________________________________
>> >>
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http://lists.puredata.info/listinfo/pd-list>> >>
>> >
>> >
>>
>> --
>> --
>> May you, and all beings
>> be happy and free from suffering :)
>> -- ancient Buddhist Prayer (Metta)
>>
>
>