[PD] chord libraries?

Wed Nov 4 06:57:06 CET 2015

http://xenharmonic.wikispaces.com/Chords

On Tue, Nov 3, 2015 at 3:38 PM, Matt Barber <brbrofsvl at 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 at 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 at 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 at 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 at gmail.com>
>> >> Date: Monday, November 2, 2015
>> >> Subject: chord libraries?
>> >> To: William Huston <williamahuston at 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 at 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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>> >
>> >
>>
>> --
>> --
>> May you, and all beings
>> be happy and free from suffering :)
>> -- ancient Buddhist Prayer (Metta)
>>
>>
>
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