Re: [MMM] Re: automated harmony/counterpoint (MIDI example)

Hello Margo!
It truly is quite a beautiful example here and more than musically
effective. Conceptually one can enjoy the fact of starting and ending in a
historical root where the middle part looks forward. Some kinda of musical
time machine. It is amazing how the beginning and end take away any real
threat of "monotony" that one can get with parallel harmony, also adding a
consonant/disonant element as well.
With the idea of expanding harmony based on perfect intervals (4th or
5ths) in the direction of 7ths instead of thirds, i have used pentatonics
with the following basic chords in various appegiated forms
D A C
F C D
G D F
A F G
C G A
D A C
Besides your normal parallels, one can alternate the chord chosen in
such a way that the melody note is doubled by a sequence where when
ascending one can progress from root to "seventh" to fifth- vice versa
descending. Hopefully i will be able to take a look at
the inversion of the tetrad you are using they all sound good to me) and
work out such a pattern just for fun.
I think stravinsky would have enjoyed your example as he liked to
superimpose different historical periods or chain them together in musical
viable ways.
It was quite informative and I truly got some things out of it i can't
express. Thanks

"M. Schulter" wrote:

>
>
> Hello, there, Kraig, and your question ties in with some "algorithms"
> for generating harmony or counterpoint at a keyboard that I sometimes
> use, or maybe quite often if we can consider passages or chains of a
> few notes as a unit of interest.
>
> In the medieval and Renaissance terminologies of Europe, this is
> sometimes known as _discantus supra libram_ ("discant" or improvised
> polyphony "over the book," while reading a chant melody upon which the
> ensemble extemporizes added parts), or _quintoyer_ ("fifthing," a
> technique for improvised discant mostly in fifths, with phrases often
> beginning and ending on octaves), or around the early 15th century,
> _faburden_ (English) or _fauxbourdon_ (French).
>
> This kind of technique is a special favorite for me in a just
> intonation system I call _Sesquisexta_, the Latin term for a ratio of
> 7:6, where two 12-note Pythagorean keyboards are tuned at this
> distance apart (~266.87 cents).
>
> Using a curly brace symbol (}) to show a note on the upper keyboard
> raised by a 7:6, I can harmonize a melody in "21st-century
> fauxbourdon" using a chain of parallel 14:18:21:24 sonorities starting
> and ending with a pure 2:3:4.
>
> Taking a simple chantlike melody in the medieval Dorian mode, let's
> say D4 E4 G4 A4 G4 F4 E4 D4 C4 D4, putting the melody in the highest
> voicee, we get a texture like this:
>
> D4 E4 G4 A4 G4 F4 E4 D4 C4 D4
> A3 B}3 D}4 E}4 D}4 C}4 B}3 A}3 G}3 A3
> A3 B3 D4 E4 D4 C4 B4 A4 G3 A3
> D3 E}3 G}3 A}3 G}3 F}4 E}4 D}4 C}3 D4
>
> Here's a MIDI file of this:
>
> http://value.net/~mschulter/seskg001.mid
>
> There are some interesting melodic aspects here. The highest voices
> moves entirely in regular Pythagorean steps: 9:8 whole-tones and
> 256:243 semitones. However, in moving from the opening 2:3:4 to the
> following 14:18:21:24 which starts the chain of parallel sonorities,
> the lowest and next to highest voices ascend by a 21:16 (D3-E}3,
> A3-B}3), a 9:8 plus a 7:6.
>
> >From there, all the voices move by identical steps in the parallel
> motion, something that makes it different from the parallel thirds and
> sixths of styles like 15th-century fauxbourdon, and maybe a bit like
> an organ mixture stop. Then we come to the final cadence, where the
> upper voice and the next to lowest ascend by usual 9:8 steps, while
> the other voices descend by 28:27 steps. It's a counterpoint of
> epimores.
>
> Anyway, thanks for this topic, which gave me a good excuse to produce
> a bit of actual music for sharing here, albeit via MIDI rather than
> with the kind of acoustical instruments you have crafted over the
> years.
>
> Also, thanks to Robert Walker for a beautiful CD I want to review here
> soon, including a wonderful chant melody in Sesquisexta.
>
> Most appreciatively, with peace and love,
>
> Margo

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

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