New music using microtones at MP3

Microtoners:

I posted a new song on my MP3 page at: http://www.mp3.com/PrentRodgers .
The piece is based on six notes derived from the otonality, taken mostly
three at a time. The ratios of the primary triad are 6:7:9. I call these
notes G, A++ and D+, which are my names for the 6th, 7th, and 9th
overtones of C. Other notes in the six note otonality I call C, E and
F++, for the 8th, 10th, and 11th overtones.

This 6:7:9 triad has a minor feel to it. The minor third (7th overtone)
is very flat compared to the minor key derived from the utonality (the
triad based on 4:3 8:5 1:1). It gives the triad a sharp edge to it. To
derive additional triads from the six note scale, I walk up the scale
through five other triads: 7:8:10; 8:9:11; 9:10:12; 10:11:14; 11:12:16.
Triads that include the 11 ratio are especially challenging. These six
chords make up the harmonic material of the piece. There is no
modulation to other parts of the tonality diamond.

The piece was made using a sampling orchestra written using Csound, with
samples taken from the McGill University Master Samples CD-ROM.
Instruments include the vibraphone, guitar, marimba, bassoon, flute,
cello, violin, percussion, contra bassoon and archlute. The feel of the
song is kind of like a medieval dance song, hence the title: Basse
Danze, a 15th century Italian dance form. It literally means low dance,
where the dancers stay low to the ground and do not leap into the air.
It is typically in 6/4 meter. Source code for the piece is at my
personal web page: http://pws.prserv.net/music1 .

Prent Rodgers
Mercer Island, WA

>From: Prent Rodgers <prodgers@ibm.net>
>
>I posted a new song on my MP3 page at: http://www.mp3.com/PrentRodgers .

More music!

>This 6:7:9 triad has a minor feel to it. The minor third (7th overtone)
>is very flat compared to the minor key derived from the utonality (the
>triad based on 4:3 8:5 1:1). It gives the triad a sharp edge to it.

Really? I find 6:7:9 very attractive and restful. I'm still
fairly new to JI and I've chosen this particular chord to base most of
my initial exploration around. In fact, one could say I've become
obsessed with the possibilities of a particular ratio: 7/6.

> To
>derive additional triads from the six note scale, I walk up the scale
>through five other triads: 7:8:10; 8:9:11; 9:10:12; 10:11:14; 11:12:16.

My first attempt was to just take a tetrachord built up from
combining two 6:7:9's based on 1/1 and 3/2. Eventually this got a bit
tedious and I was having trouble keeping up with extra-scalar notes
creeping in to allow certain things, so I started playing with a
duodene-like thing using 7/6 as the vertical axis (excuse the slightly
noisy syntax, which is from the Python library I wrote to mess with JI
ratios):

*** Duodene(vrat=Ratio(7, 6))
<14:9> <7:6> <7:4> <21:16>
<4:3> <1:1> <3:2> <9:8>
<8:7> <12:7> <9:7> <27:14>

It turns out there are a number of charming and apparently nameless
chords lurking in that simple collection. There are of course the
septimal minor triads, and the septimal majors which I don't care for
in root, closed voicing; I've found 6:7:8:9 (4/3, 1/1, 7/6, 3/2) to
have a very rich sound that I like quite a lot. The 1:3:7 (1/1, 3/2,
7/4) combination is very bright. The 18:21:24:28 (makes a square in
the chart above, say 7/4, 21/16, 3/2, 9/8) acts as a fine dominant if
you need such a thing. I've also found 12:14:21 (1/1, 7/6, 7/4) is
very useful if prepared. You can even get a useful I-IV-V-I out of
it, though I find the progression V-IV-I more effective if you keep
the relative voicing such that the top voices go 7/4 - 14/9 - 3/2
(intervals: 8/9 * 27/28). I find the small upper leading tone very
effective, probably because I listen to so much Arabic classical
music.

Do other composers take this approach to exploring the
possibilities of some system of ratios? I now understand how a book
like "Divisions of the Tetrachord" can get written. There is subtle
seduction lurking for anyone who isn't completely put off by the math,
to test, to shuffle, make some noises, and do it all again with some
small variation.

>Triads that include the 11 ratio are especially challenging. These six
>chords make up the harmonic material of the piece.

I liked it. Thanks for sharing it. At this point, anything I
hear using JI is a help to me.

--
William S. Annis wsannis@execpc.com
Mi parolas Esperanton - La Internacia Lingvo www.esperanto.org