Ode to the Polyrhythmophone

Something that I've experimented with a bit in the past is converting
"ratios" into durations. After reading a bit John Adams wrote about
Lou Harrison's "free style" JI, it suddenly dawned on me that this
also seems to me to be a simple way to go about achieving something
directly analogous to the Harrison example with an unbounded rhythmic
space sitting in for an unbounded tonal space.

To convert ratios into "note durations," I used
[(LOG(n)-LOG(d))*(P/LOG(2))] where "n" and "d" are simply the top and
bottom terms of a given ratio (the numerator and the denominator), and
"P" is whatever you want to define a given periodicity (while this
means any rhythmic periodicity, by way of the Harrison free style
analogy, this could be seen as making the octave equal the "barline"
so to speak). I almost always tried these out in conjunction with
other, more traditional rhythmic designs, and was generally content to
let P = meter. I remember finding these two rhythmic worlds all but
prohibitively difficult to reconcile; the convinces and shortcomings
of notation and "counting" did not help! (however, my drum machine
didn't so much as once complain, and nailed 'em with ease the first
time through...)

In the Harrison example, if I'm understanding it correctly, a complex
global surface of pitches are arrived at by the stepwise accumulation
of simpler JI intervals, here you no longer have the simple grid-like
duration's of halves, quarters, eighths, and the like, but rather a
collision of logarithmic and linear designs, where 5:7s, 7:10s,
12:17s, etc. are "halves," and 5:6s, 6:7s, 11:13s, etc, "quarters,"
and so forth.

ds

Dan,

Hi.

Do you happen to have musical examples of this (on mp3.com)? Please
do point me toward them if so. This is very interesting to me. This
is somewhat analogous to something I've tried with poly-tempi - which
generally involves layers of simultaneous ratio based tempos, by
which all of the performance elements are coordinated by a series of
rhythmic reference tracks (click tracks at different tempos - except
with more developed percussion parts). This is not to mention the
fact that much of this music also delved deep into poly-meters (an
area of current exploration). Ratios as applied to pitch, tempo,
meter and - in your case - durations, can be very beautiful.

Peace,

Jacky Ligon

--- In tuning@egroups.com, "D.Stearns" <STEARNS@C...> wrote:
> Something that I've experimented with a bit in the past is
converting
> "ratios" into durations.

Check out these audio files of the polyrhythmophone:
http://www.city-net.com/~moko/rvirtual.html

Darren

----- Original Message -----
From: Darren Burgess <DBURGESS@ACCELERATION.NET>

> Check out these audio files of the polyrhythmophone:
> http://www.city-net.com/~moko/rvirtual.html

Cool! Theres actually more to hear on this page:

http://www.city-net.com/~moko/samples.html

When the rhythms aren't too fast, it can sound like Nancarrow. Above a
certain speed it starts to sound like granular synthesis a la Barry Truax!

Dante

Ok folks,

I am in the process of setting up a matrix polyrhymicon instrument using
Geomaestro (http://perso.infonie.fr/hepta/GM/eGM0.html)

I am using the 8 by 8 matrix of harmonics 8-15 by subharmonics 8-15

I am currenly exploring the rhythmic relationship of this subharmonic scale:

8/8 8/9 8/10 8/11 8/12 8/13 8/14 8/15

How long does it take for this rhythmic sequence to repeat?

How would that be calculated?

The harmonic series is relatively simple rhythmically. Harmonics 8-15
repeat every 8 beats, a beat being each repetition of the 8th harmonic.

I have extended my current experimental piece as far as 300 seconds (1 beat
per second) with no repeat, and I am stumped as to how to calculate it.

Also, does this say anything about the subharmonic scale in its harmonic
relationships as well? (I recall past threads regarding the lack of
desirability of subharmonic harmonies in some cases)

I will put an audio file up on MP3.com soon.

Darren Burgess
Gainesville FL

Darren Burgess wrote:

>I am currenly exploring the rhythmic relationship of this subharmonic scale:
>8/8 8/9 8/10 8/11 8/12 8/13 8/14 8/15
>How long does it take for this rhythmic sequence to repeat?
>How would that be calculated?

I'm not sure if I've understood the question but I think the answer is to
first reduce each fraction to lowest terms, e.g. 8/8 becomes 1/1 and 8/10
becomes 4/5 etc.) then take the LCM (Least Common Multiple) of all the
denominators.

i.e. LCM(1,9,5,11,3,13,7,15)

You can calculate that in Excel, if the optional "Analysis Toolpack" is
installed.

One way to do it by hand is to prime factorise each number, then for each
prime take the highest power that occurs anywhere and multiply these
together to get your answer.

i.e

1 = 2^0
9 = 3^2
5 = 5
11 = 11
3 = 3
13 = 13
7 = 7
15 = 3 * 5

So the LCM is 3^2 * 5 * 7 * 11 * 13 = 45045

Just over 12.5 hours if 8/8 is one beat per second.

-- Dave Keenan
http://dkeenan.com

Darren Burgess wrote,

> I am currenly exploring the rhythmic relationship of this
subharmonic scale:
>
> 8/8 8/9 8/10 8/11 8/12 8/13 8/14 8/15
>
> How long does it take for this rhythmic sequence to repeat?
>
> How would that be calculated?

Though I'm not sure exactly what your doing Darren, from the looks of
it alone I would guess that it would be the least common multiple...
the LCM of 15,14,13,12,11,10,9, and 8 is 360360, and that sure would
be lots and lots of beats!

-Dan Stearns

Yes, I believe the LCM derives the correct answer, although I cannot test it
in Geo maestro as it would probably take hours of processing on my amd2 350.
LCM does derive the correct answer for a simpler example : 4/4 , 4/5 , 4/6

I can also reverse the notation makeing the 4/6 the 1/1 I get the following:

3/2, 6/5, 1/1

The LCM is 10 and this pattern repeats every 10 beats (longer than a second)
of the current 1/1 and every 15 beats (seconds) for the 3/2

Thanks for y'alls help.

Darren

>>I'm not sure if I've understood the question but I think the answer is to
>>first reduce each fraction to lowest terms, e.g. 8/8 becomes 1/1 and 8/10
>>becomes 4/5 etc.) then take the LCM (Least Common Multiple) of all the
>>denominators.
>>
>>i.e. LCM(1,9,5,11,3,13,7,15)
>>
>>You can calculate that in Excel, if the optional "Analysis Toolpack" is
>>installed.
>>
>>One way to do it by hand is to prime factorise each number, then for each
>>prime take the highest power that occurs anywhere and multiply these
>>together to get your answer.
>>
>>i.e
>>
>> 1 = 2^0
>> 9 = 3^2
>> 5 = 5
>>11 = 11
>> 3 = 3
>>13 = 13
>> 7 = 7
>>15 = 3 * 5
>>
>>So the LCM is 3^2 * 5 * 7 * 11 * 13 = 45045
>>
>>Just over 12.5 hours if 8/8 is one beat per second.
>>
>>-- Dave Keenan
>>http://dkeenan.com
>>
>>
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Darren Burgess wrote,

>8/8 8/9 8/10 8/11 8/12 8/13 8/14 8/15

>How long does it take for this rhythmic sequence to repeat?

>How would that be calculated?

Dan is right, you'd calculate the lcm of the denominators, which is 360360,
and then you'd divide by the numerator, 8, giving 45045 beats before a
repetition.

>Also, does this say anything about the subharmonic scale in its harmonic
>relationships as well? (I recall past threads regarding the lack of
>desirability of subharmonic harmonies in some cases)

It helps explain why a chord such as 1/15:1/14:1/13:1/12:1/11:1/10:1/9:1/8
is perceived as much more dissonant that a chord such as
8:9:10:11:12:13:14:15, despite Helmholtz, Partch, Plomp, and Sethares's
theories to the contrary.