Rhytmic primes

I�ve been wondering recently if there is a direct parallel between prime ratios in pitches and in rhythm.For most people,the sensation of consonance all but disappears at primes 17 and higher.Accompanied by a chord like just 1-3-5-7 for example,it blends in but by itself,17 and higher primes do not give the smooth sound lower primes has in most human ears.

While 11/8 and 13/8 meters can be difficult to play even for those who are used to them(indeed,most Western music do not contain any meters with higher primes than 2 and 3)they can be played,and most certainly"felt"in a way where they become a naturally flowing rhytmic cycle.The former,for example,when used in Balkan music,is often percieved as a extended cycle of five beats(2,3,2,2,2).

While meters like 17 and 19 can be built up in the same way of shorter and longer sub-cycles,they simply refuse to"flow"in the way the previously mentioned meters does(a subjective experience.)

Although i can learn to play it,it just doesn�t"feel"in the way 13 and lower prime meters does.I always thought of higher numbered meters being more complex than others,but i never before considered it as a prime factor thing.

My idea is not that there is a distinct limit to human perception(indeed,some Indian and Indonesian music use very long cycles)but rather that one should consider the complexity of a meter to be dependant upon prime factorisation rather than the sheer value of the number.For example,21 is not a prime.

����������������������������������������������������������������������
Mats �ljare
Eskilstuna,Sweden
http://www.angelfire.com/mo/oljare
________________________________________________________________________
Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com

Mats,

IMO there is more of a correlation between "ratios of tempos", to
that of "ratios of pitch", than there is in considering just single
meters alone. Something I have done a bit of experimentation with in
the past is to create tempo chords in midi sequenced compositions.
Since Tempo can be looked at as "frequency" it is possible to use
ratios of tempos in the same way one would use them for pitch. In the
simplest sense 60 BPM being 1/1 - 120 BPM being 2/1 etc... Perhaps
this is something you already employ in your compositions?

In another altogether different way, it is also important to consider
polymeters - and phasing between a number of simultaneous meters. I
have also worked with combining many prime meters at once (5/8, 7/8,
11/8 and 13/8 - for example), each playing on various timbres - and
passing these timbres alternately to the other poly-metrical
rhythmic "strata". Since in this scenario all are playing at the same
tempo - to me there is less of a "chordal" correlation with
polymeters. You get more of a sense of cycles phasing against one
another, than the chordal tempo effect of slow and fast rhythms
happening in juxtaposition.

As to whether or not human perception can follow passed 17, I've
found it's all about conditioning and the chosen context for such a
long cycle. If you work with anything and hear it long enough, it'll
become a valid part of practice.

I love to work in prime meters - there is nothing like the "feel" it
adds to a piece. I think that the shackles of "primes than 2 and 3"
are kind of like 12 tET sometimes.

Thanks for the thought provoking post,

Jacky Ligon

--- In tuning@egroups.com, "Mats €  Öljare" <oljare@h...> wrote:
> I€  ´ve been wondering recently if there is a direct parallel
between
prime
> ratios in pitches and in rhythm.>
> While 11/8 and 13/8 meters can be difficult to play even for those
who are
> used to them(indeed,most Western music do not contain any meters
with higher
> primes than 2 and 3)they can be played,and most certainly"felt"in a
way
> where they become a naturally flowing rhytmic cycle.The former,for
> example,when used in Balkan music,is often percieved as a extended
cycle of
> five beats(2,3,2,2,2).
>
> While meters like 17 and 19 can be built up in the same way of
shorter and
> longer sub-cycles,they simply refuse to"flow"in the way the
previously
> mentioned meters does(a subjective experience.)
>
> Although i can learn to play it,it just doesn€  ´t"feel"in the way
13
and lower
> prime meters does.I always thought of higher numbered meters being
more
> complex than others,but i never before considered it as a prime
factor
> thing.
>
> My idea is not that there is a distinct limit to human
> perception(indeed,some Indian and Indonesian music use very long
cycles)but
> rather that one should consider the complexity of a meter to be
dependant
> upon prime factorisation rather than the sheer value of the
number.For
> example,21 is not a prime.
>
> €  »»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»»
»»»»»»»»»»»»»»»»»»»»»»»
€  »»
> Mats €  Öljare
> Eskilstuna,Sweden
> http://www.angelfire.com/mo/oljare
>
______________________________________________________________________
__
> Get Your Private, Free E-mail from MSN Hotmail at
http://www.hotmail.com

--- In tuning@egroups.com, jacky_ekstasis@y... wrote:
> Mats,
>
> IMO there is more of a correlation between "ratios of tempos", to
> that of "ratios of pitch", than there is in considering just single
> meters alone. Something I have done a bit of experimentation with
in
> the past is to create tempo chords in midi sequenced compositions.
> Since Tempo can be looked at as "frequency" it is possible to use
> ratios of tempos in the same way one would use them for pitch. In
the
> simplest sense 60 BPM being 1/1 - 120 BPM being 2/1 etc... Perhaps
> this is something you already employ in your compositions?

We might also mention, in light of the conversation with Jacky and
Banaphshu, that you both certainly will recall the "biggest" of such
harmonic-rhythmic spectral efforts, Stockhausen's _Gruppen_.

The article that "explains" Gruppen appears in Issue III of _die
Reihe_, the wonderful, but short-lived German publication that
follows
the Boulez-Stockhausen-Webern post-serial schools, an article
called "Musical Craftsmanship."

The "unified field theory" of this approach is clearly explained by
Stockhausen right at the beginning of the article:

"Our sense perception divides acoustically-perceptible phases into
two
groups; we speak of DURATIONS and PITCHES. This becomes clear if we
steadily shorten the length of a phase (e.g. that between two
impulses) from 1" to 1/2", to 1/4" ... etc. Until a phase-duration
of
approx. 1/16", we can still just hear the impulses separately; until
then, we speak of 'durations,' if of one that becomes extremely
short.
Shorten the phase-duration gradually to 1/32", and the impulses are
no
longer separately perceptible; one can no longer speak of the
'duration' of the phase. The latter process becomes perceptible,
rather, in a different way: one perceives the phase-duration as the
'pitch' of the sound... Thus the transition from one time-area to
another causes a change in our perception of phases. This
observation
could form the basis of a new morphology of musical time..."

Stockhausen goes on to develop a system of what he calls "formants"
or
rhythmic pulses that consist of the ascending series of whole numbers
which also correspond to the harmonic series... i.e., obviously,
instruments will be performing at the same time a unit of 1, 2, 3, 4,
5, etc., in the _Gruppen_ texture.

Interestingly enough, this is a very similar procedure used by
Charles
Ives in his Universe Symphony and due to the fine efforts of Johnny
Reinhard, we are beginning to get a glimmer of Ives real interest in
acoustic matters and intonation. The Ives, of course, would pre-date
the Stockhausen by some time... but I believe the "discovery" was
independently formulated by Stockhausen... I'm pretty sure he
wouldn't
have seen drafts of the Ives Universe Symphony...(??)

In any case, I was startled to find that Stockhausen also derives
durations by using the SUBHARMONIC series... and he has a UTONAL
rhythmic scheme in _Gruppen_ as well.

Stockhausen states: "In comparison with a scale built on chromatic
intervals, the subharmonic scale is a MODE. The composer Messiaen
was
well aware of this when he characterised such scalse as 'modes" in
his
fourth _Study_ for piano...

Anybody know more about Messiaen and the subharmonic series
scales??... I would be very interested!!

In an additional description of his "formant spectrum," Stockhausen
continues:

"Because the fundamental phase serves as the unit of perception, the
divided values are always referred to it. Thus the fractions must
always repeat themselves until they reach the total fundamental
value. There are two halves, three thirds, etc, to one fundamental
phase. We define such a formation as a HARMONIC PHASE-SPECTRUM, BOTH
when it applies to micro-phase (pitch) and macro-phases (durations)."

It might be also interesting to consider that these overlapping
rhythmic relations and phases are certainly pre-dated by such
oriental
musics as the Gamelan... I'm afraid I don't know too much about the
subject... I know some list members do. I guess the question is
whether Gamelan music follows small integer relationships in the
overlapping rhythmic patterns. That's an easy one for somebody.
Thanks!

____________ _____ __ __ _
Joseph Pehrson

--- In tuning@egroups.com, "Mats Öljare" <oljare@h...> wrote:
> I´ve been wondering recently if there is a direct parallel
between
prime
> ratios in pitches and in rhythm.

I have a couple of CDs by Ben Neill. One of them (I think it might
be Goldbug) has liner notes which mention this. Neill is a
student/former student of La Monte Young and so is influenced by his
ideas on just intonation and rhythm.

Paolo

> [Mats Öljare, Sun Aug 20, 2000 9:38am]
>
> While 11/8 and 13/8 meters can be difficult to play even for
> those who are used to them(indeed,most Western music do not
> contain any meters with higher primes than 2 and 3)they can be
> played,and most certainly"felt"in a way where they become a
> naturally flowing rhytmic cycle.The former,for example,when used
> in Balkan music,is often percieved as a extended cycle of
> five beats(2,3,2,2,2).
>
> While meters like 17 and 19 can be built up in the same way of
> shorter and longer sub-cycles,they simply refuse to"flow"in the
> way the previously mentioned meters does(a subjective experience.)
>
> Although i can learn to play it,it just doesn´t"feel"in the way
> 13 and lower prime meters does.I always thought of higher numbered
> meters being more complex than others,but i never before considered
> it as a prime factor thing.
>
> My idea is not that there is a distinct limit to human
> perception(indeed,some Indian and Indonesian music use very long
> cycles)but rather that one should consider the complexity of a
> meter to be dependant upon prime factorisation rather than the
> sheer value of the number.For example,21 is not a prime.

Hi Mats. I'm glad you added 'a subjective experience' to your
description, because it doesn't hold for me.

I've been a big fan of Bulgarian folk music, much of which uses
complex asymmetrical meters like 11/8 and 13/8. But my introduction
to this music was thru a piece by jazz trumpeter Don Ellis, called
'Bulgarian Bulge', which is in 31/16.

(You can read a bit about this in my autobiography:

http://www.ixpres.com/interval/monzo/bio/bio.htm

There's a link to a webpage loaded with info about Ellis, and
another link to a video excerpt that didn't work when I tried
it just now.)

Ellis's band plays the 31/16 flawlessly and with a lot of swing.
I'd like to know how other listeners familiar with this tune
would respond to your comments.

'Bulgarian Bulge' was a real eye-opener for me, not primarily
because of the interest it sparked in the folk music, but because
the speed at which the band plays the tune made me realize that
we can perceive very complex meters as series of smaller chunks
made up of either 2 or 3 beats.

In this particular tune, those 2- or 3-beat units are built up
in various different combinations into larger pieces made of
7 or 8 beats, which are in turn paired off into 15- and 16-beat
units, which finally are paired to produce the 31-beat unit of
a single measure. With such a long and complex structure, each
single measure is like a phrase.

Since then, I've been inspired to use this type of construction
in a lot of my own tunes, but I've never quite approached the
complexity of this Ellis tune.

Primes are particularly of interest to me, considering the role
they seem to play in my harmonic theories. But my personal feeling
about meters is that their full unit measurements don't compare
as prime-factor _gestalts_ they way harmonic prime-factors do
(or seem to, as a template into which we fit our perception of
more complicated proportions). It seems to me that any metrical
structure can be, and is, perceived as series of 2- and 3-beat
units.

-monz
http://www.ixpres.com/interval/monzo/homepage.html