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<font face="Calibri">Joseph, are you sure that a siren turning so
slowly as to produce a frequency below, say, 15Hz, would produce a
"rhythm"? Or, more generally, that infrasounds are rhythms? And
that a scraped idiophone, if scraped fast enough, would produce a
single sound of low frequency? I do very much doubt both
hypotheses. <br>
A rhythm is made up of successive sounds within the auditory
range (a rhythm does not exist without sounds), not of waves below
the auditory limit. The idea that diminishing sound frequencies
would become rhythms seem to me analogous to considering that
increasing frequency eventually produces light.<br>
<br>
I fail to see in what sense difference tones (and hardly see in
what sense interferences) have rhythmic analogues: can you be more
specific about that? <br>
<br>
Yours<br>
</font>Nicolas Meeùs<br>
Université Paris-Sorbonne<br>
<font face="Calibri"><a class="moz-txt-link-abbreviated" href="mailto:nicolas.meeus@paris-sorbonne.fr">nicolas.meeus@paris-sorbonne.fr</a><br>
<br>
</font><br>
Le 14/09/2011 04:51, Joseph Lubben a écrit :
<blockquote
cite="mid:99BD5E95-013C-45D0-9518-477CB5FF7FA7@oberlin.edu"
type="cite"><br>
<div>
<font class="Apple-style-span" size="4">I too think that a
sincere answer should not remain unquestioned. There are in
fact a number of circumstances under which pitch and rhythm
can be understood as the same physical phenomena. Any good
oscillator, or siren, or fine-toothed comb, can generate a
periodic pattern whose frequency can be altered along a wide
spectrum, so that "kicks and blows" below 15ish cycles per
second transform into pitch above that range. Combinations of
kicks vs blows in a ratio of three to two, when sped up, will
emerge as a perfect fifth, whose quality will of course depend
on the individual timbres of the kicks and the blows. So I do
think one can speak of a "rhythm of sound waves," and whatever
its inverse would be.</font>
<div><font class="Apple-style-span" size="4"><br>
</font></div>
<div><font class="Apple-style-span" size="4">The problems arise
when making assertions about the sameness of pitch and
rhythm in a musical context, not only because of the
complexity of timbres associated with musical textures, but
also because of the cognitive divide, probably resulting
from the structure of the cochlea, whereby pitch and rhythm
are *perceived* as distinct phenomena, and processed by the
body/brain in different ways. Still, some important
physical phenomena long associated with pitch combinations,
such as difference tones and interference, have interesting
rhythmic analogs that seem to arise from the equivalent
physical properties that adhere to combinations of rhythmic
attacks.</font></div>
<div><font class="Apple-style-span" size="4"><br>
</font></div>
<div><font class="Apple-style-span" size="4">Joseph Lubben</font></div>
<div>
<div><font class="Apple-style-span" size="4">Associate
Professor of Music Theory</font></div>
<div><font class="Apple-style-span" size="4">Oberlin
Conservatory</font></div>
<div><font class="Apple-style-span" size="4">440-775-8239</font></div>
<div><font class="Apple-style-span" size="4"><a
moz-do-not-send="true" href="mailto:jlubben@oberlin.edu">jlubben@oberlin.edu</a></font></div>
</div>
<div><font class="Apple-style-span" size="4"><br>
</font>
<div>
<div><font class="Apple-style-span" size="4">On Sep 13,
2011, at 3:50 PM, Nicolas Meeùs wrote:</font></div>
<br class="Apple-interchange-newline">
<blockquote type="cite">
<div bgcolor="#FFFFFF" text="#000000"><font face="Calibri">Manigirdas,<br>
<br>
You might not receive many answers, I am afraid,
because your argument really does not resist close
examination. As I hate leaving a sincere question
unanswered, here is my opinion:<br>
<br>
There is no such thing as a "rhythm of sound waves". A
wave is not delimited by kicks or blows and its
duration (its period) can be measured between any
specific point in the first wave to the analogous one
in the second. The idea that sound vibrations were
successions of blows, i.e. of individual points, is
very ancient, and you are in the very good company of
antique philosophers in thinking so. I believe,
however, that the idea had to be abandoned with the
development of physics in the 17th century, even if a
mathematician like Euler probably still believed in it
in the middle of the 18th century. Sound vibrations
result from continuous motions.<br>
<br>
The addition of notes sounding at an interval results
in the addition of curves, involving not only the
fundamental of the notes, but also their partials.
These highly complex resulting curves can be analyzed
in their individual (sinusoidal) components through
Fourier analysis, a formidable achievement of
late-18th-century mathematical theory.<br>
<br>
You are right that these individual resulting complex
curves may individualize intervals and chords. The
problem is that they also strongly depend on
individual timbres (i.e. harmonic content of the
individual constituent notes). They certainly do
account, in general terms, for the specific sonorities
of given consonant intervals or chords, nobody denies
that. But (a) they certainly correspond in no way to
rhythms: the conditions or the respective perceptions
of complex waves and of rhythms are incommensurate;
(b) they hardly could define general physical
categories, because of the important role of timbre
(harmonic content) in their construction: consonances
and dissonances are way too dependent on timbre to
elicit "different emotions" that could be categorized
on purely physical grounds.<br>
<br>
It remains, though, that fifths definitely are
consonances, and major 7ths dissonances, regardless of
their timbre. This is because they form entities not
only in a physical context, but also in a semiotic one
– i.e. in the context of a musical "language".
Circumstances might be created where, from a physical
point of view, some fifths may sound more dissonant
than major 7ths; much as known words may sound very
bad in the mouth of some of us (me, for instance, when
I try to speak English). But even badly pronounced,
words do retain their emotional content.<br>
<br>
To sum up: you obviously would be happy to be able to
link musical emotion to physical properties. These two
realms (emotion and physics) however do not overlap,
so that your hope will not be fulfilled.<br>
There is a consolation to this, though. If musical
emotions really were linked to specific physical
properties, then very little space would be left for
alternative musics – musics of the folks, musics of
the world – and the claim of some of us, that our
Occidental music is the best (they don't usually
specify <u>which</u> Occidental music) would seem
true. Fortunately, the emotion in music <u>does not</u> depend
on physics, it can take many forms, and allows space
for many different tastes.<br>
We would like our music, or music at large, to be
"natural", i.e. founded on (physical) nature. Yet, as
Walter Wiora (an outstanding musicologist) once
claimed, any attempt at proving the "naturalness" of
some music (there have been several such attempts in
the history of music) usually aimed at proving the
unnaturalness of some other (usually more recent)
music.<br>
<br>
Yours,<br>
<br>
</font>Nicolas Meeùs<br>
Université Paris-Sorbonne<br>
<font face="Calibri"><br>
<br>
</font><br>
Le 12/09/2011 06:52, <a moz-do-not-send="true"
class="moz-txt-link-abbreviated"
href="mailto:Manigirdas@cs.com">Manigirdas@cs.com</a> a
écrit :
<blockquote cite="mid:c6e1.4f9b5edc.3b9eea1c@cs.com"
type="cite">
<pre wrap="">Musical intervals with the notes sounding together are actually very rapid
rhythns of sound waves. For example, the 5th can be represented as follows.
The distance between two marks represents the duration of each sound wave of
the fundamental partial of a note. The times involved are on the order of
1/200 of a second:
| | | | (durations of sound waves of the upper note g)
| | | (durations of sound waves of the lower note c)
---------------------
| | | | | (combined rhythm of the waves of the two notes)
We can see that the sound waves of these two notes are related in the
rhythm of 2 against 3.
Similarly, the 4th has the rhythm of 3 against 4:
| | | | | (f)
| | | | (c)
---------------------------
| | | | | | | (combined)
The octave has the rhythm of 1 against 2.
| | | (c an octave higher)
| | (c)
-------------------
| | | (combined)
And so on.
Chords are also rhythms. For example the waves of a major triad in second
inversion look like this:
| | | | | | (top note
e)
| | | | | (middle
note c)
| | | | (bass note
g)
---------------------------------------------------------------
| | | | | | | | | | | (combined)
This is the rhythm of 3 against 4 against 5.
Of course, the sound waves will not necessarily be neatly in phase as in
the diagrams. If they are shifted relative to each other, the rhythms formed
will be somewhat more complex.
These rhythms are too rapid to be discerned by the ear as rhythms, but they
are there nevertheless. They repeat continuously while the notes are
sounding.
Since each interval and chord has an unique rhythm, it may be speculated
that each rhythm contributes to a different emotion.
Manigirdas Motekaitis
Piano teacher
714 W. 30th St.
Chicago, IL 60616-3005
(312) 804-4324</HTML>
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