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<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 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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</pre>
</blockquote>
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