[Smt-talk] Structure of intervals

[Thomas Noll]

This is just a side remark to this subject: The idea of a slow-motion
performance of the idealized superposition of elementary oscillations
underlies an exhibit in the Mathematics Museum of Dresden: 

http://www.youtube.com/watch?v=Tnjfxxbx9ys

It is inspired by an instrument and a composition "Galileo" by Tom
Johnson. In this exhibit the tubes are tuned in the same frequency
ratios as the pendulums. I can confirm that every constellation of
pendulums out of the five (12 : 15 : 16 : 18 : 24) poses quite a
different task to the player and every "chord" contributes to a
different source for making mistakes. (But that's an ethical issue
rather than an esthetical one...) 
Sincerely
Thomas Noll  

*********************************************************
Thomas Noll
http://user.cs.tu-berlin.de/~noll
noll at cs.tu-berlin.de
Escola Superior de Musica de Catalunya, Barcelona 
Departament de Teoria i Composició 

*********************************************************   


-------------------
> 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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