[Smt-talk] Structure of intervals

[Manigirdas at cs.com]

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>