Why do we think some musical combinations
sound good together?
Here are four facts about music,
• A musical instrument produces sound waves that cause air
to vibrate at a particular frequency;
the pitch
of a musical note (is it a "low note" or a "high note") is determined
by the
rate
of vibration.
• When a note with
frequency "x" is produced, it has
overtones at multiples
of x, at 2x, 3x, 4x, 5x, 6x,
7x, ...
For example, if a musical note is produced by air vibrating 24
times per second,
it will have overtones with sound waves (in air) vibrating at 48, 72, 96, 120,
144,
168,
192,...
• A major chord is formed by playing the 1-and-3-and-5 notes of a major scale at the same time.
• In a Pythagorean Scale, the
ratios between the 7 notes of a major scale are
1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1
If the 1-note is produced by sound waves vibrating at 24 times per second,
the
seven scale-notes
are: 24 27 30 32 36 40 45 48
and a question:
Can you see a mathematical relationship between the overtones
of the 1, 3, and 5 notes?
You can play with the numbers and do detective work,
then look at the explanation below.
In this table, notice the "matching up" of some overtones: 13, 15, 35, 135.
1st |
24 | 48 | 72 | 96 | 120 | 144 | 168 | 192 | 216 | 240 | 264 | 288 | 312 | 336 | 360 | etc |
|||||||||||||
3rd |
30 | 60 | 90 | 120 | 150 | 180 | 210 | 240 | 270 | 300 | 330 | 360 | etc |
||||||||||||||||
5th |
36 | 72 | 108 | 144 | 180 | 216 | 252 | 288 | 324 | 360 | etc |
||||||||||||||||||
match |
13 |
13 |
15 |
35 |
15 |
13 |
15 |
135 |
Our ears perceive the "matching up" of overtone-waves as a pleasant harmony.
Due to the physiology of hearing and vision,
our ears hear simultaneous notes as harmony,
but our
eyes see simultaneous colors as a new color.
{ In other pages, you can learn more about the science of music and color. }