Download PHYSICAL THEORY OF MUSIC

Vasileios Tsitsimpis
Teacher of Physics
4th General Lyceum of Lamia Greece.
Email: [email protected]
Web site: http://4lyk-lamias.fth.sch.gr/
Cell phone:
+306972115587
ileios Tsitsimpis
Georgios Pantazis.
Teacher of Physics and astronomy,
Music School of Lamia – Greece.
Email: [email protected], [email protected]
Web site: http://gym-mous-lamias.fth.sch.gr/
Cell phone:
+306977244095
PHYSICAL THEORY OF
MUSIC
THE MUSICAL INTERVALS OF INTEGER NUMBERS OF
PYTHAGORAS AND THE NON INTEGER INTERVALS OF
EUROPEAN MUSIC.
Vasileios Tsitsimpis and Georgios Pantazis,
Lamia – Greece
Our project aims to illuminate the science behind the
music.
It is widely known that when either a string or a membrane or the air inside a pipe pulses,
standing waves are created and sound is produced. Sound is periodical motion which has
a fundamental frequency along with many multiple motions, known as harmonics.
We confirmed that the length of a string or a pipe is inversely proportional to the
frequency of the sound that is produced when subjected to oscillation.
Two sounds are in harmony when they have many common harmonics.
We achieve total synchronization when the frequency of one sound is the integral
multiple of the frequency of the other sound (In this way, they have the same
harmonics!). If their frequency ratio is 1/2, then they constitute an octave.
Pythagoras observed that strings (with the same tension and thickness) with small
integral ratio of their lengths produce fine-sounded sounds. So, he built instruments, the
ratios of which are 2/3, ¾, ½, etc (the frequencies of the produced sounds will also have
inverse ratios). a scale of notes based on the ratios of the numbers 6, 8, 9, 12 (tetraktis)
and on their combinations.
The problem is that given a fixed ratio of two integral numbers between two sequential
sounds, we can’t double or quadruplicate the frequency (It’s impossible for an octave to
be constituted!)
During the Renaissance, musicians divided an octave into 12 «equal» parts (semitones).
When we say “equal” we mean that the sequential notes have the same frequency ratio
and not the same difference. So, the frequency ratio of the first and the last note will be
½, while the intermediary ones will all own the same frequency ratio which is proved to be
the twelfth root of the number 2. This is known as integration. In this way, we can have a
choir of many instruments playing simultaneously the same melody starting from a
different base. This is something that cannot apply to Pythagoras’s scale, as it’s not
integrated. Byzantine music is not integrated either and that’s why here we have a
monody and not a chorus- European music.
Thus, we constructed Pythagoras’s tetrachords and one major scale of European music
with 8 spaces (tone-tone-semitone-tone-tone-tone-semitone). We observed that most of
Pythagoras’s sounds are included in European music.
Furthermore, we thought that we could elaborate more on what would happen if we
separated the octave in 10 «equal» parts instead of 12.In that case, the frequencies ratio
of the two sequential sounds would be the tenth root of 2. We did that because we
noticed that the ratio of the first and the seventh note is Phidias’s number φ. Hence, we
wanted to compose a music piece according to the new integrated scale and see if the
produced sound is harmonious or not.
Similar constructions were made with tubes, cut out in specific lengths so as to
correspond to the above mentioned scales.
As regards to the constructional material, we needed to have a string with equal thickness
and tense in order to use specific parts of it, to see which notes are produced when is
pulsed. For that reason, we used pulleys to maintain the same tense, as well as riders on
rails, to move them adjusting precisely the length. With a turnbuckle, we adjusted the
tense of the string and thus change the «tuning».