Fabrice Mogini
INTRODUCTION.
CONCEPT OF TUNING.
Tuning is necessary when the frequency of sounds used for a musical or sonic
performance has to be stable.
By tuning, a composer or musician can refer to a particular and satisfying
frequency with consistency.
The composer can write a tune and play the same tune the next day or even,
play it on a different instrument; this is the function of stability that
comes with the act of tuning.
Tuning is also a system. This has to do with the inter-relationship that frequencies
can have with each other in a music composition.
A tuning is a set of frequency relationships.We can quantify these relationships with intervals. A fixed frame is needed to help discriminate these intervals. The frame commonly used in most music is the octave.
The octave1 is an interval that seems fundamental musically for many cultures,
ancient or modern (Burns and Ward (1982). Starting from any chosen frequency,
the octave is twice the frequency; it has twice as many cycles per second.
A note and its octave have then soundwaves which coincide with each other
very often and regularly. This octave is then a particular note but the term
'octave' is commonly used to refer to the interval between this note and its
root.
The octave as an interval sets the limits of the tuning system. It seems that
no other interval is a better candidate for
defining a frame that other intervals can be related to.
The other intervals have certain proportional relationship to
each other while being related to the root and to the octave.
diagram 1. Example of musical intervals (in bold characters) and their relationship
to the root and to the octave.
The discussion for musicians, composers and scientists
has often been on the size of these intervals leading to
different choices of tuning systems.
1.0 A PLURALITY OF TUNING SYSTEMS.
1.1 PYTHAGOREAN TUNING.
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