We have the duple relationship, such as 4:1 and 2:1, which are known commonly as octaves and are basically the same note. We have unison, 1:1, which is actually the same note. We have the triple relationship, 3:2 and 4:3 which are the perfect fifth and the perfect fourth respectively.
Pythagorus derived from the triple ratio the circle of fifths F,C,G,D,A,E,B. C is F times three, G is F times three times three, D is the triple triple triple of F, etc... These pitches, when translated to the same 2:1 or octave becomes our diatonic scale: C,D,E,F,G,A,B. Around the 15th and 16th century the use of sharps and flats came into practice and the idea of the chromatic 12 note scale surfaced, followed soon after with Equal Temperament. For the last 400 years we in the western world have been infatuated with, immersed in, and frustrated by the equally tempered twelve tone scale.
The problem is this:
There are other ratios to be heard. Our twelve tones are only an approximation of the richness that could be possible if we could break out of our cocoon. I wouldn't dream of saying Pythagorus is to blame. I think the biggest factors that have led to our situation is our constraining notation system and the composers who have failed to think outside of its box.
next time:
the drama of fives
No comments:
Post a Comment