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lecture17

# lecture17 - Pythagorean Scale Pythagoras(born about 580 B.C...

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Pythagorean Scale Most consonant intervals: 1:1 – unison 2:1 – octave 12 semitones 3:2 – perfect 5 th 7 semitones 4:3 – perfect 4 th 5 semitones Pythagoras (born about 580 B.C.) The Pythagorean system is an attempt to build a complete chromatic scale from only two of the pure tones: the octave and the perfect fifth ... 32 243 , 16 81 , 8 27 , 4 9 , 2 3 , 1 ... 2 3 , 2 3 , 2 3 , 2 3 , 2 3 , 1 5 4 3 2 The goal was to close circle (Circle of fifths), i.e. to end up with the same note as started. Unfortunately, it is impossible. ; 7 . 129 2 3 12 128 2 7 = 2 3 4 2 3 = If octave has 12 semitones, then 7 octaves have 12x7 semitones. If perfect 5 th has 7 semitones, 12 perfect 5 th have 7x12 semitones.

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Questions: How to construct a convenient scale? How to set up an interval between notes? What is known: Perfect fifth plus perfect forth is an octave Perfect fourth up is the same as octave up and then perfect fifth down Perfect fifth up is the same as octave up and then perfect fourth down So we can use octave and perfect fifth to construct perfect fourth 12 perfect 5 th are approximately equal to 7 octaves 12 semitones! 7 notes!
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lecture17 - Pythagorean Scale Pythagoras(born about 580 B.C...

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