Week 9b

# Week 9b - Physics 1240 Today Intervals tuning and...

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Physics 1240 Tues 3/8/2011 Today: Intervals, tuning and temperament Next time: Consonance, dissonance, begin standing waves Outline - Pythagorean Hypothesis - Musical intervals - Major Scale - Just tuning - Pythagorean tuning

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Frequency and Pitch Table half step = (2) 1/12
Pythagoras • The Magic of Whole Number Ratios l 1 l 2 = l 2 l 1 2 1 diapson diapente = l 2 l 1 3 2 diatesaron = l 2 l 1 4 3 octave perfect 5th perfect 4th

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Pythagorean Hypothesis: Natural intervals in music are related to low integer ratios of frequencies.
Need to know… Interval example ratio half steps Major 3 rd C to E 5/4 4 4 th C to F 4/3 5 5 th C to G 3/2 7 Octave C to C’ 2 12 half step = a factor of (2) 1/12 = a factor of 1.05946 whole step = two half steps = a factor of 1.12246

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CQ 9.1 According to Pythagoras, the Major 3 rd interval should be what ratios of higher to lower frequencies? A) 1.25 B) (twelfth root of 2) 4 = (2) 4/12 C) Both A) and B) D) 50 Hz E) none of the above
4 half steps is a major 3rd 7 half steps is a perfect 5th

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## This note was uploaded on 05/01/2011 for the course PHYS 1240 taught by Professor Holland,murray during the Spring '08 term at Colorado.

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Week 9b - Physics 1240 Today Intervals tuning and...

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