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Musical Scales

Musical Scales. WHY NOT?. Just scale constructed from major triads:. 4 -> 5 -> 6. 1 5/4 3/2. divide by 4:. to get Hz, you could multiply by any number you like, e.g. multiply by 50: 200Hz -> 250Hz -> 300Hz. tune the white keys of the piano:.

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Musical Scales

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  1. Musical Scales WHY NOT?

  2. Just scale constructed from major triads: 4 -> 5 -> 6 1 5/4 3/2 divide by 4: to get Hz, you could multiply by any number you like, e.g. multiply by 50: 200Hz -> 250Hz -> 300Hz

  3. tune the white keys of the piano: C D E F G A B C D to three triads: C-E-G: CDE F G A B C D C D E FG A B C D G-B-D: C D E F G A B C D F-A-C: What are the required frequencies?

  4. Just Scale: white keys of the piano C-E-G triad 1 5/4 3/2 2 G-B-D triad 9/8 3/2 15/8 9/4 F-A-C triad 4/3 5/3 2

  5. if we call the first frequency (C) =1 the frequencies become: C D E F G A B C 1 9/8 5/4 4/3 3/2 5/3 15/8 2 inter- val: 9/8 10/9 16/15 9/8 10/9 9/8 16/15 incr:12.5% 11.1% 6.7% 12.5% 11.1% 12.5% 6.7% STEP: 1 1 1/2 1 1 1 1/2 the ”major just diatonic scale" black keys where there is a whole-tone step!

  6. Names of intervals: examples on blackboard: how count? how find number of semitones? minor third vs. major third when are intervals called”just”? How would we tune a keyboard? example: of A4 = 440 Hz, what freq is F4? G5? How calculate frequency ratios? example:find ratio between F4 and B4 in just tuning

  7. The Natural Scale natural scale: sequence of harmonics (bugle) frequencies relative to fundamental: 1 2 3 4 5 6 7 8 9 10 ………... example: if fundamental is F4 what tone is the fifth mode?

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