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DHC 161

DHC 161. Musical Intervals and Frequency Ratios. Dr. Andy Piacsek Central Washington University. A musical scale is a systematic arrangement of pitches. Each musical note has a perceived pitch with a particular frequency. (the frequency of the fundamental).

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DHC 161

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  1. DHC 161 Musical Intervals and Frequency Ratios Dr. Andy Piacsek Central Washington University

  2. A musical scale is a systematic arrangement of pitches Each musical note has a perceived pitch with a particular frequency (the frequency of the fundamental) Going up or down in frequency, the perceived pitch follows a pattern One cycle of pitch repetition is called an octave. The interval between successive pitches determines the type of scale.

  3. Intervals 12-tone scale (chromatic) 8-tone scale (diatonic) Note span Interval Frequency ratio C - C unison 1/1 C - C# semitone 16/15 C - D major second (whole tone) 9/8 C - D# minor third 6/5 C - E major third 5/4 C - F perfect fourth 4/3 C - F# augmented fourth (tritone) 45/32 C - G perfect fifth 3/2 C - G# minor sixth 8/5 C - A major sixth 5/3 C - A# minor seventh 9/5 C - B major seventh 15/8 C3 - C4 octave 2/1 C3 - E4 octave+major third 5/2

  4. compound intervals Adding intervals means multiplying frequency ratios major third + minor third perfect fifth octave perfect fourth + perfect fifth perfect fourth + major third major sixth perfect fourth + whole tone perfect fourth

  5. more compound intervals ratios larger than 2 can be split up into an octave + something perfect fifth + perfect fifth Octave + whole tone major seventh + minor sixth Octave + perfect fifth

  6. harmonic series Intervals between consecutive harmonics Fundamental f1 2nd harmonic f2 = 2f1 octave 3rd harmonic f3 = 3f1 perfect fifth 4th harmonic f4 = 4f1 perfect fourth 5th harmonic f5 = 5f1 major third 6th harmonic f6 = 6f1 minor third

  7. Consonant intervals Overlapping harmonics f1 f2 f3 f4 f5 f6 f7 f8 f9 tonic 120 240 360 480 600 720 840 960 1080 octave 240 480 720 960 fifth 180 360 540 720 900 1080 fourth 160 320 480 640 800 960 M third 150 300 450 600 750 900 1050 m third 144 288 432 576 720 864 1008 Dissonant intervals Perceived when harmonics are close enough for beating

  8. Intervals 12-tone scale (chromatic) 8-tone scale (diatonic) Note span Interval Frequency ratio C - C unison 1/1 C - C# semitone 16/15 C - D major second (whole tone) 9/8 C - D# minor third 6/5 C - E major third 5/4 C - F perfect fourth 4/3 C - F# augmented fourth (tritone) 45/32 C - G perfect fifth 3/2 C - G# minor sixth 8/5 C - A major sixth 5/3 C - A# minor seventh 9/5 C - B major seventh 15/8 C3 - C4 octave 2/1 C3 - E4 octave+major third 5/2

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