1. DHC 161 Musical Intervals and Frequency Ratios Dr. Andy Piacsek Central Washington University 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. Note spanInterval Frequency ratio C - Cunison 1/1 C - C#semitone 16/15 C - Dmajor second (whole tone) 9/8 C - D#minor third 6/5 C - Emajor third 5/4 C - Fperfect fourth 4/3 C - F#augmented fourth (tritone) 45/32 C - Gperfect fifth 3/2 C - G#minor sixth 8/5 C - Amajor sixth 5/3 C - A#minor seventh 9/5 C - Bmajor seventh 15/8 C 3 - C 4 octave 2/1 C 3 - E 4 octave+major third 5/2 Intervals 12-tone scale (chromatic) 8-tone scale (diatonic)

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

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

6. harmonic series Fundamental f 1 2 nd harmonic f 2 = 2f 1 octave 3 rd harmonic f 3 = 3f 1 perfect fifth 4 th harmonic f 4 = 4f 1 perfect fourth 5 th harmonic f 5 = 5f 1 major third 6 th harmonic f 6 = 6f 1 minor third Intervals between consecutive harmonics

7. Consonant intervals Overlapping harmonics tonic 1202403604806007208409601080 fifth 180360 540720 9001080 fourth 160 320480 640 800960 M third 150 300 450600 750 900 1050 m third 144 288 432 576720 864 1008 octave 240480720960 Dissonant intervals Perceived when harmonics are close enough for beating f 1 f 2 f 3 f 4 f 5 f 6 f 7 f 8 f 9

8. Intervals 12-tone scale (chromatic) 8-tone scale (diatonic)