The Physics of Sound: :The Physics of Sound: The Foundation of Music


Why Talk Physics? :Why Talk Physics? It gets us in the right mindset Of appreciating our amazing sense of hearing Of thinking about commonplace things in a new way Of realizing that you can fruitfully analyze an art It’s interesting to see how our music flows from science and mathematics And the best part of physics: the demonstrations! Not a prerequisite for the rest of the talk Though these concepts do reemerge in counterpoint


The Phenomenon of Sound :The Phenomenon of Sound Vibration within a certain range of frequencies Waves transmit energy but not the medium Individual particles of air more or less stay in the same places Particles are constantly joining and leaving the wavefront Illustrations show sinusoidal motion A gentle, mellow sound:


Another Tone :Another Tone An ordinary “sawtooth” tone: Four variations (listen for differences!) 4: 3: 2: 1: What was removed each time?


Harmonics :Harmonics In every tone we encounter, there are other tones hiding inside! Any sound of frequency f that is not a sine wave can be decomposed into a sum of sines at f, 2f, 3f, 4f, … Generated by any natural instrument Perceptible only if you listen hard for them Harmonics blend in to create tone color


Our Perception of the Harmonics :Our Perception of the Harmonics Original tone: [5f = 2 octaves + third] Four variations (listen for differences!) 4: [4f = 2 octaves] 3: [3f = 1 octave + fifth] 2: [2f = 1 octave] 1: [f = unison] Why do we hear 2f as “the same note”? Because we were just made that way! This harmonic sequence (first five listed) forms the basis of harmony. But how?


When Harmonics Clash :When Harmonics Clash When two harmonics (or any pure sine waves) approach in frequency, they give rise to an unpleasant-sounding beating Thus we are attracted to certain intervalsthat minimize the amount of beating.


The Dissonance Curve :The Dissonance Curve Generated by sliding one tone (with fundamentals) against another A dissonance score is calculated from any conflicting harmonics The dips in this curve generate/coincide with many scale degrees! Just from harmonics, we’ve generated a scale!


The Poor Man’s Dissonance Curve :The Poor Man’s Dissonance Curve


Dissonant Intervals :Dissonant Intervals Dissonance drives all our music. Dissonant intervals want to resolve into consonant intervals The m2 and the M7 are generally too dissonant for direct use But look at the power of the mildly dissonant M2, A4, and m7! Combining several intervals vertically leads to a chord As the intervals in those chords resolve horizontally, there is created a chord progression The top note of these progressions is melody


Counterpoint :Counterpoint Writing harmonies that form chords (vertical) and are singable (horizontal), yet preserve distinctness or “independence” of the individual voices Developed by consensus during the Renaissance Reached great heights in Palestrina (d. 1594) Famously summarized by Johann Fux (1660 – 1741) A rite of passage for music majors Followed to the present day In four voices, also known as “chorale writing” The method by which hymns are harmonized


Consonance :Consonance After the octave (P8), the perfect fifth (P5) is the most consonant interval. Many of a note’s harmonics overlap perfectly with that of its P8 or P5 Good for chords: consonant intervals And yet bad: these intervals can fuse into one tone, losing independence, by masquerading as harmonics The phenomenon of the “missing fundamental”


Consonance in Counterpoint :Consonance in Counterpoint Examples of chorale-writing rules: “Parallel 8ves/5ths”: A P8/5 may not move into another P8/5 “Hidden 8ves/5ths”: The outer voices may not move in the same direction into a P8/5 Unless the soprano is moving in step (a mitigating exception)


Conclusion :Conclusion You’ve heard some nice demonstrations You’ve learned a little about harmony Even if you don’t plan to write any harmonies, know that… There are rules concerning harmonies There is science behind the rules Knowing the science can improve art Now then: let’s get on with the show!