Physics and Music PHY103What does Physics have to do with Music?2. Method of Experimental EnquirySlide 4Slide 55. Physics of Perception: how does the ear and brain work?Opening song from anime series6. A way to find beauty in physics and mathMusical analogies in early astronomy and mathematicsKepler and the Music of the SpheresThe Birth of Quantum MechanicsSlide 12Musical analogies in modern physicsApproach for this classFocusSyllabusSlide 17Relation between intervals and wavelengthsSlide 19Harmonics or OvertonesModes of oscillationWavelengths and frequencies of HarmonicsOvertones of the stringPiano spectrogramTouching the string at a node after plucking`Natural’ harmonics technique‘Natural’ Harmonics in MusicPitch and frequencyTerms IntroducedRecommended readingPhysics and MusicPHY103Approach for this classLecture 1Animations from http://physics.usask.ca/~hirose/ep225/animation/standing1/images/Linear 1D Wave equation describing waves on a guitar string has solutions that are traveling waves with speed Using this you can predict the pitch of a string and how it depends on string density and tension.However, if one tries to take into account other physical effects you get equations lacking simple solutions.What does Physics have to do with Music?1. Search for understanding of the natural worldQuantitative theory. Physics provides a framework./c T r=2. Method of Experimental EnquiryFor example: By experimenting with different kinds of strings you might better understand what affects the damping time, “warmth” of tone, and durability. Different scenarios and explanations can be tested via experiment.3. Source of ideas on how to vary the way we make/record music. Yucatan Brown Jay, copyright Daniel J. Mennill 1999 this is an mp34. Hobby for physicists, musicians, craftsmen, engineers, psychologists and biologistsBird songs and spectra thanks to: Daniel J. Mennill 1999 Montezuma Oropendola TimePitchDarker is higher volume5. Physics of Perception: how does the ear and brain work? Physics and Music together encompass a wide range of intertwined scientific disciplines and methods of enquiryOpening song from anime series6. A way to find beauty in physics and math•If physics can explain something musical then physics is beautiful. Pythagoras showed that musical intervals were related to rational numbers (like 2/3) •If a physical model resembles an acoustic system it’s more beautiful and therefore better. (Kepler)•A way to explain physics. A way to catch people’s interest. (Era of classical and modern physics). Deep connections between ideas of quantum mechanics and harmonic analysis.from F Gafurio Theorica Musice 1492] [rep. Wittkower 1949.]Musical analogies in early astronomy and mathematics"The chief aim of all investigations of the external world should be to discover the rational order and harmony which has been imposed on it by God and which He revealed to us in the language of mathematics." Johannes Kepler (1571-1630) from Astronomis Nova de MotibusKepler and the Music of the SpheresIn his book “Harmonies of the World”“The heavenly motions are nothing but a continuous song for several voices, to be perceived by the intellect not by the ear; a music which through discordant tension through syncopations and cadenzas as it were progresses toward certain pre-designed six voiced cadences and thereby sets landmarks in the immeasurable flow of time.”The Birth of Quantum Mechanics“Would Kepler, the mystic who, like Pythagoras and Plato, tried to find and to enjoy the harmonics of the Cosmos, would he have been surprised the atomic physics had rediscovered the very same harmonies in the building stones of matter and this in even purer form? For the integral numbers in the original quantum theory display a greater harmonic consonance than even the star in the Pythagorean music of the spheres” --- Arnold Sommerfeld (1930)The Birth of Quantum MechanicsShroedinger equation is based on the wave equation. This combined with boundary conditions yields various modes of oscillation that depend on integers --- just like harmonics of a stringA resulting beautiful model for the quantization of the energy levels of the hydrogen atomA nice analogy to Pythagorean approach --- the beauty of nature reflected or matched by simple integral/mathematical modelsMusical analogies in modern physics1996, Astrophysical Journal, 471, 30, Hu, Wayne, & White, Martin, Acoustic Signatures in the Cosmic Microwave Background “We study the uniqueness and robustness of acoustic signatures in the cosmic microwave background by allowing for the possibility that they are generated by some as yet unknown source of gravitational perturbations. The acoustic pattern of peak locations and relative heights predicted by the standard inflationary cold dark matter model is essentially unique and its confirmation would have deep implications for the causal structure of the early universe.” August 2005 issue, Scientific American “Is the Universe Out of Tune? Like the discord of key instruments in a skillful orchestra quietly playing the wrong piece, mysterious discrepancies have arisen between theory and observations of the "music" of the cosmic microwave background. Either the measurements are wrong or the universe is stranger than we thought.” By Glenn D. Starkman and Dominik J. SchwarzPower spectrum of spatial temperature fluctuations of the cosmic microwave background (from Physics Today)Approach for this class•Exploration and search for understanding of natural world – the world of music•Exploration of physical concepts and explanations via experimentation•Demonstration and experimentation for fun•Develop skills we need to do interesting experiments and to understand acoustic systems•Understanding of musical instruments, how music is played and how we perceive it.•Instruments represent centuries of experimentation and design - can we understand some of the compromises involved in their design? We will be building instruments in the lab.Focus•Enquiry and Lab based. ------ This compliments other rich musical offerings on campus•Follow our interests and our hunches. What topics would most likely lead to new undiscovered results or original creations? •Tackle math/physics/engineering/computer skills sufficiently to allow us to investigate questions related to our interests.Syllabus•Harmonics and harmonic analysis•Spectra of musical sounds/ timbre•Resonances