Physics 341- Spring 2012

Physics of Music

Notes:

Midterm:

Reminder

Tutorials

Note: I send emails to the class vi the registrar's email lists for this course. Please make sure that you have registered your email with the university. Unfortunately some service providers see this as an indication that this is spam and dumps the mail into a junk, or spam, or other labeled folder. I do not know how to get around this as I do not want to give everyone everyone else's email, I do not want to enter all 50 separate email addresses as separate emails, but I want people to get them. Please remember to look into your junk/spam/... folder as well if you do not get the emails for this class. Note that I have now sent at least one email.

Topics

• Oscillation-- mass, stiffness, damping, externally driven oscillation, frequency, period, amplitude
• Addition of sound waves, beating.
• Frequency vs Pitch-- Octave, scales, intervals, frequency standard
• Amplitude and Energy vs Loudness-- dB, Hearing damage.
• Sound and sound waves
• The ear, structure and operation
• Addition of sound waves, Harmonics.
• Temperament and Tunings-- Harmonic melding, temperaments.
• Sound Generation and efficiency of vibration to generate sound in air. Loudspeakers
• Plucked and struck instruments
• Continuous sound instrument-- Clarinet and other wood reed instruments
• Lip Reeds and Trumpet family
• Bowed Instruments, Bow string interaction, sound box, Wolf tones.
• Voice-- Formants and vowels, speech, vowel shifts,singers' formants
• Limitations of "Physics and Music", psychoacoustics.

Notes-- various reading throughout the year.

• Harmonic Oscillator, frequency, Q
• Phase comparison of oscillations
• Modes of vibration
• Pitch -Frequency relation ~ (Correction to name of note a fifth above A5 as E6- Jan 29/09)
• This site by Dolmetsch gives a lot of history of the naming of pitches, including the Do(ut)-re-me..., clefs, pitch and octave labels.
• dB
• Noise notes
• UK Noise regulations
• Various Weighting curves for noise audibility
• Hearing Damage
• Mike Hoff's visiting lectures (From 2012-- I leave these here as they may be useful for later years as well.)
  • The Ear
  • Room Acoustics
• Fourier Transforms Notes
• Fourier Analysis of Guitar Pluck
• Temperaments
• Just tuning
  • Ross Duffin on the use of Just Temperament in Renaissance music. He is almost as opinionated as I am. See especially:
    Benedetti's Puzzle for an example where a succession of four chords repeated each tuned to Just tuning, keeps rising in pitch because the just minor third is very sharp compared with the equal tempered or Pythagorian minor third. Ie, if all perfect fourth and fifth intervals, and the minor third are kept at true just ratios, the successive runs of these chords rise in pitch by about 1/6 of a semitone each time through.
    Is Just tuning possible> which demonstrates the Hilliard Ensemble singing "The Lamentations of Jeremiah" in pure Just tuning. Note the purity of the especially the last major third chord. (E2-E3-G4#-B4-E5)
  • Ross Duffin has a large collection of articles and examples of Just tuning, of the various temperaments and of the effects of these on Music tradition. His article on Valotti-Young pitches the idea that other temperaments might have been used and be useful for late Baroque and early Classical music. The examples he give are worth the the cost of entry.
• Radiation and radiation efficiency
• Speaker Design ~ ftp
• Negative Damping
• Simulation of pressure and velocity inside a reed instrument (Java is needed)
• Brief Note on Instruments This is an email I sent to Mike Hoff in 2005 reviewing what I covered toward the end of the course on the way that the various instruments operate. These do not cover everything I said in 10 lectures, rather they are a brief overview of the material. See the class notes or the text books for a more in depth coverage of all these materials. These notes have not been edited or proof read, and so they are very rough, but I am posting them here in the hope they may be helpful. If they are not helpful, ignore them.
• Tuva Throat Singing Spectrum
• Joe Wolfe of the University of New South Wales Australia has a great web site covering some of the topics in this course. In particular he has pages on verious instruments and how they work. At times he goes into more detail than I do, at times less. He aslo has some Flash animations which may make some of the concepts clearer.
  • Clarinet
  • Saxaphone
  • Flute
  • Violin
  • Voice
  • Brass
• Sound recording of cracking of ice from within the ice. These are caused by the fact that for the transverse vibrations of ice, the velocity of the vibration of different frequencies is very different. Thus the further away the cracking is, the more the frequencies of the sound of that cracking are spread out in time. High frequencies travel faster than the low frequencies do and result in the dropping sounds.

• A series of articles on the tuning of guitars, and the difficulties of making them play an equal tempered scale.
• Large selection of resources on the clarinet . The physics is at best pretty rudimentary on these pages.

Lectures:

1. Intro, Simple Harmonic oscillator; R2; B3.3+6.1
   • Sine waves,Period, frequency, amplitude, phase
2. SHO, damping, resonance;R2; B4.8+10.1-3+10.6
3. Complex systems, Modes & nodes; R2;B6
4. Freq-Pitch;R7;B5+15.3-4
5. Amplitude-dB; R6;B13.2+13.8
   • Ear damage
6. Fourier Transform (Fundamentals and Harmonics)
7. Temperaments
8. Sound, Sound transmission
9. Ear, Hearing, and PsychoAcoustics
10. Instruments and how they make their sounds
    • Speakers and Efficiency
    • Drums, and other percussion.
    • Clarinet and positive feedback
    • Trumpet and Lip Reed-- phase shift
    • Flute and air reed
    • Violin and bow feedback
    • Voice
11. Tuva Singit Singing
12. Octave equivalence

Assignments and Solutions

• Install Mozilla. This will also short circuit the various security holes in Internet Explorer. However there has been at least one report that this can still result in beheading.
• left click on the menu bar Tools->Internet Options. On that small page click the button "Delete Files" ( which will remove the stored files it has stuck onto your computer, and will always show those instead of retrying from the web site.) Then try the link again. The problem is not consistant. A file which displays fine one day, will have trouble the next.
• Right click the link and choose save target to disk. This may also not work. It seems IE can truncate random amounts of the beginning of the pdf file
• I used to also supply an ftp version of the pdf files which you could download and view with Acrobat or whatever. However since I have not heard of this problem in the past few years, I no longer supply the ftp files. If you have this problem, please let me know, and I will reinstitute the ftp files.
• If all else fails let me know and I will make available a printed version from the rack outside my office.

Math Miniquiz

Assignments

• Assignment 1 Due next Wed Jan 19
• Assignment 2 Due next Fri Jan 28
• Assignment 3 Due next Mon Feb 6 Solutions will be posted at 5PM Wed Feb 8 for the midterm So If you are haning in late, do so before that time.
• Assignment 4 Due Mon Feb 27
• Midterm Due Mon Feb 27 by 5:00PM

Solutions

• Assignment 1 Solution
• Assignment 2 Solution
• Assignment 3 Solutions Corrected Feb 12. In question 3, the maximum times for the two cases were wrong-- I made mistakes in subtracting, and in dividing by two six times.

Readings (Whole Year )