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Music, Superposition and Chords

Music, Superposition and Chords. Physics 11. Chromatic Scale. The chromatic scale (A, A#, B, C, C#, D, D#, E, F, F#, G, G#) has been around for centuries and the note frequencies can be determined mathematically

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Music, Superposition and Chords

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  1. Music, Superposition and Chords Physics 11

  2. Chromatic Scale • The chromatic scale (A, A#, B, C, C#, D, D#, E, F, F#, G, G#) has been around for centuries and the note frequencies can be determined mathematically • Each semitone is represented by 100 cents and provided a root frequency, the remaining frequencies can be determined

  3. Chromatic Scale • Determine the notes of one full octave of the chromatic scale, using f0=440Hz and c=0, 100, 200, …, 1200 • Assuming the speed of sound to be 343m/s, determine the angular frequency and wavenumber for each frequency

  4. Chromatic Scale

  5. Basic Music Theory • A major chord is constructed with a root note (c = 0), major third (c = 400) and perfect fifth (c = 700) • A minor chord is constructed with a root note (c = 0), minor third (c = 300) and perfect fifth (c = 700) • The difference between the major third and minor third results in more destructive interference

  6. Major Chord

  7. Minor Chord

  8. Instruments • Why does a note played on a piano sound different from the same note played on a flute? On a guitar? • This is because while the primary frequency that is defined as the note, it is the harmonics that each instrument develops that is important to the overall sound

  9. Depending on the instrument, it may develop many different frequencies outside the first harmonic, or it may only establish a few Sound Spectra

  10. Open Ended Resonator • Open on both ends • 1st Harmonic is half a wavelength • 2nd Harmonic is a whole wavelength • 3rd Harmonic is one and a half wavelengths • Nodes are equal to the harmonic number plus one • Antinodes are equal to the harmonic number

  11. Closed Ended Resonator • Closed on one end • 1st Harmonic is one quarter of a wavelength • 2nd Harmonic is three quarters of a wavelength • 3rd Harmonic is five quarters of a wavelength • Nodes are equal to the harmonic number • Antinodes are equal to the harmonic number

  12. Speed of Sound • You have a tuning fork of frequency 440Hz and hold it to an open ended resonator. You hear resonance when the length is 37.5cm. What is the speed of sound? • You have the same tuning fork but now a closed ended resonator. This time the length is 19.1cm. What is the speed of sound?

  13. Problems • Page 421 • 16-20 • Page 427 • 17-23

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