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Two mechanisms producing sound of a bowed string: Stick and slip delivers periodic energy

Two mechanisms producing sound of a bowed string: Stick and slip delivers periodic energy Reflections off the end purify sound to be musical (and pitch is determined by L and v – which in turn is determined by tension T) The result is periodic, therefore harmonic sound.

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Two mechanisms producing sound of a bowed string: Stick and slip delivers periodic energy

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  1. Two mechanisms producing sound of a bowed string: • Stick and slip delivers periodic energy • Reflections off the end purify sound to be musical (and pitch is determined by L and v – which in turn is determined by tension T) • The result is periodic, therefore harmonic sound.

  2. For an ideal string: fn = n f1 For a real string: fn = n.f1.[1+(n2-1)A] where A ~ r4 E / TL2 (p.313) So what is the difference between harpsichord, an upright, grand and baby grand piano? However: the sound of a bowed string is periodic, therefore the spectrum is harmonic in spite of inharmonicity of the partials ! Similarly for pipes: the end corrections are (not surprisingly) frequency-dependent, so the “passive” spectrum is inharmonic. But the two mechanisms which cooperate to produce sound create, again, a periodic sound => spectrum is harmonic. So what is the difference between the sound of a pipe with large diameter, compared to small diameter?

  3. Open/open, closed/closed (or cone!): fn = n f1, f1 = v/2L, n=1,2,3,4,… Open closed: fn = n f1, f1 = v/4L, n=1,3,5,7,… Notes: what is v? For strings, open end is not practical For pipes, closed/closed is bizarre (but open/open is identical, and a question of definition ..)

  4. Inharmonicity of piano strings requires the technician to make adjustments, in order to prevents octaves from beating. What seems strange about these results?

  5. “Quality” of the “musical” interval as function of f2/f1.

  6. A suspicious “confusion table” in musical instruments recognition test, when the initial transients are removed. Why is it suspicious?

  7. Reeds: “hard”: frequency determined by the reed (organ, harmonica, “vocal chords”) “soft”: frequency determined by the timing of reflections (clarinet, oboe, saxophone, …. ) So: what happens when the temperature in the church increases by 10 C? (hint: about 2/3 of the stops are flute-like, 1/3 have reeds)

  8. So: at what musical interval does the clarinet overblow? And what about a recorder? Flute? And what about an oboe?

  9. Formants: broad resonances modulating the spectrum

  10. So: what happens when I inhale Helium ? (hint: speed of sound in air/He = 340/970 m/s )

  11. Difference tones: Nonlinearity somewhere in the chain (production/propagation/perception) Produces, from initial f1 and f2, sounds with 2f1, 3f1, … and also (f1-f2), (f1+f2) …. The sound with 2f, 3f etc. is called “harmonic distortion” The sound with (f1-f2) is called the “difference tone” – it has nothing to do with beats! A (bad: why) example of musical use of the difference tones Spectacular use of difference tones: what if you could not hear the two original tones? Make them ultrasound, say 100,000 Hz and 101,000 Hz …. And modulate one of them by speech/music

  12. Physics of the Pipe organ: • Pipes sit in holes of the channels supplying air if a stop is pulled. • The valve at the foot of the pipe opens when the appropriate key is pushed.

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