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Physics 371 April 9, 2002

Physics 371 April 9, 2002. Acoustics for Musicians. Brass Instruments lip-driven oscillations (feedback) adjustment of natural modes mouthpiece and bell playing a chromatic scale: slides and valves. pressure distribution for different modes.

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Physics 371 April 9, 2002

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  1. Physics 371 April 9, 2002 Acoustics for Musicians • Brass Instruments • lip-driven oscillations (feedback) • adjustment of natural modes • mouthpiece and bell • playing a chromatic scale: • slides and valves

  2. pressure distribution for different modes

  3. adjusting the natural modes of a brass instrument f (a) (b) (c) (a) natural mode frequencies of a cylindrical tube closed at one end; (b) upper shift of frequencies of the lower modes caused by replacing part of the tube by a bell; (c) downward shift of the higher modes caused by adding a mouth piece. it’s a misconception to think of it as an open pipe!

  4. for a periodic excitation, the partials are by necessity exact multiples of the fundamental x x x but misconception: brass intruments play in JUST tuning table on p. 267of Backus shows that e.g. 8th resonance is as much as 54 cent off

  5. Tuba players have a sense of humor about their instrument...... note: Tuba has a long conical section

  6. a home-built tuba Tuba reminder: conical horn has same modes as OPEN pipe f0, 2f0, 3f0,4f0, for trumpet, pedestal note is out of tune, but tuba has a larger conical section than a trumpet or French horn so that pedestal note (lowest mode) is more nearly in tune

  7. note: if the conical section is nearly 50% of the horn length, the pedestal tone is in tune (Tuba)

  8. Playing a chromatic scale (sequence of half-steps): one method: the slide (trombone) to bridge the gap from mode 2 to mode 3 (a fifth) requires 7 slide positions Bb-A-Ab-G-Gb-F-E how long should I make the trombone if I can extend arm by 0.5 m? Answ: no longer than 3 m when slide is extended -> 2m for pos 1

  9. another method: valves to add length of tubing entire scale with only three valves - how? Trumpet French Horn

  10. example of a piston valve: valve depressed adds more length (lowers pitch)

  11. need to bridge the gaps in the natural scale: if first mode is not used - biggest gap is FIFTH (1) 2 3 4 5 6 7 8 9 10 fifth fourth major minor third third # semitones: 7 5 4 3 lower pitch 1 semitone by adding length l1 to original length lo 2 l2 3 l3 4 l1 +l3 5 l2 +l3 6 l1+l2 +l3

  12. problem: the lengths do not add up properly! example: take trumpet of length 137 cm lower pitch by added # cm new length (cm) needed: 1 137x1.059... = 145.1 8.1 2 137x(1.059..)2 = 153.8 16.8 3 137x(1.059..)3 = 162.9 25.9 4 137x(1.059..)4 = 172.6 35.7 but 8.1+25.9 = 34.0 off 1.7cm/172cm = 1% 5 137x(1.059..)5 = 182.9 6 137x(1.059..)6 = 7 solution: thumb slide or add more valves

  13. Schematic airflow through a French horn: F horn on top, Bb horn on the bottom. Each numbered valve pair is operated by a single lever

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