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Understanding Brass Instruments: Acoustics and Tuning Techniques for Musicians

This article delves into the acoustics of brass instruments, focusing on lip-driven oscillations and the adjustment of natural modes through mouthpieces and bells. It covers how to play a chromatic scale using slides and valves and discusses the pressure distribution for different modes of brass instruments. Additionally, it clarifies common misconceptions about the tuning of brass instruments and presents practical methods for bridging gaps in the natural scale, including using slide positions on trombones and valves on trumpets.

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Understanding Brass Instruments: Acoustics and Tuning Techniques for Musicians

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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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