So I played trombone for 7 years or so back in grade school. For those who don’t know how trombones work, you can play a B-flat with the slide all the way in (known as first position). Bend the note up a little, and it’ll jump up to an F, then a high B-flat (this is generally how most brass instruments work). Bend the note down from the original B-flat, and you go all the way down a full octave to a low B-flat, skipping the F.
So what causes the instrument to skip notes and “lock” to a different one? If you buzz through just the mouthpiece, it doesn’t do this.
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Instruments based on a length of tube resonate at some lowest note, but you can also get them to resonate at some whole multiple: 2, 3, 4, 5, … The first factor is 2 which is exactly an octave in music. Going from 2 up to 3 is a factor of 3/2, which is a perfect fifth or 7 semitones. The factor of 4 is two doublings, so two octaves above where you started and a major fourth or 5 semitones up. Now 5 is 5/4 above that which is a major third or 4 semitones. 6 is an octave above 3 which is also a step up of 3 semitones or a minor third.
Because the ratio between consecutive whole numbers gets progressively smaller, the number of notes skipped reduces with each new harmonic. Music pitches are all ratios; notes at simple whole ratios sound good to us.
what you are discovering is called harmonics. each note is a standing wave vibration in the length of the instrument.
sound waves have pitch or note that is determined by their frequency. the number of wavelengths that fit inside the trombone from the mouthpiece to the bell has to be an odd integer multiple of the natural frequency to make a sound. for each additional wavelength in the instrument the note produced jumps or bends up to the next higher frequency note.
“ A trombone produces resonant standing waves at a fundamental frequency (the lowest resonant frequency of a vibrating object) and then at odd harmonics (integer multiples of the fundamental frequency). The air at the closed end must stay in place, which forms a node. Open ended air columns can produce all harmonics because they are not restricted to having a node at one end.”
https://prezi.com/w3c0pgajn_wm/the-physics-of-the-trombone/?frame=9d6b3c54170bab63b5436867f5439b9627567267
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