Fourier Spectra of Trombones

Below are Fourier transforms of a low Bb played on various trombones and other low brass instruments.

The low Bb was recorded on the built-in microphone of an iMac using GarageBand. The soundwave was exported in mp3 format at a sampling rate of 44,100 Hz and transformed by SOX into a dat file at a sampling rate of 4410 Hz. The dat file was imported into Excel and a Fourier transform was performed on 4096 points. Based on the sampling rate and the number of points used, the resolution of the transformed spectrum was approximately 1.077 Hz, and the Nyquist frequency (the highest frequency that could be resolved) was 2205 Hz.

Since the recording system is admittedly weak, the absolute magnitudes of the peaks are likely inaccurate. However all recordings presented here used the same equipment, so comparisons between spectra may be useful.

The first eight peaks that appear, going from left to right, correspond to the following pitches:

  1. Low Bb (~116 Hz)
  2. Middle Bb
  3. High F
  4. High Bb
  5. Double High D
  6. Double High F
  7. Double High Ab (~)
  8. Double High Bb

 The instruments used, in order of the graphs below, were:

  • Blessing Scholastic Trombone with 0.500" bore, 8" bell and 12C mouthpiece.
  • Bach 36 Trombone with 0.525" bore, 8" bell and 7C mouthpiece.
  • Blessing B-88-O Trombone with 0.547" bore,  8.5" bell and 6.5AL mouthpiece.
  • Maestro Bass Trombone with 0.562" bore, 9.5" bell and 1.5G mouthpiece.
  • Besson Sovereign Baritone with 9.5" bell and Wick 6BS mouthpiece.
  • Allora Euphonium with 12" bell and 6.5AL mouthpiece.
  • Meinl Melton Spezial Eb Tuba with 15" bell and Canadian Brass Arnold Jacob mouthpiece.

The trombones, which are cylindrical, tend to have more high-frequency harmonics than the euphonium or tuba, which are conical.  As the trombones get bigger the high frequencies are also diminished.

Surprisingly (to me) the baritone looks more like a conical instrument than a cylindrical one. I suppose this is to be expected from a horn that has a small bore mouthpiece, but flares to a 9.5" bell.