slide positions for alto, tenor and bass trombones.
The harmonic, slide distance and slide
position are then given for the notes available on a slide
of normal length.
The harmonics are given as a number, with
"1" representing the pedal tone (a half-wavelength), "2"
representing the octave above (a full wavelength), etc.
Slide positions are calculated up through the 20th
harmonic. Harmonics may also be referred to as 'partials'
The slide position is given relative to standard positions of a Bb instrument played on a Bb harmonic. For instance, with an F attachment engaged, a low E would be played at a position equivalent to 2.32, i.e., a flat 2nd position for a standard Bb horn.
I've been taught that the high F harmonic is especially sharp, so positions must be noticeably extended. However this calculation indicates that the deviation is small. On the other hand the D harmonic just below is quite flat, and ideally the slide would need to be brought in by over a centimeter to achieve a well-tempered pitch.
For an explanation of some of these
calculations, see this
page. Thanks to Benny Leonard for suggestions on
improving this page.