Although conventional slide-position charts give useful basic information, the use of staff notation is cumbersome, and this means that precise quantitative locations of respective slide extensions for equitempered tones (and differences between positions of equitempered tones on higher harmonics and reference positions based on the first harmonic) are not available. Perhaps even more importantly, precise slide-extension relationships between different equitempered tones (or the same tone) on different harmonics are not immediately obvious. The ETSP chart is a precise graphical portrayal of Equitempered Tones (vertical axis) versus Slide Position (horizontal axis)--for a theoretical prototype trombone in which the harmonics follow the full harmonic series: 1 x, 2 x, 3 x, . . . a fundamental frequency.

The following is the ETSP Chart for a Bb tenor trombone. For reference, <I>lines</I> of the treble and bass clefs are shown. Number of semitones above Bb1 is indicated along the right-hand boundary. Vertical lines show reference positions. The shaded regions are bounded by shortest slide positions (orange) and longest positions (blue) for a chromatic scale. Where the boundaries of the two colours touch, there are no alternate positions. The unshaded regions show, at a glance, where alternate positions are available. Heavy lines sloping down to the right show available tones along each harmonic. Light solid lines show semitone increments between adjacent harmonics; dashed lines show whole-tone increments between adjacent harmonics. Generally speaking, more facile slide technique corresponds to regions where the dashed lines are steeper. Note that any tone of the chromatic scale can be played above the fourth harmonic in any three adjacent slide positions. Also note the tenor gap: five missing equitempered tones between E2 and Bb1.

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Thanks