twice as sharp as the third) the eleventh and twenty-second are 49¢ flat (i.e. In these fixed reference positions, compared to their nearest (in frequency) equitempered tones, the third, sixth, twelfth, and twenty-fourth natural harmonics are all 2¢ sharp the fifth, tenth, and twentieth are all 14¢ flat the seventh and fourteenth are 31¢ flat the ninth and eighteenth are 4¢ sharp (i.e. The reference positions correspond to fixed positions for natural harmonics one, two, four, eight, and sixteen. We must add seven new (different) positions for each odd harmonic above that. Mark McDunn’s “The 51 Positions” chart goes from the first natural harmonic (pedal) up to the sixteenth harmonic. When they get note-wise close there is just not enough room to display everything on paper, but the mind's eye can zoom in on the detail to follow the paths. And most charts do not well handle the compression of partials as they go up. The ear can then recognize in aural context there are position paths available for play, not just notes.Īnyway, this chart does not support that kind of thing. So melody becomes a path of connected positions in the chart. (Lower in his visual model is higher in pitch-don't get that part.)Īnyway, the internal visual model allows one to think visually about lines, and Greg does that in his chart. The best representation of such chart I have seen is in Greg Waits' book, but for some reason his internal model is upside down relative to mine. What I mean by internal model is an internal visualization of the position chart. This chart does not align with my internal model, though it seems pretty accurate for someone with a horn that behaves in that way on his own face.

Trombone note chart and positions