problem: the lengths do not add up properly!
example: take trumpet of length 137 cm
lower pitch by added # cm
new length (cm) needed:
1 137x1.059... = 145.1 8.1
2 137x(1.059..)2 = 153.8 16.8
3 137x(1.059..)3 = 162.9 25.9
4 137x(1.059..)4 = 172.6 35.7 but 8.1+25.9 = 34.0
off 1.7cm/172cm = 1%
5 137x(1.059..)5 = 182.9
6 137x(1.059..)6 =
7
solution: thumb slide or add more valves
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