example: if the air column of a horn is 2.6 m long
how much additional length is needed to lower
the pitch by one semitone? by 3 semitones?
by 4 semitones?
answer:
one semitone: lower pitch requires larger length (inverse proportion)
new length = old length times semitone ratio
new length = 260cmx1.0595 = 275.5cm.
additional length needed = 275.5-260.0 = 15.5cm
three semitones: new length = 260cmx (1.0595)3= 309.2cm
additional length needed = 309.2-260.0 = 49.2cm
four semitones: 260cmx (1.0595)4= 327.6cm
additional length needed = 327.6-260.0 = 67.6cm
Note: the way the horn is used, when the player want to lower
the pitch by 4 semitones he adds 15.5cm + 49.2 cm=64.7 cm
but should be 67.6 for correct tuning! He is off 3cm/327cm
or about 1%, which is 1/6 of a semitone. Not perfect but not bad.
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