Difference in succesive frequencies in open pipe
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If you start with the same fundamental frequency for both open and closed, say f0f0, you'll notice that for the Open pipe, the harmonics are:
f0,2f0,3f0,...f0,2f0,3f0,...
While for the closed,
f0,3f0,5f0,...f0,3f0,5f0,...
And you'll notice that the closed pipe has greater spacing of harmonics compared to the open pipe.
That is for a given single note. You have to lower the note of the closed pipe by 12f012f0 (1 octave) to produce the same spacing of harmonics as the open pipe
f0,2f0,3f0,...f0,2f0,3f0,...
While for the closed,
f0,3f0,5f0,...f0,3f0,5f0,...
And you'll notice that the closed pipe has greater spacing of harmonics compared to the open pipe.
That is for a given single note. You have to lower the note of the closed pipe by 12f012f0 (1 octave) to produce the same spacing of harmonics as the open pipe
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