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Simple acoustic theory is often quite inadequate to explain what really happens in musical instruments. Take organ pipes, for example. The sounding length differs from the physical length by the end correction, but this is frequency dependent (and the simplest accounts don't even mention that) and so the harmonics should be out of tune. Add phase locking to the account, and we see why the harmonics really are all in tune, unlike the nasty harmonics of a piano with its stiff strings. Now in simple terms, celestes and angelicas should sound the same. When tuning one pipe against another the beats don't tell you whether you are above or below pitch until you change the pitch slightly and observe whether the beat rates get faster or slower. So what are the extra factors which determine any difference in sound between the two?