Consider the "law" that a clarinet puts out only odd harmonics.
This law is based on:
1) Physics: clarinet is a tube closed on one end; such tubes
put out only odd harmonics; QED.
2) Authority: the text says in several places that clarinets
put out only odd harmonics.
3) Observation: musicians can tell the difference -- just by
listening -- and if a so-called clarinet put out even harmonics
it would sound wrong.
The only problem is, quantitative data doesn't follow this law.
This is true even for the lowest note the instrument can play,
i.e. all tone-holes closed. http://www.phys.unsw.edu.au/music/clarinet/E3.html
To roughly describe the data:
a) when played pianissimo, you get the fundamental and the 3rd
harmonic, and maybe a little bit of 2nd harmonic, and then not
much else above the noise floor.
This makes a mockery of the textbook request to describe the
"next three" harmonics.
b) when played mezzopiano or forte, the 2nd harmonic is pretty
weak ... but the other harmonics are up for grabs.
1) How are you going to grade a test when the student says a
clarinet puts out even harmonics? Mark it wrong??
2) What is the point of teaching the "law" about no even harmonics
in a clarinet?
a) If you think this is an important topic, why are we saying
wrong things about something so important?
b) If you think this is not an important topic, why are we
covering it at all?
Here's my best guess: First: the textbook author claims it is
an important application, but it isn't really. Sure, tone color
is important, but it's determined by a lot of factors, many of
which are more important than the alleged absence of even harmonics.
Second: Since it isn't really important, the author can get the
facts wrong, and almost nobody will bother to call him on it.
It seems like a perfect match: wrong physics coupled with a false
claim of importance.
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Small constructive suggestion: When writing a textbook, don't just
rely on beautiful "artist's conception" diagrams; put in some real
data. If somebody had looked at *even one* real power spectrum,
this whole chapter in Glencoe would have been written differently.
Writing a book is hard, but on the scale of things, tracking down
some illustrative real data is not the hard part.
As the saying goes:
"When all else fails, look at the data."
Similarly: I know a lot of folks on this list have a hand in selecting
books for adoption. Simple suggestion: Look for real data.