I understand that only odd harmonics (1st, 3rd, 5th, 7th etc.) can be formed from a closed-open pipe such as a clarinet. So (from my physics book) why in this graph of harmonics of the waveform of a frequency produced by a clarinet does it show odd & even harmonics?

 

Any note can be produced from a length of pipe such as a clarinet (Or in my case, saxophone)

The note depends on the distance between the reed and the nearest open hole.

If I play a middle C. there's about six inches of pipe in operation between the reed and the hole

The 1st, 3rd and 5th denote musical terms which are more useful and easier to understand from the musicians point of view (Rather than writing the actual frequencies or ratios in full.

the 1st 3rd and 5th can be any number of frequencies, depending on the tuning and which scale you're using.

e.g. in C major, the 1st 3rd and 5th would be

C, E and G or

261Hz, 327Hz and 392Hz or

1:1, 81:64, 3:2

 

In F major they would be

F, A and C, or

359Hz, 392Hz and 523Hz or

1:1, 81:64, 3:2

 

(Notice how the 1st and fifth are much simpler ratios, they exist in every musical culture)

 

I've added this image below to illustrate the relationships between notes

Many thanks for your informative reply, I'll study it carefully. Can I just ask what the 'cents' axis represents?

 

Thanks

The 'cents' axis represents the musical scale, which is divided into 1200 cents.

There are 100 cents between each semitone.

Notice that each of the markers (1200, 2400, 3600 & 4800) are each marked underneath each 'C' note. They are evenly spaced on the Cents axis.

Each time we go up an octave, we double the frequency, giving us the exponential curve illustrated in the graph.

Each vertical dotted line represents a key on a piano keyboard. In the graph, only the white keys are illustrated by dots.