h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

http://www.h2g2.com/A473528: Brass instruments, tuning and harmonics.

Having read the Entry about low brass instruments, I felt that the Guide was in need of a more generalized view into the world of brass instruments, with a focus in the correlations between tube length, bore, harmonics, tuning, and the more theoretical background of the brass family.

I'm sorry if it's not too easy to understand (esp. the calculations), and I'd appreciate any help to make this Entry an easier read without loosing too much information.

Gnomon gave me some important hints to improve my Entry. Please have a look at it again.

I disagree with Jeremy on the fact stated in his entry, that the length of the ideal pipe is equal to the wavelength of the sound produced. I say that the length of the pipe is equal to half the wavelength of the sound produced. I have done experiments to prove this.

Other than that, this is a good entry. There are one or two spelling mistakes, but the content is good.

Gnomon, I have to admit that you are right. Shame on me.

I did not consider the difference between open pipes and closed pipes.

If you have an open pipe, the harmonics are in a ratio 1:2:3:4: ... whereas in a closed pipe it's 1:3:5:7: ...

I'll have to correct my entry. Thank you for not giving in to my obstinacy.

Closed pipes do not occur often in brass instruments. They do happen from time to time in woodwinds: the clarinet, the chalumeau, the crumhorn, the pan-pipe. When I finally get around to doing an article on woodwinds, I will be sure to mention them.

My Entry has been worked at again. I have found some graphics on the subject of tubelength / wavelength, but I don't know how to include them into the Entry. Just in case it is picked, I could provide a link as a suggestion to the Graphics Department.

Hi Jeremy! I see that I've persuaded you that a tube open at both ends has a wavelength twice that of the tube length. Now I have to persuade you that a tube closed at one end supports a standing wave with a wavelength four times the tube length! This is a fact. Since it does not apply to any brass instruments, I suggest you omit your comment about half-open pipes. I will mention it in my article on Woodwind (which I *am* working on), because it applies to clarinets and pan pipes.

Two other minor points:

1. The correct spelling of "cornet" has only one "t". There was a different instrument called a cornett in times gone by. This instrument was also sometimes called a cornetto. It was a wooden brass instrument with finger holes. It was often used as the top part in a four part ensemble, with three sackbuts (mediaeval trombones).

2. The formula,

(1000 ft/s divided by 5 ft) x 2 = 100 Hz

No it doesn't! You should divide by 2, not multiply.

Thanks Gnomon, for your help.

You're far worse than any of my teachers ever was .... and I really appreciate what you do for me.

I think I'll omit the whole wavelength-tubelength thing and set my focus more on the harmonics and tuning problem.

SCOUTS ATTENTION PLEASE:
This Entry is under construction again. Please do not pick it for inclusion to the Guide!!

Gnomon, I did some muck out on the topic of tubelength / wavelength. I hope everything is clearer now, and I would appreciate an expert's look at the Entry again.

Jeremy,

There are still two problems where it is not exactly right:

You have "double tubelength = double wavelength". This should be "double tubelength = wavelength".

You have "(1000 ft/sec divided by 5 ft) x 2 = 100 Hz". It should be "(1000 ft/sec divided by 5 ft) / 2 = 100 Hz".

In general, you are right with all your statements, but the whole thing is beginning to get very confusing. I think it is worth having information like this in the guide as a reference, but I really don't think that the whole thing makes a very good entry. In order to get something complete and accurate, you are sacrificing readability. But being easy to read is what good guide entries are all about.

Please move this Entry from the PR to A473528.

I withdraw this Entry from the Peer Review. Gnomon has convinced me that it's no longer readable, and I have to admit that he is right. I'll continue working on it, perhaps I'll split it into two seperate Entries (Brass Instruments <-> Tuning and Harmonics).

Thank you for all you Help.

That's the problem with rather 'exotic' entries which the Guide so desperately wants, but neglects to foster... how many instrument builders do we have around here?

Oh, and I might be a little late here, but if you plan on dividing this entry... (DO it!) "Tuning and Harmonics" perhaps, and "Brass Instruments" the other.

Anyway, now that I've finally quit procrastinating to read this entry:

Para "Third question":
"... a 100 hz tone and a 200 hz tone have an interval of exactly one octave and sound absolutely harmonic." I suggest adding: "In fact, that is precisely how an octave is defined: as a factor of 2 between two tones. The 'octo' there comes in because this frequency span is divided into /eight/ natural tones in our musical system" (if the latter is correct).


Para "What happens if we build one octave from identical intervals?"
Could you consider a shortcut to this paragraph... something like
'Adding a major third is equal to a factor of 5/4. Doing this three times yields 5*5*5/4/4/4, or 125/64 which is slightly /less/ than 2. For example 110*125/64 yields 214.84375, but not 220. Unfortunately our ears are ....'

In the Table following this: the column 'natural frequency' should explain what 'natural' is, and how the numbers 132, 137.5 ... were constructed (Ok, 132/100 = 6/5, but it's missing).

h2g2 puts the dimension immediately behind the value: 1,000ft/s not 1,000 ft/sec (and 's' rather than 'sec', that's the SI unit of time)
Hertz is 'Hz', not 'hz'.

Footnote 1: lentgh --> length

These are all minor things, Jeremy! You've got a real big mistake in footnote 1!

There /are/ bigger instruments! Disaster Area has them!


Apart from that ugly mistake : Very comprehensive article!

Bossel,

thanks for your support.

I will, however, propose to move this thread to the Writing Workshop. I'll have to work on it, but I have no idea when this work will be finished.

Perhaps I'll re-submit it later.

Well, I'll wait...
And see: this threat /is/ already in the Writing Workshop!

I would like to bring up one minor nitpick about the differences re: flugelhorn/cornet vs. trumpet. It is not just that the bore is wider, but that it continues to widen conically on the flug/cornet, whereas the trumpet retains the same bore size until the flare begins.

all the best.

Author has elvised - Flea Market?

I'll take this one on if it goes into the Flea Market.

I'll add this to my list.