Sounds of Music - Science of Music
November 29th, 2007
This page is dedicated to video clips and short text segments on everything from building simple musical instruments for Science Olympiad to “general musical science.”
The Science Olympiad segments are NOT intended as full fledged design projects. There are plenty of sites and resources already, and any students looking into this page should know this already. Instead these clips are intended to advise as to how to both “tweak” your design for better positioning in the competition and to give ideas of some of the theory behind your instruments. As a judge at regional, state and national level for this event, I have often found the students have blindly built their instrument from plans they found in a book or on the internet, and yet they have no real clue as to how it works. The Science Olympiad means for the students to learn both building skills AND the science behind them. The idea is to DESIGN a musical instrument. Simply building one from plans is not designing. The plans should serve as a starting point and then let your minds and imagination wander! Surprise and dazzle the judges!
There are four classes of instruments I have found in judging these contests.
1.) Metal chimes (hollow and solid tubes/bars)
2.) Wind columns (pan flutes and flutes or recorders)
3.) Strings (mostly guitars and violins)
4.) Percussion (”tuned” drums or Blue Man Group types of instruments)
I have rarely seen brasswinds or woodwinds (reed instruments as opposed to flutes).
One thing that is nice about the Sounds of Music competition of Science Olympiad is the fact that much of the math theory you encounter in designing is relatively simple. However, the complete understanding of any instrument is very complex. For example, drums seem like they should be simple but the math analysis that describes the various modes (types of standing waves that form in any resonating medium) involves Bessel functions in two dimensions! The more thorough your ability to discuss the theoretical aspects of your instrument, the better you will fare at the competitive level.
The first segment is on metal chimes.
Metal Chimes Theory - Part One:
At this point let’s discuss some design parameters. You could, of course, download some plans and build your tube chimes to someone else’s specs, but this can be risky. The materials constant can vary from one batch of electrical conduit to another (1/2 inch electrical conduit being the preferred material for most student chimes). You really need to measure the constant and then do your own calculations. The following video shows how to do this. Here is the math:
L = k/(f^.5)
There is a list of frequencies and the corresponding notes of a 12 tone chromatic scale provided at the bottom of this page, but this list can be found in may places. Once you get k per the video, pick your notes and calculate your lengths. You’re predicted notes and the notes that actually sound will be much more likely to be correct at the outset (without having to resort to trimming to fine tune them).
For more ideas on how to build the basic chimes, check out this article:
“Hollow Tube Chimes,” volume 36, April 1998, The Physics Teacher page 209
Now, you can be creative as to how to PLAY these. Certainly, most students rig them up as a glockenspiel of some sort or hanging chimes. I have see a few rig them to be played as a sort of keyboard instrument with elaborate “Rube-Goldberg” type lever apparatus to play them very quickly and easily. Again, dazzle the judges with your creativity.
Metal Chimes Theory Part Two - design and tuning:
The PVC Natural Trumpet
This is an easy instrument to build and understanding how it works involves some nice physics. As a judge at Science Olympiad, I must say that whenever a group can do something to set itself apart or stand out in some way, it catches my eye. Regardless of how nicely made a chime instrument is made the fact remains that a huge percentage of the students presenting will make chimes of some sort, along with strings and the odd percussion instrument. Over the years I’ve been judging, I have seen one copper trombone and one “bugle.” The copper trombone was excellent and that group would have won had they known their physics a bit better. Here is clip that is on my Online Lessons page for trumpeters about how a trumpet works. I hope some of you might be inspired to try making one.
The biggest problem students have with considering a brasswind is that they are indeed difficult to play if you have NEVER played a brasswind before. However, if someone on you S.O team DOES play trumpet or trombone, you are in a position to get the judges attention.
The touch part is making the tapered tubing and the mouthpiece.As per the video the thing only works well when you have some really good taper in the mouthpiece/leadpipe area and with the bell. Making the mouthpiece can be accomplished with a lathe and it doesn’t have to be metal. There are commercial moutpiece manufacturers actually selling wooden mouthpieces. You could ake one from wood, too. For that matter, the bell could be wood as well. Flaring PCV could be done with heat, but this could prove difficult. You’ll have to be creative here.
Beats and Multiphonics on a Bass Trumpet:
This is a minimally technical discussion about how beats frequencies work in both tuning and in the general sound of music. I use this to dovetail into the idea of mixing two notes together to get a third tones as is done with multiphonics on a bass trumpet. I demonstrate the so called Tartini tones or difference tones in which two notes a whole step apart are sounded at the same time and a third note three octaves under the lower note is clearly heard. The process in multiphonics is slightly different from the beats, in that it invloves mixing in a non-linear transfer function, but you can get the general idea of how this works from a visceral level.
There is one slight “faux pas” on the bass trumpet segment. I say that I’m going to play a low Bb, which is what I did. Then I say that I’m going to sing the G (hum it) above it. That was a Bb trumpeters transposition slip-up. In Bb speak, I play a low C and hum the G over it. An E above that is now audible. However, I started out NOT transposing, So if you’re keeping track, in concert pitch, the notes are Bb, F and D. When I slide the hummed note (announced as an A), I’m sliding up to a G concert. In the contemporary parlance, “my bad.”
Timbre and Harmonics and Pedal Tones as Applied to Trumpet and Flugelhorn:
This is a minimally technical discussion about why one instrument sounds different from another, even if playing the same note. While there is a brief flirtation with Fourier synthesis, this is a very qualitative discussion.
While this is a discussion revolving around brass winds, the ideas here are very useful to know for any potential tests and oral examinations that might occur during the course of the sounds of music competition.
Frequency Note List:
Frequencies are in HzC4 = 262…………………………….C5 = 523
C#4 = 277…………………………..C#5 = 554
D4 = 294…………………………….D5 = 587
D#4 = 311…………………………..D#5 = 622
E4 = 330…………………………….E5 = 659
F4 = 349…………………………….F5 = 698
F#4 = 370…………………………..F#5 = 740
G4 = 392…………………………….G5 = 784
G#4 = 415…………………………..G#5 = 831
A4 = 440…………………………….A5 = 880
A#4 = 466…………………………..A#5 = 932
B4 = 494…………………………….B5 = 988
C5 = 523…………………………….C6 = 1047
References, suggested reading and web sites:
Hyper Physics on Wave Theory and Acoustics - Concept Web
Books:
“The Science of Sound Second Edition” by Thomas Rossing published by Addison - Wesley copyright 1990
“The Acoustical Foundations of Music by John Backus published by WW Norton and Company - copyright 1977
