Musical Mathematics

on the art and science of acoustic instruments


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Also available from the publisher at Chronicle Books, San Francisco.


20002018 Cristiano M.L. Forster
All rights reserved.


17 November 2003


Hi Katie,


In the last email you wrote, For science olympiad I need to build an instrument that plays two octaves from C3-C5 so I was thinking about making a system where one can play multiple notes on the same string like a guitar. What do you think about that?


Yes, you are right. The bridges of a canon play the same role as the fingers on the frets of a guitar: the bridges and fingers stop the strings at varying string lengths, which, in turn, produce tones of varying frequencies.


In the figure below, please note that the octave, C4, requires a bridge at length ratio 1/2, and the double octave, C5, requires a bridge at length ratio 1/4. Regarding the latter ratio, make sure that the sound hole is not near the 1/4-length location, otherwise the bridge would drop into the sound hole. 


It might be a good idea not to put a sound hole in the soundboard or top of the Little Canon. If you drill small holes into the front and back sides (like on my Harmonic/Melodic Canon and Bass Canon), then you can place the moveable bridges anywhere along the lengths of the strings between the left nut and the stationary bridge.


Finally, I would urge you to consider building a canon with 13 strings. If you leave the first string open (i.e., no bridge) and tune it to C3, this string would act as the first tone or tonic of a 12-tone scale. Then, if you place bridges under the remaining 12 strings, you would have a complete scale that would enable you to play a lot of songs. The advantage here is that you don't have to continuously slide a bunch of bridges around to play a melody. Of course, by sliding the bridges to different locations, you could also tune a lot of new scales and modes of your own creation.




Little Canon Design Considerations