PVC Flutes

an experiment in cheap instrument production

Hannah Rossman

Math 5

May 30th 2005

Method

• Tools• 3/4 inch PVC piping

• serrated knife or (preferably) hand saw

• tape measurer

• calculator

• permanent marker

• Method of Construction• piping cut to desired length with handsaw

• mouthpiece carved at calculated length

• finger holes carved at calculated lengths

Mathematics• Calculations

A FLUTElength 0.34 effective length 0.38 add 0.04As an open-open pipe

# in scale ideal f real f L=nC/2fA4 0 440 437 0.386363636 0.34636364B4 2 493.8833013 448 0.344210868 0.30421087C#5 4 554.365262 486 0.306657021 0.26665702D5 5 587.3295358 513 0.289445685 0.24944569E5 7 659.2551138 558 0.25786679 0.21786679F#5 9 739.9888454 590 0.229733193 0.18973319G#5 11 830.6093952 621 0.204669007 0.16466901A5 12 880 660 0.193181818 0.15318182

As an open-closed pipe L=(2n-1)C/2fA4 0 440 437 0.386363636 0.34636364A#4 1 466.1637615 448 0.364678712 0.32467871B4 2 493.8833013 486 0.344210868 0.30421087C5 3 523.2511306 513 0.324891797 0.2848918C#5 4 554.365262 558 0.306657021 0.26665702D5 5 587.3295358 590 0.289445685 0.24944569D#5 6 622.2539674 621 0.273200347 0.23320035E5 7 659.2551138 660 0.25786679 0.21786679

Obstacles

• Mouthpiece• Original mouthpiece too small. Widening the mouthpiece made it easier to play, also

made it possible to tune by adjusting position of the air source.

• Realizing the effective length• Real world calculations of pipe length must take distance to mouth into account

• Calculations inaccurate• Is the effective length changing? I noticed it was different for smaller pipes than larger, leading me to

believe it was altering throughout the flute. • Mathematical model fit better if flute was open-closed. Why?

• Difficult to play• Instrument is difficult to play. This became easier when I made the decision to close one end of the

pipe, less air required to make the flute sound.• It is made out of PVC. Total cost per flute- $1.25. Not too disappointed with sound quality

Analysis

• Sound quality• Problem of 2 modes being excited simultaneously• Hard to achieve a non-airy sound

• Pitch quality• Proceeding up the scale, notes get more and more flat.