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Completing the Cone

Investigate the conjecture that the volume of a saxophone mouthpiece completes the volume of the conical instrument.
by

Walter Martin

on 18 January 2016

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Transcript of Completing the Cone

Completing the Cone
Fact or Fallacy
1) Get the horn in tune.
2) Measure how much of the neck is inserted into the mouthpiece.
3) Measure the volume of the neck.
4) Measure the volume of the mouthpiece.
5) Measure the neck radii.
6) Calculate the theoretical mouthpiece volume.
measured volume = 24ml
24.0 - 6.86 = 17.1
vs
a theoretical 14.9
Mathematical Analysis
Experimental Procedure
Data Analysis
Mathematical Analysis
Experimental Procedure
This is our saxophone
Data Analysis
7) Calculate the effective mouthpiece volume.
1 2 3 4 5
Median
(1 + 2 + 3 + 4 + 5)/5
Mean or Average
A Whirlwind Tour of Statistics
Boxplot
Bar #1
Salary Survey
patrons - 48
median - $43,500
mean - $42,140
Bar #2
patrons - 52
median - $42,950
mean - $5,750,019,786
Problems with the analysis
Reliance on individual player's skill in tuning (Maybe alto and tenor players always play sharp?)
Small sample size
Measurement resolution (scale only measured to the nearest gram)
Faulty geometric assumptions
Full transcript