PVC Pipe Instrument

Goal: To make a unique instrument out of PVC Pipe

Jim Pepper

Where We Left Off…

Pipes Completed

Frame Needed to be Built

Objective- Portability, Easy to Assemble

Legs and Lower Frame

More PVC

The Finished Project

Not screwed together, straps needed for support

Playable in the same way as a xylophone

New “mallet”- Wood with mouse pad that is looser

Off?

Note Desired FrequencyTube Length Estimate Freq Ratios Length Exact

Difference- Estimate to Exact

Ratios to Exact

C 130.81 48.27814196 49 48.25 0.028141962 0.721858038

C#/Db 138.59 45.61006386 46.2315 46.25 -0.639936143 0.621436143

D 146.83 43.0925475 43.659 43.23 -0.137452496 0.566452496

D#/Eb 155.56 40.71629114 41.1845 41 -0.283708858 0.468208858

E 164.81 38.47317365 38.8815 37.75 0.723173655 0.408326345

F 174.61 36.35595756 36.71 36 0.355957563 0.354042437

F#/Gb 185 34.35625 34.643 33.75 0.60625 0.28675

G 196 32.47018495 32.7075 32 0.470184949 0.237315051

G#/Ab 207.55 30.70498073 30.8455 31.5 -0.795019272 0.140519272

A 220 29.00980114 29.1305 28 1.009801136 0.120698864

A#/Bb 233.08 27.42391561 27.489 26.25 1.173915608 0.065084392

B 246.94 25.9267889 25.945 25.25 0.676788896 0.018211104

C 261.63 24.51316267 24.5 25 -0.486837328 -0.013162672

Some lengths were off.

First, the estimate from the equation (Length=12434.3125/(2*Frequency) + Radius)

Second, estimate based on frequency ratios

Third, exact measurement from instrument

-1

-0.5

0

0.5

1

1.5

1 2 3 4 5 6 7 8 9 10 11 12 13

Series1

Tubes

0

10

20

30

40

50

60

130.81146.83164.81185

207.55233.08261.63

Frequncy

Length

Tube Length EstimateFreq Ratios Length

Exact

Is the Pitch Off?Predicted Pitch Pitch Desired Freq. Actual Freq. Difference

Predicted length

Actual Length Difference

48 48.25 130.81 132.715498 1.905498 47.59574391 48.25 0.654256

49 49.1 138.59 139.394167 0.804167 45.35126555 46.25 0.898734

50 50.1 146.83 147.682975 0.852975 42.84798887 43.23 0.382011

51 51 155.56 155.563492 0.003492 40.71539404 41 0.284606

52 52.05 164.81 165.290467 0.480467 38.3635197 37.75 -0.61352

53 53.05 174.61 175.11915 0.50915 36.25243506 36 -0.25244

54 54 185 184.997211 -0.00279 34.35675658 33.75 -0.60676

55 55 196 195.997718 -0.00228 32.47055427 32 -0.47055

56 56 207.55 207.652349 0.102349 30.69021636 31.5 0.809784

57 57.3 220 223.845532 3.845532 28.52431467 28 -0.52431

58 58.1 233.08 234.43211 1.35211 27.27007116 26.25 -1.02007

59 58.8 246.94 244.105284 -2.83472 26.21915885 25.25 -0.96916

60 59.85 261.63 259.368544 -2.26146 24.72035563 25 0.279644

Using a chromatic tuner, found each pitch difference in cents

Used the equation 440*2^((Pitch-69)/12) to get the actual frequency

Frequency Difference

-4

-3

-2

-1

0

1

2

3

4

5

1 2 3 4 5 6 7 8 9 10 11 12 13

Series1

Sound

Pipe, 2 open ends

Wave Equation

∂²p/∂²x² = 1/c²*∂²p/∂t²

End Correction-

From Benson

Effective length longer than actual length by approx. 3/5 of tube width

-Sound coming out of it

If this were the case, each would have to be shorter

Difference is scattered, both + and -

-1

-0.5

0

0.5

1

1.5

1 2 3 4 5 6 7 8 9 10 11 12 13

Series1

Could then be cutting error

Conclusion

Despite slight differences in length, each pitch is still identifiable with its respective note

Full 12 note octave can be played as well as all intervals