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8 b from Risskov School presents. M u s i c a n d M a t h e m a t i c s. Tones in Glass. 12 tones in one octave. Spreading of the 12 tones by means of The starting point is the concert pitch a a has a frequency of 440 Hz When you multiply with , you get the tone above

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8 b from Risskov School presents

Musicand Mathematics

Tones in Glass

12 tones in one octave
12 tones in one octave
  • Spreading of the 12 tones by means of
  • The starting point is the concert pitch a
  • a has a frequency of 440 Hz
  • When you multiply with , you get the tone above
  • Divided by , you get the tone below
conditions for tones in glass
Conditions for tones in glass

We have examined if the following has an impact on tones in glass:

  • Temperature
  • Connexion between quantity of water in the glass and the frequency
  • Other materials than water in the glass
temperature
Temperature

Thesis: When the water gets warmer, the tone becomes deeper.

Conclusion: Temperature has no influence

quantity of water and the frequency
Quantity of water and the frequency

Thesis: There is a connexion between quantity of water and frequency.

Our researches showed:

  • Two different glasses with the same percen-tage of water in proportion to the volume of the glasses do not give the same tone.
  • You can not find more tones in the same glass simply by adding x ml water (or removing from) the glass.

Conclusion: We were wrong!

other materials than water
Other materials than water

Thesis: It makes a difference to put other materials than water in the glass.

Vi made experiments with:

  • Pure water
  • 10% salt
  • 10% sugar
  • 10% oil

The speed of one oscillation/wave in pure water

The speed of one oscillation/wave in 10% salt

other materials than water continued
Other materials than water continued

Water:

  • The speed of one oscillation/wave is 0,001 s
  • Number of oscillations per second (frequency):

1/0,001 s = 1000 Hz

10 % salt:

  • The speed of one oscillation/wave is 0,0012 s
  • Number of oscillations per second (frequency):

1/0,0012 s = 833,33 Hz

other materials than water continued9
Other materials than water continued

Percentage the ”salt-frequency” is less than the ”water-frequency”:

(1000 Hz – 833,33 Hz)/1000 Hz · 100 = 16,7 %

other materials than water continued10
Other materials than water continued

Conclusion:

  • The numbers do show a difference in the tone.
  • You could not hear a difference in the tone. The ”oil-water” did sound different, though.
  • A very questionably experiment.
found tones
Found tones

Method to find the frequency of the tones

  • The speed of one oscillation/wave (from one wave top to the next) – in this situation 1,8 ms
  • Frequency: 1/0,0018 s = 556,56 Hz
  • 556,56 Hz/2 = 278,28 Hz. It is the tone cis (275 Hz). 556,56 Hz is cis one octave higher.

This is how we have found all our tones.

Science Workshop-program. By the use of a microphone the program shows a tone’s speed of one oscillation/wave.

found tones continued
Found tones continued

The speed of sound in air is 340 m/s

The speed of sound in glass is 5000 m/s

Wavelength = speed/frequency

The tone cis in glass: 5000 m/s / 555 Hz = 9 m

The tone cis in water: 340 m/s / 555 Hz = 0,61 m

found tones continued13
Found tones continued

Percentage the wavelength in glass is bigger than the wavelength in air (the tone cis):

(9 m – 0,61 m)/0,61 m · 100 = 1375 %

conclusion
Conclusion
  • You can spread the 12 tones in one octave by means of .
  • Temperature of water in the glass has no influence on the tone.
  • There is no connexion between quantity of water and frequency.
  • Mathematical there was a difference in the frequencies, when the material is different from water. But you could not hear it (a very questionably experiment).
conclusion continued
Conclusion continued
  • We found our own method to find the frequencies of the tones by the use of Science Workshop. Our starting point was one oscillation’s speed.
  • The tone cis’ wavelength in glass is 1375% bigger than the wavelength in air.
  • We think it is a fine instrument, and you can be very good at playing it. In Denmark we have professionals.