M u s i c a n d M a t h e m a t i c s

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# M u s i c a n d M a t h e m a t i c s - PowerPoint PPT Presentation

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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Presentation Transcript

8 b from Risskov School presents

Musicand Mathematics

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
• Divided by , you get the tone below
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

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

Conclusion: Temperature has no influence

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

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

• 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

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 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 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

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

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 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
• 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
• 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.