Presentation on theme: "Music andMathematicsMusic andMathematics Tones in Glass 8 b from Risskov School presents."— Presentation transcript:
Music andMathematicsMusic andMathematics Tones in Glass 8 b from Risskov School presents
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 12 tones in one octave
The frequencies of an octave ToneFrequency Calculated frequency ToneFrequency Calculated frequency c2528 Hz523,25 Hzf1352 Hz349,23 Hz h1495 Hz493,88 Hze1330 Hz329,63 Hz Bb1475 Hz466,16 Hzes1317 Hz311,13 Hz a1440 Hzd1297 Hz293,67 Hz as1422 Hz415,31 Hzcis1275 Hz277,16 Hz g1396 Hz392,00 Hzc1264 Hz261,63 Hz fis1367 Hz369,99 Hz
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
Thesis: When the water gets warmer, the tone becomes deeper. Conclusion: Temperature has no influence Temperature Temp.14°C20°C30°C80°C ToneDDDD
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!
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 Other materials than water 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.