Mathemtatics of music, Computer Science and Music Technology Outreach.
Dr David Greaves
Fellow and Director of Studies
Corpus Christi College
University of Cambridge
Copies of slides used to accompany the 'pocust' music software: SLIDES.
Link to pocust on sourceforge sourceforge.net/projects/pocust.
Question sheet for break-out session: LINK.
List of Interactive Demos
- Look at microphone and see oscillogram of ruler twang. See SHM, decaying sine wave.
- How many books can a blindfolded person have added to his stack before he notices: not additive, but a ratio: should be about the 10th root of ten (one decible).
- Demonstrate wavelength with Swanee Whistle. Relate to stopped organ pipe.
- How high and low pitch can you hear. How high and low in volume: should be 20Hz to 20kHz for youngsters. Volume experiment will be limited by ambient noise and PA system.
- Poly-VCO: listen to sine, square, saw and triangle waveforms while viewing them on the
pocust scope. Explain their characteristics. Adjust pairs to hear the tonality of the
octave and perfect fifth: then use this to justify the twelve note even-tempered scale. Note that
the 12th root of 2 is quite a lot smaller then the 10th root of 10: why does nature give
us such accurate pitch perception ?
- Midi organ: Someone plays a chord on the midi organ and then someone else adjusts the pitch of the notes using the GUI. Should sound out of pitch at about 10 cents error. Turn up the 'random pitch error' control to see where people think it's nasty.
- Sampling rate and precision: using the wav player in random mode
to select a random TV signature tune, how many quantizing levels and
samples per second are needed to recognise it. Concentrate on the bps
product (displayed in large font) to compare with the MP3 results
later. Can also demonstrate the LPF to avoid alising and explain Shannon-Nyquist if time
- Lossless compression and PK-zip: show pkzip does not help and show how an mp3 encoder does help.
I use BladeEnc on linux. Also use -binaryview option on a wav file to see the real ones and zeros.
- Vocoder demonstration: show vocoder operation on pop track. Look at spectogram and explain
that the signal has been transformed into many low-rate signals containing the same information.
- Psychoacoustic masking demo: move a pair of points close to each other using the poly-VCO
GUI. See that within a semi-tone you need nothing louder than -15 dB re loudest tone.
- Enable the interactive MP3 encoder and adjust the mask shape and discard aggressiveness
while monitoring the BPS product. Compare the quality at around 50 kbps with what was
earlier achieved. See how low you can go and still recognise speech or TV signature tunes. Explain
about vocoding for submarine comms.
- Program up the wavplayer to make a farm yard or nature ambient sound track, using
random triggering of samples. Explain how stereo effect of river is achieved.
List of Sound Clips