Mathematics, Music, Illusions and Paradoxes

1986: “Tritone paradox” – by using a pair of carefully selected Shepard tones, our signal processing mechanism can be tricked.

1964: “Shepard tone” – a careful selection of harmonics can create an ever-descending/ascending tone.

• Pythagoras: A combination of two tones will sound pleasant if the ratio between their frequencies is a ratio between two small whole numbers.
• Fourier: Any periodic wave is a sum (A combination) of many sine waves.

Analysis (MSC2010#97I99)

·   Sine function

·   Periodic graph

·   Frequency

·   Amplitude

Arts, Music, language  (MSC2010#97M80)

·   Tone

·   Harmonics

·   Loudness

·   Pitch

·   Tone-quality/timbre

·   Spectrum

·   Octave / Fifth / Triton