This Demonstration generates music pieces based on seven mathematical constants in different bases: pi, e, the golden ratio, Euler γ, and the Catalan, Khinchin, and Glaisher constants, up to 300 digits. The constants were "sonified" by assigning notes from several instruments to the digits 1 through 9, taking 0 as a rest of the given duration. The "simultaneous" option plays the constants pi, e and the golden ratio at the same time with different random instruments for each one. The "shift" control allows you to shift the note spectrum to a higher or lower frequency.
Jazz musicians use a very sophisticated approach to harmony. Instead of thinking in terms of simple major, minor, and dominant seventh chords as Mozart, Beethoven, and the Beatles did, they first think of a "modal" key center like Lydian or Dorian, and create chord "voicings" that are built up from all the available intervallic relationships of that mode. Armed with this point of view, jazz musicians' aesthetic goal then is to control the "tension" in the voicing. They do this by grouping the intervals into roughly three classes: (1) the major and minor seconds combined with the major and minor sevenths create "dissonance" and attack our ears; (2) the thirds and sixths are "consonant" and sound sweet; and (3) the perfect fourths, fifths, and octaves are "neutral" and sound somewhat hollow. Make note of the voicings that intrigue you. Just like cooking, there is no right or wrong use of these aural spices!!! Press the "create random jazz voicing" button to create a jazz C major seventh chord. Change to C minor seventh chords with the scale setter. The bullseye chart on the right shows you the compositional makeup of the various chord voicings. With time and practice, your ears will tell you the same thing, and you will be on your way to taking Giant Steps as a jazz musician!