I have a strange habit of using a graphics calculator as a synthesiser.
There are a few benefits to making music this way:
when the maths-brain is in the pilot’s seat, weird stuff happens
novel interactivity (the Cartesian plane is your keyboard!).
There are also a few reasons why other people don't do this:
rhythm and pulse is hard to acheive on a graphing calculator
building waveforms from scratch, always
What follows is a basic interval synthesiser. The red dot represents two numbers, one for the horizontal position and one for the vertical position. These numbers are the frequencies of the pitches you hear (if you click the unmute button in the top-left of the frame below).
The grid is spaced so that adjacent lines are an octave apart (that is, 256Hz is an octave above 128Hz, etc.) to make it a bit easier to play.
Make sure to click the unmute button and then collapse the expression list to get a full view of the pitch-grid interface. Have a play around!
If this is the first time you’re hearing the phrase “equal-temperament” then boy am I excited for you! A whole world of alien sounds awaits when you dive down the rabbit hole of tunings, and this synth will hopefully provide a good introduction to the sounds, if not the theory, of equally-tempered tunings.
If you want to get playing right away, click the unmute button in the top-left of the frame below and drag the coloured dots around to change their pitches and volumes (radially for volume and around the circle for pitch).
If you want to know a little about the theory, then the basic idea is this: on a piano there are 12 notes between the A in the middle of the keyboard and the next A to the right of it. We say that the octave is split into 12 equal intervals (called semitones). The piano is tuned in 12 tone equal temperament.
But what if we jammed a few more keys between the two A’s? Say, 4 extra keys so that the octave was now split into 16 equal intervals. Well then every note, except for the two end A’s, would have shifted slightly to accommodate for the extra tones. So we couldn't play, for example, Frère Jacques exactly as we know it; some notes would have to be slightly sharp, others slightly flat, and the whole thing might sound a bit alien.
But what possibilities have we opened up by allowing ourselves to not only play more notes, but play different, previously unavailable ones, too? See if you can make some sounds you like in tunings other than 12et, and then switch back to 12et to see where your new notes lie in the scheme of things.
A note for the nerds: I've chosen to display the angles against a linear rather than logarithmic frequency (Hz) background because I think this gives a good intuition for why certain chords (say, second inversion major triad in 12et) sound nice: they are arranged in a geometrically satisfying way which corresponds directly to the relationship between harmonics.