Questions on the Mathematics of Computer Music

  1. MIDI was established in 1984. It was designed so a person could have one master keyboard that could play a range of sounds, as opposed to multiple keyboards programmed differently.
  2. In an 8 bit system……. Data bytes are numbers with a 0 in the left most column, status bytes have a 1 in the left most column. The highest data byte is 01111111, which equals 127. The lowest status byte is 10000000, which equals 128.
  3. Three occurrences: 1) note-on on channels 1-16 (a status byte between 144 and 159) 2)a data byte between 0 and 127 (which note) 3) data byte 0-127 (volume). I.e. The note is being played, its velocity, and the channel it’s on. Two data bytes are necessary. All note-on messages have 1001 (144 as the lowest).
  4. Controller message- whether the pedal is down or up and/or whether there are any sliders or joysticks that have been moved- this is what it represents. 2 data bytes necessary?? The initial status byte represents controller data. The first status byte says a controller has been moved, the data bytes say which controller and how far. Range of 10110000 to 11001111 (192-207 respectively).
  5. Patch, telling a synthesizer what pre-programmed patch to play. There is only one data byte because it just needs to say which patch needs to be accessed.
  6. MIDI notes are turned off by giving a note-on signal at 0. A data byte sent with a velocity of zero makes it turn off.
  7. MIDI is a 16 channel system. Numbers 144 to 159 hold the 16 channels. 144 being 1, 159 being 16. Each is followed by corresponding data bytes.
  8. MIDI does not care about duration because the player usually decides the duration of notes, simply by playing. If music is being programmed, then the duration will be another data(?) byte.
  9. ?
  10. A sin wave is simple. Every sound can be simplified to a sine wave. Sound waves (sine waves) disturb the air. Most sounds create several sine waves at once. Overlapping and interacting sine wave frequencies is what makes any given sound unique.
  11. One needs to multiply whatever frequency you’re given by 2 to make it go an octave up. To go another octave up, you need to multiply it by 2 again. The harmonic series has 100Hz between each note, which means that notes get closer together at the end of the series. 100, 200, 300, etc… Octave, 5th, 4th, 3rd, etc… Any lower frequencies in any given series sound good together.
  12. A simple sine wave does not have overtones, it has no additional harmonic content. Triangle waves sound similar to sine waves, it contains other frequencies, the inverse of the square of the harmonic number. Sawtooth waves are buzzy, this has the inverse of the harmonic number. Square waves are clarinet-y, it has weird partials in it at eh inverse of the partial number.