## Synthesis

• Make a sound: contrast with analysis, effects

• Many popular approaches

• Wavetables

• Frequency Modulation

• Some really fancy stuff

## Notes

• A "note" is a sound with a fixed frequency

• Briefly: Western music uses a "12-tone scale"

• Remember that the ear hears frequency on log / exp scale

• An "octave" is a frequency that is twice some other frequency

• We divide an octave into 12 parts: with a base frequency f, we have

$$\textrm{note}_i(f) = f \cdot 2^{i/12}$$

• For example:

\begin{eqnarray*} \textrm{note}_{0}(f) &=& f \\ \textrm{note}_{12}(f) &=& 2f \\ \textrm{note}_{-24}(f) &=& \frac{f}{4} \end{eqnarray*}

• There is a bunch of music theory here for future

## Key Numbers, Note Names

• For Western scales, the base frequency is 440Hz, because reasons

• We can use a numbering based on piano keys as a standard: MIDI "key number"

• In MIDI 440Hz A is key 69; we call this the A in "octave 4" or A4

• We give the notes letter names with a possible "sharp" or "flat" modifier

  Key   Freq    Name    Octave
69    440     A       4
70    466.16  B♭/A♯
71    493.88  B
72    523.25  C
73    554.37  D♭/C♯
74    587.33  D
75    622.25  E♭/D♯
76    659.26  E
77    698.46  F
78    739.99  F♯/G♭
79    783.99  G
80    830.61  A♭/G♯
81    880     A       5

• The "why" of all this is a future lecture

## Note Timing

• Notes start at a particular time, have a particular duration (how long they continue to play)

• For now, will think of this as an "on time" and "off time" for the note

• There's a whole complicated theory here, but we don't need it yet

• Typically start times are 4 to 30ms apart or thereabouts, durations are 4ms and up

• Notes may overlap: "polyphony". Some instruments (including some synths) are monophonic: one note at a time, so start of next note is end of current