Oscilators: emit basic waveforms, which can be represented graphically as waveshapes by an oscilloscope, a mechanical device which analyzes waveforms; measures rise and fall of voltage from 0 to maximum positive/negative and back to 0

• while transients (ie envelopes) contribute to the nature of a sound, the chief reason we distinguish between different sounds is due to their harmonic content.

1. sine wave: most noncomplex sound; contains no overtones

2. triangle wave (delta)

• contains harmonics, but not a full set

• contains all odd # partials

ƒn ƒ1 ƒ3 ƒ5 ƒ7 ƒ9

1/n2 1 1/9 1/25 1/49 1/81

Hz 100 300 500 700 900

3. sawtooth wave (ramp)

• contains all harmonic overtones of the fundamental

• harmonics have relative amplitudes that decrease exponentially as they exist higher in the harmonic series

ƒn ƒ1 ƒ2 ƒ3 ƒ4 ƒ5

1/n 1 1/2 1/3 1/4 1/5

Hz 100 200 300 400 500

4. pulse wave (rectangle)

• variable shape

• instantaneously positive, then negative, whereas above types exhibit gradual rise & fall between +/- states

a. square wave- "on" portion is 1/2 portion of cycle

• considered to be a basic wave shape

• 1:2-indicates haronic content

• duty cycle is "on" portion of entire cycle

• harmonic=normal inverse relationship @ 1/n strength

• ratio of duty cycle to rest of wave gives indication of waveform harmonic content

• 1:2• every 2nd harmonic is skipped ƒ1 ƒ3 ƒ5 ƒ7 . . .

• 1:6-every sixth harmonic is skipped ƒ1 ƒ2 ƒ3 ƒ4 ƒ5 ƒ7 . . .

• any pulse not a square wave is called a rectangle wave

• when "on" portion is slight, resulting waveform is known as a "spike wave" 1:30