I have a very basic question-- what's the difference between a sine wave and a saw wave? I'm not sure I can phrase this to make sense. I do know what a sine wave looks like, and a saw wave, in general, but I guess the question is what is happening in the instrument to make the two different waves?

# Saw wave vs Sine wave

Posted: 4/18/2007 12:38:35 AM

A sine wave is a waveform that corresponds to the sine function. If you have a graphing calculator and graph the sine function, the result will be a curved waveform -- a sine wave!

The sine wave is a pure pitch with no overtones.

When one adds another sine wave (an overtone) to a given sine wave (the fundamental) the waveforms are summed and the result is a new waveform that is the sum of the two. Natural overtones occur above the fundamental at integral ratios to the wavelength of the fundamental. For instance, a fundamental of 100hz will have overtones at 200, 300, 400, ... that is in the ratio of 1:2, 1:3, 1:4, 1:5... etc. Each of these overtones (partials) are sine waves. If they all start together (in phase) then as partials are added, the resultant waveform approaches that of a sawtooth.

As a practical matter, the sawtooth wave has ALL the overtones and one can remove (filter) unwanted overtones (i.e., a low pass filter filters out the high partials and passes the low). This technique is sometimes referred to as "subtractive synthesis".

Sine waves can be summed together. In fact, one method of synthesis (Fourier synthesis) deals with sine waves -- timbres are controlled by controlling the level and phase of discreet sine waves. This is sometimes called "additive synthesis".

This answer is probably more than you wanted to know. The simple answer is that a sine sounds mellow and a sawtooth is buzzy! If you have access to an oscilloscope and oscillators with the various waveforms you can learn about this faster than written explanations. :)

You asked what is happening in the instrument?

They all are different. For instance, the theremax's detector produces a sine wave.. the sine wave is, in turn, sent to a comparator (a Schmidt trigger) to produce essentially a pulse wave. In other cases, the mixer/detector may produce a bright waveform and then a low pass filter is used to convert it a sine wave.

Thus the answer is "it depends". Terrible answer, I know... however it is almost midnite and my brain cells are taking leave. Hope this info helps. :)

The sine wave is a pure pitch with no overtones.

When one adds another sine wave (an overtone) to a given sine wave (the fundamental) the waveforms are summed and the result is a new waveform that is the sum of the two. Natural overtones occur above the fundamental at integral ratios to the wavelength of the fundamental. For instance, a fundamental of 100hz will have overtones at 200, 300, 400, ... that is in the ratio of 1:2, 1:3, 1:4, 1:5... etc. Each of these overtones (partials) are sine waves. If they all start together (in phase) then as partials are added, the resultant waveform approaches that of a sawtooth.

As a practical matter, the sawtooth wave has ALL the overtones and one can remove (filter) unwanted overtones (i.e., a low pass filter filters out the high partials and passes the low). This technique is sometimes referred to as "subtractive synthesis".

Sine waves can be summed together. In fact, one method of synthesis (Fourier synthesis) deals with sine waves -- timbres are controlled by controlling the level and phase of discreet sine waves. This is sometimes called "additive synthesis".

This answer is probably more than you wanted to know. The simple answer is that a sine sounds mellow and a sawtooth is buzzy! If you have access to an oscilloscope and oscillators with the various waveforms you can learn about this faster than written explanations. :)

You asked what is happening in the instrument?

They all are different. For instance, the theremax's detector produces a sine wave.. the sine wave is, in turn, sent to a comparator (a Schmidt trigger) to produce essentially a pulse wave. In other cases, the mixer/detector may produce a bright waveform and then a low pass filter is used to convert it a sine wave.

Thus the answer is "it depends". Terrible answer, I know... however it is almost midnite and my brain cells are taking leave. Hope this info helps. :)

Posted: 4/20/2007 5:09:40 AM

Aha, I notice from another thread that you have a Kees Enkelaar theremin.

The sine wave setting is pretty much like a sine wave, as Kevin says - a very pure tone, without harmonics.

The sawtooth setting is not a sawtooth - it's a half-wave rectified sine wave - loads of harmonics. As Alexander says, "zzz" instead of "ooo", and as wikipedia says (http://en.wikipedia.org/wiki/Rectifier#Half-wave_rectification), there's a diode in the output line.

The sine wave setting is pretty much like a sine wave, as Kevin says - a very pure tone, without harmonics.

The sawtooth setting is not a sawtooth - it's a half-wave rectified sine wave - loads of harmonics. As Alexander says, "zzz" instead of "ooo", and as wikipedia says (http://en.wikipedia.org/wiki/Rectifier#Half-wave_rectification), there's a diode in the output line.

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