Speaker A
This is a sign wave.
Explore overtones, harmonics, and additive synthesis using sine waves to build complex sounds and understand musical timbre.
Key Takeaways
- Sine waves are the purest form of sound and the basis for all complex tones.
- Overtones define the unique timbre of each sound and can be harmonic or non-harmonic.
- Additive synthesis uses sine wave harmonics to construct complex waveforms like sawtooth and square waves.
- Harmonic relationships follow integer multiples of the fundamental frequency, preserving musical tonality.
- Amplitude scaling of harmonics is crucial for accurately recreating waveforms.
Summary
- A sine wave is the fundamental building block of sound, representing a pure tone with a single frequency.
- Sound waves are visualized using an oscilloscope showing amplitude over time.
- Higher frequencies have shorter wave cycles, while lower frequencies have longer cycles.
- Overtones are additional frequencies that shape the timbre of a sound; they can be harmonic or non-harmonic.
- Harmonic overtones are integer multiples of the fundamental frequency and maintain musical tonality.
- Additive synthesis builds complex waveforms like sawtooth and square waves by combining multiple sine wave harmonics.
- Square waves include only odd harmonics, skipping even ones, which affects their sound character.
- The amplitude of each overtone in a classic sawtooth wave is inversely proportional to its harmonic number.
- Musical intervals between overtones become smaller as frequency increases, reaching microtonal ranges.
- The video demonstrates how additive synthesis recreates common waveforms and explains their harmonic structures.
Full Transcript — Download SRT & Markdown
Speaker A
A sign wave is the basic building block of sound.
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The sign wave gets its name from the sinusoid function which describes a circle in two dimensions.
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Since sound only exists on one dimension, the time dimension, the graph cannot go back on itself to create a real circle.
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So basically, a sign wave is audio circle.
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Just as can create a complete drawing from small dots, you can also create any sound conceivable by mixing together several sign oscillators.
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Let's listen to the sign oscillator.
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The graph you are looking at is an oscilloscope.
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The Y axis represents the amplitude.
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This is the zero point, this is the maximum and this is the minimum.
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And in the X axis represents time.
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The Y axis acts exactly as your speaker would.
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When the graph is on top, your speaker is pushed forwards towards you.
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When it's down, the speaker is pulled away from you.
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When it's on zero, then your speaker's driver is centered on an ideal state.
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When I play high notes,
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more wave cycles are compressed into the view.
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This is because high frequencies are shorter.
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And our graph has a set time window.
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If we play low notes, we can see that there are less cycles in our view.
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This is because they are slower and they take more time to evolve.
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Let's look at the sign in our frequency analyzer.
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As you can see, the sign only has one peak and has no frequency content on any side of the spectrum.
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This is why a sign wave is often referred as a pure tone.
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As it is the only sound that consists of a single basic frequency.
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This basic frequency is called the fundamental frequency.
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If we look at other wave shapes such as the so or square.
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Now we are looking at a so wave on an oscilloscope.
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If we look at the frequency analysis of this sound, we can see that it has many spikes.
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Those spikes are extra high frequencies that construct the sound timbre.
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Those are called overtones.
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Overtones construct each sound that we hear each day.
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Overtones can be harmonic or non-harmonic.
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Non-harmonic overtones result in noise or sounds with ambiguous speech.
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While harmonic overtones support the fundamental frequency and keep its tonality intact.
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So as you can already guess, we can make a so oscillator out of many sign oscillators.
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The lowest frequency of the sound is the basics on which the sound is built.
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And is called the fundamental frequency.
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The rest of the spikes here are called overtones.
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Harmonic overtones will always be the fundamental frequency multiplied by a whole number.
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Let's take for example the note A 110 Hz.
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It has a fundamental frequency of 110 Hz and its first harmonic is its fundamental frequency 110 Hz.
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Its second harmonic would be the frequency times two, which means 220 Hz.
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The third one will be 330 Hz.
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Times four.
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Times five.
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And so on.
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The idea behind the system is to keep our wave cycle repetitive.
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And the only way to do that is to have the overtones start and finish at the same phase of the fundamental frequency.
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As you can see here, we have a green, blue, we have small sign waves here that represent the harmonics of the sound.
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The first harmonic would be the fundamental frequency.
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The second harmonic has two cycles per one cycle of the fundamental frequency.
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And because of that, it starts and it ends at the same point.
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And it's the same with the third harmonic, which has three cycles per one.
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Or here we have four cycles per one, and you can actually follow it, it's pretty accurate.
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And so on to infinity.
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Let's listen to those harmonics.
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Does it sound musically familiar?
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Of course it does.
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This is the building block of all music.
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It occurs naturally in nature, and it exists in all human music.
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Personally for me, it reminds an Indian flute or something like this.
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Let's see how a so wave is constructed from many sign oscillators.
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By adding them one by one.
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Let's start with the fundamental frequency.
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And now we add the second harmonic.
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Third harmonic, as you can see, there are three slides here.
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And it's starting to resemble a so shape.
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We are going to add this harmonic here.
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And I could go on forever.
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But my CPU doesn't have enough horsepower, and 16 is enough to demonstrate the idea.
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A so wave has all of the harmonics.
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But not all waves have to have all of the harmonics.
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For instance, the square does not have any even harmonics.
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It skips the two, four, six, eight and so on of the harmonic, adding only the odd harmonics.
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So one is the odd harmonic.
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As you can see, two, we're not mixing inside.
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We're skipping it.
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Straight to three.
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And voila, it starts to look like a square.
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We skip the fourth.
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We add in.
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We skip the sixth.
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We add the seventh.
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And so on.
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Let's look at the same thing on the frequency analyzer.
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Here is a so wave.
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This is our fundamental frequency, and now we're going to add the overtones.
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The first one.
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Second one we skip.
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Third.
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Fifth.
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Seventh.
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Ninth.
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Eleventh.
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Thirteenth.
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Fifteenth.
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Let's look at the relations between frequencies.
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I've selected 220 Hz as my fundamental frequency.
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And my next overtone will be an octave higher.
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The fundamental frequency times two.
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That's 440 Hz.
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The next overtone will be a fifth higher than the second overtone.
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Or an octave and a fifth higher than the fundamental.
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The fourth one will be two octaves higher than the fundamental.
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And a perfect fourth higher than the previous overtone.
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And as you can see, as I go up the overtones,
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the interval with the previous overtones gets smaller and smaller and smaller.
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As I go up, it reaches microtone.
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The recipe for making a classic so oscillator is having each overtone amplitude divided by its harmonic count.
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So for instance, the first overtone would be on maximum volume.
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The second one would be half the volume.
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Third one would be third the volume, you can see it here also.
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And so on.
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That's it for this lesson.
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I hope you got a little bit wiser.
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If you want to download this device and explore the world of harmonic sound or generally learn about synthesizers and how to make great sound,
Speaker A
just visit our website www.synthschoool.com.
Topics:sine waveovertonesharmonicsadditive synthesisfundamental frequencysound timbreoscilloscopefrequency analysissawtooth wavesquare wave
