What is timbre? Topic: Square,Sawtooth, Triangle and Pulse waves

 Find out how harmonics affect waves.

 Odd harmonics... ...are the 3rd, 5th, 7th, 9th etc harmonic above a fundamental pitch. Square waves The Clarinet is a closed pipe and produces odd harmonics only.  The sound waves from a clarinet are Square waves. Here's a diagram of a Square wave: The fundamental frequency or pitch is shown at number 1.  Numbers 1, 2, 3, 4 ...... 9 are its harmonics. Notice that only the odd harmonics seem to be involved here and that the amplitudes are in inverse proportion to them. Listen again to the Square wave sound on the screen at the start of lesson 4. It sounds like a clarinet.

 Here is an animated version of a Square wave. You can see it changing from a Sine wave pattern to a Square wave pattern in the following diagram where the red lines are numbered 1, 3, 5, 7, 9 and the scale of the vertical line is in fractions of 1:

 So, a Square wave is composed of only odd-numbered harmonics with amplitudes in the ratio 1/n  (f, 3f, 5f, 7f... with amplitudes of 1, 1/3, 1/5, 1/7... )

 Even harmonics... ...are the 2nd, 4th, 6th, 8th etc harmonic above a fundamental pitch. Sawtooth waves An Oboe looks a bit like a Clarinet and also has a reed in its mouthpiece. However, it is an open pipe and produces both odd and even harmonics. Sawtooth waves give a richer sound. Here's a diagram of a Sawtooth wave:         Listen again to the Sawtooth wave sound on the screen at the start of lesson 4.

 You can see it changing from a Sine wave into a Sawtooth wave in the following diagram where the red lines are numbered 1, 2, 3,  .... 20 and the vertical scale is in fractions of 1.  The sound is richer than a Square wave sound because all the harmonics are involved here:

 So, a Sawtooth wave has both odd-numbered and even-numbered harmonics with amplitudes in the ratio 1/n   (f, 2f, 3f, 4f... with amplitudes of 1, 1/2, 1/3, 1/4...)

 A Triangle wave... ... has odd harmonics with amplitudes in the ratio 1/n²  (f, 3f, 5f, 7f......with amplitudes or  loudness  of 1, 1/9, 1/25, 1/49, 1/81........)

 This is an animated Pulse wave It seems to have a constantly repeating peak of amplitude.

 Timbre mainly depends on harmonic structure.