The Science Behind the Arts: The Maths Behind Music

[jeremytrilingue]

I've spent the whole day watching videos about maths in music and this is BY FAR the best one! BRAVO!!

[brandinfisher]

Come on give me more! 3 minutes is just not enough for something so interesting

[Jimforxst]

This is a great way to display and talk about the Harmonic Series, Pitch Frequency, and Intervals.
Fantastic work!

[themadcaplaughs]

Would be awesome if you guys expanded on this in more depth, maybe go into some music theory and try explaining it through visualizations similar to this video.

[trevormathews]

When a string is plucked it vibrates at a particular rate. The rate at which a string vibrates is called the frequency and is usually measured in hertz the number of vibrations a second. What determines the frequency is four factors : the string thickness its density the string length and the string tension. We humans perceive frequencies within a certain range as pitches. The range starts roughly at 20 Hz and goes up to about 20, 000Hz or 20 KHz. Notice that the shorter the string is, the higher the frequency or pitch is. [f=(1/2L) √(T/μ)]. In fact, the string length can be thought of as wavelength and there's an inverse relationship between wavelength and frequency. The higher the wavelength the longer the string the lower the pitch and the shorter the wavelength or sting the higher the frequency or pitch. So musical instruments like the guitar, use this principle to create different pitches. For a string of a particular type thickness and tension you can change the string length or the wavelength to create different pitches. So different string lengths create different pitches. How do we decide which ones to use? Well one pitch difference or musical interval is called the octave and it's created by halving the string length. There by doubling the frequency. So, doubling a frequency gives us an octave quadrupling it would give us two octaves. but we can multiply a frequency by different integers to create different intervals. For example, tripling a frequency gives us an octave and a fifth. Multiplying a frequency by five will give us two octaves and a major third. What we are building here is known as the Harmonic series. The set of musical intervals created by multiplying the frequency by whole numbers. One way to create scales is to take these intervals, usually the lower ones, and bring them down to the same octave and they sound sonorous together. Chords and melodies emerge naturally from this.

[normanspurgeon]

You have the right instrument to explore intervals and tuning- this is tremendously fascinating. I'd be very interested to see more videos, with a discussion and demonstration of the pure intervals available on guitar, and the untune- able ones, and how to achieve the former and co-exist with the latter. thanks-great, valuable subject

[QuackersMcCrackers]

Masterpiece, brava, this is truly a piece of presentational art!

[billsurrette]

This is a great video. I've got a MS in math but I have zero musical knowledge. All I know about music is I turn the knob to the right to make it louder. I've always wanted an explanation that taught all the musical terms in mathematical terms, and that's exactly what's being done here. It should be noted that the equation given 45 seconds in is incorrect. Rather than 1/2L... it should read 1/(2L). Hearing his explanation of the inverse relationship between frequency and length made me quite confused as it was inconsistent with the equation. I found other resources and confirmed what the equation should be. (Also, less of an issue, the graph shown at 1:12 shows a linear relationship, not an inverse one.)

[MomentForever]

nice intro, and the guitar sounds great, but is there anymore to this? I would like to see more in depth stuff

[gstech]

Wow never thought of it this way thanks!

[adelia]

You're the reason I have Holiday Homework :/

[vectorshift]

They should show the waves travelling away from the guitar.

[maysonsonntag]

Unfortunately, the harmonic series displayed @3:10 is incorrect. The 6th, represented by 6/5 as 6/5 is less than, not greater than 3/2, meaning it's wavelength would be longer, placing it far lower in the scale.

[opreaiulian]

Maths is just a detalied language that describes a certain phenomeon. You can explain the phenomeon in any language.

[jackkoumi]

 μ is mass per unit length, or density times cross-sectional area of the string

[oldandnewpieces]

It's actually f = ( 1/(2*L) )* sqrt(T/miu)

[Skydraa]

This deserves so much more attention than those Kardashian vlogs...

[AstinOne]

does anyone know what measurement μ represents?

[akshaypuradkar]

this is so much easier.
"harmonic series", check.

[artrock]

Nice video, except that scales don't come from the harmonic series, which seems to be the main premise here. Only the major triad, the second and the octave - there is no fourth, sixth or major seventh as presented at 3:08