Math of Musical Scales, Part 1 of 3

[havokca]

I’m just starting to try and really dig into music theory, and one of the frustratingly-annoying parts of it is how absolutely arbitrary it seems. Thank you so much for taking the time to show the math behind it.

[alitajvidi]

Patrick, you are an amazing teacher! The demonstration of oscillation was something I could never visualize or understand before. Thank you so much for your help!

[halasimov]

Overtones visualized as one combined wave is mind blower!

[jpuzebb]

I want this to be the only video that survives past humanity, or sent into space. So that whoever watches it has all this knowledge....but argue over what that drawing of 7 white and 5 black boxes could be called!!

[mercedesayris]

we have 7 notes and 12 chromantic because of how interwoven music and astronomy and geometry were together in previous times, you can find this in the work of Ptolemy and Kepler commonly attributed to pythagoras. the circle divides well into 12 parts, which is what is used for the 12 zodiac, 7 classical planets, aswell as 12 months, 7 days. and the 7 colors of the rainbow.
this concept is also illustrated highly in renaissance textbooks where they identify certain days with certain planets and modes of a scale.

they chose 360 degrees for the circle in babylon because it was the closest degree to the yearly cycle of the sun and the 13 month cycle of the moon that divided into so many whole numbers. they perceived time as cyclical of course. the whole system is beautifully put together when you think of it, everything is energy frequency and vibration just as Tesla stated.

[MabookaMabooka]

If we look a bit close at a few first harmonics (let's start from A == 110), we might notice that within the 4th octave (880...1760) there are 8 tones (not 7!!!); These A) all lie within the same octave; B) represent a non-interrupting sequence of small relatively denominators which C) is located as close as it gets to the base frequency.
110 220 330 440 550 660 770 880 990 1100 1210 1320 1430 1540 1650 1760

So I think that would be a natural way to divide an octave: into 8 intervals, not 7. The argument that on earlier instruments overtones sounded more loudly only supports this idea. And probably that system was the case sometime in the past but then "historically" or just as an artifact of the way musicians tuned their instruments the 8th note was "lost in translation".

[sunnymittal]

I wish you had more subscribers, you deserve it! I'm a huge math and physics nerd but have also played music most of my life. This connection is super important but so few musicians really understand or appreciate it. True you don't "need" to know it to write music, but the physics of music brings even more beauty to it for me. Love it!

[davidwalker]

Very well explained. I've been struggling a bit with some of these concepts for a while. This is just what I've been looking for. Great clarity and perfect integration of words with visuals. Bravo!! Moving on to parts II and III.

[TEXAS.NV]

Thank you very much for sharing this information. This came across my search looking into the connection between sound and the 3 to 2 ratio. I’m researching the connection between the pentatonic scale and the mathematical concepts embodied in several native ceremonial rituals and glyph paintings.

[wellsqs]

Very nicely done. I really appreciate the math/physics.

[dsomlit]

Thank you sharing, it's better explained than what I read in theory of music book

[bennybundi]

I can't believe i only just learned this. If this was taught to me at some point when i took music when i was younger i would have had a much deeper appreciation for it.

[joaolemes]

I can't see double frequencies as the same note for the life of me.

[TotalDec]

The reason we use 12 notes to make an instrument, is easily understood when looking at the 16-64 frequencies of the H.S.

[pavelsurkov]

I have watched all the videos on this topic, and this one is one of the most clear and accurate ones. thank you.

[thomashoffman]

This video is dopeee. I truly appreciate your way of condescending the phyics --> math --> auditory layers of this. The animation is on point too. Thanks for this.

[bwinsky]

Great integration of music theory and frequencies. Great series! Thanks!

[mikechad]

The intro is actually my favorite scale. When I first discovered it, I've always wondered when I spread the notes out, they kind of sound like "merging" in the same note. I first looked it up and it's called Lydian Dominant. But I found a name that actually made more sense, the acoustic scale. This video explains alot

[rainerausdemspring]

Erm - there is a good reason to stop after 5 or 12 (or 53) notes generated from the overtone series. As you certainly know this has to do with the continued fraction expansion of log(3)/log(2).

[oliviawang]

This is super interesting, thanks for explaining it all so well!