Math of Musical Scales, Part 1 of 3

[@alitajvidi5610]

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!

[@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.

[@Xonatron]

I had the same issues initially.

[@sunnymittal1906]

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!

[@halasimov1362]

Overtones visualized as one combined wave is mind blower!

[@youtubevideor265]

I perceive both as different at 3:38

[@thomashoffman5217]

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.

[@bennybundi9671]

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.

[@pavelsurkov2853]

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

[@davidwalker41]

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.

[@Lee_yourboylee]

My struggles with these concepts echos yours as does my appreciation of this video. It's outstanding.

[@MESSENGER-of-JESUS-CHRIST]

Brilliant! Thanks! Subscribed!

[@lmao4982]

Love it, i've been wanting to find this video for years.

[@wellsqs1]

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

[@anonkiddo]

Only half way through - and oh my god man, this is simply genius. KUDOS to you for creating such an amazing piece of content.

[@mikechad27]

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

[@TEXAS.N8V]

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.

[@PianoTechMaggie]

I love this video! Well done!!! 👏

[@bwinsky]

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

[@LuisTorres-qz5kr]

GREAT job explaining this in such a simple manner! Thanks for sharing.

[@shahedatutorial6328]

Seriously BRILLIANT!! I've been struggling with this for so long!

[@edzielinski]

Outstanding. I've seen a lot of videos on this topic and this is one of the best. Thanks for your work and for sharing!

[@oliviawang6324]

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

[@comrunyousefzadeh758]

Awesome work! This vide answered to a lot of long standing questions I had.

[@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.

[@lmahesh26]

This was wonderful! Connected a lot of dots for me, thanks!

[@florentinosanchez3969]

This is the best video ever

[@ratikanto]

one of the best teachers i came across

[@mistershaf9648]

I am really into music theory. I’ve heard of this interval called the 77th harmonic (325 cents) and I never really understood it until now!

[@mercedesayris9436]

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.

[@tuliothx]

Just to clarify. The 7 white keys (diatonic scale) or all 12 black & white keys (chromatic scale) had nothing to do with the zodiac, planets, or rainbows. It is a mathematical progression of taking 3/2 of a tone and then repeatedly increasing that tone by 3/2 until it begins to repeat itself. When that mathematical sequence is repeated 12 times, it repeats itself at the 7th octave of the scale.

[@mercedesayris9436]

@@tuliothx I’m saying it’s all In synchronicity not by coincidence. They are all related everything is connected like a unified theory, just because they are not related in the system you have doesn’t mean they are not connected to other people, do you play music or know astrology? If you had sufficient knowledge of both you’d see they are in fact related. I am well learned in both areas. Pythagoras referred to the heavens as the music of the spheres, he saw the solar system as a giant orchestra. This ‘occult’ type thinking was used by many of the great western composers and onward to jazz musicians such as John Coltrane, Pythagorean’s believed that the ratios in music were also important in astronomy

[@joaolemes8757]

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

[@samstits5136]

I mean I don’t think they are lol

[@elijahjflowers]

Same! Fourier series is literally a contradiction to modern music theory. Music theory needs a linguistic update.

[@desanctisapostata]

@@elijahjflowers why?

[@somasundaramsankaranarayan4592]

Yeah. Chord inversions exist for a reason.

[@austinline2621]

Seems it's more to do with the structure of our inner ears (Basel membrane of the cochlea), the subjective way our brains process the info from it and perhaps some wave physics to guide the way.

[@wetplutonium9787]

great series, glad i was able to find it again (phew) 👍👌

[@bengoldman6003]

This was a great explanantion. Thank you!

[@curtpiazza1688]

Very well explained...very well illustrated!

[@user-jp1uz9eb5b]

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!!

[@navneetyadav3941]

Very impressive, Thank you!!

[@rajdohadwalla8847]

Wow sir great video

[@GMAtheory]

Great explination....thank you!

[@TheModo]

Awesome video 😼

[@lawrencetaylor4101]

You bring out the inner Geek in moi. Merci.

[@Algardraug]

Ah, yes this is so fantastically explained!

[@dduay]

Thank you so much! I spent 30 minutes finding this video.

[@mustaphadiallo2134]

IRON MONTAINS KASH KARD IRONNE

[@dwukMUSIC]

Thank you for sharing.

[@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".

[@Freespirit.444.]

Godeeper bro

[@SwimnBird]

Great video! Subbed

[@shrishailctalukar]

Thank you.

[@fuckyoutubengoogle2]

7:33 I think for some instruments, the fundamental is not the loudest among the overtones. I'll look it up to be sure and get back to you.

[@saimon174666]

this definitely deserves much more views, awesome explanation

[@roberts8783]

using an app like spectroid to show the spectrum on chart adds a lot of context and colour to the explanation

[@rainerausdemspring3584]

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).

[@muraxn]

@9:32 The Aha moment when the math-music-magician reveals his Trick behind his world famous masterpiece @10:30... 👏🙏

[@CraigCameronmusic]

You are my kind of nerd!

[@MarkWadsworthYPP]

Thanks. I'd always wondered about that. Why don't they teach this in maths lessons at school? Or in music lessons?

[@sagittarius_a_starr]

3:25 I played it over and over but I swear i could hear a difference between the tones that were only different by 2 cents... it might be suggestion or expectation but i swear i hear it... i'm really sensitive to this stuff, to the point that when i got true temperament frets... omg, the d chord (1st position) finally sounded correct to me, for the first time. still.. i'm probably only thinking i'm hearing a difference in tones, b/c i know that they are different

[@asainpopiu6033]

You can take a test here if you want to know if you can hear a 5 cents difference: kzbin.info/www/bejne/i6i5oYeXr8yln9U I cannot hear the 5 cents difference in this test. I can't even decide what to guess, but I definitely can for 10 cents even if it's more an impression than a certainty (but the test says the impression is right). On the other hand, in Patrick's video, I cannot distinguish the two audio samples for the 10 cents difference and the 2 cents difference... in both of them I feel the second note is higher (which is the right guess). But a spectrum analysis of the sound says that in the 10 cents difference there is a 3 Hz difference in the third harmonic and only 1 Hz difference for the 2 cents difference... So the two sounds samples are not identical.

[@Ashtree81]

Great explaination but the notes played at 10:31 are C D E F# G Ab Bb C so it doesnt add up to the C major scale played at 10:56

[@ratikanto]

GOLD

[@HaridevV]

I could perceive the difference between the two tones in both cases. I guess my threshold of hearing is less than even 5 cents. Anyone else?

[@sarahaprincesa]

👏🏻👏🏻👏🏻

[@manuelr7121]

wow

[@milesborowsky8140]

Is there any way i can access that applet?

[@RMarch3]

Patrick, I really don't understand the logic behind the "rescaling" business in 10:30...can you explain?

[@Music-zl1go]

Why C major has to be all natural notes, why not alphabetically have A major with all natural notes? What is the naming convention starting with C why not A.

[@amarkantkumar4233]

7 notes also in ancient tradition in India

[@jubjubbird56]

Well thought out. Humble brag. I legit percieve the difference in pitch when he says humans cant'. Internet, Im going out on a limb here.... Doesn't matter that the duality of tones demonstrated MATTERED... the order of pitch to pitch is the same between both examples. The first one is sharper both times! I know you hear it too don't lie/ (call me out if I'm wrong I dare you)

[@DaveDG]

If i could put 3 likes, i would!!

[@mustaphadiallo2134]

RABID TUNE RABID RED

[@rwharrington87]

What is the 100 cents = (1 cent)^100 at 3:20? Isn't this saying 100 cents = 1 cent? Then you make the jump to the 12th root of 2 = 1 cent without explaining the math steps that led there. Maybe you explain it later in the video. But I'm baffled about this part so far.

[@mockingjayu2210]

Yes I was trying to warp my head around this relation 100 cents = (1 cent)^100

[@rwharrington87]

@@mockingjayu2210 Yeah, I mean (2^(1/1200))^100 = 2^(1/12), so that makes sense. But he doesn't really show where each piece prior to the last step comes from. It almost reads better in reverse.

[@jhonya.zavaleta6736]

I don’t understand the math. @3:27 1^100=1 not 100

[@mockingjayu2210]

same here, I too don't get that

[@ryandevens4726]

False, Wendy Carlos Super Just is the best scale... well major at least

[@jwjwjwjw2997]

trans women are real women!!

[@awittypilot8961]

Might be interesting for a geek....but AC/DC SOUNDS good and that is in the end ALL that matters. On a gig I have never one time have someone come to me and say...hey...that 2 to the 1200th power note in there ROCKED! or that overtone in there sucked.... For me, none of this correlates with "pleasing to the ear". Music is about making memories and causing you to FEEL something that you like to hear. I guarantee you I will never tune my guitar and say...hey...that's 8 cents too high. Van Halen didn't either. He played what he wanted to hear and made the band to to his guitar for sync. The ONLY time a few cents makes a distinguishable difference to me is when I'm trying to sync something I'm trying to learn with my instrument. If it's a few cents off you're never going to get it right. But if you adjust the program up or down a couple of cents, the rest of the tune will stay true. And never one time have I looked at our bass player and said...dude that G is 14 cents flat

[@alvodin6197]

There's no need for any math, beyond counting to 12, and understanding simple half and whole steps. Anything else is redundant. You use your ears to figure out what scales, chord progression and melodies you want to make, not math. Let's ask Chopin, Beethoven, Mozart, Debussy etc what kind of math they used. We can't, because they're dead.. If they weren't dead, they would say that they used their ears first. You are overcomplicated something which is completely unnecessary. It's like teaching people to read before speaking and understanding a language, makes very little sense.

[@radeum1010]

Hi Patrick, I know the answer is more than likely in your excellent video but could you please explain with ‘exclusive’ detail why you can hear the Bb overtone when hitting the lower E note (first) on a piano..? A very good long time retired musician / producer friend of mine is captivated by this phenomenon. 🇦🇺🦘