Is The Major Scale A Fractal? Harmonics Explained

MSS #1 - Learn about harmonics and the recursive patterns that govern harmony. Identify harmonics, their ratios, and how the major scale deviates from the acoustic series.
Subscribers update : It has been more than a year since the release of my last video. I've been wanting to come back to this channel for a long time, trying to find what I want my content to be about, what schedule is sustainable, etc. I'm starting the Music Space Station show as a result of this process. The MSS will about all about exploring interesting music ideas in a free way, with a sci-fi touch. No schedule, just following my interests of the moment in a playful manner. I hope the content resonates. Happy to be back, thank you for sticking around. All the best!
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[@ownedcoot1046]

HE’S BACK!!!!!!! 🙌 🎉

[@KevinTPLim]

The F/F# and B/Bb thing is super interesting! Great video ☺️

[@nathanlewiswilliams8985]

I loved the ending with the references to classical modulations - I’d never thought of the F and the B that way before. Thank you

[@grtamericanseahorseseahors9094]

The “major scale” is adjusted from the physical harmonics specifically to create a linear division of the octave into discrete half steps. The purpose of having equal half steps in a musical context is that it allows an instrument to play in different keys in the spectrum. If an instrument were to be tuned to the harmonic series…then as one changed keys the relationship (ratio) of one tone to the next would be constantly changing and less predictable/pleasing. Of course the major scale is tuned (currently) to an equal Equal Temperament and became standardized with the creation of the Piano. The piano changed the future of music. The piano allowed a composer to have access to the musical spectrum on one instrument and therefore musical “research” became more easily conducted and as a result musical became more complex (key changes and modulations became more frequent). Having said that….the harmonic series (part of the electromagnetic spectrum) is non linear as it allows for all things to exist. If the harmonic series were linear then all of the “nodes” would align with 12 realities…vs the infinite division of frequency. That last bit is a piece of my own insight…aka not particularly present in the literature.

[@pinheadnick8540]

could you go into why the harmonic series is non linear and the equal temperament division is?? also how does that relate to a fractal? pls help

[@joshuasanford]

​@@pinheadnick8540 Generating function behind equal temperament is Frequency = Reference_Frequency * (2^(n/12)) n is the number of semitones above (or below, when negative) the reference frequency. output is always going to be some frequency that is in the same chromatic scale as the reference frequency - assuming n is an integer. the 2^(n/12) implies 12 pitch classes which repeat across all the octaves. if a pitch's frequency is doubled, it has been increased by 12 even parts (semitones). if a pitch's frequency is halved, it has been decreased by 12 semitones. the function is an exponential function. as n increases, the gap between adjacent output values gets larger. The way human hearing works, we hear a doubling of frequencies as a 'similarity' in pitch called a pitch class. 220hz is an A and 440hz is also an A, etc. Note that as pitches get 'higher' their next octave becomes a higher and higher frequency, just like i explained with the function. The exponential nature of the equal temperament function and the logarithmic nature of human hearing have a 'canceling out effect' causing the human perception of the equal temperament system to sound linear. The harmonic series is a very definite acoustic phenomenon that involves a series of frequencies generated via sympathetic resonance from a base tone. The gap between each successive note in the harmonic series gets shorter as the series progresses because divisions 1/x have shorter gaps as x increases (this represents the subdivisions of a base vibration). The frequencies still get higher as you ascend through the sympathetic vibrations of shorter and shorter length. I your answer is that the equal temperament system allows you to evenly maintain 12 pitch classes repeating across octaves indefinitely. The harmonic series is an uneven distribution of pitches related to a fundamental tone by sympathetic resonance. That is what is 'non-linear' vs 'linear'. The equal temperament system evens out all the tones equally, while still achieving quite close intervallic relationships to the desirable consonances and dissonances found in the harmonic series. Some of this wasn't explained that clearly in the video, and perhaps was described in a misleading way. I've actually enjoyed writing this out more than the video because I left the video wondering if I just watched some bullshit, but I don't want to be impolite because this is the first video I've seen from this channel. It felt a bit too much like taking some concepts and trying to talk about them until something made sense. I've done a lot of thinking about the fundamentals of our music system so I think my comfortability with my knowledge tainted my ability to appreciate this video.

[@davidrjbrown8808]

Fair enough for common practice era. Blues and jazz make more sense make more sense through the lens of the harmonic series, and transpositions of it, IMO.

[@grtamericanseahorseseahors9094]

@@pinheadnick8540 Well, I think I can sort of speak to this. The harmonic series is non linear with respect to dividing an octave into 7 diatonic pieces. First let me answer it directly. The harmonic series exists as a physical manifestation of reality…aka it isn’t arbitrary, the equal tempered scale is arbitrary. As mentioned in the video, the 1st new harmonic is the simplest ratio (the octave as a doubling of the fundamental. The 1st new harmonic is the perfect 5th. Without going into too much theory, the 5th is the strongest relationship to the fundamental…to the ear, but also to the physics…as it is the 1st “new” harmonic in the series. So here is the basic theory: All 7 tones of the major scale are derived from the harmonics but are modified by the relationship (ratio) of the P5th in Equal Temperament. This is to say that if you have one tone, a fundamental, you can derive all the other tones from it using the 5th simply stated…F - C - G - D - A - E - B. Each one of these tones is a P5th Higher than the previous one. One could go backwards as well. As you will see, if you added one 5th above the B you would return to F in an endless cycle. This is why I mentioned that the harmonic series would not align with these tones as in equal temperament. I don’t aim to put up the math as that will just convolute the simplicity of this. The harmonic series as it exists in nature is a fractal….but the slight modification made to create equal temperament is not a fractal as it is by nature arbitrary. This is not to say that harmonic series music is bad or unpleasant….it just prevents the history of Western Music that we all primarily deal in.

[@grtamericanseahorseseahors9094]

@@davidrjbrown8808 There is a huge body of work speaking to the nature of blues. There are a few modifications or techniques employed in blues that lean on the harmonic series, but as a whole blues music is just Western Music. It uses 8 tones (7 diatonic plus 1 non-diatonic) as its scale and is usually played on Equally Tempered instruments.

[@uazuazu]

One practicality of having notes in the scale tuned perfectly to harmonics is that they "disappear", i.e. if there is a C and you play a perfectly harmonically tuned G or E, then you don't hear the G or E any more as it kind of merges with the C into a single sound. Having the very slight dissonance to perfect tuning makes the note stand out as a separate entity. It also gives movement to the sound as the fundamentals beat against each other. (I did experiment with different tunings at one stage with harpsichord sounds and early music.) The possible role of the almost-F# and the Bb in harmony is interesting, though.

[@chadyonfire7878]

This is crazy, I love it

[@mackinbox]

So glad you’re back man. Your videos have taught me more effectively than any other music teacher on KZbin

[@joshgunn1973]

Always considered mixolydian to be more natural than ionian for this reason. The way you related the F# and Bb thing to classical composition was very cool, I'd never noticed that. Was boggling my mind how an 11/8 F# could possibly be more natural than a 4/3 regular F... But you can't get a 4/3 from any harmonic related directly to the fundamental, but you can between the 4th and 3rd harmonics obviously. So an alternative way to build a scale from the harmonic series would be to take the fundamental as your root, then the first more consonant interval is an octave at 2:1, followed by a purrfect 5th at 3:2, then 4:3, 5:4, 6:5 etc. 7:6 would be the first unusual interval you'd get, being a sub minor 3rd, then 8:7, a sharp major 2nd. Only issue is this would populate a diminishing lower slice of the octave with more and more notes while leaving the upper section barren, so you'd have to invert the ratios to populate the top of the octave. So you'd still get your 'harmonic 7th' at 7:4 because that is an inversion of 8:7. Either way seems any ratios involving 7 or 11, and then any higher primes have not been favoured for use as musical intervals, I don't know if this is for mathematical simplicity, or whether the harmony produced by these ratios is innately less compelling. Thanks for this great video, I'm glad I came across your channel.

[@purpasteur]

Thank you for commenting. Indeed Just Intonation (I think is what you’re referring to) is a fascinating temperament, and the ratios are indeed much simpler.Maybe future video!

[@davidrjbrown8808]

That half sharp F sounds great when bending up from the F

[@KalebPeters99]

i cant wait to return to the music space station!! 😅 this was a fantastic exploration of harmonic series, and i really loved your thoughts on why the major scale is a useful tool despite (or perhaps *because of*) its discrepancies with the harmonic series! 👏 as someone attempting to explore the boundaries of modern music theory myself, i hugely appreciate your videos!! 🙏🙏🙏

[@BasperMarshall]

welcome back

[@mr.wigman]

Dorian and gypsy major are something like fractals. Not really, but they are symetrical and dorian is the most neutral diatonic mode. Its darker than the three major modes and brighter than the other three minor modes. Dorian is somehow special in terms of structure and position. If you play close atention, the note d devides the keyboard in two symetrical halfs. The fractal of tonality is more going through all tonality beginning with perfect fifths, pentatonic, lydian, ... ending with total chromaticm eventually steping in microtonality until infinite small intervalls. There are fractal rhythms btw that sound quite trippy. Virtual riot made a video using an polyrhythm technique. Cool stuff

[@Azubi_Meatball4349]

Woah only 8k subs?? Gyahdayum this is a good video

[@pinheadnick8540]

you say that we perceive later harmonics (like 8th and 9th) less than the more fundamental ones because its simply how we perceive it, could it not be that more fundamental frequencies are more baked into sounds than the higher unstable harmonics?

[@thegeeeeeeeeee]

Cmixo with half sharp 4? I have to try that fractal scale! Thanks and great video 👍

[@Oddity12]

UR back 😇

[@Noone-of-your-Business]

So *_that_* is why some plugins differentiate between _even_ and _odd_ harmonics! 🤯 The even ones are just the *octaves* and do not add as much "color" to the sound, we perceive them as "cleaner" but also less interesting... I wish I had learnt this sooner. There is *_SO_* much marketing BS to cut through in music tech, and I bet half of all recording engineers do not even know this one. They ought to teach this in school! Well, _music_ school at any rate. Then again, maybe they _do._ Who knows. Any experience from others here in the comment section?

[@pinheadnick8540]

i didn't understand how we can consider the harmonic series a fractal :(

[@DarksTunes]

Would the pattern scales be the closest in 12 TET to fractals? Like the repeating intervalic pattern (W, W, W, H) giving every note a 5th?

[@joeywisedrums]

No, the diatonic scale is not a fractal. However, the harmonic series (adjusting the out of tune notes a few cents) fits perfectly into the key relationships between the 1, 4, and 5 chords. For C F and G it works.

[@althealligator1467]

2:29 The reason it's called the first harmonic is... what else would it be called? If the complex waveform is constructed by adding sine waves of frequencies that are whole number × fundamental frequency, then 1 × fundamental frequency counts, since 1 is a whole number. Hell, it's the most important one since it's almost always the loudest. The thing that causes this confusion is that this first harmonic isn't the complex waveform, it's a sine wave like every harmonic, it only happens to have the same frequency as the complex waveform (the fundamental frequency). Not including it would be completely arbitrary, because the while the point of the concept of overtones is to look at harmonics that have a frequency higher than the fundamental, that's not the point of the concept of harmonics.

[@Ivan_1791]

Scriabin mystic chord

[@mondellomusic]

There’s bound to be burps and farts with that much gas

[@talos.fractal_author]

Your thumbnail looks like a spongebob squarepants title card.

[@clarkbowler157]

Symetric

[@GJOstudio]

Dude, what if you tune your instrument first to 443 hz ? I know the harmonic relations remain the same, I guess but mathematically this might give different outcome