The Clock Diagram

Note: Clock Diagrams are all about expressing Pitch Class and Interval Classes. So when you hear or seem some weird octave displacement, that's why. It's irrelevant to the lord of clocks!
Patreon: / sideways440
Twitter: / sideways440
Twitch: / sideways440

[@AdamNeely]

This was a great introduction to set theory!

[@AMOW42]

02352T0.... 😏

[@Ololoshaish]

Hey Adam! Can you recommend any books or online courses to learn more about math in music theory concepts, like sets, classes, groups, symmetry, etc? ty!

[@shneancy220]

I found your channel yesterday and now you are here, coincidence? yes, probably, but a nice one

[@rodrigorebolledo9918]

Not at all, Adam 'the lick' Neely has commented various Sideways videos.

[@Unkraut]

you

[@flikkie72]

As a maths major, this was the most sense that music has ever made to me.

[@KevinSmithGeo]

Comp sci major here and I very much agree.

[@bamesjond7495]

Accounting major, I'm right there with you guys.

[@Whatismusic123]

Sorry to say, you still don't understand it, as this is a pseudo-scientific concept that only seems to work on paper.

[@louisaruth]

@@Whatismusic123 no, it works. i figured this out mostly by myself thanks to the harmonagon app. you can use this system to model music like it is a torus

[@alexrodriguez4643]

I spent thousands of dollars to learn this in a class. You made more sense than my professor

[@nowhereman6019]

I have no idea what you're talking about but I love it.

[@thomashodgkins6233]

He’s as blind as he can be, just sees what he wants to see. Nowhere Man can you see me at all?

[@solseeker7502]

I see we are all part of the same tribe. It's probably because we all live in a yellow submarine.

[@gustavosousa3554]

He’s a real nowhere man sitting in his nowhere land making all his nowhere plans for nobody

[@Evangelionism]

*Lmao!!*

[@cheesecakelasagna]

Nowhere Man I'm so with you. (also, where did you get your dope profile pic from?)

[@Ruhigengeist]

Jesus christ. Thank you for this, really puts music into terms I can understand, as a computer science major. Set theory is everywhere.

[@thedolphin5428]

No, set theory exists only in the minds of mathematicians and musicial theorists.

[@vvolfflovv]

I can C Major benefits, using this.

[@dariocaporuscio8701]

wolfflow ahahah

[@Legotankt34]

I see A minor flaw in this concept, you won't be able to communicate your ideas to those who do not know this system. (Sorry for the bad joke)

[@arturmizuno]

what A sharp joke

[@egkeagle8520]

Disliked

[@erikw4193]

Don't try so hard to be funny on the internet, you have to B Natural

[@sasimitra5871]

Okay. I'm alarmed at how similar Mathematical Set Theory and Musical set Theory is.

[@CheCheDaWaff]

Err... I don't see how this is like mathematical set theory at all. You're interested in unordered tuples of objects, I guess?

[@sasimitra5871]

Modus Ponens I mean the basic terms, and how they are related. In retrospect, it does make sense why.

[@wkingston1248]

Modus Ponens it is like math set theory in the basic concepts, sub sets, super sets, symmetry ect.

[@Ceviche4K]

Sasi Mitra Music is just sound maths tbh

[@kenhimurabr]

The creator of this theory for musical analysis was mathematician.

[@flamingmuffin666]

To go into an entirely different field of mineralogy (or crystal chemistry in general), this clock diagram concept is incredibly close to how one classifies a crystal lattice structure, and how two different structural arrangements can be related by operations of rotation, mirror planes, roto-inversion, etc., of one another. A crystal, much like music, is just a mathematical repetition of its constituents, and being such I’m kind simultaneously (un)surprised that they can be mapped along the same principles.

[@Awesome20801]

This is like mathematical group theory at it's finest!

[@TTALeapMonster]

It would be so cool if we could apply notes to a crystal lattice structure and play it like the notes on these diagrams.

[@Whatismusic123]

This is a pseudoscience, it doesn't work specifically because it's trying to mathematically analyse music.

[@Simrasil_]

8:26 pronouncing that name was actually the most impressive thing in the video ^^ jk this is a really cool and helpful tool to analyze music :D

[@Trowa71]

Takes 12 hours to make video. Takes another 12 to google name.

[@james_subosits]

Simrasil I have a feeling that Patreon donor just wanted to fuck with him and see if he'd get it right

[@halian.vilela]

I thought the exactly same think!!!

[@danielf3623]

It's alike Sideways and 3Blue1Brown had a baby and it was this video. Awesome.

[@primarysecondaryxd]

Wait wait wait, you're a genius. That should totally happen. This is happening. This needs to happen.

[@qwertyuiopaaaaaaa7]

I play piano recreationally and have never been interested in music theory, after 15 years of piano I still can't read music. But your videos really inspired me to listen to different types of music, especially Debussy (he's always been my favorite), and also to think of music and the math in music as an interesting magic system that I'm working on now. I think your channel teaches me more than any other educational channel I'm subscribed too just because its so far out of my usual interests. Very well done, thank you.

[@lissykate2037]

I keep being reminded of Inception

[@wenjunhuang419]

This guy copied Andrew Duncan's video：kzbin.info/www/bejne/hX6npaNubr2kotk

[@huhneat1076]

*MY NEURONS ARE FIRING FASTER THAN MY BRAIN CAN HANDLE IT*

[@bobbykearns1386]

well... I don't know what you said, but I like the way you said it.

[@ameliajones2266]

Woah. Mind blown. Great video

[@patrickramos1748]

I dont even know music theory, But you are still VERY entertaining even If i only understand 20% of what you say. Great job. This goes for all of your videos btw

[@BaneDane_JB]

I have no idea what your saying, but Im enjoying trying to understand.

[@lawrencecalablaster568]

I utterly love fascinating representations like this one. This helped me understand chord inversions. Thank you for making this video!

[@shmunkyman33]

To be clear, the "inverted" chords here don't have anything to do with what most people are referring to when they say a chord is inverted. In these "inversions" (which are better called "reflections") the notes in the chord change, whereas when someone asks you to play, for example, an F major chord in 2nd inversion, the notes of the F major chord (F A C) don't change, but the order does. Instead of playing F A C, in second inversion you play C F A. In first inversion it would be A C F. (Sorry if you already knew this, I could just immediately see the confusion that could be caused by his use of the term "inversion".)

[@comiclover99]

This video was extremely useful in helping me understand set theory in music so thank you. My only issue with this way of looking at things is that although the maths may dictate that a major 6th and minor 3rd are the same because the shortest intervalic distance is the same, sonically the distance matters. There is a big difference in sound between a C and C# next to each other and those notes displaced by an octave. The level of dissonance is completely different. Its much easier to account for a semitone in chord construction than a b9 interval. So this method is extremely useful for some things but I find that the way that a lot of music based on mathemathics (including twelve tone serialism and the like) ignore aspects such as octave displacement really frustrating. But again, thanks for another amazing video.

[@theappleboom5391]

It's a hammer nail problem. If you only have a hammer, all you see are nails, but if you recognize that more tools exist than a hammer, then you can build more fully formed structures. Your issue, as I understand it, isn't so much the tools themselves, but the obsession over those tools by many theorists and the lack of tools to wholly describe and implement other aspects, like octave displacements as you put it.

[@comiclover99]

The Apple BOOM Exactly. These theories of harmony and harmonic analysis are great in certain circumstances but multiple theories are necessary. I had no issue with this video but just with the usage of this information by some theorists and the fact that Im sure many will take this information as "the best" form of harmonic analysis.

[@ILoveSoImAlive]

well. every single model is only viable inside some borders, where it is precise, relevant and somewhat usefull. the only other thing would be world formula, or just inapropriate model. all music models are very simplified and abstract, and have low range of accuracy. one of main purposes of models IS to blend out irrelevant details. if you want to go deeper, you need to take into account the nature of sound and nature of perception of sound. and that means at least inner structure of any sound(with overtones, energy destribution, phaseshift, aso), nature of sound medium (inertia, pulsresponse, frequencyresponse in magnitude and phase, and all the funny things that result out of that like interference of the sound within itself), add to that geometrical properties of propagation (like reflection and refraction), and then go one lvl higher and think about what happens if you suddenly have 2 of this monstrosities, where each component of this 2 interacts with each component of another one, and then each result of this interactivity interacts with each component and each another result of this interactivity. wrap everything you got into additional mechanics your brain implements to process the sound data, and you will forget where you started. you will realy fast lose everyone. most people will not be able to see the forest behind the trees, if you dont abstract to the lvl, you are working at, but instead go into details below this lvl.

[@nametry3]

I think that you could define an interval as the _clockwise_ number of spaces between two notes (instead of the smaller number of spaces) you can recover the other intervals while keeping the concepts of this video. I don't know anything about music set theory (I do know math set theory) but maybe we can extend these techniques to a more specific interval definition

[@themandownstairs4765]

okay but his pronunciation of "Ḟhłōwrhîåń Ṗìrhchqër" at the end was so smooth

[@theorodgers4991]

‘All of them are wrong because I’m right’ - Sideways Really cracked me up!

[@Pandaplaya123]

This sounds like a round or spiralling instrument based off of a clock diagram would be godly in jazz. Please tell me these exist.

[@citrusblast4372]

What does a spiraling instrument mean? Like its shaped like that?

[@Euphist15]

Citrus Blast yes

[@daanwilmer]

There's a sort of spiralling instrument based on the circle of fifth, called the Striso (developed by Piers Titus van der Torren for extra googleability). Is that similar to what you're looking for?

[@tuckersmith7991]

Not jazz, but this reminded me of these strange hang instruments. This one is chromatic kzbin.info/www/bejne/eJLRpqx9jbd2pqM

[@rodrigorebolledo9918]

Dude, that's a genious idea, you should really try to make something with it.

[@CorruptPianist]

DUDE I'M TRIPPING THE HELL OUT RIGHT NOW BC I'VE BEEN THINKING ABOUT MUSIC IN THESE TERMS FOR YEARS BUT MY DUMB ASS NEVER THOUGHT TO ARRANGE IT INTO A CIRCLE

[@jfredett]

I'm a mathematician, I'ven't seen "Set Theory" (in the context of music, it's a pretty common idea in Math) before. This is very neat. There's some cool Group Theory stuff going on there (specifically this looks pretty similar to the dihedral group with 12 letters; flips, rotations, etc). It has a concept of 'addition' in the form of intersection, but also you could come up with a sort of multiplication with Unions (units are 'no notes' and 'all the notes' "selected", resp.) Punchline is this is a very cool way of looking at music theory. Especially once you start mapping out alternative scales (what if music had more than 12 notes, i.e., microtonal systems?), or comparing this group structure (assuming it's there, which I haven't actually proven, but it does seem to be there) to other groups. There are basically 2^13 - 1 ways to choose some set of notes from this clock, that number happens to be prime, assuming that each of those ways is achievable, and this really does form a group like I suspect, that fact means this is the _only_ group of that order, and also implies a few other properties. That means if you can build two groups (using the union and intersection methods I mention above), you can actually draw a isomorphism between them (that is, the two methods are equivalent -- they represent the same underlying structure), indeed, it's an isomorphism from the group to itself (an automorphism) which has some additional implications. Very very cool way of looking at this. People often talk in passing about the symmetry structure/group structure of music, but I've never really bothered to dig into it. This is pretty neat.

[@jfredett]

I literally had this pop up in my feed again, forgot I had seen it, watched the video in full thinking, "This is kinda familiar -- oh it must be because these things look like a Field." Came to write the _exact_ same thing only to see my name having already done it almost 4 years ago. Good job past me. This really is a cool idea.

[@01Micha]

I know almost nothing of music, but I do know a bit of math as a hobby, so whenever you touch on the subject of math I am amazed by how closely related both of these truly are. And hearing you explain it all so passionately is also super engaging and great. Honestly, subscribing to you has been nothing but a treat every time you upload a video. Keep up the great work!

[@medicalbar]

As a math enthusiast with an interest in music, this video was incredibly interesting, mind-opening, and delicious. Keep up the great work! I loved it

[@CratthewF]

nerd

[@Derptastification]

I played in an orchestra for a few years but have only touched my instrument here and there a couple times since going to college. Your videos make me yearn for that knowledge and understanding and have stood as a good supplement for the time being. I cant wait to graduate and take lessons again and hopefully be a part of an orchestra once more. Thank you for your videos!!!

[@ccalvac18]

This is the whole negative harmony thing every jazz person is going nuts over after the Lee-Collier interview. The clock diagram certainly is easier than drawing the circle of fifths, the big difference being that the prior is arranged chromatically. What should be noted about negative harmony and other atonal mirroring techniques is that the prime importance in execution is voice leading (duh, I guess), a lot of people are going crazy over negative harmony w/o understanding that something being the mirror of the dominant doesn't mean you can use it the same way and that your mirror might just imply another dominant function (G7---> F-6 which implies Backdoor iv VII7 I which is F-6 Bb7 Cmaj7) which is a little redundant imo. Not 100% on topic w the video, I know, especially since this video had a focus on scales and here I am talking about harmony. I'm excited to have another tool at my disposal!!! Thank you so much sideways! You rock!!

[@stupidhatonthefloor3]

I think this might be my personal favorite of all your videos! Takes me back to my days in Theory 4 :)

[@95CamaCazzie]

Fantastic as always

[@thxqrop5765]

true

[@thxqrop5765]

sideways best channel

[@edmbm00]

Fantastic as sideways

[@alexalani10101]

I remember watching this in high school when it came out, and now I’m in the middle of Music Theory 5 and when we started learning Set Theory I recalled this video in the back of my mind lol.

[@gd_xl]

I’m in AP music theory rn and your videos are like a drug for me gah I love this channel

[@GUIM1797]

Man, this is a really great video for people getting into this stuff. Thanks for doing this! It's hard to find videos on more advanced concepts that are both accurate and well-done, but also accessible!

[@benpriest9555]

Thank you for helping me understand an area of music I've never heard of and probably never will again

[@Lys1998]

This video was so interesting! I always get excited when you upload :)

[@MirnaXavierG]

You are amazing! One thing people take for granted is how visual tools help us understand a theory or basically anything. But not you. You know the power of images, shapes, frames from another video. Whenever you mention another video from the channel and let some frames from said video roll, our brains immediately remember the video and what you've said there, so you use that tool to help you. I know some teachers use that tecnique but I wish people valued it like you do.

[@chrisrichardson6294]

I don't know much about music, but I'm in the middle of a class called Algebraic Structures, and all of the math we've been doing just showed up in your video! Amazing stuff.

[@Caiphex]

That was amazing! As an absolute nervous in music videos just enough to get himself in trouble this was so fascinating

[@barryhowardbrake]

Very interesting. I guess this counts as a mesofact for me! I graduated with a composition degree in 1990, right when this article came out, and totally missed it. This is my first introduction to the concept, as a lifelong professional composer. Crazy! Thanks.

[@slaughterround643]

Fascinating, entertaining and educational; what more could you ask for? Great video as always!

[@constantinosstylianou]

Damn this was amazing!!! All your videos are top-notch quality, but this one was something else! I know more maths than music, and I had a thought like this many times: "There MUST be some kind of 'purely' mathematical branch that discusses relations between notes, and represents scales in a numerical way". But I never got to search for it, it was just a passing thought for me. But now one of my favourite youtubers made a really cool video for it!! Thanks for this amazing material, man, this really is one of the finest channels in here!

[@maciejczajka3495]

What an amazing video! You are really getting better at this!

[@AngelBolt]

Wow this reminds me a lot of color theory, ad seeing scales as palettes.

[@maz.s]

Wow! I’ve been watching your videos for a while, but this is the first time I feel like I really understood it. I’m tempted to go back and watch all your old videos with my newfound understanding of what all these music terms actually mean. Or maybe just draw a bunch of clock diagrams and throw some math at them.

[@TheLockeNessaMonster]

Oh my @*#&%$ gosh, you opened my eyes. This is a great visual way to see notes. I swear, every video you put out gets me more and more excited to play music using some kind of theory rather than simply playing what I hear by ear.

[@LucasPreti]

Your videos are amazing, man, I always get exited when you post something

[@fisk8804]

Are you guys hyped for shrek 7 or what

[@DoartYT]

The fact that going backwards is unnatural and to see how that is so well linked to music, its pretty fascinating and creepy.

[@nikkin3752]

This is so cool!!! I loved learning about this, and I feel like if a lot of my music theory courses had been explained like this, I would've found it much more engaging a lot sooner. Thanks!!

[@mitchelcsermak6993]

A day with a Sideways video is always a good one

[@ollerich32]

037 .. 😊 Reminds me how we used to build chords in Trackers. Good to see that this ancient technique is being re-explored. Great Video!

[@leahs2068]

New Sideways Video? *Drops everything* I love this nerd, time for some nerdy music time whoo!

[@daltonwade3853]

Man this blew my mind, no joke, put together a M7 chord, threw in Re for shiggles, mapped it on this clock, flipped it, rotated it, flipped it again. It brought out these amazing sounding chord progressions, that took some thinking about how complex the relationships were. This is Amazing!

[@petarmilic9729]

I feel like this is the most important video youve ever done. Certainly my favorite

[@Xeroskia]

This was one of the most eye-opening music videos I've watched in a while. I feel like I just watched a segment on quantum relations and comparisons to the macro scale of the universe. But in the universe of musicality..

[@huruey]

I have been looking for this information having heard about set theory here and there. Now I can finally unify this with some other ideas I'd been working with and it's a total epiphany. Great video thanks!

[@calc8017]

I'm a Cs major who's only ever learned about music theory from this channel and this video was the most interesting alien-speak I've ever heard

[@zekebeckman]

That last set of notes and cluster chords made me laugh out loud. Never heard of this before. Super cool.

[@jeshweedleon3960]

Set theory: Topology for Music .....yay

[@alexanderreynolds6018]

This is way, way above my head and I still watched all the way through for some reason.

[@SalamaSond]

Wow, whiplash, from the sudden enlightenment. Thanks for this bridge between the glandular and the visual brain. I see it now.

[@billygarvey633]

WOAH Negative harmony!

[@stuartjones8787]

Exactly

[@Bahimo3154]

In symmetrical way yes .. but not the same with ernst levy thematic

[@AbhiBass96]

Not really, you see that flipping the C minor doesn't give you C major.

[@afkaralp]

@@AbhiBass96 negative harmony puts Cmin into Fmaj not Cmaj

[@Raftaf13]

WOW ! this looks awesome, it's almost like seeing the hidden gears of scales !

[@Mixu.]

This is the first video I was pretty much completely lost in lol. I could follow the (admittedly little) math, but that's about it. Somehow my laughably small musical knowledge seems to be enough of a base for most of your videos... also you're excellent at explaining complex topics.

[@LordQueezle]

This is fantastic. I just started set theory the other day in class, and I found this and it blew my mind

[@srbelnap]

I'm late to the party, but you went hardcore music nerd on this one. Absolutely great!

[@usedtobesomeone9149]

Dude this awesome man!! I’m totally going to mess around with this once I get home!

[@revilo2099]

“Imagine that we had a keyboard” Ok that’s easy enough. “With all the notes labels on it like so” Umm.....

[@ClankyClanky]

We just talked about set theory in my Theory IV class and I was confused as hell but this video really helped me understand it a bit more. Thank you!

[@MarushiaDark316]

My dude, this video is a god-send, since I've been using a similar system for color theory and color harmonies for years using pentatonic and major / minor scales with key systems (the way the Impressionists did). My teacher always said it was analogous to music theory, but I'm shit at music theory, so this helps tie the two together in a way that I - a visual learning - can totally grok.

[@louisac303]

so i played violin and studied basic music theory as a kid, and i can't believe I was never shown a clock diagram (though i suppose that if we're similar ages then at that time maybe they weren't widely recognised enough). trying to explain to a kid why certain minor and major chords are complimentary is really difficult and most of us just end up learning it by memory without fully understanding it in a way we could right down on paper, and end up hearing that they're complimentary and intuiting it based on years of having it hammered into your brain that it's just true without a satisfactory (for an eight year old) reason why. this is freaking awesome.

[@egbertkind]

This channel is like vsauce but for music It’s fucking amazing

[@NotRightMusic]

Somewhat related, but just as curious is Miles Okazaki's study and books on visual references for musicians.

[@NotRightMusic]

DIg it: www.milesokazaki.com/wp-content/uploads/2016/02/visual-reference-smaller.pdf

[@WadWizard]

I love this kind of stuff

[@wenjunhuang419]

This guy copied Andrew Duncan's video：kzbin.info/www/bejne/hX6npaNubr2kotk

[@fractlpaca6285]

First heard about this concept looking into tone clock theory and Peter Schat and Jenny McLeod. It seemed very interesting and this video definitely was! Thanks 👍

[@DG-gx8pn]

I might toy around the guitar using this diagram.... Thanks once again Sideways!

[@MyronDavismd]

Fascinating! Thank you for posting this!

[@BuckshotBill118]

This is pretty trippy but also very useful. Thanks for sharing!

[@virginiapeterson1404]

Im using this to learn music before i learn what notes compose different chords. I love it.

[@dkcholo5281]

this entire video is just a series of mind explosions

[@Diegoalfonsocrespoya]

I Loved this video. Thank you for making it!!

[@HighlandViolinist]

You just explained three months worth of my set theory classes in 8min, 41sec. Quite impressive!

[@ehudzechariahschmidt7036]

Wonderful video! Thanks sideways!

[@chockydoe]

i find it kind of ironic that you’re the only video-essay youtuber that i watch about music and you’re also the only video-essay youtuber that doesnt use background music in videos

[@pieza43]

This video is incredible, thanks for talking about these issues

[@SquidgytheGreat]

Much of my inspiration comes from Hisiashi's music. As I've played his music so much, when it comes to composing, I've subconsciously been playing those marvellous tetrachord/pentatonic scales - is has literally opened up my whole world. My compositions have become much more fluid and flexible!

[@carsonstadler6921]

God damn these kids putting advanced calculus concepts into my music

[@VioletStone100]

Confusing? Yes. Fascinating? Yes. Something I will watch again in the future after some more music theory? Yes.

[@michajanik9277]

This is one of the most awesome things, I have heard in a long time :D

[@Foxarocious]

I put this video on at half the speed because I'm bad with fast numbers. It makes you sound drunk, but it honestly helps xD this is an informative ass video!!

[@V1rusFPS]

I know literally nothing about music but I love your videos

[@Haridnar]

I really enjoy these music theory videos that I am barely capable of comprehending. (They're well explained but out of my field of expertise.)

[@TrebleWoofer1]

Excellent! You are very clear and concise in your explanation - - especially for the 'fairly' complex topic of set theory. Well done :)

[@morganburt2565]

I am a VERY visual learner so this stuff is so helpful for me to learn theory. Thank you!!!

[@Em-ic3vm]

Ok I know nothing about music, and I know you explained this very well, and I’ve accepted that i still have no idea. I just really like these videos because he actually sounds really passionate about music. it’s really interesting to listen to someone talk about something they love.

[@haydenaron2533]

thank you for helping me with my music theory hw

[@dokkabaerpg7896]

Holy shit. I never thought of music this way before. This is definitely super interesting

[@poliestotico]

I was locked without internet one summer with my mathematician friend and we decided it was a great idea to rewrite how to represent music on paper and we came to this exact same conclussion wow this was usefull

[@GiantButterKnife]

This makes me want to change my major to analytical music theory, if that's even a thing I could do.

[@SoGraphitesify]

Holy shit, thanks! I was looking for a simple way to explain some stuff to my bf and this is just perfect!

[@malekibrahim7697]

What an interesting concept. Love the video!