This Music Trick Shouldn't Work
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- Опубликовано: 4 июл 2024
- But it does. What's up with that?
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One thing I've always believed is that music theory is more than just a toolbox. It's useful, sure, but it's also an art form, a way of constructing new kinds of beauty and meaning, and when I get the chance, I like to try to show that side of it. There's lots of great examples, but one of my favorites has always been Jack Douthett's infamous Cube Dance, a deceptively simple map of triads that both hides a ton of insight about harmonic relationships and also just looks really frickin' cool!
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Script: tinyurl.com/yeysmtcn
And thanks as well to Henry Reich, Jon Hancock, Gene Lushtak, Eugene Bulkin, Oliver, Adam Neely, Dave Mayer, OrionWolfie, David Bartz, CodenaCrow, Arnas, Caroline Simpson, Michael Alan Dorman, Blake Boyd, Charles Gaskell, Tom Evans, David Conrad, Ducky, Nikolay Semyonov, Chris Connett, Kenneth Kousen, h2g2guy, Andrew Engel, Peter Brinkmann, naomio, Alex Mole, Betsy, Tonya Custis, Walther, Graeme Lewis, Jake Sand, Jim Hayes, Scott Albertine, Evan Satinsky, Conor Stuart Roe, ZagOnEm, רועי סיני, Brian Miller, Thomas Morgan, Serena Crocker, Adam Ziegenhals, Mark, Amelia Lewis, Justin St John-Brooks, DialMForManning, Andrew Wyld, JD White, Graham Orndorff, gunnito, Douglas Anderson, Foreign Man in a Foreign Land, Tom, Kyle Kinkaid, William Christie, Joyce Orndorff, Isaac Hampton, Mark Mitchell Gloster, Andy Maurer, William Spratley, Don Jennings, Cormag81, Derek Hiemforth, Bryan, Mikeyxote, Milan Durnell, Dan Whitmer, Thel 'Vadam, FAD3 Chaos, Michael Morris, Bill Owens, Martin Romano, George Burgyan, Marc Testart, Carlfish, Matthew Soddy, Flavor Dave, Alin Nica, DraconicDon, John W Campbell, Megan Oberfield, morolin, An Oni Moose, Ken Birdwell, Blue 5alamander, Cliff Hudson, Olivia Herald, JayneOfCanton, Ethan Savaglio, Robert Bailey, Deirdre Saoirse Moen, juneau, Sina Bahram, Ira Kroll, Patrick Minton, Justin Katz, Roahn Wynar, Chuck Dukhoff of The Stagger Lee Archives, Bob D'Errico, Robert Shaw, David Shlapak, Donald Murray, JD, Rennie Allen, Travis Briggs, Claire Postlethwaite, Greyson Erickson, Matt Deeds, Jordan Nordstrom-Young, Brian Covey, Miles_Naismith, Jay Harris, Sean Murphy, JasperJackal, Tommy Transplant, Wolfgang Giersche, ParzivaLore, Amanda Jones, Olaf, Colleen Chapman, Gil, d0d63, Jon Purdy, Ken Brown, Colin Kennedy, The Mauses, christopher porto, Billy Abbott, William Wallace, Karel P Kerezman, Ted Trainor, mightstill, Nick Loh, Randy Thomson, rpenguinboy, Antarct, Erika Lee, Mikaela, Vinayak Nagaraj, sandra zarbatany, Aenne Brielmann, Simone Andolfo Andolfo! Your support helps make 12tone even better!
Also, thanks to Jareth Arnold!
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Some additional thoughts/corrections:
1) Do I actually think 19-tone equal temperament is the future of Western tuning? Nah. The argument is mathematically reasonable but the practical implications seem daunting enough for relatively little gain that I suspect we'll just coast on 12 notes until we move on from equal temperament entirely. But I thought it was interesting how the system relies so heavily on current musical norms and breaks immediately if you change basically anything, and 19-tone is a good way to demonstrate that.
2) I couldn't find a way to fit this into the script, but another way to think about how the augmented triad can replace all the other bridges from A to its various 2-step neighbors is that, no matter which bridge chord we used, the process of getting to any of those minor triads _always_ involved raising E up to F. And since you can do your voiceleading work in any order, we can just put that step first and boom, A augmented every time.
3) To be a bit more explicit about the process of combining moves to measure distance, it might seem like there are so many options that it'd be impractically difficult to find the shortest path, but that's actually not true, thanks to one little fact: The two-steps moves are only useful for moving between cycles. Anything else can be done with just the one-step moves. That makes the process a lot easier. If the two chords are in the same cycle, just do parallels and mediants, and if you're hopping between cycles, use whichever of the two-steps will put you closest to your target. One of the beautiful things about this system is that it's fully navigable with a basic greedy algorithm.
4) Those of you already familiar with Cube Dance and Neo-Riemannian Theory in general may be wondering why I bothered including the other bridge chords at all, as they exist nowhere in Steinbach and Douthett's original paper or in Cohn's descriptions of it in Audacious Euphony. The short answer is that last time I made a video about Cube Dance, I followed Cohn's basic approach, and I got a lot of people asking how diminished triads fit in, so this time I wanted to explain why they don't. They work perfectly well as secondary bridges, but their function is superceded by the augmented chords, and I thought it'd be good to show that.
5) I suppose I didn't mention the major(b5) chord, so there's still one possibly-reachable triad left out of this analysis, but uh… I don't care about the major(b5) chord. Sorry. It's useless here anyway.
6) Did you know that the original Douthett/Steinbach version of Cube Dance is different from the one Cohn uses in Audacious Euphony!? Not structurally, but it's mirrored, so the bit where I talk about the clock numbers had to be rerecorded 'cause I wrote the script based on Cohn's version, used Douthett's version as a reference while filming, and didn't notice the difference until it was too late. This means you lose Cohn's mnemonic observation that, in his arrangement, the clock numbers represent the sum of the pitch classes in each chord mod 12, but I wasn't gonna talk about that anyway and also you have to be pretty familiar with pitch classes for that to be useful.
All those alternative EDOs into 17,19,31,41 or 53 steps may certainly approximate the harmonic series better than 12 EDO. But they all lack the symmetry of 12 EDO since 12 is a highly composite number with factors 2,3,4, and 6 allowing the modulations you described.
My god, you know even more than you teach in your videos which is already so much... Really impressive! Tbh i would love to take classes in person from you like at a university for a year, to learn everything you have to teach and have the time to find day to day implementations of these theories for my own music. Because i do find the theory fascinating, but all i can realistically see myself doing in my head in real time is think about how many half steps away a chord is from the one i played before and that only with enough practice. No chance i can remember and implement the specific 1 and 2 step motions in real time 🤔
the first one only matters to people with *frets*
@@russellzauner what about pianos, brass, woodwinds, tuned percussions...?
Hi 12tone,
First, thank you for your Videos! They are always a joy to watch and to learn from.
2nd Nebenverwandt means a bit more than 'related'.
'Verwandt' means 'related' and 'neben' means 'next to' or 'on the sie of' depending on usage.
Greetings from Germany!
You've heard of the Circle of Fifths. Get ready for the Cube of Augmented Triads
the dodecahedron of
You saying this made me realize that the circle of 5ths should actually be the dodecagon of 5ths.
Too hard for my brain
I'm waiting for the dodecahedron of diminished 11ths.
@@jackielinde7568Would prefer the Tesseract of diminished 11ths.
I feel like the words "Hamming distance" should come up in this work.
The STEM is strong with this comment
This looks like a hypercube in the 4th dimension in that sense
i was thinking the same. like we just need an obsessive theorist of music theory that has learned computer science. there must be one person at least.
Indeed it should.
@@hellNo116Roger Shepard of the Shepard scale was the inventor of nonmetric MDS. Lots of math already around, I guess is what I’m saying.
If you squint really hard you can see Coltrane's ghost smiling.
🔥
He is in heaven writing interdimensional steps around the weird music cube
These are my absolute favorite kind of 12tone videos. Don't get me wrong, I love the song analyses, but this channel is so great at expanding my understanding of music theory, especially on niche topics like Cube Dance. As a lifelong music nerd and very, very novice composer, these theory videos truly challenge and elevate my thinking. It's awesome. Thanks, y'all.
So true. I like how it highlights the exploration aspect of music theory, which is my favorite part. just sitting in front of the piano and trying out specific things.
@@fllamingbarfi7126 Exactly! I've been singing since I was a child but have VERY little theory knowledge. Over the past few months I've finally started to get my head around basic theory/composition, and I owe a lot of it to videos like this. They make the "sit at keyboard, figure things out" process so much clearer.
Youre entering what used to be my territory. This is Group Theroy, in Abstract Algebra.
Add some Hyperbolic Geom, and some non-Euclidean stuff and you get music.
Maths really need to make a branch called Music lol. I mean we already have brain melting topolgy
You also need vibes, man
@@darksecret965check out regular temperament theory for brain-melting music maths
@@darksecret965There are mathematical theories of music, but they don't seem very popular. A few books on this topic that were just recently released are "Exploring Musical Spaces" by Hook, "A Geometry of Music" by Tymoczko, and "Computational Counterpoint Worlds" by Augustín-Aquino et. al. The math in them is really cool (I'm also planning on being an algebraist), but I don't really understand the music theory so I can't really say anything about that.
Hey, I'm planning on being an algebraist (enumerative algebraic geometry), and I was thinking the same thing. This thing looks like a Cayley diagram for some small group I've seen in the past, so I'm looking into what group naturally acts on it. My guess is it's a semidirect product of Z6 with one of the order 4 groups (most likely Klein-4), but if it isn't, it should be some extension of Z6. If you're curious and haven't figured it out already, I'll let you know when I do.
The Term "Nebenverwandt" rather means something like secondary related.
Neben = Next to
Verwandt = Related
It is a compound word, but it is quite old and has no use outside of a few very specific areas of application, such as music theory.
“…and that’s why Surfin’ Safari is so catchy.”
Funny fact. In English words "note" and "tone" looks very similar and sometimes they are used interchangeably. But the word "note" comes from "notation". Enharmonics C# and Db are not the same "notes" - they are notated diferently - but they are the same tone. The tone is related to their pitch.
You randomly throw a Feynman diagram in beautifully. What's the Venn diagram overlap of quantum physics geeks and music theory geeks?
I don't know, but there's at least the two of us!
"I don't know why this works, but it does"
Circle
@@flanger001 "Sorry I'm late to tune your piano Mrs Jenkins, CERN phoned to discuss my experimental proof that antimatter is regular matter travelling backwards in time."
The overlap is huge. Recently a French horn player in my orchestra brought up quarks and gluons in a casual conversation and we all just followed along.
i smiled so wide when you drew cat-dog, such a classic
"In spite of [Dinosaur], we still need to [Platypus], when it used to be [Apples and Oranges] - It's a [Big Bad Wolf]. Arguing that these two notes are [Ditto] [Disgruntled Villager] on [RUclips] gets people [Reddit] me. When we [Megazord] our [Airplane] of [Snowman], that'll tell us how [Battletoads]..."
Have you ever considered putting your music sheets up for sale? They are works of art.
So are you!
I would frame one and put it up.
@@doctorsteveb4906 Same, in a heartbeat
would be a good charity thing! if they save them
100% agree
'Nebenverwandt' is Not German for 'related'
'Verwandt' is German for 'related'
Whilst 'Neben' means 'next to'
I can also mean that Something is less important than its Main counterpart.
I'm glad Cube Dance came back up because it's been living rent free in my head since you last brought it up.
Xenakis took the phrase “cube dance” in a totally different direction
I wonder if this has got to do with how easy it is to evenly divide 12. We divided the octave into base 12.
That might make it interesting to divide octaves into other easily divisible numbers. Weird that we then use 7 notes out of those 12 notes. Make a 16 note octave and use 11 of them, what do you get?
Yes, divisibility is one reason. The other reason is that it approximates the overtone series quite well. Not perfectly - there are better approximations, like 31 steps - but it's the combination of those 2 reason which makes 12 TET so useful.
16 can be challenging harmonically, though coincedentally it does have an 11 note scale with enharmonic notes that i think is probably the best one its got, it has 3 dominant chords and the seventh is closer to 7/4 and the major third is closer to 5/4 making it almost a 4:5:6:7(a harmonic seventh chord), trouble being that the fifth is closer to 28/19 or 40/27, 25c flatter than the fifth in 12. Also 8 is a chain of neutral tones right between a semitone and a wholetone, 2 make a minor third, it then proceeds to hit some very unfamiliar intervals like 450c and 750c which are half a major sixth and half a minor tenth respectively, that is somewhere between a major third and a fourth, and between a fifth and a minor sixth, and which they sound like really depends on the context... and they can be quite dissonant. Another quirk is that due to the flat fifth if you build a major seventh chord up as M3 m3 M3 the major seventh becomes a neutral seventh, in order to reach the major seventh you would have to build an augmented chord(which doesnt close at the octave cause 16 isnt a multiple of 3) or you would have to make one of the major thirds into the aforementioned 450c intervals.
Theres also a 7 note scale like diatonic except the minor thirds and major thirds are swapped so instead of a diminished triad you get an augmented triad and the wholetones become neutral tones and the semitones become supermajor wholetones, in a pattern like 2 2 2 3 2 2 3 for what is called anti ionian, the pentatonic that is part of this is (2 5 2 2 5) also wierd in that instead of minor third and wholetone steps its made of major thirds and neutral tones, you do however get a chain of minor thirds and (supermajor)wholetones in the 9 note scale you get from stacking more fifths from the 7 note scale to get 2 2 2 2 1 2 2 2 1 or superlydian, except the chain is capped off with the familiar diminished triad. Alternatively you can stack major thirds to make a 7 note scale of 4 1 4 1 4 1 1 which has a very dramatically augmented sound and continues to a 10 note scale (3 1 1 3 1 1 3 1 1 1) and then a 13 note scale (2 1 1 1 2 1 1 1 2 1 1 1 1) tbh these 3 i havent really explored much...
This is to say both that theres a lot of interesting stuff to explore there, and also that you cant just pick one and expect it to work quite the same way, diatonic is actually relatively rare compared to other scales, it shows up first in 12 then 17, 19, 22, 26, 27, 29, 31 and so on(just add 5 and/or 7 and you can find more that have them, just keep in mind if its a multiple itll likely just be the same one like in 24) that leaves a lot of other divisions in the gaps, after 35 though every division should have some form of diatonic, even if its a very extreme tuning. As far as 16 is concerned, unless you are open to wierdness and driven toward novelty(like me) i cant really recommend it for most people, 15 is nice though.
@@WadWizard omg it's wad wizard
My thought would be a 24 note octave with 13 note scales... 24 is the next highly composite number after 12, and 13 is one more than half of 24 as 7 is one more than half of 12. Plus, 7 is a centered hexagonal number while 13 is a Star number and both are primes with lots of mystical significance to many cultures.
Granted, I don't really understand all of the math and it's always felt kind of weird we call a ratio of 3:2 a fifth or 2:1 an octave(I know it's because the way we decided to divide the interval between octaves, a fifth is the fifth note along the cale that starts on C and is all the white keys and none of the black keys on a piano and the octave is 8 notes if you count both endpoints and exclude the black keys, but those are labels dirived from the final scaling system, not from the ratios themselves)... plus hearing is weird and logarithmic(each octave covers twice the range of frequencies of the octave below, but sounds just as well populated with the same number of notes in each octave, and a 10 decibel increase in volume is a 10-fold increase, but sounds like a linear increase...
18 is also equally composite to 12, its just not a peak
This hurt my brain. I'm going to revisit it after I have coffee.
Instructions unclear: I think I made benzene
At least it's not fish-shaped ethylbenzene!
Music theory is amazing it’s like a ouiji board where you can take someone’s music and make it say all kinds of interesting things, even ones the people who made it didn’t have in mind
5:16, A F Db reminds me of a song from Einstein on the Beach by Philip Glass, who does A LOT of one unit voice leading work (I guess, because I just learned it was a thing with a name in this video)
Gonna have to rewatch thin and take notes to fully understand it. Very very interesting stuff!
While you were discussing the various paths chords could take to change into one another, it made me think about series and parallel resistance in electrical circuits. I don’t know how useful it would end up being, but it could show chord “resistance” rather than distance. Do chord changes that could take multiple paths feel like there’s less resistance than chords that can only take one path, assuming they’re the same distance away in the Cube Dance?
i love these more advanced videos of yours! thank you so much for making them!
The Nebula version of this video still having the Nebula sponsorship in it😝
There's a lot you can do with a good stick: sword fights, world War 1 or 2 reenactment, fight the Sith, be a wizard. Lots you can do with a stick.
You were clearly having a lot of fun here. I thing I laughed more times at this video than I have at any of your videos, which are always clever and funny. Also, the presence of six chords, and the use of the word "hexatonic" produced not one, but two invocations of the bicycle from "The Prisoner" as an added bonus. Thanks! I continue to attempt to do my best to keep on rockin'!
Regarding 12EDO being a goldy locks zone for this concept, you'll find other EDO tunings also have amazing relationships enabled by their particular evenly spaced intervals. I particularly love more granular ones, but go very granular and you sort of lose what makes EDO so special to me. 22 is my favorite sweet spot where you can still clearly hear the angular and symmetrical nature of EDO, the chromatic motion is REALLY nice. Conversely, you'll run into problems when relying on 12EDO tendencies, you can sort of drift far from home with more granular tunings, a bit like how we do with just intonation.
You go through all these chords and it sounds a bit odd but smooth, then you wanna return to the beginning and... we're suddenly a 22nd of an octave lower or higher.
With long progressions, that gets obscured and it can be a cool way to subtly get brighter or darker, but with shorter ones that jump all over the place, it can be very jarring.
Also notice 21EDO, for example, is 3x7, whereas 12 is both 2x6 as well as 3x4, this ruins some of the interval cycles/stacks and general symmetry devices we might otherwise use, but this can also potentially be used to move back into place when already offset. And, of course, we get that unique 7EDO effectively embedded within 21EDO, a very cool sound.
And yes, that does mean that if you made a piece entirely in whole-tone, for example, you've written in 6EDO.
I personally like the sound of 15 and 22 EDO, but I wonder if part of what makes 12EDO so useful is its splitting of the octave with a trio of small prime factors (i.e. 2x2x3). You see echoes of that in things like the hexatonic (6=2x3) cycle, quartet (2x2) of augmented triads, etc. It makes me wonder if one could find similar embedded cycles in other EDOs with three small prime factors, like 18 (2x3x3), 20 (2x2x5), or 30 (2x3x5).
Hurray for 22EDO!
Regarding prime factors:
That only makes those relationships simpler. You can use them in EDOs that don't devide evenly. For example, diminished seven chords in 22edo (minor third, subminor, minor(, subminor)) aren't isomorphic, but still feel the same and can be used like 22 edo.
12 edo just makes some relationships easier to "see".
@@Buriaku I find there's a certain kinda neatness to the sound, you can get diminished either way, but those perfectly even intervals really lean into that even property of edo. It's especially cool when you wanna say go down a full cycle of minor thirds, they're the exact same and you end up exactly where you were. However, like I said, when it doesn't land you where you were, you may be able to use that to deliberately offset it or get out of already being offset. Cycles/stacks being flat or sharp compounds so I often make use of when it doesn't
your speech is so good now man wow. You're a great teacher and you have a great voice to back it up. cheers for all the awesome content.
I love following along to your videos with my isomorphic keyboard in front of me (specifically the Striso, which uses the DCompose layout). Patterns that never made sense to me on a piano nor on sheet music become obvious. I mean, the negative transformation literally rotates 180 degrees around the root (also, negative harmony is just flipping the board around 180 degrees rotated around the spot between the root and its fifth - I love this thing).
I don't understand a single thing he's talking about but it is super interesting to listen to
I want to recommend a music theory book (if you haven't read it already):
Desire in Chromatic Harmony: A Psychodynamic Exploration of Fin de Siècle Tonality / by Kenneth M. Smith
I found it fascinating, if difficult to read. The hardest (and for my purposes the least important) elements are the "psychodynamic" ones, which are often too postmodern for *me* to grasp, even after two close readings of the whole.
The music theory overlaps with many of your topics, including this one. A RUclips search for "desire in chromatic harmony" will get you several eduCreate videos of his. I feel enlightened about the unfolding of deeper structures in highly chromatic music that's not serialist.
In any case, thanks for everything you do!
a new way to view things and something to work on, i look for this everyday, thanks!
It was driving me nuts why the notes C, F, D, B are ending up as the "roots" around the edges, since those all represent symmetrical augmented triads, and otherwise there's no discernible consistent relationship between those four notes, whether ascending or descending. After plotting all the chords out, I see there are fully diminished 7th chords in there (as in, all three of them) if we choose different ostensible roots using one of those chords: the C+ can be kept, the F+ could be A+, the B+ could be Eb+, and the D+ at bottom could be F#+, this results with the very same augmented triads (whose roots now spell out a dim7), and that makes this diagram bilaterally symmetrical; going counter-clockwise you are descending the chord in minor thirds, going clockwise you are ascending the chord in minor thirds, corresponding to the stepwise direction of the triadic transformations being shown. If you mentioned this then my apologies but I didn't notice discussion about the outer roots as to which ones and why. At any rate the simplest story is that it's all about common tones, just like the circle of fifths, which exhibits the same bilateral symmetry and serves the same function but with regard to keys (ascending vs. descending fifths, representing one degree of transformation with each tick, which conveys degrees of relatedness across keys). Hm, so it's a "circle" of diatonic chord relationships, with augmented triads being the "engines", each yielding three pairs of triads, three major and three minor, overarchingly organized by a diminished 7th chord (another symmetrical structure), encoding common tone relationships when undergoing the most gradual transformations possible, up or down.
This also means the structure can be reversed and still yield the same type of information: three diminished 7th chords organized by an augmented triad, which would yield a triangular structure, with each "node" connecting four major and four minor triads in either direction, representing the four dual-mode resolutions of a dim7 chord (leaving off 7th chord resolutions resulting from one semitone alteration of a dim7 for the moment, which reveals the same type of interrelatedness between some (but not all) 7th chords). Symmetrical chords, having symmetrical intervals, are not only unstable gateways, but also underlying organizational structures, different in character from fifths/fourths, being the only asymmetric intervals in the whole system (they don't divide the octave equally).
From the moment I saw those triangles in the thumbnail I immediately knew we were in for a wild ride
REQUEST: Please show us how Cube Dance can be used to analyze songs and genres, as you alluded to in the end of the essay. Also would be neat to see if Cube Dance can be used to help create music. (I have to admit, I was playing around with A, Am, F, Fm, Dd, and C#m in a four-voice part to see what they sounded like.
So many of your videos are about Neo-Riemannian Theory and tonnetz'es on the background. Love it.
Musical Hamming codes? (edit) possibly Gray codes?
I saw the thumbnail and immediately went "Oh, huh. That's something I have drawn myself once"
"We need not just equal temperament, but specifically 12-tone equal temperament"
me: YOU SAID 12TONE !!!!!!! THAT'S THE NAME OF THE CHANNEL!
Cube Dance is such a three dimensional concept that you are doing it a disservice by drawing it on a two dimensional surface, rather than constructing it with balls and sticks or some other three dimensional construction method.
A 4D Structure like a tesseract would fit even better.
You can't do anything with a stick
@@darricshhh Speak for yourself. I can do a great many things with a stick. My ancestors brought down mammoths with sticks.
@jpopelish I was just quoting a part of the video. I can do lots of things with sticks too...
This reminds me of a trick I use regularly, pulling borrowed chords from other keys that have leading tones back to the root, or to whichever chord in the key I’m going to next.
can you list some examples please
@@Zakk_Ross Keeping things in C for simplicity:
E - C (G# and B leading to G and C)
G#min7 - C (G# and F# both go to G, B to C, D# to E)
Amaj7 - C (C# to C , E stays put, G# to G. This one also works for Cmin)
On the minor side: E7 - Cmin (same as before but the D goes up to E flat)
Fmin(maj7) - Cmin (E to E flat, A flat to G)
Dmaj7 - Cmin7 (D to E flat, F# to G, A to B flat, C# to C)
Really, it’s just an exercise in, take any note that’s not the root, see what chord you’d have to built around it that have half-steps away from your root’s root, third, fifth, sometimes seventh. Like a lot of these sort of things, best done in moderation, and you need your be mindful of your melody as borrowed chords can clash easily.
@@alexgrunde6682 thank you I appreciate the examples! I was trying to reharmonizes notes that were a half step away but all of them were pretty standard chords and I was struggling with my brain! So I appreciate this a lot and I'm excited to mess with it
Awesome explanation and thinking 💭 this is how music theory should be!
I was experimenting with raising the 1 in a major chord a half step to move up and down between diminished chords and their Major neighbours - and it seems your video fills all the gaps I never would have guessed by my own 😀😀😀
Very cool! As others have noted, some similarity to Hamming codes. A few months ago I used the idea of minimising "voice leading work" (though I didn't call it that) to compose a 28-bar cycle of chord changes through a number of different 7th, maj6 and min6 chords. This ended up as an album track. It's a very productive idea, I think.
Now this is the good stuff! The analysis of pop and rock songs is fun, but I first found this channel by searching for Tonnetz theory, and I’ve missed these deep explorations into non-functional harmony, tuning systems and other more esoteric aspects of music theory.
I remember seeing a video with Pat Martino talking about exactly this thing of how the augmented triad can collapse in all these different directions to give you all the major and minor triads. So major and minor can be derived from just the four augmented triads.
The counterpart to this is that all the dominant 7 chords can be reached with half step voice leading from the three distinct diminished 7 chords by lowering any one note of the chord in turn. (Raising a note instead gets you to the min6/half diminished inversions, depending how you look at it)
It's a fun way to look at it, that from a certain view these 'exotic' chords can actually be seen as the fundamental building blocks that functional harmony emerges from.
@6:54 Equal Temperament strikes again! Take that, "just intonation"!
If you wanna hear what a base 19 octave sounds like, check out Easley Blackwood’s microtonal etudes. Super cool to experience your ear getting used to a new tuning system over the course of a few minutes of music!
I actually saw JC talking about augmented chords as a train station to hop off and on directions you want to move around. In my own music I actually use these kind of related chords to change colours. It’s probably gonna take me quite a while until I will find a “beautiful” melodic way around these triads, bc they kind of go into different directions. So to me they feel more like a split way.
Anyways, I really enjoyed your tour de force around the keyboard. 🎹🤩🙏🏼
18:05 - "Ah, a cube". Moments later: "Oh, a *hyper*cube".
I think you'd find cymatics pretty interesting. Chladni figures can map frequency ratios into geometric shapes really well, and really beautifully.
How about more odd scales?
Modes of neapolitan major.
Persian
1 b2 3 4 b5 b6 7
Double harmonic lydian
1 b2 3 #4 5 b6 7
Loc nat 7
Harmonic minor b4
I really like the scale theory
Thanks 12 Tone. Makes cents.
You are a gem.
I feel like this is a rabbit hole that Thom Yorke fell a long LONG way down.
Another great video. Love for you to dissect the cure’s pictures of you. Thx
This is super cool - I'd never heard this idea before. The distance between two chords reminds me of one possible way to analyze Richard Strauss' Metamorphosen, one of my all-time favorite pieces of music.
This type of analysis was designed for music like Strauss’. I’ll have to give metamorphosen a listen, I don’t know it super well, but there’s a famously hard chord to parse in Salome as well.
@@KingstonCzajkowski Cool. I was never taught this type of analysis myself, but I had to teach a simplified version of this back in my adjunct prof days - but it was part of a refresher course for grad students, and it wasn't considered as important as techniques for music earlier in history than this, so we didn't get to spend much time with it.
The topic itself is interesting but I'm more amazed by some of your choices for illustrations. C19 from Dragon Ball? Fucking CatDog? I love it
Ludowic did an album using simialr tricks.
Linescapes, all based on paintings of lines for rhythms.
You end up talking about it as a series of connected cubes, which feels a lot like the definition of a tesseract (which is really just a fancy name for the 4D cube). My mind immediately wonders what the remaining edge movements on that tesseract would be. This might be utter nonsense - my second thought is that there might not be anything to occupy the remaining vertices - but it's an interesting concept.
Then again, it might just be Newton's attempt to connect optics and music all over again.
One of my biggest impact (IMO) progressions is one semitone- a major chord to the same minor chord. In a context of otherwise very conventional progressions it can really stand out and give a sense of decay or loss.
I see what you are doing, but this seriously melted my brain.
6:04 Reminds me of Arvo Pärt's Fratres. Wonder if he used a similar technique in that piece?
Is all of this, first limiting to major and minor triads, then adding bridges which could be other triads, really better than just measuring the number of half steps necessary, as discussed near the end? Maybe I'm missing something.
Anyway, if the cycles are hexagons, you can build two staggered tetrahedra on each side pointing up and down to the augmented triads, and the tips touch another tetrahedron vertex connecting to another hexagon. That's how I like to imagine it.
The time cube once again appears before us.
It would've been great to see you using 31TET as the alternative equal temperament instead of 19TET, as that would be hilariously the QCM (basically) fighting back.
Does 31TET contain the same intervals as quarter-comma meantone?
Holy flirking cube dance! I got lost at the elephant then the penguin but it made sense when he drew Zoidberg!
I'm all like "what now?"
Nice use of the Old Man of the Mountain!
music theory is an occult art where we draw weird sigils based on tables of correspondences to invoke spirits of the air... change my mind.
3:59 wait is this how Brilliant Corners was composed??
Great stuff, I laughed out loud a couple of times.
And of course I watched it on Nebula😎
✌✌
Thank you for this breakdown
I remember learning about Cube Dance in the music theory course at musical summer camp (Blue Lake). I, uh... do not remember what it is (commenting before watching the video, like a heathen)
Edit: I very quickly started remembering once you got into it. Guess all those years of summer camp weren't for naught.
This heavily reminds me of Barry Harris's theory around chord derivation from diminished chords. I've really been eager for you to delve into his music theory
The farthest chords by this model are a whole-step up, a whole-step down, or a tritone. I feel like that's not a coincidence.
It's the tesseract of music
I love this!!!
Ahh, another chance to wake up my long (like probably longer than some of you have been alive) dormant college-music-theory encoded synapses ... like stretching after being bedridden following an accident, the experience was both energizing and more than a bit ...uncomfortable ... but definitely worth doing!
Thanks for keeping me company while I did mindless chores -- and here's hoping those errant drops of dishwater that escaped my dishtowel won't short out my laptop , lol!
@12Tone Does the cube dance help at all in figuring out which melody notes outside the key are most likely to sound “good” over the diatonic chords at all?
This is the way Pat Martino approaches the guitar! It's bonkers but it works
With the mediant transformation example here, "Someone Like You" by Adele started playing in my head immediately.
I can't wait for the second channel 19 tone
This is essentially 12-tet viewed as a manifestation of Augmented temperament. Augmented means the major third is exactly 1/3 an octave and therefore tempers out 128/125. This is the case not only in 12-tet but essentially any equal temperament that is a multiple of 3 so this works in other equal temperaments like 15-tet or 27-tet. In 19-tet this does not work as mentioned in the video but you do get something else neat instead: Magic temperament, where 5 major thirds gets to the perfect fifth above the octave.
Funny, cus to my ear A minor sounds much more related to B minor and the segment that followed was really frustrating as it felt like 5 min lapse into hell trying to prove my ears wrong. Mind you I have no clue about music theory, or even music lol. I just know the sound it makes when I put four in the floor. Umchiumchi.
I have been playing around with my grand kids Magformers (squares and triangles with magnets that hold sides together) to try to build the Cube Dance structure. But I quickly realized that, though a cube has the 8 vertices needed per quarter, it is not, perhaps the best solid to model these relationships. As you draw it, the cubes have to be badly distorted to connect them into a 4 cube ring. If you replace the cubes with rhombohedrons with equal sides, you get what are essentially stretched cubes that keep all the distances between chords similar, but allow 4 of these units to be connected, directly into a 4 unit ring, with the 4 augmented chords the same distance from their 6 neighbors as each of the other chords is from their 3 neighbors. If you like, I can email you a photo.
Hey, something I encountered in a movie recently that made me think of you: the soundtrack to the movie "Kinds of Kindness". The whole movie is this bizarre, alienating absurdity of a triptych. But the soundtrack was quite striking in it's sparseness and discomfort.
Outside of a slim handful of basically diegetic songs, the only soundtrack I can remember is this hauntingly empty piano that seemed to be specifically playing the OPPOSITE of chords. But they were still strangely melodic. It was clearly not just key smashing. There was some kind of non-Euclidean progression, notes changed in tone and intensity. But it's main affect was "YOU ARE UNCOMFORTABLE. THIS IS REALLY UNCOMFORTABLE."
And, I dunno. If you saw it or can get some sound bites, I'd love to hear your breakdown of what the hell they were doing.
I took a listen to “Kindness (Dream)” from that movie and it sounds like pretty standard triadic harmony with arpeggios. It’s really pretty but I don’t think it’s too unusual. I found a couple of choral bits that have much more dissonant harmonies, still elements of tonality but some weird stuff.
Cube Dance, Power Towers… it’s all about parsimony.
“All it reveals is what we set out to show”……….damn
Incredible. Thanks!!!
The geometry of 4 note chords is also really interesting. For this and other interesting things see A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (Oxford Studies in Music Theory) 1st Edition by Dmitri Tymoczko (Author)
But 3 note chords are the foundation don’t you think? And four note chords are variations on the 3’s. I’m not sure, I debate myself on this. I’ve watched some of Dimitri’s videos, I thought his thing was more about movement within movement within movement. what does he say about 3 notes vs 4?
@@HamCar1000 In Jazz almost all chords are (at least) 4 notes (though they may be incompletely voiced.) I find the geometry of the 4 voiced chords interesting, with two 4 voiced chords adjacent if they differ by a one note semitone change.
For some reason the chords you started out with sounded vaguely reminiscent of muse's exogenesis pt 1.
From an a minor chord: The halfstep c# to c can be described by the relatio 25/24 yet the halfstep e to f is clearly 15/16. A chroma and a diatonic step are two complete different worlds. People simply dont understand equal temperment and for what its meant for, treating it as a magical invention derived from the heights of heaven lol, its like thinking there are 12 different notes on the piano or the 12tone-technique consists of 12 fixed notes. There are infinite notes, the cycle of fiths is in reality a spiral operating with the pythagoryan comma. And there are misty ambivalent notes, too, which you cant really determine at all. And thats why i abandoned my theory study after writing hundreds of sites over this topic and developing my own theory. Quite mathematical. Nobody could or wanted to understand, because academia itself has no interest in overthrowing old lines of thought and create something new, its selfreproductive, even with profs being kind or open minded. And thus theories like the one presented here are more valueable. Academics will always prefer academic logic and academic knowledge over knowledge.
At a certain point, it becomes ASMR...
The Prisoner sketch for hexatonic cycle is a pun that has no right to exist.
My problem with these analysis devices is that they don't take into account 4 note chords, which are, at least for me, the foundation of my musical vocabulary
Now do the same thing with tetrads and the diminished seventh. Raise any degree of °7 to get a m6/m7b5/ø. Lower any degree to get a 7. Gotta love the symmetry of a highly composite number like 12.
This is the only episode ive watched in half speed ❤🎉😂
As a football chant. NEO. REIH.MANN. *clap clap clapclapclap*
Okay cool but is this just for analysis or can you derive cool music from it? Have you got examples I could listen to and recognise it's application?
I worked this stuff out without any musical theory training when I was 18.
androind 19 reference made me instantly like and sub lol