Bela Bartok's Infinite Tonality
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Bela Bartok is often considered one of the most important composers of the 20th century, but his works leave us with a bit of a conundrum: He often claimed that his compositions were based on tonal principles, but, well... they kinda weren't. At least, not ones that theorists of the time would recognize. Bartok seemed to think about chords completely differently from his contemporaries, and thanks to the tireless work of theorist Erno Lendvai, we have some idea why. Axis theory reconciles Bartok's revolutionary practices with the traditional principles of classical harmony, opening up whole new realms of possibilities for what we can do with chords.
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Expanding brain meme:
1. Bringing a guitar to a party
2. Playing the host's piano at a party
3. Bringing your accordion to a party
4. Bringing sheet music in case there's other musicians at a party
5. Arguing whether the iii chord has tonic or dominant function at a party
6. Not learning music theory outside scales
this is amazing
So shall it be done. imgur.com/a/j8OJs0H
I have actually been at a party where someone brought their button accordion and played it
@@jeffirwin7862 i'm not familar enough with the comment meta on youtube, so take this: !redditsilver
i.imgur.com/5pgnDKF.jpg
Very cool! I had never heard of this particular approach to tonic, subdominant and tonic, but it's really nifty. Also, seconding the idea of "I'm a music theorist, and we are very fun a parties" merch.
It's disappointing that they didn't cover this at Berkeley.
love you adam
Arne Hanna I definitely learned this at Berklee, in “advanced harmonic concepts”. We applied this same concept to the Coltrane changes. Think about giant steps, it changes between G B and Eb, which you may have noticed is the same relationship as the three chords that the OP chose (A F and Db). They’re all major thirds apart. So you can analyze giant steps for example as a multitonic system of symmetrical key centers, or as sub dominant-dominant-tonic with pitch axis, etc etc
You forgot dominant.
@@captainalex8003 you forgot he didn’t giv a fuck boi
"I'm a music theorist, and we are very fun at parties" with a drawing of a slice of cake with a candle in, is a Merch idea I would buy!
It definitely made me laugh.
As a music theorist myself, I would absolutely buy one as well!
I second this!
I want that t-shirt!!
I need this in my life
Another feature of the axis chords is they are related through the fully diminished 7th chord, which as a symmetrical chord, is enharmonic to the 4 keys on the axis points.
I learned this from Barry Harris videos.
same with augmented chords! the 6th diminished scale/harmonized bebop stuff can be thought of with augmented chords and can help connect modulations easily and if you use the bebop scale as your harmonic foundation you are left with a 4 note compliment not in the scale to form the chromatic scale.
You should look into Bartók's polymodal chromaticism!
He often superimposes a Lydian scale ontop of a phrygian scale on the same root, giving us acces to all chromatic pitches.
By using the "guide notes" from each scale (Let's use D as the tonic) b2 (Eb) resolving to the 1 (D) and b6 (Bb) from the phrygian scale to the 5 (A) and the #4 (G#) to the 5 and the 7 (C#) to the 1 from lydian.
If we were to use the hungarian minor scale (1, 2, b3, #4, 5, b6, 7) and it's chromatic complement sharing the 5 (1, b2, 3, 4, 5 6 b7)
We get even mote "guide notes"
In G for example:
2 -> b3 = A ->Bb (Not the other way around because of the minor scale)
#4 - > 5 = C# - >D
b6 - > 5 = Eb - >D
7 -> 1 = F# - > G
and
b2 - >1 = Ab - >G
4 -> 3 = C - > B (Because it is the b7 from the Dominant)
6-> = E - > F
So we get these 2 chords. One with a Dominant function and one with a Tonic function.
A C# Eb F# Ab C E
to G Bb D F
a nice tonic Gm7.
If you think there is no way Bartók is using this in his music, check out his 2nd string quartet, or pretty much most of his music!
Thank you for such a lovely explanation
I'll save it for later use
His second string quartet is amazing! My favorite probably
Truly fascinating
you must be fun at parties
@@rafadawabe probably more than you that have nothing to add
7:10 giant steps
Or a really fucked up row row row your boat
Nice! I'm totally trying this when I get home...
as soon as I got to 1:46 I look for Giant Steps in the comment
The "dominant chords" in this theory are exactly the dominant-seventh chords that have three notes in common with the viidim7 (and one note a semitone apart). This might be another explanation for why they work as dominant function : they "emulate" viidim7.
Indeed, in C : viidim7 = B D F Ab
V7 = GBDF has three notes in common
bII7 = Db F Ab B (I write notes in equal temperament without caring about enharmony to make my point clearer)
bVII7 = Bb D F Ab
III7 = E Ab B D
For sub-dominant function, a similar reasoning could explain that F, B, D, Ab have it : they have three common notes with vidim7 = viidim7/vii, so they can be seen as "secondary dominant" for the same reason.
The weirdest part is considering say F# as a tonic chord in C. Most people probably... wouldn't agree. (for Eb and A, this is reasonable)
I like how people have been comparing your example with Giant Steps, this is a funny coincidence : Coltrane changes are basically the same principle as the one shown here but with major 3rds instead of minor 3rds. (there are not a lot of other options, because 12 doesn't have that many divisors).
Oh those Bartok chords are savory.
Moving (resolving?) across the branches is such a strange sensation. It feels equally consonant and dissonant.
This is also incredibly helpful for understanding chord function
As a music theory nerd myself, I very rarely get to learn anything new. On this video, not only did I learn something new, I also learned something exciting that I can put into my own music. Thanks 12tone :D
Novel and actionable
Yvan Cluet Same. I came here to comment that this was the best video on 12tone that I have ever watched as a music theory nerd - but you beat me to it :P
@@kathrynschekall9160 glad you discovered this cool thing too !
@@kathrynschekall9160 cool channel btw ;)
I agree although I have used bII, III and bVII as substitutes for V I never thought to extend it to tonic and subdominant. Doh!
The progression at 7:10 reminds me of the first few changes in Giant Steps
Absolutely! 👌 I heard it too 😂
Love what youre doing here and your content is extremely impressive!
this is one of the coolest videos I've seen Thanks! Mr.12tone
Fascinating video over a topic I'll definitely have to look more into! At first, when you played the A -> F -> Db -> A progression, I wasn't so sure that it sounded like Bartók to me, but then when you made the split chords, the resemblance was almost uncanilly perfect! Awesome video!
brilliant presentation. thank you. the picture illustrations were well drawn out and made sense well. Thank you.
What Bartok pieces would you suggest checking out to hear this in action?
One that Lendvai cites a couple times is Bluebeard's Castle, which uses this model to move back and forth between C and F#.
12tone also it’s worth mentioning that Bartók’s maj/min chords are also called “bitercial” chords (I think?), something that Jimi Hendrix used frequently, so much so that it was dubbed the Hendrix chord among guitarists. Sorry for being a year late haha
Suite for piano, opus 14
LOVED this video. Completely fascinated!
I'd argue the the functionality of the IIIm chord is ambiguous, and can go either way. It has equal parts of the tonic (1 *3 5* ) and the dominant (2 *5 7* ). How it functions depends on whether you emphasize the 3 or the 7.
The VIm chord also has this issue. But it has the relative minor to fall back on that makes it feel like it's most often a tonic chord.
Or you can use the system I prefer, where only I is actually tonic, and VIm and IIIm are both pre-pre-dominant, since they aren't perfectly at rest.
amazed wanderer But the IIIm7 has a leading tone in its fifth: 3 5 *7* 9. I'd say the real problem is that it's just a IM7 chord without the root which makes it still sound tonic.
Maybe that's it, actually. A IIIm chord is just the IM7 chord without the root, but is not any extension of the V chord. Thus it feels tonic in a jazzy context.
Hello ! I would say that the axis theory was making sense only for Lendvai, which was a way for him to reconnect Bartok's music with his own background in Riemanian theory as you explained, but overall it seems that Bartok himself wasn't really thinking in that perceptive. And not a lot of theorists followed Lendvai's idea. I suggest one article by Janos Karpati titled "Axis Tonality and Golden Section Reconsidered", and I assume you are familiar with Elliott Antokoletz's book on Bartok's music which don't use this approach at all.
I liked the topic, one of my favorite videos from you in a while. The function of chromatic chords is something that isn't talked about enough. I chalked most of them up as pre-dominant before I saw this video
Absolutely wonderful! Thank you.
Thank you so much for sharing your knowledge. If not for you and others like you. It would be likely that some of us would not have access to such knowledge. So again thank you and God bless!!!
I'm totally gonna play around with this when making songs now thank you
Awesome channel. Congratulations!
That final Bartok's way to afford the chord progression is amazing, Using both minor and major thirds at the same time it's a thing even Hendrix has done his own way, and the results, well...we still talk about it today :)
This is quite fascinating. I must use this as inspiration.
Props for explaining this in under 8 minutes! I learned a lot.
Nice, I've really been needing a video on this, I've been pretty unsuccessful at researching axis theory on my own.
EDIT: Excellent video, axis theory personally appeals to me a lot. I love "edges of tonality" type stuff. Also, the four pitches associated with each axis(?) form a different diminished seventh when sounded together. Probably not useful for anyone but there you go.
That diminished seventh thing explains why it works so well for dominant-function chords, I think
4:46 Garnet)
Damn thats such a cool concept, you can do so much with this if you combine it with just 251s and Minor to major and vice versa reharmonizaion. thank you for sharing!
Amazing! Definitly gonna try to use this theory in something I'll compose
i stumbled onto this EXACT theory on my own in a sketchbook after my first music class... I'm about to study tf out of Bartok's book. O.o
Wonderful! Nice to follow even if it's definetly a heavier topic!
The "Garnet" bit was great :)
7:08 sounds like giants steps
As a big Bartok fan, thanks for spelling out his harmonic ideas. Can’t wait to discuss this at my next party.
A - F - Db - A progression also can be described using lattice concept. Lattice is just organized n-dimensional ratio space, where step in each dimension meaning multiplication of previous pitch by some multiplier (prime number). If we have 2d lattice, where horizontal axis correspond to multiplication by 3 (basically step by perfect fifth) and vertical axis is correspond to multiplication by 5 (major third) and we pick notes from some major scale in this lattice (where tonic is in the center of coordinates) then we will see, that major scale is consist of three corner-like overlapping structures (triads) - first (tonic) in center of lattice, second (subdominant) on the left from center and third (dominant) on the right. If we rotate this structure by 90 degrees then subdominant will be beneath tonic and dominant above (or vice versa, depends on direction of rotation), what means they will be one major third apart from tonic, just like F and Db in A - F - Db - A progression. So this is basically "major" scale, but S and D are major third apart from tonic, not a perfect fifth.
Although scale created from covered pitches will have only 6 notes, but also it is possible to build both major and minor version T, S and D triads.
This video is now my favorite on all of TH-cam
From which we derive the following: chords move down by semitones, by major thirds, by perfect fifths; and up by whole tones, and perfect fourths.
Cool! I remember checking Lendvai out about 20 years ago, randomly picked up his book because it looked interesting, and it was - I think it had a big influence on the way I think about harmony, but I think he's pretty obscure....Thanks for reminding me. It's worth pointing out that AFAIK this is something that Lendvai invented to describe how Bartok's music works, I don't think Bartok ever expressed these ideas himself.
Barry Harris would call this 'Brothers and Sisters' - he uses the same axial symmetry but mostly for dominant chords as you demonstrate. Also the common technique of parallel minor modal interchange fits into this theory, although things like the Neapolitan 6th chord don''t preserve their traditional function.
My high school didn't have theory as part of music we just played music. Now that i'm at college and got some theory experience I understand most of your videos. I feel like if i'm slowly being able to decode your video. Slowly but surely.
This was super cool! I've been wondering about ways to interpret existing modern music and create more of it, and honestly, the traditional functional harmony theory isn't doing it for me - it seems way too simple and I keep thinking there must be more to it. The axis theory is something I hadn't heard of before and it too seems a little too good to be true, but it's interesting at least (it looks similar to Coltrane's studies of the circle of fifths). I also wonder what would happen if you combined the axis theory with the "negative harmony" theory.
Nice video. I like to think of these axises as families of diminished chords.
Interesting observation on the "collapsing scaffolding". I like it! And yeah, I'd be in for a T-shirt too
Thank you for makin' music theory more awesome and fun
I love when people do anything with Bartók, he's one of my favourites. Thank you!
"Axis Theory" sounds more like a contemporary djent band to me. :)
This video has really love with me up. In the struggle to understand what the hell is meant by median and what the hell is that kind of function could possibly be for the three cord I figured that since the three is dominant of the six it might as well just be a dominant. And now there's a good explanation for that outside of what I thought
This is awesome!
Great video
Wow, first 12tone video I understood all of, we're getting somewhere!
Correction: the label "subdominant" applies only to the IV chord. The function that leads to dominant function is called "predominant."
Another video Adam Neely will like. I didn't know of Bartok before he brought him up in his videos.
I knew of him but he made me appreciate it even more, specially his quartets
I cracked up in a public library when you mentioned Bartok's split chord use. He was utterly, gloriously insane. Thanks for the video?
Thank you❤
this seems like a very good way to conceptualize the variety of extensions dominant chords get in jazz
not to mention chromatic mediants sound hip af
Damn this channel is so good
love it!!
This is so interesting!
I think I need some sleep right now and tomorrow I'm going to watch this over again, maybe in half of speed and with memo.
There was quite much interesting theory of tonality presented in fun way thou
I wonder how many composers who delved into chromaticism (like Bartok) also thought about microchromaticism? At the end of the video you mentioned that Bela Bartok made use of "split chords," which use both the major and minor third. This reminded me of the neutral chord, which is used a lot in other tuning systems and is constructed using a root, fifth, and neutral third, which is between a major and minor third.
Speaking of, if you haven't already you should make a video about other tuning systems, like 5- or 7-limit tuning, or even 19, 31 (my personal favorite), or 313 EDO (which sounds really cool). Sevish is a really awesome artist who works a lot with those.
Could you explain John Coltrane’s “Tone Circle”? I think its fascinating but dont know how it functions.
Thanks!...now playing "Wild Thing" with all the new options
🙌Giant Steps🙌
Twenty years (almost) now I've played music and read books and papers and websites from every corner of the globe across centuries. Hard to find boring junk that nobody cares about. I've read my copy of Harvard Dictionary of Music cover to cover and followed many sources it cites. I breathe this nonsense.
I've never heard of this theory before.
I'M SO EXCITED!!!!! THIS IS AWESOME!!!
Music theory parties are the best parties. Especially with costumes!
How have I never heard of this?
I'll be honest. I had no idea what the video title mean and my first response was to pass on the video. Then I remembered that your videos are always interesting and worth my time and I clicked. (Might have had the same first response to a baiting title but probably wouldn't re evaluate clicking)
Really liked the video
I remember being taught that the function of the III chord is very context sensitive, and also down to inversions and voice leading. Since there's only one leading tone, it can be easily obfuscated, and thus lose the dominant function, if it's not featured prominently.
Coming to your party about 2 years too late, but it was fun anyway. Another way to think about all this is to ignore chordal harmonies altogether and look at the notes in the scale and where, in a tonal framework, they go. Bartok was a brilliant contrapuntalist, and his contrapuntal voicings create all of these harmonies in passing. So all of those related or substitution chords are ways that the 12 tones in the scale move towards and away from resolution.
Hey, you should do a video outlining the arguments for iii being dominant or tonic. I personally believe it's dominant because Persichetti has a chapter in Twentieth Century Harmony where he discusses chords based on cycles of thirds rather than the cycle of fifths and in that cycle, iii replaces the usual V, and he gives several examples where he freely switches between the cycles to end the phrase in V-iii-I rather than a V-I
This is my only exposure to the use of iii chords besides my theory teacher just saying not to use them, so I'd see to see some other arguments
I first heard about it and thought this is rock guitar pentatonic/ blues scale theory, except for the tritone which is more of a jazz concept. Love Bartok
Did he draw Garnet at 4:50?
He totally did!
As if I could love this video channel even more! 3-lights-in-eyes -> single tear
In Hungarian, Bartók is written with an ‘ó’ which is a long ‘o’, pronounced like the ‘o’ in ‘boat’ for example
You might want to specify which dialect of English, because in Australian English, the "O" in "Boat" is two vowels smooshed together, whereas (if memory serves), Hungarian 'O's are single vowels.
@@Wigof99Flowers The IPA is /ˈbeːlɒ ˈbɒrtoːk/
@@eyestreet My point was more that the IPA for Boat is /bəʊt/ (or /bəʉt/), and not /bo:t/ :)
@@Wigof99Flowers Fair enough
@@Wigof99Flowers Australian English does have a long /oː/ though; it’s the vowel in ‘north’ or ‘thought’.
Re: the function of the III chord: I'd argue that, much like the bVII, the III's function is largely dependent on context and voicing. If you use it in second inversion, or use the leading tone as a focus of the melody, that note's drive to resolve more than outweighs any stability from the key's third. If the leading tone is in an inner voice (or just omitted, as the fifth of the chord often is), then its function is more tonic than dominant.
had a couple "OH THAT'S WHAT THAT IS?" moments. Well done, thanks.
At 1:57, I love your topology reference!
Hungarian axis theory specialist here :) (kinda - sorta)
At 5:30 you messed up the fourth option, it should be C#7 , you're a semitone off.
C#7 would be the dominant of F#m, that is the minor tonic, instead it resolves to the major tonic, kinda makes sense and sounds good. The strange thing is when you resolve C#7 to Am, really sounds off-key, but as I hear it Herbie Hancock uses this resolution often times.
From the jazz point of view, you can also say that the upper structure of (say) E 7 b9 is a dim7 (g# h d f) ,all of the "axis tones" make sense with all these notes of the other axis (e g bb c#) the bass notes could be interchanged for similar tension. And see, the 1:2 scale forms with these 8 notes.
To me, this system makes a lot of sense. From the jazz point of view, considering a II-V-I, if you could interchange the dominant on minor 3rds, why couldn't you interchange the II on minor thirds? Note that the IV of also a minor 3rd from the II.
You can also consider the II-V as a similar fall of a five as the V-I is a fall of a five.
If you can interchange the dominants, why couldn't you interchange the I's? I mean if you go like G7- C you could also go Bb7 - C. But B7 is also a dominant of Eb so you cold say C F G Eb. It modulates a whole lot, but this theory can explain why some progressions sound the way the do.
For me the tension-release system kind of stays the same, but the overall mood of progression changes with the substitution of the chords, especially when you "don't go home" to the original I chord, but you choose another home.
Check out alpha, beta, gamma etc chords in Lendvai's study of Bartók's music, they are also very interesting.
Check out "music for string, percussion and celesta", he uses this theory a lot of times.
My favourite from Bartók is the sequence of "Roumanian folk dances". I might have heard even Him playing it, but if you can't find it, listen with Zoltán Kocsis, he was considered the best interpreter of Bartók's works.
Anyways, thanks for the videos, your works are lovely :)
Thanks! I _believe_ I played the right chord there, I just wrote D instead of Db. I could always be wrong, though: MIDI mistakes happen. But yeah, sorry about the transcription error.
As for the rest, I'll definitely look up more of Lendvai's work: I have his book now (Or at least one of his books...) so I'm planning to go through and talk about more of his stuff, just wanted to focus on one theory at a time. But Bartok's work is so dense and complicated that I'm sure I could make like a hundred videos just about cool things he did.
...Did you increase the intro metronome's bpm by a couple beats for this vid??????
Came to this video because of Bartok, came out with Frank Sinatra?! Best 12tone video yet. Thank you so much for this.
Also, I'd love to hear your take on why the IIIm is overall a tonic-functioning chord. I personally think it's a little less restful than I or VIm, but it's not as directional as V7, V, or even IV in my opinion. I use it in my compositions as both a tonic-functioning chord and to start moving e.g. into a IV to begin setting up some movement.
I would argue that it usually leads to a pre-dominant chord, rather than a tonic chord.
Though I do like the system that has a pre-pre-dominant chord, and only I (or I-minor) is tonic.
@@ZipplyZane I've never seen that system before, but that'd be how I'd classify it too. When composing, I usually think of a continuous spectrum of directionality, with I or Im on one side and, say, V7b9 on the other. IIIm would fall maybe 30% down the line starting from the "tonic" side on that spectrum.
is there a writing-mistake? in #05:24? it should be D-flat major. thank you for uploading this brilliant video!
That was a horrifically good explanation of something quiet fiddly (!) :)
I forget the name of this method, but I was taught functional harmony differently. The "vi has tonic function" thing is nowhere to be seen. How it goes is that (in Major) I is the tonic, V and viidim are 1st class, ii and IV are 2nd class, vi is 3rd class, and iii is 4th class. The higher class, the more distant it is from resolving to the tonic. This is basically because much traditional harmony moves by fifths or fourths in the roots, meaning that iii would tend to go to vi, vi to either 2nd class chord, then either 1st class chord (more often V), then to tonic.
iii and vi are viewed as "de-stabilizing" chords in this system, I assume because they blur the line between the two relative keys. For example, if I start by playing C, then a. It is impossible to determine whether that is I-vi in C, or III-i in a until some further progression clarifies the context.
Could you do a video on transposing music maybe? I've been wondering about that for awhile. There's only so much one can learn from high school band
When the music theorizing gets serious, my head spins, but think I got a little better idea of why I like Bartok. Something about changing the harmonies a lot but not so much that I can't recognize the familiar harmonic functions.
This one I will have to watch again lol. I think I missed pretty much everything
Hey there. Great channel ! I would like to suggest analysing a tune called "Once in a Lifetime" from Michael Ruff including the Piano Solo
Could you do a video sometime on Schenkerian analysis?
I do think to myself in terms of modal interchanges of neighbour and relative keys, like in A F Db A I see:
A, the tonic ,
F, from A minor,
Db is not Db, is C#, the V from F# minor, the relative minor of A major.
A, the tonic.
Seems more simple.
I think I can make a video that explains this more clearly. I'll begin working on it right now.
For anyone wanting to hear a modern example of this, I believe the tapping part in 'satch boogie' by Joe Satriani uses pitch axis theory :D
That's a different pitch axis theory. He basically stays on the same root and cycles through various modes from it.
@@TheDjangofan My bad. Should've looked it up more before I commented.
question on the tritone substitution of the backdoor resolution: why does the G# not act as a leading tone in the resolution to A, shouldn't it? Should it not then be a stronger cadence? Why is it so week if it has both the backdoor resolution and a leading tone resolution?
That's a good point! The main reason I consider it weak is just that root movement by 3rd is generally the least powerful motion. All the other resolutions are going by either a perfect 5th or some kind of 2nd, which feel more resolve-y to my ears.
What Bartok pieces (instrument solo) would you suggest analysis about axis system?
Essentially, the Neapolitan chord is very emphatically a subdominant chord - resolving to the tonic as a plagal resolution - whereas the chord of the leading tone is always very emphatically a dominant chord.
Well, the thing is that degrees other than I IV and V have a kind of duality... The way I see it, vi for instance is mostlyTonic and a bit of Subominant (e. g. vi V I, vi sounds like a subdominant there), and the iii chord is mostlyTonic and little Dominant too....
At last someone has verbalized what I suspected from the very beginning.
3:20 How is the Ab subdominant though? It Also has a leading tone
Before seeing this video I genuinely thought I invented a new system. Which made me think I must have listened to too much jazz and broke my ears then come up with this like I could have thought of anything and still found it sounds good anyway. But now I know I just had the same idea someone had 50 years ago. It's actually reassuring, I wasn't coming up with bullshit but simply deluding myself into thinking I was the first to have this idea because of my own ignorance of already known somewhat advanced theories, feels great actually.
Keep going, you've got a mind for the theoretical in music, perhaps you will come upon a new system.
I'd argue that the mediant has its own function, which is different that tonic or dominant - but can be used as either depending on how it resolves.
Also here's my intuition for functions on the circle of fifths:
A♭ --- S
E♭ --- M'
B♭ --- D
F --- S
C --- T
G --- D
D --- S or D
A --- M''
E --- M
B --- D
F♯ --- ? (S or D)
C♯ --- S
But (when the tonic is C) D maj and F♯ maj or min have the explicit function of modulating to the dominant
Moreover I'd argue that there are five harmonic qualities, based on the motion (either up or down) of the tonic:
(1 & 2) if it moves by a fourth (or fifth) or step, or half-step there's a dominant/subdominant relation (the two can be equated to some extent, e.g. as the subdominant resolves to the tonic in a plagal cadence)
(3) if it moves by a minor third there is a type of mediant
(4) by major third, a different type of mediant
(5) by tritone - which is so distant that it can resolve to anything and it most useful for modulation.
What do you think?