Great video! The “your/you’re” analogy is awesome, I’m going to be using that more. There’s lots of microtonal augmented sixths that are distinguished from minor sevenths too, for people who are interested in that stuff.
For those interested, jazz has long been in love with such tritone subs, and if you have any interest in jazz improvisation you'll find their study and usage pivotal.
In 31 equal or quarter comma meantone, {F, A, D#} has a clear F root because that becomes a very good approximation for the just ratios {1, 5/4, 7/4}, or 4:5:7 which is directly a bunch of harmonics over an F two octaves down. At least to my ear, this does almost as good a job at suggesting its root as the 4:5:6 major triad. Also, the minor 7th, with Eb in place of the D# sounds different and functions differently -- the Eb being a couple of perfect fourths over the F, so a ratio of (4/3)^2 = 16/9 rather than 7/4, carries a lot more tension and helps dominant function. All the points about meaning and spellings make a mind-exploding amount more sense if you ever get your hands on an instrument that can play in a larger meantone tuning and so distinguishes sharps and flats. Especially quarter comma or 31 equal which both have really solid approximations to the 7th harmonic that lie just sharpward on the circle of fifths, as three whole tones gives you a 7/5 tritone, and when you line that up with your 5/4 major third, you get (7/5)*(5/4) = 7/4, which is an octave of the 7th harmonic. This means you get all kinds of ratios with 7 in the numerator when reaching sharpward out of key, or 7 in the denominator when going flatward. For example, C to D#, becomes a septimal minor third, 7/6, a beautiful interval a bit narrower than a minor third that's quite characteristic of Middle Eastern music, where C to Eb is our familiar minor third, 6/5. The parsimonious impact all these additional strange consonances contribute to key changes is quite magical. Both the septimal and ordinary minor third occur in the German +6 example at around 4:30 with {C, E, Fx, A#}, the E to Fx would be a 7/6 in order to allow Fx to A# to be a 6/5. There's a good bit more dissonance using Fx than using G, with the Fx/C interval perhaps functioning as 35/24 (awkwardly close to 3/2 of course), but since it's not unrelated to the other chord tones, it's not entirely out of place, and by comparison, {C, E, G, A#} would be a very stable C harmonic seventh chord, and wouldn't feel as much like it needed a resolution. There's a kind of fundamental tension in the fact that our music notation and a lot of theory comes from a time when people often *did* use larger tuning systems like quarter or fifth comma meantone (or at least subsets of those), and so makes distinctions that are inaudible in 12 equal, but would be immediately crystal clear in 31 or 43 equal or one of these meantone temperaments. As someone who recently got a Lumatone MIDI controller, with enough keys to play all these extra notes, I'm grateful people have so diligently preserved these distinctions that perhaps haven't mattered quite as much for a long while.
Loved learning about them in school and enjoyed this history of 500 years of confusion even more. Maybe the best lesson here is the old adage: “Theory follows practice”. Not only does it follow but, in the case of aug 6ths, it may never really catch up!
Wow, I am not even totally through the video but the connection to modal harmonies of Renaissance music is like a bolt from the blue! I'm just imagining a Renaissance singer being tut-tutted for a realization in the Phrygian that would, centuries later, become a commonplace and beloved harmonic device!!
This was fun. I studied harmony 25 years ago, hoping to be a symphonic composer, but life interrupted and I never got past 7th chords. Augmented 6ths were literally the next chapter when I had to stop. And I never became a symphonic composer, though I can write a fine SATB harmony. And I can tune a mean piano.
This is by far the most comprehensive survey of the augmented 6 I’ve encountered. Even in grad school, we didn’t dig this deep. In musicology we talked about how it worked narratively, how it plays on our expectations. We spent more debating the labeling of the cadential 6/4 chord (is it, in reality, already the dominant?). Thanks (a year later) for doing this. RU-vid videos are great but I often find myself either abandoning something I missed or having to stop. I’m a pretty good sight-reader but with several of the examples you were off and running before I had the lay of the land. It sometimes felt like a speed analysis marathon. It’s a minor quibble over an excellent presentation. Cheers!
@@ClassicalNerd Yeah - which is what I did a few times. I just finished watching your sonata video - also a great survey. I studied with Hepokoski in grad school in the 80s at the University of MN. I wrote the best paper of my college career in his class - on Mahler’s 2nd. When you said ‘medial caesura’ I knew where it came from and was glad to hear you speak well of their book. I just discovered your channel and I’m really enjoying it. Thanks for producing really good pieces in classical music. Cheers!
Love the subtle soft Aug 6th orchestral sound samples playing under you dialog! That's pretty slick. Jazz players call the Aug 6th chord a Dominant 7th chord a half step above the destination chord. So a C Aug 6th chord to B would be called a C7 (C Dom 7th chord!) to say a B Major 7 target. It wasn't until I understood the origin of the voice leading of the outer voices of the properly spelled and named Aug 6th chord di this common chord progression in Jazz make sense.
Great video, always fascinating to see how old theories were formed and what held up over time. I've never been able to shake the reductionist jazz take that all those aug.6 chords at 30:38 are just Ab7 with different extensions. For example to me the Italian is a "shell" voicing, just root/3rd/b7. The German adds a natural 5th, the French has a #4( or #11), and the others add various 9ths, 13ths, etc That doesn't respect the spelling, inversion, or voice leading which definitely matters a lot in a classical context but I feel like it's the most intuitive harmonic reduction: just a bVI7 chord preceding V7, with whatever extensions you want! The fact that the tritone sub is so closely related is more evidence to me that aug6 chords were kind of early glimpses of blues/jazz non-functional harmony.
As a student I used to ask if we could not have theorie combined with musichistorie. At last 62 years later you are doing it. Thank you in behalf of every new student.
Great video. It's funny that the discussion of these chords take up so much space in modern theory books. When I taught theory at a University some forty years ago, I came across several texts from the 19th century which only devoted a single a paragraph on the topic (maybe Ebineezer Prout?). These texts considered the A6th as a double leading tone to the root of the dominant; that is, a leading tone from above and below.
If we thing enharmonicly, we could say that in C major, the french+6 is an Abaug6 or, enharmonicly, Ab7. And, what is a tritone away from Ab? D, which if we make it a dominant becomes a V7/V7! So thinking in reverse, the Abaug6 would actually be the tritonic substitution of the V7/V7! So we could write it as a SubII7, or SubV/V I would guess, as it is the substitution of the secondary dominant!
The B Minor Mass example might be the most useful contextual example- though certainly not the only. Nor necessarily representative of the best explanation in all cases. Which is to say: often melody has primacy, and what someone choses to call a “rounding” of a vertical interpretation, in these cases, is really besides the point. Great overview btw!!
I think that for explanatory purpose it’s always helpful indeed to show and clarify all those chords and passages in the key of C Major and thus to avoid an unnecessary complications of different respective keys. Otherwise it’s very difficult to be followed especially by someone who is not a native speaker and whose musical terminology is different in his mother tongue.
Two things interest me in life: Music and Physics. I've read quite a bit about physics theories and, although I've played music all my life, I realize watching this that I understand more about physics than music.... but I loved watching... Maybe I'll catch up.
Man I just discovered your channel and am binging everything. One of the best channels on RU-vid. I see you’re working on a Milton Babbit video and you did a great video on Leonard Bernstein, I was wondering, if it’s not too outside the “classical” tradition, if you would think about doing a video on the late Stephen Sondheim?
In meantone, the augmented sixth approximates almost exactly the 7th harmonic. Kirnberger attributes its use to being a consonance disguised as a dissonance.
1/6 comma meantone is a counterexample. Your comment is valid only in tunings (it doesn't have to be meantone ) where augmented sixth is reached by two major thirds + two fifths (octave reduced).
I know it was intended to be merely in the background, but I really liked whatever I could hear of the background music in this video! Considering it's maybe original work, anyway you could upload it separately on your other channel? Me likey chromatic resolutions
9:46 Wow. This was the first time I've ever heard of an "Azeri Sixth" chord in context. I always thought that this cross relation came from a kind of cadence that sometimes happens in performances of de Machaut's pieces where the triplum sings F#-G#-A and the tenor sings F natural-E-D. Some performers wanted to avoid augmented and diminished melodic intervals regardless of the harmonic results.
Correction: 11:12 it's spelled Jean-Philippe (1 L, 2 P's), not *Phillipe. I was named after Rameau, and people misspelling my name that way is a big pet peeve of mine. 😅
I have noticed a slight correlation between the type of augmented sixth and the nationality of the composer, possibly stronger in some cases than the stylistic correlation that Calcott used to name the chords. I see the Italian Augmented Sixth often in works of Italian composers or composers of other nationalities that nevertheless often composed in a more Italian style(Mendelssohn would be an example of the latter). I see the French Augmented Sixth often in works of French composers or composers who lived a lot of their years in France, like Debussy that you mentioned in the video, but also Liszt for instance. And I see the German Augmented Sixth often in works of German and by extent, Austrian composers, like the whole Classical Era Trifecta that is Haydn, Mozart, and Beethoven. That is not to say that I won't see augmented sixths outside the composer's nationality being used. The Italian Augmented Sixth especially is also commonly used by for instance those same German and Austrian composers that often use the German Augmented Sixth. And Schubert is well known, at least by theorists for, among other things, using the French Augmented Sixth quite often. I'm just saying that there is a slight correlation between composer nationality and augmented sixth type.
I will love you forever if you cover Ruth Crawford Seeger. Her chamber compositions changed my music composition life. I find she is not in nearly as many discussions as she should be.
26:29 I'm having trouble understanding how that is an augmented sixth chord. I would have said that that's a Bb7b5 (in this case bII7b5) chord in second inverson (4/6). Do you mean it is enharmonically a French augmented sixth chord? Amazing video as always, anyway.
Damn I'm actually working with an augmented 6th then in one song. Use Spanish eight tone scale and take out the minor third. Yeah it's super weird. gives a nice nightwish sound though if you're careful. Very hard to work with. You're definitely ahead of everyone out there, damn 😵
@@avantagonist It's not really equivalent. Zam+6 is Ab7#5 going to G, what I described is Bbaug/Ab going to G. They have the same chord shape (in inversion), but are differently positioned in the tonality. Zam+6 has three notes moving downwards (one of them by a whole tone) and only the F# moving upwards. The J-pop+6 has one shared note, only the Ab moving down and two notes moving up; and all the movements happen by semitone.
A quick question: so is the only reason that the aug 6th can’t be considered a convenient collection of passing tones because together they have a very clear predominant sound and thereby must have a Roman numeral attached to them since passing tones shouldn’t be able to have clearly discernible functions? TBH I really don’t get what is uncompelling about Fux’s opinion on this. Admittedly it’s not fully satisfying, but then, neither is any other theory. For the record, at least to me, it sounds most compelling in the Viennese classical examples where they seemed least contrived in context, perhaps because of Fux’s posthumous influence over that style?
It's not so much the clear predominant sound (technically, you can +6 your way to _any_ chord, as in the Chopin example) as much as its common use, and composers' treatment of it as a coherent, functional sonority. The irony is that, yes, it _does_ in fact derive entirely from a more horizontal, Fuxian view than it does from the vertical, Rameauvian position-but since the latter position won out, you get the few centuries' worth of logical twists that I track in this video. More than any other "tonal" chord, it problematizes what we mean when we say "tonality" and the Roman numeral-based theory that underpins it.
C = cadential. There's a huge theory debate over whether to call it V64 or I64; my elegant solution is to call it by a name upon which both can agree. See elsewhere in the comments.
No. C = cadential. Of the three ways I know how to express that chord, it's my preferred method. (What to call C64 could be a whole video unto itself.)
@@ClassicalNerd Gotcha. I'm old-school trained. I'd mark that as I-6/4 (i.e. "one-six-four"); no need to state the cadential function because it's implied. Thanks for clearing that up. BTW, I never got around to posting a compliment on your serialism video a few years ago. It was a stunner, possibly the most sensitive discussion of the subject I've ever come across. I was amazed.
Actually we do know where the names came from. See this reference, …These names were given to these chords by the English theorist, John Callcott, in his book, “A Musical Grammar,” published in 1806 in London. These names refer to subjective qualities that Callcott “felt” each of these versions of the chord possessed. He called the “Italian” the chord with “elegance.” The “German” chord referred to as the chord with “strength.” The “French” was the chord with “feebleness.” Than name “Swiss was given to the Doubly-Augmented Sixth Chord by the American composer and theorist, Walter Piston, in his harmony book, first published in 1937.” (Kendall Briggs, The Language and Materials of Music Vol. 1, pg. 553)
The country names come from John Wall Calcott in 'Musical Grammar' or that is the furthest I could trace. The names were more or less ethnic and country stereotyping. EDIT!!!! Never-mind you got to it in the video. HAHA.
If, during the 12th through 16th centuries, 'musica ficta' applied to those notes outside common usage/notation, could the various augmented sixth chords employed after 1600 "that broke theory" be considered 'musica afflicta'? On a more serious note, in the Adagio of his Seventh Symphony In E Major, Anton Bruckner composed what is first perceived as a dominant seventh chord on the V of Db Major and then transforms it into an augmented sixth chord modulating into the key of C Major which coincides with the famous cymbal crash inspired by the death of Richard Wagner. See the score and hear this transformation of the dominant seventh in one key into the augmented sixth of another key from the last measure of letter V climaxing into letter W at 18:08-20 of this link: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Ue3Sdrg3Hnw.html
Augmented sixths did not break theory. Theory was broken to start with. ‘Harmony is a fairy tale told about counterpoint’ (Nadia Boulanger or someone probably.) EDIT: I am slightly being tongue in cheek….
Surely, you jest. The Petrushka chord is The wackiest harmony known to man. Stack two major chords on top of each other - but wait, their roots are separated by a tritone! This vid really got 10k views in one day? People actually care about music theory? Maybe I should give grad school a chance?
Polychords may sound quite a bit spicier, but that's not the point. Theoretically, they aren't really _that_ weird. The wackiness of 6+ chords is a function of their inability to be explained through the lens of what is most commonly taught as "music theory" (i.e. Roman numeral analysis).
Fantastic work. I love the video. While we’re on the subject of different spellings and functions (as your “your” vs. “You’re” example), may I offer a pedantic remark: you don’t “build off of” something and you don’t “base [something] off of” something else either. You build on something or upon something. You base something on something else. It all goes back to the meaning of the words “base” and “build”. It drives me a little nuts to hear a brilliantly articulated sophisticated explanation with such banal language mistakes. Such is the world of RU-vid, I suppose. Good work otherwise. I’ll keep watching.
A lot of this was over my head but I picked up a few things and will be coming back to this as I learn more. Thanks for doing all this hard work too. Excellent presentation!
Are you implying that the person who made this video had to struggle to accomplish it because it pushed the limits of his intelligence? Maybe it was not that hard for him to make this video because he's smarter than you think.
@@virtualpilgrim8645 "A lot of work" tends to refer to putting a lot of time and effort into something. It doesn't imply lack of intelligence. It's more the production value and the well-researched nature of the video.
Notwithstanding this excellent presentation of the history of the use and analysis of these chords, the centuries-old debate reminds me of that scene in The Matrix where a young candidate explains that to bend a spoon one must not "try" to bend it, but rather realise the truth: that there is no spoon. This moment by moment vertical analysis - giving labels and finding roots for each new aggregate of notes - is a longstanding obsession of European theorists and IMO one of the worst ways to analyse European tonal music in a meaningful way. The analytic layer that it creates does little to convey the harmonic meaning and directionality of a piece, instead forming a kind of an opaque 'scientific' list of components, like trying to analyse a story by giving different labels to various combinations of letters. This is one of the downsides of having a notation-based music: now there's all this lovely stuff to analyse AWAY from the actual music, regardless of how it sounds... Having been brought up on this kind of vertical analysis, the Schenkerian approach was a revelation to me. I felt like there was now a clear representation for the harmonic-melodic vectors in the music, and I could actually HEAR the music through the analysis. My two cents...
Hindemith’s Craft of Musical Composition lays out a cool, handy system for determining the root of any chord, regardless of most context, and no matter how crazy it is. The rule is essentially “lowest, best interval”. Basically, perfect 5ths (or 12ths, etc) are the best guide, followed by perfect 4ths, then 3rds (maj>min), then 6ths (min>min), then 2nds and 7ths. If there are multiple perfect 5ths or other intervals, whichever is lower “breaks the tie”. This is mainly interpreted in a 12TET context, and gets tricky with augmented or diminished intervals that Hindemith likely avoided by writing with enharmonic equivalents except for tritones which he considers to not really have a root, but the root-substitute is determined by which notes most smoothly leads to the root of the next chord. So, the root of the italian 6th shown at 12:40 would be Ab, as the M3 between Ab and C is the most harmonically stable interval present. The root of the french 6th at 13:00 would be Ab also, as the M3 between Ab and C is lower than the one between D and F#. The German 6ths’ root is also Ab, and less ambiguous because there’s a P5 between Ab and Eb. Also it’s essentially just a dominant 7th chord if you respell f# to Gb. I like this system because it focuses on actual acoustic relationships and not somewhat arbitrary name-games (say between F# and Gb) or appeals to tradition.
It is dense and ultimately has some strange takes but fascinating and comes with such useful frameworks to analyze music with, that can applied to any style of music. Harmonic fluctuation (the flow between more and less stable chords), root progression, ranking the relationship of all intervals to a given root note, his chord categorization system, and the notion of melodic step-progressions as a significant contribution to the theory of melody are all concepts that should be taught in conservatories. A neglected masterpiece for real. My favorite music theory text ever.
I was taught theory using Hindemith's writings but I don't recall this particular system, which otherwise seems both interesting and rather utilitarian.
I get them confuse because people COMPLICATED the living shiet out of it. From the KEY of C MAJOR....I do know I can INSERT b2........b3.........b5.........b6........b7 chord degree as ANY TYPE of chords if I simply VAMP these modes over any of those chord degree as GUIDE lyd #6....Lyd #5, #6....Lyd #2, #6..or even Ion #6. well...if you can play A aeo , maj7 = A harmonic min A dor maj7 = Melodic minor A phry maj7 = Harmonic min b2 = Bb lyd #6 A dor b2, nmaj7 = melodic min b2 = Bb lyd #5, #6 D double harmonic min = = B lyd #2 #6 i also KNOW...you CAN play Maj, min. dominant or diminished every b3 intervals G7........Bb................Db.............E7 C Harmonic MAJOR D dor b5............F lyd b3........ Ab lyd #2, #5 B loc bb7 A Harmonic min D dor #4 F lyd #2 G# loc b4, bb7 B loc maj6 D dim/Bb....... F dim/Db.........G# dim/E..............B dim/G well... I know I can play C Maj7 F min G7 into C Maj ( C Harmonic MAJOR) I guess C Maj7 F min Db maj7 G7 into C Maj.....sounds cool I could C Maj7 F min Db maj7 Gb min G7 into C MAJOR ...............A min G#7 into C# min F# min G7 into C MAJOR There;s a million other things I could do..aside from worrying about the French....German or Italian The price of gas is $8 p/gallon...F#@K that. AMERICA FIRST !!!!!! well..... .A harmonic MAJOR B dor b5, D lyd b3 F lyd #2, #5 G# loc bb7 F# harmonic min.........G# loc maj6 B dor #4 D lyd #2 F loc b4, bb7 C Harmonic min..........D loc maj6 F dor #4 G# lyd #2 B loc b4 bb7 Gb Harmonic MAJ Ab dor b5 B lyd b3 D lyd #2, #5 F loc bb7 Eb Harmonic min F loc maj6.....ect................ect......................ect
When I was composing, my music was all based upon chords. This brings back happy memories Tom. Brilliantly described and superbly explained. An excellent masterclass.
I love these explanations of the augmented sixths. My personal favorite explanation is that they’re just weird predominant chords. In my own writing, I’ve found that predominant chords can be very chromatic or unusual as long as they lead nicely into the dominant chord. The German sixth as the tritone substitution of the V/V is the way I personally analyze it.
