One of the things I think is cool is that a standard chord sequence in Jazz is the ii7-V7-IM7 (e.g., Dm7-G7-CM7) which, if you do the tritone substitution turns into ii7-II♭7-IM7 so you get this nice little chromatic descending sequence happening in the bassline.
It’s also worth noting that when comping, the most important notes to be sure to hit are the 3rd (which expresses whether we’re major or minor) and the 7th (which gives the flavor of the chord), since the root is likely covered by the bass player and the fifth is implied by the 3rd (if you’re at a piano, try you can see this by, e.g., playing C-E-G-B in the right hand and C in the left, and comparing that to E-B in the right hand and C in the left. A jazz pianist soloing will likely do their melody line in the right hand and hit 3-7 with the left), so the tritone substitution will be made/implied by whatever the bass player does against that.
The other fun thing is to just vamp on a II♭7-V7 sequence. Some notable places you’ll encounter this in music you’ve heard include the Simpsons theme and the Beatles’ “I Am the Walrus.”
you get this nice little chromatic descending sequence happening in the bassline
If and only if the chords all stay in the same inversion and the bass line doesn't make leaps. That might be what you want and it is idiomatic in some genres/styles. But it might not be what you want or even what you get from the notation depending on how the musicians interpret the notation.
"Music theorists tend to bombard their audience with more information than nonexperts can swallow in one sitting." groaned the mathematician, in cognitive dissonance.
I don't think there's usually so much information in music. It's more like a language problem.
Depending on context, it can take a whole paragraph of music theory to describe a handful of chords that would otherwise be instantly recognizable to a trained ear.
I didn't hear that spot as a tritone substitution, personally, but a sort of non-harmonic counterpoint move ("passing tones" or "setup tones" to 19th century theorists).
More broadly, a lot of people like to point out wild 20th century chords in baroque music, but they really didn't think in terms of chords, and as such these pseudo-chords don't have the same function that modern versions of chords do. In particular, Scarlatti was a prolific user of the partimento method of composition, which is a slightly of abstracted version of counterpoint, and his sonatas are pretty good examples of pieces written with this in mind. The method revolves around intervals and movement between voices rather than chords. It's normal for someone thinking in counterpoint to produce some very "modern" "chords" because that's a common consequence of following nothing but voice leading to produce a piece of music.
But JS Bach apparently did love those modern sounds, see BWV 542/I But indeed it doesn't make much sense to apply jazz theory on classical or early music.
I've never quite understood that POV, although my piano teacher had it. Clearly she had another way of understanding it which I'm sure is more useful. I lack that training.
Pick an example everyone knows: Bach's Prelude in C. I wrote in chord symbols over every bar of that, except for that one very weird bar near the end. It helped me a lot in memorizing it.
IMO when you're playing music, everything you want to do is on the table. If you're going to make music theory and music history arguments, you should be sensitive to the theory and history you are arguing about.
By the way, a 19th century functional harmonist would also find that prelude sort of odd. Not in terms of the chords themselves, but they don't always obey their usual functions.
Also, many modern players and theorists reach toward Schenkerian analysis and its derivatives to sort of explain why music sounds the ways it does. Unlike counterpoint and harmony, Schenkerian analysis is almost entirely descriptive, not prescriptive. I have no idea what your teacher would have suggested.
> IMO when you're playing music, everything you want to do is on the table. If you're going to make music theory and music history arguments, you should be sensitive to the theory and history you are arguing about.
I don't even understand this paragraph. I'm not arguing.
That wasn't directed to you, but rather toward your teacher and the OP. The intent was that as a player, I think you should go ahead and use roman numerals or jazz theory or any other form of analysis that helps you think about things. However, if you are publishing an analysis of a piece (which you did not do), you should be thinking differently than that.
As someone with a significant background in historical performance, my books of Bach preludes are still full of Roman numerals because that is a really good way to "compress" information about what notes to play.
I mentioned this in a sister comment, but I will add:
* Schenkerian analysis is probably the modern method of looking at Bach. A sister comment also indicates that Schenker was a controversial figure (he was a German fascist), but I believe the follow-ups from other theorists on his methods are the modern ones to use for analysis.
* Analyzing otherwise in the context of counterpoint and intervals - see Gradus ad Parnassum and Kennan's book on counterpoint.
I guess you could use figured bass notation. It's more complex than modern chord notation because it tells you which inversion to use, and it notates secondary dominants (e.g. V of V, which you'd write simply as D7 in jazz notation if you're in C). Personally I know too little about it to use it effectively and therefore I would stick with modern chord notation even when talking about classical pieces.
While not disagreeing with anything you’ve said (music theory is one part acoustic physics to several parts history and sociology), the specific primacy of Schenkerian analysis is a particularly American trait.
It’s also, interestingly, illustrative of your argument. Musical analysis is necessarily socially contextual and therefore revealing of the author’s values and priorities, and Schenkerian arguments often imply, or directly come with, some really quite right-wing positions. Schenker was very much into motivated reasoning to defend his deep-rooted racism; many Schenkerian analysts have, deliberately or otherwise, wound up following in those footsteps.
Schenkerian analysis is, broadly speaking, a rediscovery and popularization of melodic reduction approaches that were well known to composers and performers in the 18th century. There's very little that's specifically American about it, let alone German. See Nicholas Baragwanath, The Solfeggio Tradition: A Forgotten Art of Melody in the Long Eighteenth Century. And of course, Schenker's "imaginary continuo" is readily understood as a popularization of historical partimento (and closely comparable approaches such as the so-called Partitura known from German sources).
It's true though that Schenker's treatises included plenty of political asides of such an extreme chauvistic character that to call them "quite right wing" is a huge understatement. (It's also true that, as scholarly research has pointed out in recent years, he seems to have expressed similarly extreme views in his private correspondence and other private writings.) Part of this might perhaps be explained as Schenker's awkward overcompensation for what would've been his remarkably humble origins back then (he came from a small village in what was then Austrian Galicia, now in modern Ukraine). Regardless, I think we nowadays have so many sources proving the relevance of melodic reduction/elaboration approaches (some of them quite early indeed, from the 16th-17th centuries) that to tie these analytical approaches polemically to Schenker and his specificities is really quite pointless, perhaps even misleading.
Ah yes, the good old "fascist dog whistle" argument. Schenker himself was an outright fascist. However, many theorists from the late 20th century who have come up with methods for analyzing tonal music have done so mostly on the back of Schenker's work. I'm also not suggesting you should read Schenker himself - his own work on what we call "Schenkerian analysis" is quite primitive and limited.
I'm curious what you would suggest to perform a modern analysis of Bach (what the original comment chain on this was about) if not Schenkerian analysis. I didn't see any alternative analysis tools proposed in your post, even though it sounds like you are educated on the subject.
For an alternative (but still very valid) interpretation, Wanda Landowska playing BWV 903 on a harpsichord in 1935 totally blew my mind: https://www.youtube.com/watch?v=h-tsbumcyVc
My piano teacher pointed me to this recording when I studied the piece with him. It was scandalizing at first, but the free improvisation in the arpeggiated chords is almost miraculous. (I also love Paul Badura-Skoda's take on the piece: https://www.youtube.com/watch?v=Xx5gojkXdeI)
Scarlatti's sonatas contain many chords, apart from pure polyphony. In fact they're particularly notable for their early inroads toward functional harmony. The tritone substitution in K420 is a clear example of this. Bach much less so, and certainly not in the case highlighted by Beato there.
Whether it contains what a modern ear hears as chords or not, he wrote the piece using polyphonic methods. Bach's music also contains plenty of chords, but that doesn't change how it was written.
When theorists talk about Scarlatti laying the foundation of harmony, partimento is probably the foundation they are referring to. Functional harmony of the 19th century is just a more powerful abstraction.
I don't get how it depends on "how it was written." First, Bach did write chords. Bar 2 of the famous Toccata and fugue ends in a chord. Bar 10/11 has a big chord. Bar 12 starts with a chord. There are chords everywhere. In case you doubt the authorship, plenty of other toccatas have chords. The whole idea of figured bass is chords.
Second, while they did think differently about harmony, you can describe it in modern terms. A description like Cmaj7 doesn't mean anything else than a set of pitches.
A tritone substitution is somewhat different, since it depends on what the analyzer thinks the chord could/should have been. There's a recent YouTube video (by David Bennett, IIRC) that shows tritone substitutions in songs, but he mentions that he doubts Paul McCartney knew he was writing one. But does that mean it isn't? No, it means you can see it as a tritone substitution.
Music theory is a subjective tool to describe and compare, nothing else.
It's interesting that you cite the Toccata and Fugue in D minor because some theorists believe that was actually written much later. The original theory was that Mendelssohn wrote it in the 19th century, but I believe there were some sources from the 1700s. It clearly has a very non-Bach character, including the octave doublings in the chords you mention.
It's very clear that the man wrote chords. It's also very clear that harmony (ie vertical music theory) was not the tool used to write those chords. If you listen to BWV903, for example, there is a long section of arpeggiated chords that defy 18th and 19th century harmony.
The OP's idea of a tritone substitution from Scarlatti does not have the same harmonic function as a tritone substitution in modern music. I would agree with you that if the function matches, you can certainly analyze things in the context of a later theory, but the function does not match.
Finally, figured bass notates intervals, not chords. A crude realization can neglect voice leading in the upper voices, but more skilled realizers of figured bass will preserve voice leading between the intervals in the upper voices. The idea that figured bass is about chords sort of maps backwards the modern abuses of figured bass (which IMO should not be taught as a "basic music theory" subject - but that is for another day) onto the original method.
I think this might be missing the point a little bit - the bassline in figured bass has more primacy than any of the sonorities above it. The most relevant feature of "chord"-based approaches to music (as found historically, e.g. in performance methods for the Baroque guitar, and to a far lesser extent in repertoire for the lute) is that the vertical sonority (such as "Cmaj7") is all that matters; individual "voices" or "parts" are of secondary importance at best. This maps well enough to how lute- or guitar-like instruments might be played in an accompaniment role (since these instruments obscure the sense of a "melodic line" or a "part" the most, for a variety of reasons) but music includes a whole lot more than that.
Fux's Gradus ad Parnassum is something you can find. A lot of the partimento stuff was practical in nature, and consisted of some rules and several exercises. A great online source on Partimento and historical solfege:
If you think of a dominant 7th chord as four notes in a 4:5:6:7 resonance, then it seems the 7/5 interval is the "correct" tritone in this context. But a proper tritone substitution means turning the 7/5 into a 10/7 or a 10/7 into a 7/5, which means one or the other of the chords will be out of tune with itself.
Alternatively, one could just hold one note fixed and move the other three, so you end up with both chords being self-consistent. That seems more mathematically satisfying at least.
Ultimately, though, I suppose the only real standard of correctness in music is whatever you can get away with.
It's a shame to describe the tritone sub for G7 as C# F G# B, when the proper way to spell it is either Db F Ab Cb or C# E# G# B. Of course, then you'd have to explain about enharmonic equivalence and how chords are usually spelled with every other note.
The C# grates on my eyes, since the V7 tritone substitute is IIb7. However, preserving the F and the B notation emphasizes the tritone interval that is inverted and shared with the substitute.
The explanation is that a seventh chord is defined as a set of third intervals. So it cannot jump from C# to F, it needs to go from C# to E#. Even though these tones are the same, the C# to F doesn't make sense. The same can be said about F G#, it doesn't make sense because it is not a third.
I transcribed the music on the ghost ship in Monkey Island 1, which features a lot of chords in the background involving fourths, fifths, and whatever we want to call the half-step in between fa and so.
Working with a MIDI file and without much grounding in music theory, I had and have no real way of determining whether to represent notes flat or sharp. I consulted several people and generally got a response of "Oh, interesting stuff! It's not clear how you should transcribe that."
The note between fa and sol is fi or se, depending on if it's the sharp 4 or flat 5 functionally. Sharp 4 would be most common, since it comes up as the leading tone of the dominant's key, e.g. in an secondary dominant, like V7/V.
But I guess you could get the flat 5 if you did the tritone substitution of the secondary dominant of the IV, which would be bV7.
I know that fa sharp is fi and so flat is se. The point of my comment was (1) that I was having difficulty labeling the note in question, meaning I couldn't use either name; and (2) that the heuristic "use the enharmonic that doesn't interfere with other nearby notes" doesn't work, because the notes a half-step away in either direction are both in use.
Oh sorry, I misread your comment and that you were referring to a specific piece. Are you talking about the vibraphone part in the beginning? If so, I think you did it right. I wouldn't consider those little dips of the top note to be a chord change, but just a neighbor tone (https://en.wikipedia.org/wiki/Nonchord_tone#Neighbor_tone). So I'd treat it melodically and just put it on the adjacent line, with whatever accidental works. Like you did!
And then I think you may be talking specifically about measure 11. I'm pretty rusty on my analysis, but it seems like it's the iv7 chord, but starting and ending with a chromatically raised root, which is slick because it acts as a passing tone from the i chord in measure 10 and the V in measure 13. I would probably do Gb -> F -> Gb, because the F is the chord tone, and the Gb is the nonchord ornament. But yeah, probably doesn't really matter!
- Match the type of accidentals used by the key signature.
- Use sharps when the melody is moving up, and flats when it's moving down.
- Use whatever accidentals give you a visually pleasing spacing of notes in "thirds" as represented on the staff. (As advocated here.)
- Use the accidentals that are physically compatible with other notes in the chord. (Only a concern for certain instruments, but e.g. I understand that the pedals on a harp affect many strings at once, so playing a particular combination of notes may require a clever approach to the pedals, indicated by what might otherwise look like an unnatural set of accidentals. This wouldn't apply to a piano, where G# is just a separate key from G, not a modification of the G key.) I think this is what you're going for?
Another example would be the bass side of an accordion where Db and C# imply different buttons (though not different sounds - there are duplicates) and they’re quite far away from each other.
The accident you use really depends on the context. If you're talking about chords, then you should follow the "stack of thirds" explanation that I gave above, it is how chord theory works. However, the other rules you mention also can be used depending on your situation. In a melody, you normally want to add accidents only when needed.
Yeah, I've seen things spelled this way before in barbershop arrangements. Usually because it's less accidentals. I think it makes sense from a "what notes should I play" perspective, but seeing these chords spelled in a weird way gives you insight into how some composers actually think, and all that REALLY matters is what the music sounds like.
I came here to pick this nit but you beat me to it. I think calling it Db7 is the best way to think of it, especially since in jazz it's often part of a descending sequence of II-V-I, where the tritone substitution turns it into II-bII-I. So in C major (where G is the dominant), it has to be Db.
I don't think this is correct. I think colanderman's answer is the right one, which is that when we're descending, we generally spell out the pitches with flats. If this were ascending, then we could have I-#I-II. But as I noted, in jazz this particular descending pattern is fairly common.
I, bII, etc. are chords not pitches. II-bII-I is a chord change. Pitches may go up or down and voices may go away or arrive. They may be part of those chords or not. And there may not even be a root pitch.
Or if you want formal theory, chords are scales [1] and there ain't no such thing as a scale with a sharp I. If you sharp the one it’s a different scale starting in a different place.
The b in bII is not an accidental and bII is how to communicate the chord in passing. I/bII is also possible to communicate a modulation (as would be vii/II, etc. if the modulation is elsewhere).
There are “enharmonics” for chords that aren”t the root of course, e.g. #IV and bV depending on intent, convention, or playability. But #I will be marked wrong on the entrance exam and only raise you standing among an avant guard that isnt accepting new members.
> If you sharp the one it’s a different scale starting in a different place.
It depends on what's the function. If you want to use the tritone-substituted G7 to modulate to the sharp fourth, you'd write it C#7 and resolve it to F# (or F#-).
C#7 is the name of a chord not a pitch and not Roman Numeral Analysis. [0]
The Roman Numeral analysis would be V7/#IV if you are modulating in C. And something else if you aren't in C. Roman Numeral Analysis is independent of key or tonal center. The Roman Numeral Analysis would be bII if you are not modulating because that's how Roman Numeral Analysis communicates.
Thinking about Phrygian mode. The two is always a bII.
{0} As an aside, in The Common Practice the bII is often notated N6 (for Neapolitan 6th) to set up a perfect cadence, i.e. I-N6-V-I.
Question for music theory experts who are also coders: does it feel like understanding a programming language, or something else? Admittedly I've never really made any serious independent effort to learn it, or to retain whatever I tried to learn, but it is very difficult for me to even grasp a mental model of how understanding it is supposed to work, or feel, in my head.
I can read a piece of code and know how the bits affect one another. When I read basically anything on music theory it feels like a string of non-sequiturs basically. Maybe there's just some skill floor where that all starts to feel organized?
I think the only "universal" part of music theory is the integer resonance stuff, "a perfect fifth is a 2:3 frequency ratio", because integer resonances do seem to have biological significance for us. The rest is culturally dependent: it's not describing some uniquely necessary mathematical object, but more like describing the spoken language of a certain region and time period. The best way to understand it is to play music from that period, notice some common "moves" (like the move from dominant to tonic), and realize "hey, music theory has a name for that".
You wouldn't use music theory to write music, same as you wouldn't use a grammar book to write a novel. You write music by intuiting the sequence of moves you want to make, guided by your ear and listening experience, and maybe even coming up with some new ones. Then if you're successful, theorists will make theories about it.
Some people will naively say "All music has pentatonic! Universal!" but ignore vital cultural context. One example in the video is ragas: they can look a lot like Western scales and modes, but they have a time and context.
Western music also has a time and context, but it doesn't stand out as much to us unless someone goes full ham breaking that context like with the Imperial March in a Major mode: https://www.youtube.com/watch?v=B9MShtCg4fk
It changes the mood from "this is the bad guys!" to something more positive and triumphant.
There are also several traditions that have scales/modes where certain note sequences (typical pairs) are only "allowed" in one direction (i.e you can play #3 after #1 if you're ascending from #1 to #3, but not the other way around).
This adds additional confusion to comparing scales/modes between cultures.
We do have at least one such mode/scale in the western european classical tradition, but it is not widely used.
I would disagree with the second point. Music theory has definitely changed how I make music. The initial idea is typically still conceived intuitively, but I definitely use music theory to develop it into a whole piece. Before knowing music theory, developing an idea further felt a lot like applying a brute force algorithm. Now, I can recognize what my initial idea is doing and I know where I could take it - both by following conventions and by breaking them.
So it's not biological significance... You are born loving the sound “shush,” white noise. This is also the great irony of people complaining about distortion and thick bassy kick beats, we actually like it because it's warm and “takes us back”: indeed even to the noisy slushy womb and the heartbeat there.
Rather it's that things that hit one tone either also tickle the hairs in your organ of Corti at 2x, 3x, 4x, 5x the frequency (strings) or at 3x, 5x, 7x, 9x the frequency (half-open acoustic resonators—guitar bodies, panflutes), and your brain feels comfortable when those tickle together as they are familiar.
Music theory is descriptive, not prescriptive. Oodles of people make music without knowing a lick of it, and people who learn it in academic environments still typically make music starting from other concepts. "Listen to records and vibe with what they are doing" is typically a much more effective way of learning to improvise seriously than "learn the theory rules", for example.
"Music Theory" also typically is very tightly bound to harmonic analysis modes that are focused on about two centuries of western european music. This is necessarily going to limit its effectiveness when applied in other spaces (even here, when applied to jazz).
This is exactly what I got wrong when I started learning jazz piano as an adult. My wife is a lifelong musician and I got to the annoying point where I'd be playing and she'd walk by and go "that third chord sounds wrong." I'd ask why and she'd be unable to elaborate until she sat down and played the better version intuitively. Then she'd retroactively analyze what she did to explain it to me. I understood the theory, she understood the sounds. It was always humbling and helped me understand that intellectualizing comes second.
A bit. Music is a bit like programming but I think there are 2 distinct ways to practise music: performance and composition. Theory helps you with both. I think that there's less of a "performance" aspect to programming, it's more "composition-like". Chess is an area where you have a combination of theory and skill that, to me, is more music-like (because you can play chess in a "performance way" and also in a "composition way").
If your goal is to be able to improvise then the purpose of theory is really ear training: it allows you to develop an instinct about what to do with your body to produce a desired result. Improvisation is a bit like "composition in the moment", like speed chess.
There are contrived situations where people treat programming as a performance activity but it's not the way most programmers spend their time.
This was my favorite reply to the question. Music theory is great, and it really can be helpful with composition. But I've also found that what I'm really looking for when trying to improvise, or perform, is having studied and worked on the theory - specifically on the ear training and the process of connecting that to my fingers - to the point where I don't have to think about it any more.
The composition vs performance framing is very useful I think. Some musicians might just want to do composition, and can spend a little more time between the notes figuring out what ought to come next. (Although even in this case, it's easy to get bogged down in analysis and forget about what feels right). But a lot of musicians want to be able to improvise - and the difference is like being able to write down a compelling argument vs being able to make a compelling "speech" off the cuff.
Yeah, in both cases, you're going to need a good understanding of grammar and vocabulary - but when you're trying to make that speech (or improvise a solo), you're just not going to have the time to think about "the sound I want to hear next is the sound of the 5th of the chord the band is implying." All our practice and theory homework is in service of the fingers just doing what's in our heads automatically - and sometimes, even surprising ourselves with what comes out.
> But I've also found that what I'm really looking for when trying to improvise, or perform, is having studied and worked on the theory - specifically on the ear training and the process of connecting that to my fingers - to the point where I don't have to think about it any more
"The purpose of all theory is ear training" is actually a Warne Marsh quote, although one that I can't verify. My dad (who is/was a jazz musician) read it in an interview in Coda Magazine in 1976 and while I can find references to the interview I can't find a copy of it online.
My dad used the quote "The purpose of all theory is ear training" as the inscription on his self-published basic and advanced keyboard harmony books. It's certainly a quote I've heard him repeat many times over the years.
That makes no sense. They've internalized the theory so much that they can focus on the magic, and each of them has their own kind of magic, but they absolutely know the theory.
There’s a bunch of theory that goes into understanding why a tritone sub works for a Dom7 for the 5 chord, but it’s not something you think about when you’re using it. You learn how it sounds and you start using it instinctively.
Other people can probably figure out better analogies, but I’d say it’s something like the difference reading an article about generics or monads vs actually using them every day. To an outsider these seem like a ton to think about, but when you use them every day they’re just part of your toolbox.
I fit the bill. There are obviously similarities: music notation is a formal language like programming languages. When you read notation, you can pretty quickly grasp certain relationships and substructures within the piece. With jazz notation especially you can quickly figure out what the general strategy of the piece is and once you’ve got an ear for how it works, you can theorize or write little melodies or complementary bits just from sight alone.
I would also say that the obvious impact of the ear and/or the tools you’re using to play music make it very different than programming. Without the knowing how you would actually play a piece of music, it can be difficult to visualize or interpret notation, whereas code is pretty straightforward in how it’s made or what it actually does. The “feel” is really abstract and interacting with the piece is more akin to observing a running system than it is to touching code.
Sure, music theory involves learning the "syntax" of music notation, the "semantics" of e.g. key and genre, and the "programming pearls" of common musical idioms like tritone substitutions. There are analogs.
But what distinguishes music theory is:
1. The language and notation is hundreds of years old. It's been with us in one form or another 200 times longer than COBOL has. Maybe longer.
2. You don't have the peculiar challenge of having to speak it in the very precise form that a computer requires of a programming language. The terminology and communication between musicians is much fuzzier than that, much more like a human language.
Western Music theory is an attempt to formalize certain things about music. But it's better with proper context. Like, say, a song is not about the music theory you put in it. A good song starts with a good story--and that's another craft altogether--which you make into good lyrics. Good Lyrics combine story, language quirks and phonetics. The lyrics are a heavy ingredient that needs spacing and intonation which are good-sounding and practical to a human singer, and that needs to mesh with melody and rhythm. Then comes harmony and the doses of emotion you can put into it, and that's what this article is about.
You can certainly code lots of ingredients. For example, you can use embeddings to find better rhymes faster when composing a lyrics, or even LLM help to check if your lyrics make sense (If ChatGPT can guess what your lyrics are about, a human may be able too). You can use a host of computer utilities to find harmonies, and even use voice synthesizers to sketch the singing. But at the end, what makes a piece of music interesting is how well it meshes with its listener...you can model that with statistics, if you are pedantic enough, but at that point the maws of hell open and suck your soul out.
Haha this is the second time my degree has come in handy after getting me a job in a record store after college.
I’d say “music theory” as a general concept is closer to understanding computer science principles like managing complexity or the memory hierarchy. Individual disciplines, such as orchestrating for a specific kind of ensemble (string quartet, big band…) or writing in specific forms (fugue, AABA popular song…) are closer to mastering practical programming tasks like working fluently in a given programming language.
[I am not a music theory expert but just finished two semesters of music theory at community college and have several decades of experience as an adult]
Functional harmony is usually what people mean by music theory.
Functional is the key to my understanding. Functional Harmony is what has been done harmonically and melodically in styles of music derived from The Period of Common Practice. Functional Harmony describes what some people did. Using it makes music that sounds like what those people did.
From the street where I live, I see cultural institutions that ascribe moral value to the conventions of The Period of Common Practice. There’s an industry built up around The Period of Common Practice and the flow of money means there are jobs for those of jobbing age and careers for those of careering age.
To me it's one of those midtwit memes where on the left and right side, it's like "they're so similar" and in the middle "they're totally different".
On the left, they're similar because on the surface level, you're basically executing scripts and there's a lot of jargon to describe higher levels of abstraction.
In the middle, they're different because, as others have said, music theory only loosely maps to how people write music, whereas software development seems much more algorithmic.
But as I became more experienced, I realized software is way more of an art than a science, and that all the best practices are contextual.
As someone who has come back to jazz improvisation after many years, and being a coder, the performance aspect is a little like playing a video game.
But this game has 1) very short levels (1-2 seconds), 2) repeated patterns in the levels and sequence of levels, 3) strong incentives to solve levels in novel and interesting ways, but 4) there are hidden mines everywhere which can damage you, but 5) you get points for hitting the mines in the right way so that you avoid damage. The mines are “wrong notes.”
Music theory gives you power ups to see the mines, quickly plot paths, and treat sequences of levels as part of a meta-level. But you have to be FAST.
(I have been known to stretch an analogy too far..)
Yes - well, almost. As coders, theory scratches the itch of understanding what's happening "under the hood." We might say that "Bach's music is brilliant", but why? Theory helps make the music, and the things that make it sound interesting, explainable.
That said, making music is not merely a technical exercise - there could be multiple theoretical ways to describe a harmony. You still have to listen to it and ask, "what makes the most sense? Is this functioning as a resolution to some tension?" It's easy in a classroom to lose sight of the fact that the theory was invented after the fact.
If you're programmer-brained, lots of things will feel like understanding a programming language to you. There's no particular programming-ish qualities to music theory.
I asked some classical music people once if there was a history of harmony. Someone retorted that the modern concept of harmony was an inadequate way of understanding counterpoint, and that the primary concept should be voice leading, not vertical harmony. I suppose it makes sense — that our categories of musical analysis have histories, and it can be misleading to apply them out of context (as the rest of this thread is commenting).
But I still wish someone would write a history about "what kinds of harmonies do people think sound good/melodious/interesting, and which do they consider bad/ugly/weird/useless at a given moment." Or if that history already exists, I wish I knew how to find it.
"Harmonielehre" by Dieter de la Motte is an excellent book that does exactly this. He explicitely points out that harmony must always be understood and analyzed in context. "Kontrapunkt", his book on counterpoint, follows the same principle and is just as good. I think/hope there are English translations.
You also need to locate such a project in place as well. There isn't just one music history, each culture has its own. They've only begun to somewhat converge in the last couple centuries, but there are at least dozens of distinct, independent musical traditions with at least a thousand years of continuous development.
A great deal has been written on this but the vast bulk requires a solid understanding of theory, Cambridge's History of Western Music Theory gives a lifetimes worth of material to study on this topic.
From a jazz musician's perspective, classical theorists tend to confuse the map with the territory. Classical theory is (at least historically) often prescriptive rather than descriptive, which tends to cause some friction when applied to music outside of that idiom.
Interesting. John Baez is the brother of Joan Baez, the famous singer. Didn't know he was into music too.
That being said, Tritone substitutions sound good in some circumstances, but seem over the top in others. Use with care, as always. They'll always seem more appropriate in jazz genres
Toxic by Britney Spears is basically built on secondary dominants and tritone substitutions (i-VI7-II7-V7 becomes i-IIIb7-II7-IIb7), so they definitely have their place in pop music too. Whether the composers thought about it that way, we can't know, but in any case what matters is whether the bass line sounds good.
Music used to be treated like a science… the pythagoreans, for instance, conducted the first hypothesis driven scientific experiment on a musical question (whether whole number ratios affected chords with bronze chimes). Descartes’ first book was all about music theory.
Up until fairly recently the only people who treated music like a science were people who did not have much if anything to do with music beyond listening and thinking about it. When composers and musicians started treating music like a science (or math) people tended to complain about it and "reduce" it to academic wankery.
Pythagoras and Descartes had more to do with criticism and theory than anything anyone was listening to or composing, which was instrumental in the development of western theory. I don't think we have any music following the ideas of the Pythagoreans until the mid/late 20th century, anyone know of earlier examples?
There is pretty strong evidence that Bach, for example, was also very much into math and thought about music in a very mathematical way. Some other composers definitely did the same, but I agree with you that mathematical thinking was never a prerequisite for composers.
I would suspect that many of the ones from the early periods were far more "mathematical" than 20th and 21st century composers, but there is very little writing either way.
I don't think many early composers get as mathematical as someone like Xenakis or even Schoenberg. Or maybe its just the way in which the math manifests in composition, Xenakis was far more direct with it than Bach. I can't see how one could make a viable case for pre 20th century composers being more mathematical but the argument could be interesting and worthwhile.
I'm not sure how you're defining "mathematical." The definition really changes who is on the list. Schoenberg and the 12 tone crowd had some of the most obvious applications of math, but composers of the Baroque era treated music a lot more like a logic puzzle than anything the 20th century composers came close to. For example, I encourage you to do some research into canons and how they are written. That is what I meant by "mathematical," rather the idea of doing arithmetic on notes (which I happen to think is a crude excuse for creativity).
>rather the idea of doing arithmetic on notes (which I happen to think is a crude excuse for creativity).
That is a very crude view of the relation between math and music in 20th and 21st centuries. The puzzles Bach was working out had more to do with the theory than the math and we can support this, the math aspect is more interesting conjecture than something we can demonstrate, at least from what I have read on the subject which tends to be filled with assumptions and generalizations.
Schoenberg and his ilk are more music influenced by math, set theory in music is not set theory in math. We don't really see math literal in music until the rise of computer music and they are often doing things more than just seeing what the math results in. The thing with much computer music is that it is deeply tied into how music works on a computer right down to the way sound is generated which requires us to throw away traditional ideas of orchestration and form to understand it as something other than just a musical representation of math. I lack the math to get much of this stuff but I find it very interesting and it certainly provides me with a good number of ideas.
I gather that you have defined math completely differently than me, or at least defined it in a way that gives computers primacy over every other form of math.
> The puzzles Bach was working out had more to do with the theory than the math and we can support this, the math aspect is more interesting conjecture than something we can demonstrate, at least from what I have read on the subject which tends to be filled with assumptions and generalizations.
This sentence structure is very much beyond me, but from what I gathered, you do not consider propositional logic as created by harmony/counterpoint to be "math" and you believe that those rules are arbitrary and not based on math at all. That is sort of a fringe view that is facially false. Around the world, rules of harmony have a lot to do with the harmonic series, scales, tunings, and other building blocks that are hugely based on math. A lot of that was actually up to the composers and producers of music in the 19th century and earlier (around the world).
> We don't really see math literal in music until the rise of computer music and they are often doing things more than just seeing what the math results in.
I see that you have defined "math as math" in terms of the totality of the math involved in the process of composition. Most 21st century composers and producers I know do absolutely no math (defined in any way) when writing music. I will also say that the producers of computer music absolutely do not throw away "traditional ideas of orchestration and form" unless they are lazy or bad. Many of them very clearly understand that stuff and riff on it in ways that can only be done when you combine a deep artistic instinct (0 math) with a computer (that does all the math for you).
well the Pythagorean comma and how to divide it amongst the octave was the central objective during the whole evolution of temperament (from meantone to modern day 12-tet).
So that takes us back to at least the 15th/16th century
That is more theory than practice unless you want to reduce Pythagoras down to a comma. I was referring more to people who decided to take Pythagoras and related writings as gospel.
According to Vitruvius, Roman engineers had to learn music so they could tune the ropes of ballistic devices to the correct tension by listening to their pitch when striking them.
Music was part of the quadrivium as well, on par with astronomy and math.
Does one normally learn any theory as part of learning to play an instrument?
I played in middle and high school concert band and took private lessons in addition to that for a few of those years.
I never learned a lick of theory from any of my instructors. Maybe because as a horn player you can't play chords. All I learned was to read notes and play my part. After a year of high school band I came to the conclusion that this was just work and gave me no enjoyment at all so I quit. Everyone seemed surprised.
Not unless you want to or someone does it for your own benefit. Especially if you play an instrument where getting a baseline level of competence in reading and playing written music is all you need to be able to do to be part of the ensemble, and especially when it's a relatively casual ensemble like most high school bands.
Not just theory though. I've met people who continue to perform in orchestras decades after high school and college, who play with really good groups, and who have literally no interest whatsoever in the music they play, let alone its theory. It's always bizarre to me to talk excitedly to someone about the piece their orchestra is playing to only be met with confused indifference about it and the composer. For some people it's just an activity to keep busy and nothing more. This is not necessarily a bad thing, it's nice that there are many ways to engage with music and be able to choose how involved you want to be.
In the US, theory is typically part of post-secondary musical education. Some high schools might have it, but in a lot of high schools filling out the marching and symphonic bands with warm bodies will drive a lot of a music program.
Typically, piano is part of post-secondary music program requirements and keyboards make it practical to apply music theory to make sounds...arpeggiation will get your ear so far. Polyphony gives a much clearer picture of what music theory is describing.
If you're interested in learning music theory, a polyphonic keyboard that makes sounds without a computer (maybe one with speakers, but at least with a headphone jack) is my recommendation. Maybe it's better if it is small and portable. A MIDI controller with a phone or tablet might be ok, but phones and tablets have email and the internet and those can interrupt what you set out to do.
Anyway, theory usually comes later in the US system. There are exceptions of course.
Yes, and yes. The reason you weren't taught much theory is because on a horn you're only playing one note. But I think that's really a shame, because you were deprived of the understand of what you were playing and why, in the context of the notes and chords that the rest of the band was playing. And even when playing a horn solo piece, there is always an understandable, chord-based structure to the piece.
Edit: Also it really doesn't take much effort or theory to understand most of what would be interesting. Like many subjects, the 80% of what's helpful can be written on just a few pages and learned in a few hours - but whole college curriculums can be made of the details and nuances. Go read up on 7th chords, cadences, and simple chord progressions if interested.
This is an oversimplification imho. Many of the greatest jazz musicians like Miles Davis and John Coltrane played instruments that could only play one note at a time, and they still manage to convey harmonic concepts.
I don’t have an answer for why most music teachers don’t teach theory (and improv) other than it’s more challenging and they might not know it themselves, and it’s easier to teach rote memorization.
There are plenty of people who learn piano (which obviously doesn’t suffer from the single-note “limitation”) and also learn almost no theory.
Horn players can always outline chords, perhaps with outright arpeggios or by choosing chord tones on downbeats. That said, even if your teacher had armed you with theory its still just comes down to an assload of work. But maybe that might have helped you connect with a feeling of reward.
Interesting article, but FYI, I'm not sure if it's because of my mild color blindness, but making out some of the colors on those first couple pictures is next to impossible.
A tritone interval by itself (only 2 notes sounding) sounds quite dissonant to me.
But in the context of the dominant 7th chord, the only note dissonant with the bass is the 7th. The tritone itself is not so prominent since it occurs between two non-bass notes.
Yes, this understanding would mean the 12-bar blues and blues music in general are an extremely dissonant form as they use the dominant seven chords as tonics.
How many people consider the blues dissonant?
It reminds me of my first counterpoint assignment. "Fourths aren't dissonant" I said, and it came back covered in red marks
7 chords are dissonant. That’s why a (ii-)V7-I works. Dominant creates tension that gets resolved, or not.
But the chord function is only one third of the picture. Dominant chords can have greater or lesser tension depending on which extensions are used. A closed voicing will sound more dissonant than an open one.
I understand dissonance to be how big the numbers are when you express an interval as a reduced frequency ratio. By that metric it's pretty dissonant. How can it be considered moderately dissonant?
Yes, a tritone is dissonant because it isn’t close to any simple ratio of frequencies. It has a spiciness that makes the music sound interesting without it being overly unpleasant.
Avoiding dissonance entirely can also be unpleasant. e.g. barbershop harmony can sound saccharine because the human voice can hit those simple ratios much closer than 12TET can. 12TET gives us some dissonance for free, which people have learned to appreciate. Like spice tolerance, dissonance tolerance is learned not inate.
A minor second is very dissonant, you can hear pronounced beating between the tones: https://en.wikipedia.org/wiki/Beat_(acoustics). This makes it stick out more than a tritone, so it has to be balanced more carefully.
For me, I don't think it's meaningful to think of two notes in a vacuum as anything. The logical part of me wants to think about it with math like you're suggesting, but 2 notes lack any context to give them meaning. Add another two to the chord or add other notes around it temporally, and now they don't sound bad at all. The idea of consonance and dissonance only makes sense to me within the framework of tension and release.
“A tritone is very dissonant, so the dominant seventh chord really wants to ‘resolve’ to something more sweet.”
“I see you shiver with antici——”
It’s not dissonance that makes you want to hear the completion of the sentence, rather, it’s grammar. If you play a tritone out of context, there is no need for it to resolve, but you can cast context around it by adding a resolution to a tonic just after. The tritone has a culturally-learned grammatical role in western music; and that role is not a universal law of aesthetics.
To answer for the other JCB, no, because (my inference) she in her own words was abused by her mathematician (mathematical physicist?) father Albert Baez.
In switzerland, one has to take a course (with official binder but no longer homework) and pass practical and theoretical (written and oral) tests in order to call themselves a horseman. I used to say "in the Old Country, all you have to do is fall off 7 times", but the older I get the more I suspect an unreasonably effective way to filter for horsemen is to ask if they have a favourite wheelbarrow.
On that note, among my favourite anekdoty, "nasha" Natasha Ilyinichna is at a dance. (the following should be shaggy-dog extended when told, but I'll spare you all) First she dances with Andrei Nikolayevich, but when she notices a fleck on his shirt cuff he apologises profusely and begs pardon to leave so he can change. Then she dances with Pierre Kirillovich, but when she notices a crumb on his cheek he apologises profusely and begs pardon to leave so he can wash up. Then she starts dancing with a Hussar, Rzhevsky, but when she notices a large splotch of mud on his boot...
— Oh baby, don't you worry your pretty little head. That's not mud, it's shit, so when it dries up it'll fall off all by itself.
Oh aha, good to see the subtle pointouts are back! (This mode of convo can be helpful for local ( intrapartitional) terraforming) This one had me in stitches!
Dropping the innuendos a bit, I'm truly sorry for the hamfisted way I go about doing it (what with the shit on my uniform from transporting manure)
All I can say for now is, I see why you'd think it's impt that I rewrite that bit of firmware (and that three-way with mrmann was a precious moment in time --- but it could still be a moment that can rewrite firmwares in the future..)
It’s also worth noting that when comping, the most important notes to be sure to hit are the 3rd (which expresses whether we’re major or minor) and the 7th (which gives the flavor of the chord), since the root is likely covered by the bass player and the fifth is implied by the 3rd (if you’re at a piano, try you can see this by, e.g., playing C-E-G-B in the right hand and C in the left, and comparing that to E-B in the right hand and C in the left. A jazz pianist soloing will likely do their melody line in the right hand and hit 3-7 with the left), so the tritone substitution will be made/implied by whatever the bass player does against that.
The other fun thing is to just vamp on a II♭7-V7 sequence. Some notable places you’ll encounter this in music you’ve heard include the Simpsons theme and the Beatles’ “I Am the Walrus.”