Music Theory for the 21st-Century Classroom

(musictheory.pugetsound.edu)

130 points | by aanet 5 hours ago

12 comments

  • ultrasounder 4 hours ago
    https://musictheory.pugetsound.edu/ link takes you to the homeworks/assignments and everything else for a self-study/auto-didact to follow along. Neat!
  • SeanLuke 1 hour ago
    I dunno. On first glance, for a "21st-Century" textbook, this seems to place a high emphasis on classical music theory, and moves very highly influential modern styles to the back burner -- notably jazz. And there is essentially no discussion of music theory in other cultures (middle eastern, african, east asian, indian), nor current analysis of pop and rock music.
    • WhompingWindows 27 minutes ago
      I have a BA in Music Theory, I think maybe you should consider again. First off, Jazz relies on the same fundamentals and extends them, everything from Classical music is somewhat relevant in Jazz. So if it's only Jazz theory exclusive to classical, it'd be an advanced book indeed.

      Second, it literally has a chapter on Popular Music and another on Jazz Theory, and "Classical" is not found in its chapter titles. So I don't think your critique is accurate.

      Third, history and time matter. "Theory" came first in "classical" contexts, with codified rules pre-dating even Bach. Jazz was a much later invention that built upon these and other traditions. Both of the Jazz theory books I used in my BA in Music Theoryhad many elementary topics already covered in Classical contexts.

    • analog31 55 minutes ago
      I know a lot of people with music degrees. This is a widely acknowledged problem. It doesn't have a simple answer, especially as academic music programs are shrinking. You can't teach everything except at a survey level. You have to find faculty who can teach new topics at a college level. And students who are prepared to dive in. Music students tend to already be damn good musicians by the time they start college.

      If programming is an analogy, it's said that once you've learned your first language, you can learn any other language in a jiffy. Also, a lot of higher level learning is "learning how to learn." Maybe it's better to have a standardized "first language" that students can learn in depth, and then let them move into other areas at their own discretion.

      I don't have a college degree, but for me, classical music lessons were a great preparation for learning jazz, and I've picked up pop, rock, and folk music on my own. In fact, on the instrument that I play, the double bass, gaining proficiency and experience in jazz without that background is a brutal learning curve.

      • viccis 30 minutes ago
        Anecdotally, I know a few people who spent decades working on and/or teaching middle eastern music in conservatories abroad, and they struggle greatly to find music departments in the US who will hire them. A problem I've seen firsthand is that there are a lot of senior professors who teach it hand wavy versions of it filtered through whatever books Euro orientalists wrong mid century and are threatened at the prospect of someone coming in there who has studied and practiced it for years in places where it's more of a living art form cutting into their position of expertise.

        Where this ties in to your point is that part of the reason they really don't want experts is that they rarely have someone whose job it is to teach middle eastern music. They might have a guitar teacher with some experience with oud, a flute teacher who can passably play ney (usually with awful intonation), etc. For most schools, these other types of music are "add-ons" that they have their existing faculty teach.

    • aanet 1 hour ago
      > And there is essentially no discussion of music theory in other cultures (middle eastern, african, east asian, indian)...

      To me, that above ^ looks like the biggest gap.

      To be fair, the book doesn't claim to demonstrate theory of the "world music" (sic, a phrase as bad as it sounds).

      My (brief and shallow) understanding is that most scholars of music in the western world just do not have enough knowledge to talk intelligently about non-western genres. Exceptions exist, of course, but they are quite rare.

      [Other reason is that there is a lot of gate-keeping. I've seen that in Hindustani/Carnatic classical studies, FWIW, which is one my areas of interest]

    • sambapa 15 minutes ago
      "Oh no, math degree... Where is 2+2=4?"
  • tantalor 3 hours ago
    Very cool but what does this have to do with "21st-Century Classroom"? Is that just a meaningless phrase to make it sound modern, not old-fashioned?
    • colonwqbang 2 hours ago
      If you subtract the "meaningless phrase", the title of the book is just "Music Theory". Do this for every book written about music, art, mathematics and you'll just have a lot of books with identical and quite dull titles.
      • odyssey7 2 hours ago
        Insightful. The title being more to distinguish than to describe.
        • ithkuil 1 hour ago
          "Music Theory, Bells and Whistles"
    • Dfiesl 2 hours ago
      I guess the 21st century classroom is the free online classroom you connect to from your portable device
    • gowld 3 hours ago
      It's a new presentation, an online hypertext, and uses YouTube publications of 21st Century music as example.

      https://musictheory.pugetsound.edu/mt21c/frontmatter-5.html

    • bwanab 3 hours ago
      Could just be because it is the 21st century and this was written for classroom use.
  • stackghost 1 hour ago
    Suffers from the same problem that all music theory texts seem unable to avoid: they require the reader to simply accept a bunch of random facts to memorize with no context.

    Example: memorize the major scale as a series of whole and half steps but we won’t provide you with any context or motivation for why this is so.

    Similar: in a major scale all notes are played and none are skipped or repeated. Except if your scale goes D–E–F#–G, in which case you skip F. The only way for this to be correct is apparently we consider F and F# to be the same note for purposes of scales even though this directly contradicts a previous section.

    I was expecting a “21st century” music theory reference to have an emphasis on building intuition. Music theorists are apparently allergic to good pedagogy.

    • strenholme 1 hour ago
      We recently had a long discussion about this. I come from the “music theory makes a lot more sense once one understands that 2:1, 3:2, 4:3 sound really whole and good to the human ear, 5:4 has a little more tension, and 6:5 has even more tension” school of thought [1] but for other people it is a distraction from understanding basic stuff like “this is a minor scale”. See here for the long discussion: https://news.ycombinator.com/item?id=49541888

      [1] I understand ancient scales were 3-limit instead of 5-limit scales, and that modern equal temperament has thirds which significantly deviate from 5:4 and 6:5, but once polyphony became a thing, 5-limit temperament made a lot more sense because they reduce beating.

      • Drupon 40 minutes ago
        Man that top comment is such a combination of "sneering to show off" and completely wrong that I'm shocked I'm not on reddit.

        Recommending The Jazz Theory Book to someone starting from scratch, especially someone self studying, is like recommending CLRS or TAOCP to someone who asks "I'm curious about learning the basics of algorithms and data structures, any good books for self study?" And of course that happens all the time too. Chapter 1 is "here's what intervals like major 3rd and perfect fifths are", Chapter 2 is "here's the major scale and all its diatonic modes and ii-V-I progressions", Chapter 3 is "here's how you might use the Phyrigian mode to play over a Sus flat-9 chord" (pg 48).

        Recommending Schoenberg and Messiaen as steps to get a sufficient surface of topics covered for "music theory" is performance art in its own regard. Bravo!

      • stackghost 40 minutes ago
        > I come from the “music theory makes a lot more sense once one understands that 2:1, 3:2, 4:3 sound really whole and good to the human ear, 5:4 has a little more tension, and 6:5 has even more tension” school of thought

        Ah, well, that makes sense. I come from the "music theory is a quintessentially rigid, British-Schoolroom-coded subject that emphasizes rote memorization over actual understanding" school of thought. The musical equivalent to Americans requiring their children to recite the Pledge of Allegiance before they can even understand what the words mean.

        The student seeking to build their understanding asks: why is the order of sharps FCGDAEB? Why is the mode with a sharp 4th note the Lydian mode?

        Music theory responds: Because fuck you, that's why.

    • scottious 1 hour ago
      A better way to think about it is that all letters in the musical alphabet are represented in a musical scale. Some are sharp or flat

      D major: D E F♯ G A B C♯

      D minor: D E F G A B♭ C

      Db major: D♭ E♭ F G♭ A♭ B♭ C

      Db minor: D♭ E♭ F♭ G♭ A♭ B♭♭ C♭

      • stackghost 1 hour ago
        Sure, I knew what they meant. But if they are sloppy with their terminology on the knucklehead stuff then it doesn’t bode well for the esoteric stuff to follow.

        My point was not to showcase my confusion, rather to reinforce the fact that music theory texts are just generally low quality, and music theory as a field seems to be okay with that.

  • xcf_seetan 3 hours ago
    Happy to see serialism covered! thanks
  • cbondurant 2 hours ago
    I was hoping to see if by "21st-Century" it meant "music theory that is applicable to the way modern music is generally written and interacted with". With details on things like microtonal music, increased focus on rhythmic theory, an increased appreciation for the role that timbre plays in the sound of music, the theoretical frameworks that underpin long standing musical traditions of other cultures and contrasting what makes each musical theory unique as a way of better understanding both western theories of music as well as the breadth of musical expression....

    Nope! Just the same old, well beaten, rotting corpse of a horse in the form of a musical theory that entirely exists to prop up schenkerian analysis. The one that that racist, elitist music programs have been teaching since well before the 21st-Century. (The way you can tell is because it includes figured bass, which is totally irrelevant to any discussion that isn't about the harmonic style of 18th century european musicians.)

    God forbid I want to, oh I don't know, make music that's similar to the kind that I actually listen to on a regular basis? Better understand its underpinnings and what makes it work in the ways that it does? No. Figured bass.

  • aanet 5 hours ago
    Book: Music Theory for the 21st-Century Classroom

    by Robert Hutchinson

  • chrisjj 2 hours ago
    > On the piano there are 88 notes.

    88 keys (usually) and unlimited notes.

  • waffletower 2 hours ago
    How can this be fairly labelled "for the 21st-Century Classroom" when even 20th-century techniques aren't adequately represented? Electronic and computer music techniques are conspicuously absent. Microtonality has a rich history as well which is not even footnoted here.
  • IvanK_net 4 hours ago
    Am I the only one who thinks that the classic music notation is 3x harder to learn than the basic music theory (without the rules of notation)?

    I think that you can learn music theory (to play an instrument or to compose music e.g. in a "piano roll tool" / MIDI editor) much faster if you skip the classic notation. And I think that it is even better to learn the notation AFTER you understand the music theory.

    I even made my own guide to music :D https://www.jampea.com/learn

    • Hunpeter 4 hours ago
      This is a bit off topic, but since you mentioned your guide: I hope this doesn't come off as hostile, but the guide you linked contains a number of inaccuracies and oversimplifications - it's kind of naive in an endearing way, but also leaves the reader with the impression that it covers all there is to music. I guess what I'm saying is it's fine to restrict yourself in what you include in the guide, or even simplify things, but it should be clear that the topic (i.e. music) is far richer and more complex.
      • tracnar 3 hours ago
        To give an example, this it of course not true:

        > Only a limited set of frequencies is used in music. All these frequencies (that exist in music) can be played by a piano.

        • PaulDavisThe1st 3 hours ago
          You're saying its not possible to tune a piano to an arbitrary set of 88 pitches?
          • BigTTYGothGF 2 hours ago
            That's clearly not what was meant, even without the context of this following bit:

            > To describe tones that exist in music, we can describe tones that exist on a piano. There are only two rules:

            > the first key must play a tone of 27.5 Hz each next key must play a tone 6% higher than the previous key

            (This is not to mention that at a 1.06x increase per half step you're going to be sharp by 1 cent / octave which starts to add up).

          • organsnyder 3 hours ago
            Of course you can, but that's not what's implied by the quote.

            In addition to microtonality, many instruments (and the human voice) are capable of infinite tuning, and musicians will deviate from the "correct" note (as played by an even-tempered instrument) based on chord structure, voice leading, etc.

            • BigTTYGothGF 2 hours ago
              Also quarter step bends in guitar and vibrato in general.
          • jpitz 3 hours ago
            there are absolutely pitches that an arbitrary piano cannot be tuned to. it is also non-trivial to tune a piano.
    • bonzini 4 hours ago
      https://youtu.be/Eq3bUFgEcb4 explains why music notation is the way it is. There are very good reasons for it.

      The parts that are really weird (like the C clef) have mostly been obsoleted, unless you play the viola I guess.

      • jerf 2 hours ago
        It kind of reminds me of the periodic declaration someone makes on HN that textual programming sucks and we all need to switch to something else, usually visual programming in this case.

        If someone takes time to deeply understand the advantages of the textual approach and then builds an alternative, I'll listen.

        But at this point, anyone who is doing this and their criticism of the original approach is shallow and uninsightful, where it's basically just "it's old and it must therefore suck", is unlikely to produce a good answer.

        I think that applies to the music notation case too. "Conventional" music notation isn't just a staff and a couple of types of notes. By the time you handle all the use cases that conventional notation handles, or even just a solid subset of it, your brand new notation is probably a lot less elegant than it started out as in someone's head.

        • TheOtherHobbes 2 hours ago
          Exactly. Music theory is a programming language for musical composition and performance.

          Unlike most languages it's inherently two dimensional because music includes both horizontal (time, rhythm) and vertical pitches (chords/colours, harmony) information.

          And - especially important - melody is an element that needs both.

          You can't represent the same information with text without losing a lot of important content, which is why toys like Sonic Pi are more limited than they seem.

          You can kinda sorta represent the same information on a piano roll, but it's not any easier to read than dots - in some ways harder, because you're not going to see the relationship between a bass line and chords as clearly.

          Is it a good programming language? It's quite dense, but not denser than some code idioms. The 2D element is unique, and hard to represent in other ways.

          The learning curve is steep, but it's probably as good as it can be given the requirements and constraints.

        • jaggirs 2 hours ago
          Have a look at http://terpstrakeyboard.com/about/ and the janko keyboard

          I know neither is about music notation per se (but about fixing the piano), but it is analogous: Music notation has exactly the same problem as the piano -> it defaults to C, which makes everything else relative to C and overly complicated.

          For the record, I don't think this means we should switch to a new system, but it is usefull to recognize that it is suboptimal, if only to be able to accept it and continue (because nobody is going to translate everything to some new notation)

      • song_synth 3 hours ago
        love that video, it made me lol so hard the first time I saw it :D

        Classical composer and software engineer here. One of my goals is to help update score notation. I use something called "harmonic coloring" which is like a reduced MIDI notation: You color a note by its functional role (harmonic value) rather than an arbitrary hue in 0-11.

        What this view shares with MIDI: Long rectangles representing the applied durations. How it is different: Occupies a minimal amount vertical space.

        The color palette I'm using is intended to support people with colorblindness. The shades/hues of a color encodes the functional harmony. The root key signature (origin) is always the same color; and chords some distance r away on the circle of fifths is the shade/hue at that offset r.

        There is a similar concept described in the Tantacruel video towards the end.

        You can explore it here on Monic Theory. (mobile view should be fixed within 48 hours)

        https://monictheory.com/project-templates

        • PaulDavisThe1st 3 hours ago
          Note that in historical Byzantine musical culture, there are no absolute pitches at all. Their notational form is entirely intervals from some arbitrary root note.

          Similarly, in Carnatic and Hindustani classical traditions, the note names (Sa, Re, Pa etc) do not denote pitches - Sa is always the root, whatever it is, and the rest have a somewhat well defined intervallic relationship to it.

          I personally would not use "harmonic value" to describe this, since it occurs in music that (broadly speaking) lacks harmony. The key point, IMO, is that what matters are sets of intervals (ratios, if you prefer) rather than actual pitches (as frequencies).

          • aanet 3 hours ago
            ^^ THIS

            Hindustani (and Carnatic) music indeed do not denote pitches for a very sound (pun intended) reason: They let singers choose the root note (Sa), and thereupon the melody is built. Most (all?) of Hindustani music is melody-based, not harmonic based (like Western music). And the melodies are themselves created within the Raga framework. Raga is like a mode (but not exactly that), and is hard to explain within the constraints of Western music theory precisely because that concept does not exist in western music per se. Which is why most Indian classical theorists call a raga a "melodic framework", and leave it at that (or expound on it, as the case may be).

            A great reference for Indian classical music is [1] and and more recent one [2]

            [1] The Ragas of North Indian Music, N.A. Jairazbhoy, https://archive.org/details/dli.ministry.26725

            [2] Rāgs Around the Clock, A Handbook for North Indian Classical Music, with Online Recordings in the Khayāl Style, https://www.openbookpublishers.com/books/10.11647/obp.0313#r...

            • song_synth 2 hours ago
              much love for the Just Intonation in the house
      • jaggirs 3 hours ago
        I suppose it makes historical sense, and even ingeniously designed.

        But it, and the piano black keys with it, are definitely not optimal. It makes playing in C easy, and playing in anything else hard. I've picked up a new instrument since ~2 months, and 1 month in I could already play all scales by by deliberately staying away from music notation, learning the raw distances/steps that make up a scale and how to play them, rather than the 'delta from C', which is how classical training taught me to think. (Same story for chords etc)

        • BalinKing 2 hours ago
          > But it, and the piano black keys with it, are definitely not optimal. It makes playing in C easy, and playing in anything else hard.

          I don't think this is true—I was under the impression that, at least on piano, keys other than C major are sometimes chosen specifically to make things easier on the fingers.

          • jaggirs 2 hours ago
            Easier on the fingers - maybe (I don't know what you reference), but not easier on the mind: Instead of learning each chord once, you have to learn it 12 times (for each key).

            See http://terpstrakeyboard.com/about/

        • PaulDavisThe1st 3 hours ago
          I have some great news: you're a nerd ! :))

          ... or is it geek, i can never remember the difference ...

    • kian 3 hours ago
      It's all about the integers modulo 12. Classical notation obscures that (while making it easier to figure out which of the integers modulo 12 you're using, minus being able to assign them to integers in an obvious way).
      • BigTTYGothGF 2 hours ago
        > It's all about the integers modulo 12.

        Only in 12TET.

        • kian 2 hours ago
          24, 128, approach infinity -- I know there are microtonal systems, but if you want to understand them, choose the nearest multiple-of-twelve (or really, choose whatever TET contains the closest approximations to the exact notes) TET and look where their intervals land with respect to the symmetries (factors) within that TET, and where those symmetries are broken by a note moving by a perceptual 'slide' (one note 'moves' into the other position) rather than sounding like a new distinct voice.
          • bonzini 1 hour ago
            More like, only if you're playing Schoenberg it's about modulo 12.

            Almost all sheet music that you play uses 5 or 7 unequal subdivisions of the octave, and occasionally the rest. Sure, sometimes you'll have one or two of the rest on a regular basis (blues, harmonic/melodic minor), but still most music won't use all twelve.

            • drdaeman 1 hour ago
              Isn't modulo-twelve (if we ignore microtonal) the core underlying structure, and then you pick scale (like 2 2 1 2 2 2 1) and a key as a mapping, and then use degree as an 1-based index into the scale?

              I don't really know a thing about music, so I could be wrong here - but that mental model at least made some sense to me when I tried to map all the concepts I've heard about into some sort of a mental system.

              • bonzini 1 hour ago
                The point is that to a player the mapping is more important than the core 12-note structure, because highly chromatic (12-note) passages happen but they are the exception.

                At least in western music you pick the seven basic notes on the scale, and that gives you the sharps and flats you place at the beginning of each line. That choice, from the point of view of notation, is even more important than the exact scale. And the choice is constrained to 15 sets of sharps and flats because it implicitly tells the player (veeeery roughly) to expect some patterns that probably will occur.

                It doesn't always work great, for example if you want to write the Simpsons theme the set of notes in the scale doesn't fit any of those 15 sets. But it uses an unfamiliar scale in any case, so there's not much to gain and as a player you just deal with it.

                See around 32:30 in https://youtu.be/Eq3bUFgEcb4?t=1950

  • Eduard 4 hours ago
    didn't find a single audio file; only links to unaffiliated YouTube videos which want me to watch ads first.

    “Writing about music is like dancing about architecture.”

    • mcbuilder 3 hours ago
      I feel that quote more likely is pointed at "music appreciation" as a written work, versus understanding the theory. I know a few musicians who are happy to use terminology from theory, "I love to write songs with diminished and sustained chords".

      This seems like a great resource to me, a classically trained pianist who is now playing different types of music.

    • aanet 3 hours ago
      There are several music samples in there...

      Example: https://musictheory.pugetsound.edu/mt21c/DiatonicChordsInMaj...

    • rc5150 3 hours ago
      skill issue.
  • larodi 2 hours ago
    Music theory for the 21st century with notation from several centuries earlier. Hmm.... sorry but tracker's table-like views are much easier. And so are most DAWs gantt-like editors. 100 times easier to comprehend than notation having the same not written in three different ways, and then some.
    • dfltr 2 hours ago
      The English language is messy as hell, and yet, here we are using it because it's a shared set of rules and symbols that pretty much everyone who wants to join in on this conversation already knows.

      Same with staff notation: If you want to communicate music to other people, learning the slightly clunky but universally-known written language is generally the way to go.

      • nwatson 1 hour ago
        The choir director at my church, Michael Dodds (UNCSA), covers the early development of musical notation, "From Modes to Keys in Early Modern Music Theory" [0]. Currently on sabbatical at Cambridge. Once in a while during rehearsal he will give an impromptu lecture on music history, always interesting.

        [0] https://a.co/d/0bLcrlyE

      • odyssey7 2 hours ago
        > learning the slightly clunky but universally-known written language is generally the way to go

        A certain Amazon Web Services comes to mind…

    • odyssey7 2 hours ago
      I’m sympathetic to this viewpoint, but most music students in the classroom will be playing instruments or singing rather than working in DAWs.

      The instruments, music, and notation all evolved together in a shared tradition that make them well-suited for one another.