Music Theory for the 21st-Century Classroom
musictheory.pugetsound.edu
musictheory.pugetsound.edu
Thing about the snooty elitist vibes of the "classical" chamber music world, then realize that almost every base assumption made have real-world counter-examples. 12 equal-tempered subdivisions to an octave is (possibly) obvious one, but most people don't realize that many musical cultures don't subdivide measures into even pulses, or have even/equal-sized measures (see "additive rhythm").
Also as an alternative, the jazz piano site has a really good intro to music theory from a jazz perspective, including videos demonstrating everything in each lesson.
On a related note: https://www.youtube.com/watch?v=ga_7j72CVlc
sidenote: this is sort of part of the problem: a lot of the academic world has positioned one specialty of music as the default and everything else in the wide world of sport in to one "world music" bucket.
Also, there are absolutely schools of music theory that place other aspects of theory "above" pitch. For example, while Hip-Hop and EDM are based on western harmonic structures, I would argue that there is a much larger emphasis placed on rhythm and timbre, as the other comment mentioned. Many American Indian and African musical traditions (which may not have a "widely accepted academic tradition" but should not be viewed as less valid) place much less emphasis on a specific pitch at all, as opposed to the motion of pitch over time, and very percussion and rhythm forward.
If you're interested in theories around tonal shaping, look up electro-house and dubstep sound design tutorials. Dead serious, these guys do things that would never occur to us mere mortals because of the understanding of timbre and the tools they use. A personal favorite of mine is Virtual Riot. His "4 producers 1 sample" entry was truly mind bending: https://www.youtube.com/watch?v=zvKY_DnM1PA&t=7m43s
Essentially, the theory is that longer lines are harder to read. A US Letter or A4-width page is just too wide for normal body text size according to most professional typographers. LaTeX provides typographically sound defaults.
Something like this should probably still be supplemented with an instructor who can provide the student with some immediate, fun, and practical exercises to make the process more exploratory and engaging, though. Something that will get them thinking musically right away.
He doesn't realize that the chords sort of follow a ii-V-I pattern, and I'm sure eventually he learned it. Would he have learned the song faster if he'd known that? Maybe.
To be clear, I have seen first-hand that people well-versed in music theory can "understand" and also create (e.g. improvise) music more readily. But I can't seem to find joy in approaching music analytically...
It's like understanding syntax or grammar for a language. Making explicit names, categories, and systems to take apart what you're doing/saying. 99% of the time though people don't think about that, they go by "feel."
But if you can understand the underlying framework, you can also work to intentionally use those to your advantage such as by reinforcing expectations or subverting them in clever ways. Obviously you can also do this by "feel," but an understanding of the underlying mechanics and systems gives you a better framework to spot the points where you can get away with things. When you want to get deeper and push the boundaries of a craft it also helps to understand what "best practices" are in place and why, and then look to exploit them.
I have a friend who was self-taught guitar and a variety of other instruments and only recently started on piano and proper theory. It's been fun watching him recognize and get a framework for why things he's intuitively known, such as how a cadence works or key transitions through a circle of fifths, be brought to the surface explicitly.
Using music theory they can understand why certain composition works and then use the listeners intuition against them to subvert those expectations while still providing something coherent.
An example is something like Bleed by Meshuggah. Most people assume it uses some complex time signature but I am pretty sure its just 4/4. Periphery will have pieces that sound 4/4 but are actually 6/8s. Basically most time signatures (if not all, idk) are effectively extended 4/4, so they can create a riff that eventually hits the 4/4 your internal clock expects to hear but in between you can't necessarily find the pattern.
But like you said, music theory tells you all the rules so you can break them. It's sort of like any other set of rules. You need to understand why they are there so you can understand the right why to subvert them.
He uses the terms "guest" and "host" to describe complex time in the songs he analyses. So in Bleed for example, I think he'd say the "host" was 4/4, but the "guest" is definitely not.
> Conversely, there appears to often be many ways to "explain" a certain composition in terms of music theory.
Remember that music theory is descriptive, not prescriptive. It's a description of existing musical practice, not a set of rules that say what is right and wrong.
This was certainly not the case for western music since the reintroduction of polyphony.
Music can't really only sound good or bad to you? Bach may sound good or bad, but there is surely something more to it than that when comparing it to Shostakovitch, right? Understanding why requires theory.
Not being from the US I was always taught with semitones and tones. Whenever I saw YouTube videos with half steps and whole steps I thought they were dumbing down for the audience.
a tone is whole step. a semitone is a half step.
Sort of like semi/hemi/demi quavers and the like versus whole/half/quarter notes
I thought half step, whole step was a grade school thing mostly. But I really wouldn’t blink at either style, it’s all the same to me.
As for the 88 keys, Steinway once produced a grand piano with that many keys and after that other manufacturers copied this and it became the standard.
But before then the Harpsichord was mostly standardized around 60 keys (which is why you can play most of Bach on a 61 key keyboard just fine, and why many organ keyboards are only 61 keys or sometimes even less wide).
There are also larger keyboards, for instance the Bosendorfer Imperial has 97 keys, there is also a 92 key model.
And narrower pianos exist(ed) as well, very rarely you'll see these with anywhere from 64 keys and up.
So it's like many other things in music, a combination of practicality, standardization, fashion, price/economy, but not necessarily any underlying hard logic as to why it should be that way.
> why does piano have 88 keys?
I'm only ok at music theory, so I might get bits somewhat wrong, but the gist is right.
Notes with wavelengths that are integer multiples/fractions of each other sound the same. 440 Hz sounds similar to 220 Hz and 880 Hz (and this makes sense if you just look at the waveform), so we give them the same name. Western music slices the range between ω and 2ω into 12 points evenly divided along a log scale (we call this an octave). The log scale means the relationship of nearby notes is always the same; it takes an exponentially growing scale (frequency) and makes it linear.
You said 7 have names, but there are 12 notes in an octave. You'll learn more about that difference with scales, but the short answer most western music won't use all 12 notes because, for a given key; a specific subset of 7 sound a lot better together than the others.
88 keys is somewhat arbitrary, and there are pianos with more or less. What's important is how many and which octaves the piano covers.
Why is it called an octave when it has 7 named notes? I guess so we can repeat the first one and drive home the 2ω relationship.
I think it's because of 1-based numbering. Two identical pitches are called a "unison".
"Music theory" is almost always "European academic music jargon and notation patterns" with near-zero theory at all. If you actually want theory, you want something like "Music and Memory: An Introduction" by Bob Snyder which is written for creative multimedia artists and others with no formal music notation training, and it doesn't even ever show notation and never gets into harmony at all, but it explains the rest of the basic perception of music.
1. Watch a lecture series that focuses on listening to music
I have been watching the following lecture series: Listening to Music with Craig Wright. This is provided as a free resource from Yale on YouTube. It will answer pragmatic questions (e.g. why 88 keys) you may have encountered.
2. Learn through workbook exercises
Believe it or not, the keyboard offers a convenient interface to learning music theory. The individual keys fit in your hand. Pressing on them makes a consistent sound. In many ways, you don't have to worry about the logistics of making noise.
With that being said, by using a simple keyboard (e.g. digital), you can start the following workbook series: Basics of Keyboard Theory by Julie McIntosh Johnson. This series is available on Amazon. You can start with BKTPREP (preparatory) or BKT1 (level one).
The idea here is to learn something new, in each lesson, and then test your knowledge by working through the workbook. What this series does is it focuses on the foundations of Music Theory without throwing you deep in the water. Like math, you don't progress unless you understand where you've been.
3. Learn an instrument with a teacher
Having a teacher will help you tremendously. While they may focus your attention on the instrument, they will also introduce you to music that applies what you are learning in theory. As you progress, you will start to identify patterns the composer uses in their music. This in turn will correlate to what you have learned in music theory.
4. Compose your own music
Just like the workbook exercises above, you will understand music more by writing it. Maybe you came up with a catchy tune while fiddling around with your instrument. What other notes would sound good with it? How should this catchy tune start and end? How can we make it sound unexpected or delightful?
Always have a goal in mind when learning music theory. Many times, that will motivate you to progress further.
Ideally you'd do this alongside a teacher or someone who knows more so you can bounce questions and applications off of.
There may be better theory books out now, I haven't kept up.
what do you mean by "the basics"? Every kind of music theory is based around assumptions from elsewhere and prior experience
I'd share with people anything from Bernstein otherwise, but for music theory, these particular lectures are not what I'd recommend sharing.
https://www.maa.org/external_archive/devlin/LockhartsLament....
Music must be enjoyable or it ain't music.
1. Cadential six-four chords are only listed briefly under the "figured bass" section. But cadential six-fours are a concept from Roman numeral functional harmony, which is outside the scope of figured bass. (Figured bass only tells what intervals make up the chord-- or in some special circumstances hints about voicing-- but not about how those chords function.)
2. The section on cadences-- which precedes the section on figured bass-- does not treat cadential six-four chords at all, nor AFAICT include any examples of them.
In other words-- this text burrows away a fundamental pattern for ending phrases in tonal music. That makes a special case of most of the endings found in most Christian church hymnals, for example.
Those intervals are relative to the bass. A six-four has a sixth and fourth above the bass (i.e., a second inversion).
To be completist about my criticism here-- the author could stick only to figured bass analyses and give enough examples that the reader/listener starts to implicitly hear the bass patterns, phrase structure, and voice leading that help them differentiate between passing 6-4 chords and cadential ones. Eventually, we've sung enough chorales that we can quickly start parsing these patterns easily enough.
However, the author chose to introduce Roman numeral analysis which is the explicit approach to demarcating how the chords in an example function harmonically. That explicitness is quite useful. E.g.
* the piece begins to modulate using this specific chord as a pivot, specified with roman numerals for both the old and new key
* this second inversion chord gets special notation because it's a cadential six-four which will soon resolve to a V in root position
That would all be fine and appropriate, except that the author then relegates cadential six four chords to an ancillary part of the tutorial. But demarcating cadential six four chords is one of the big reasons to go the route of Roman numeral analysis in the first place! Teaching students how to explicitly spot and notate the difference between passing moments in the phrase and cadential moments for the same exact chord is key to them understanding how phrases of tonal music operate.
In a normal harmony class, the lessons dealing with cadential six four chords make it easier for students to more quickly analyze difficult music. E.g., is the first chord of Wagner's Liebestod a "one six four" chord or a cadential six four? In Roman numeral analysis one must resolve that ambiguity by making a choice. When one does, the structure of that part of the opera becomes obvious-- it's an ending full of little endings, each of which get elided through chromatic voice leading.
You can eventually come to the same conclusion using only figured bass. But chromatic 19th century music can get pretty hairy and so the explicit tool of Roman numeral analysis can come in handy there.
But if you learn Roman numeral analysis without learning about the quite common cadential six four, it strips out one of the fundamental lessons for figuring out how phrases of tonal music build and release tension in time. Consequently, analyses like this become more difficult for no good reason.
https://www.youtube.com/watch?v=uPExIXkBOus&t=0s&ab_channel=...
Anyway, this content is "Western Art Music" academic, *dated* sort of stuff, it's not at all appropriate for a globally-aware 21st century classroom. Serialism?? And no mention of any non-Western traditions or pitch systems etc. etc. This is more like mid-late-20th-century Eurocentric textbook just put on the internet.
Which is why all this stuff is still taught.
What do you think is "appropriate for a globally-aware 21st century classroom"? Do you have any music degrees? I've got a couple. If you've studied at a music school, then I'm sure you'd be aware that non-Western musical traditions and tonal systems are covered; just not in the core Theory 101/102 classes. They tend to get covered elsewhere.
You can fuss all you want about how this is dated and academic; whatever. It's still highly relevant to the vast majority of music out there, both classical and not, that Westerners will run into. So of course, if you go looking for a music theory course in an academic context, in a Western context, this is what you're going to get. What do you expect to get?
Woopteedoo Mr. Argument-from-authority. Well, that's the snarky tone I might have if I stick to replying in a triggered-reactive state. But better for me to engage with the reasonable points and not focus on imagining you feeling defensive and me being reactive in reverse.
Yes, you are right that "Western Art Music" is too narrow, many many aspects of pop-music and jazz and so on do indeed use these same structures. And furthermore, several aspects of this sort of "theory" are decently universal.
I do still object strongly to the presentation of these ideas as if they explain music. I'm not going to prioritize getting into this in depth here. I would be happy and probably not really object if this stuff were all just labeled as Standard Patterns of 12-tone Western Music instead of "Music Theory".
P.S. Yes, I have a music degree, and I also did a bunch of grad-level stuff too and almost started a music PhD, but life went in other directions. As it stands though, I have learned more about music away from academia than in it. However, I did find some people within academia who seemed to really have broader understandings, and I was pursuing working with such folks when I was still engaged in that world.