It's licensed under Creative Commons BY-NC-ND, and Toby W. Rush is the author. Great resources by the way, better and more concise than a lot of theory info for beginners (bordering on intermediate, if you are able to get to some of the more advanced scales, structure and basic part-writing/voice leading at the end).
I updated the mirror that ewoodrich referenced; what was up there before was a slightly older version. The new one has a few more pages in it and a few typos fixed here and there.
I've also swapped out the page on my site with a redirect to the mirror, since my web hosting service has rebooted the server twice now. The mirror is on my faculty web space at work, so we'll let them worry about it now! :)
No worries, though. Glad you all are finding the materials useful.
(Normally we'd point the post at the URL that's working, but that pdf is already downloading so slowly that I fear we would just topple the next server over as well.)
Take computer programming as an example. After 15 minutes of HTML lesson, a newbie can already look at her creation in a browser and the html file on hard disk, and have fun tweaking it (<html><body background="green">My home page</body></html>, remember the days?). An hour of Java lesson can
result in several variations of "Hello World!"
programs, created by the student. Basically, people can put their hands on the knowledge and use it to produce somewhat useful/tangible stuff.
Not so much when learning music theory. After enduring the bombardment of names/concepts/terms/maths and other stuff for quite a while, I don't have the slightest idea where I can practice in using them to analyze or write some music.
I wish there is a lecture in the format of "One hundred songs for one hundred music concepts". The songs should be
stupidly simple (children's songs, simple pops, short classical pieces, etc.). Each lesson concentrates on only _one_ concept appeared in the piece, explains what it is, how it is used, why it is used in that way, and how its application makes nice sound, etc. Basically, show me the _effect_ for each concept in a simple real world setting. Then more importantly, give me exercises to write a few bars of music using this concept, no matter how bad my writings are, as long as I am applying the new knowledge.
You can teach almost everyone to perform "Twinkle Twinkle Little Star" on piano or "Smoke on the Water" on guitar within 15 minutes, both of which are de facto "Hello world!" equivalents to many aspiring musicians.
EDIT: Removed attempt at drawing a HTML/music analogy which could be closer to truth. It is really fruitless endeavour, makes no sense.
Also, I think although knowing theory would help you play a song with an instrument, it's not required, is it? More likely knowing music theory is for understanding/appreciation of the composition/structure of the music. So no, playing "Twinkle Twinkle Little Star" on an instrument is NOT equivalent to writing "Hello world!" program. On the other hand, composing a super simple but complete song is closer to writing a "Hello world!" (or a Fibonacci series) program.
As a couple of commenters have said, your HTML analogy just doesn't seem to fit here, music theory is descriptive, not prescriptive. The best way to learn it is through playing music, a lot, and then using concepts from music theory to go back and gain more insight into why certain things sound the way they do, why certain progressions work well, why an F natural sounds ethereal and sublime on top of a B∆9 chord while an E natural sounds awful, and so on.
Again, I believe the optimal way to learn music concepts is to play (not study) music.
If jazz doesn't interest you, I would ask you what your musical goals are, and what genres do interest you, and just encourage you to play, and then play some more. Ideally, play with musicians who are better than you - you'll learn more, faster, just like anything else. It takes thousands of hours to get good at this stuff.
I know for me, the stage at which I was doing the very simple HTML examples you listed was when I was 13. Back when you're that young, just playing around with that stuff was SO FUN for some reason. As a 29 year old guy if I were just starting out I'd be much more inclined to try to skip that step and make stuff more real-world.
The equivalent in music theory would be simply playing around with the white keys on the piano (C major). Making interesting melodies (but ultimately kinda boring melodies like mary had a little lamb). To your young ears, this would be very interesting and fun. You'd play around with this for weeks and weeks and make small observations. For example, you might notice B->C has a sense of resolution to end the melody, or internalizing what C->G feels like by just playing it a lot and singing it. You might notice that E->F feels smaller and has more of a "pull" to it than A->B (in the context of C major). It's this stage that's so crucial for later understanding music theory.
Adults want to skip the simple exploration and just dive right into Beethoven. We think we can use our strong analytical sense to just book-learn music theory. What I've learned is that it's much more fruitful to make observations first and then learn what music theory calls those observations.
When you're writing HTML at 13 years old, you don't really know the high level concept of a "mark-up language" and how it might be manifested, you just know that there are parts in angle brackets that don't show up on the page but control the content. Later in high school when you learn the concept of a mark-up language you make that connection to HTML with extreme ease because all those memories of changing background="green" to background="black" flood back to you.
Maybe I have not found the right learning materials or correct way, or maybe because I am the type of persons who need to have lots of hands-on exercises to be able to grasp new concepts.
Sure, programmers also need to know all sorts of things you listed, but armed with only a few concepts, a newbie can start to write simple programs from the very beginning, in the forms of piecemeal topic-focused little exercises. The result of each exercise is a fully functioning program. I wish I can find a similarly structured music theory course that uses the same approach. Also, are there projects in music which are similar to ProjectEuler.net or the likes, where you can do focused practice on specific topic? I would be happy to pay for those services.
I understand the desire but it's also very important to realize that these things take a LONG time to develop. You can't really expect yourself to grasp chord progressions until you have a firm understanding in scales and you can't just gloss over it and be familiar with it, you have to internalize it. You have to get scales under your fingers... you have to feel the pull of the leading tone to the tonic... you have to be able to sing them and know them inside and out or your knowledge of chord progressions will be built on a shaky foundation.
The equivalent to project euler would be to just compose your own songs. Seriously, compose then analyze. Since music is subjective there's no way to say, "you're song is correct, move on to the next song". Also, there's no real correlation between song writing and theory knowledge that I know of. You can know about theory a lot but still not be good at writing songs. Also knowing theory doesn't make you a good musician by any stretch of the imagination. Music theory is descriptive, not prescriptive (i.e. it doesn't tell you HOW to write or what you should write, but rather is just a language to describe what you've written)
You can know about programming like if you're good at math you probably have a sense of what programming is about but until you sit down and type out some code, you're likely to not be any good at programming.
> My main goal is to be able write songs of quality at least slightly above total crap.
You will write total crap. The best thing you can do is come to terms that you'll write crap probably for years and that's okay. Here's the first song I ever wrote way long ago:
Bleh... not exactly something I'm super proud of other than the fact that I did indeed finish it and I was honest with myself about what level of song I could write at the time that I wrote it. I'm still not a super great musician, but I've at least improved every song since that one!
> Since music is subjective there's no way to say, "you're song is correct, move on to the next song".
Are there some kind of music "compiler" or "linter" for educational purpose out there, which check for a song's obvious and blatant violations of fundamental composing principles? This might helps beginners to hone in on the basics. I know the rules are meant to be broken later, but at the beginning, the 'compiler/linter' is efficient and cost effective in guiding the student and checking their practice work.
I think a "linter" like that would be kind of like a linter for analyzing poetry or short stories. It's so subjective that the most it could do would be offer very superficial suggestions without really understanding context. Things like "does it have a rhyming scheme and meter". And that's not that useful because some poetry doesn't rhyme, and some doesn't adhere to a meter.
Like, is 50 Shades of Grey bad writing? some might say so... but can you deny the popularity of it? Are the people that enjoyed reading that book wrong for enjoying it? Trying to apply an objective measure to quality of writing or music is futile, I think. Same goes for music. You might write a song that some stuffy old classical music PhD would scoff at but maybe children LOVE it. How could a linter possibly know that?
I say embrace the subjectivity of it. Write a song, ask people what they think of it. Accept that you will not write super great songs right away and just keep writing and experimenting. Use theory as a language to explain what you've done in songs you wrote and songs that you like.
I have a music degree and learned all this stuff and a lot more. This presentation is an excellent, high-quality overview of this non-theory junk.
It's extremely culturally-biased and, again, offers no real theoretical explanation.
If you want real understanding of music in a useful way for real people, I recommend Bob Snyder's book "Music and Memory: An Introduction" which was actually written to teach creative artistic people about how music actually works rather than how aristocratic European music notation works.
For some other perspectives, check out http://sethares.engr.wisc.edu/htmlRT/contents.html and http://sethares.engr.wisc.edu/ttss.html (normally I wouldn't push these on average folks, although they are superb but the HN crowd should be fine with them)
Secondly, why would you call this junk? This is actually very useful for people learning to play, and for those who want to understand the basics of harmony and rhythm.
What you are talking about is typically called "music perception theory", "music cognition", or "music psychology".
Teaching the notation by the hypotheses about music that the canon of "music theory" gives us is like teaching chemistry by 100 year old diagrams and names of chemicals.
To be perfectly fair, the post here does do a BETTER job with the Western-notation-scope than most other examples.
Now, explain to me the music theory of the
D major section of the Bach Chaconne! Say
the first few notes of that section after the
opening open D string and the D an octave
higher on the A string; or if want to avoid
the open string, play the D of the open D string
on the G string and the other D on the D string.
Then what is the role
of the notes repeated three times, and those
triplets repeated several times? These
triplets are insistent? Heifetz played them
this way, but not all violinists do!
Then what is
the connection from the last few bars
of the D major section and the first few bars of
the following D minor section? Or the last of
the D major is the climax of the piece, and
the start of the D minor is a catharsis?
For more, at the beginning of the second to
last bar of the D major section, there is a chord
the first G above middle C, the next G up,
and the B above that. The notes are quarter
notes except the upper G is an eighth note
and changes to the D just below, also an
eighth note. Well, what is the role of the
change from that G to that D? Some violinists
emphasize that change from the G to the D
a fourth below, that is, make the D easy to
hear and the fall something dramatic, say,
as some kind of resignation. What's
going on here? What likely did Bach have in
Rostropovich, with his recording with von Karajan
of the Dvorak concerto, made something really
special at the beginning of the second movement:
He has some depiction of remembered pathos. So, how'd he
(Dvorak and/or Rostropovich) do that?
From Rostropovich I hear
emphasis with vibrato, volume, and tone color
and careful timing, phrasing. It's passionate music.
What's going on? It sounds a little like
some abstraction of some speech with pathos.
Maybe easier is the Prelude of the first
Bach piece for solo cello and, there, the rising
chromatic passage to what is apparently the
climax of that piece. So, what else is going
on there just besides that rising chromatic
Then there is the cello solo early in the
first act of Die Walkure, maybe representing
the girl? How to write a cello solo that sounds
like a compassionate girl?
For some more, there is the duet, "Presentation
of the Rose" in Der Rosenkavalier with Barbara
Bonney and Anne Sophie von Otter as at
Some parts of the duet with the two voices are
just marvelous, and I'm not understanding how
Strauss did that. What's going on? How'd he do it?
For more, there's too much going on in Ein
Heldenleben, but I'd be happy knowing a little
about what Strauss did there, even how the
girl, that is, the violin solo, worked, or even just
how Stauss made the girl so comforting in the
Are such issues what you have in mind as
How'd I get into such questions? One night
on a radio I heard Beethoven's 7th symphony,
and it seemed easy to like, e.g., the dance.
Occasionally Dad gave me some money, and I
bought some recordings, Vivaldi through
Rachmaninoff. Then I was a grad student
in math at Indiana University in a dorm next
to the music building, and a Stern protege
put his old Italian violin under my left
chin, gave me a lesson, and I took a violin
course, starting with how to tune the thing.
I learned the music theory of perfect fifths,
that is, three times the frequency of the lower
open string is the same frequency as two times
the frequency of the upper open string, and the beats
between those two can be used to tune to perfect
fifths. Not long after making it in some form
through much of the Chaconne I got too busy
to continue on. So, I like the music but don't
fully understand just why. Music theory
has an explanation?
The first thing to understand is that written music notation is not music. Partially, this is like the way that written English is not spoken English. All the notation we've inherited from Bach specifies certain things and leaves other elements unspecified, in much the same manner as this text really fails to carry the tone and delivery you would hear from me in real life.
I can read some English text in different ways and bring out an amazing range of meaning and interpretation in how I express it. Likewise with music. We can speculate about what Bach had in mind, but we can only use various bits of evidence, writing, known practices, etc. to guess about anything not present in the notation.
There are tons of parallels between music and speech, and I recommend the book Music, Language, and the Brain by Ani Patel for more in-depth about this.
The stuff in the book I mentioned originally (Music and Memory) gets into a lot of the issues too. Our processing of all these interacting parts has to do with the various psychoacoustic factors that make things merge together or heard distinctly in our perception. Auditory stream segregation describes the factors in how we follow a line of music and why we relate one note to another instead of in a different way. And some things are really distinct, so everyone hears them the same way. Many others are ambiguous so you and I can hear the exact same sounds and actually parse the music quite differently in our heads.
I actually could sit down with you and make sense of all the subjective experiences given understandings from psychology and explain much of what is going on in each of your examples. It's a bit hard to express in text though, easier in person with the ability to gesture and intone and sing while discussing and experiencing the different examples.
Finally it dawned on me, the G to D change
was while in D major and, thus, back to the
tonic! So, there, in the next to last bar,
right before the top of
the climax of the section, Bach touched on
the tonic again! So, artistically this
tied the motion and emotion of the other
notes back to the tonic and not left partly
lost out in the ozone -- or some such.
This afternoon, I listened to the Heifetz
and Piatigorsky performance of the Andante
of the Brahms Double Concerto: Finally it
dawned on me: Brahms had an abstraction
of some kind of speech, say, of just the
sound of the speech, the sounds that
conveyed the emotion without knowing the literal
words. So, it sounded like speech, maybe like
speech in a foreign language where didn't
understand the literal meaning of the words
but, still, got much of the emotional
expression. It appears that you have a book
that expands on such a thing.
Edit: Okay, at
I found a book review of
Aniruddh D. Patel.
Music, Language, and the Brain.
He's deep into some apparently fairly speculative
research and makes me like more my little idea
that some of music is like listening to some
passionate talking in a foreign language were
know none of the words but, still, get the
emotional content -- that is, the music and the
emotional content of the speech can be similar.
So, back to the opening cello solo of the
Brahms Double, we can imagine some
passionate speaking where a person says
something, just a few words, then says it
again a little differently, then again with
a little different emphasis, then again
using maybe different word order. Well,
that's much of what Piatigorsky playing
what Brahms wrote is doing.
Or, back to the beginning of the D major
section of the Bach Chaconne, we have
F# G E, F# G A D, E F# G F# E E A F#
[this example would be still more clear
with the actual music with the
note timings -- maybe the harmony
would also help!] Here I am inserting
commas to separate what I am regarding
as the separate phrases repeating
the same basic emotional content.
So, an idea is that that music is
like a speaker saying much the same
thought three times, each time
with mostly the same words and
in a similar but different way,
that is, with variations.
Why three times
with variations? The speaker is
passionate and, maybe even, pleading,
and trying to get their meaning across
if not the first way then maybe in one
of the two other ways. Besides, the third
way is more complete than the other two
and, even, with the rise to the A, has a point of
high emphasis and emotion. Maybe.
See something similar at the beginning
of Silent Night where there are four
variations of basically the same
I suspect that Bach and Mozart could
"search their feelings" (Star Wars),
think of some corresponding speech,
hear the corresponding music, and just
write it down.
The book review suggested that different
languages have different patterns in
the speaking and, thus, for each such
language, music written in that language
will use similar patterns. So from that
might argue that the Bach Chaconne
was not written by a native speaker of
French or Greek. Or Massenet just does
not sound like Bach, Mozart, Beethoven,
Mendelssohn, Wagner, or R. Strauss! Maybe
Massenet sounds more like Debussy or Ravel!
Regarding the language relationship, many people have discussed the ways that music, especially harmonized singing, is like a super-voice, it's triggers our emotional reactions to expressive language but at a higher order of magnitude.
The real interest comes when we realize that all the valid elements of the notation-jargon-style theory actually can be themselves described psychologically. So, the books I've mentioned, don't deny the classical ideas of tonality and chords and voice-leading and all. They just explain these phenomena in ways that are actually more meaningful and more universally applicable than just recognizing the notation patterns.
Of course. But knowing how to spell is the first step towards learning to write -- my four-year-old will tell you all about it. :-)
Music theory is more than just spelling. It's also grammar -- it puts together rules for harmony and rhythm, and allows you to analyze music and communicate ideas by giving names to patterns (such as scales, chords, cadences, functions, meters, etc.) It allows you to learn for yourself how to break these rules and deviate from these patterns.
You can learn the theory without learning the notation, which is quite common among guitarists. You can also make music without knowing any theory at all, but it is always more helpful to know some theory.
> I think the parent is trying to explain that there's a cultural bias and inscrutability with respect to how music theory is taught.
Maybe, but the parent is also trivializing what is commonly referred to as "music theory" by calling it just "jargon" and "non-theory junk."
One can be a western musician in, say, a jazz tradition, understand theory, have theories and play music and have never used the system of notation explained in the otherwise awesome comic.
True, but it's pretty unlikely. Most people who play music pick some up theory (in the sense of this submission) along the way if only so they can have meaningful conversations with other musicians.
I think most people are actually thinking, "I want to understand music more." when they search for "music theory", and instead of learning deeper understanding about the nature of music, they are taught about notation traditions. Then, most people decide they do not especially care about "music theory" anymore. The folks who continue are those who like studying notation patterns.
Like you I'd much rather read text about the psychology of musical perception and the why of music. I disliked the notation drills etc. when I had piano lessons as a kid, but as I never had a natural ear for chords or harmony (and thus frequently found myself wanting to improvise things but without a good understanding of how to go about it) I came back to the theoretical stuff as an adult, and ended up getting interested in other musical traditions like Arabic and Indian styles as well as the western one (though I don't want to oversell my knowledge or skills here). Different traditions use different schemes but they all have some way to codify things, because unless you stay within a single tradition or are blessed with an eidetic memory chances are you'll need to note things down at some point.
Where I'm disagreeing with you is on the terminologyl I hold that when people search for 'music theory' it's because they want to be conversant with other people on the basics, even if they just want the bare minimum of how to distinguish between major and minor, construct a few basic chords, or read/write a melody outside of a piano roll. It's unfortunate that the label 'music theory' has become associated with this basic stuff; it's as if we used 'literature' to refer to basic spelling, grammar, and vocabulary and used some other term to describe the actual study of artistic writing - but that's how it is.
Only in the way that the label mathematics has become associated with arithmetic. The stuff here is what you need to know in order to get started analyzing music of the common practice period (you'd need set theory to talk about the pitch content of most music after 1900). But when people get doctorates in music theory, they are not stil studying the circle of fifths. They use these concepts to describe music in order to come to some understanding of how and why it is structured.
What system of notation do you think jazz musicians use? I don't think you'd have any luck trying to find employment as a jazz musician since at least the 1930s unless you could at least read music, and be fairly good at sight-reading as well. And as far a composing and arranging? Those guys not only knew tons of theory, but very consciously developed their own extensions to it. They were very familiar with Western classical music, as well as Blues.
That's true, but if you take the "observed phenomenon" to be "Western, common-practice tonal music (and notation)," then this certainly helps to explain it. It's certainly what gets taught in undergraduate music theory classes (much of it in "fundamentals" courses). Graduate work in music theory involves doing exactly what you say: explaining observed phenomena, in both "classical" music as well as about any other musics you might imagine. That's not to say that all music is Western, common-practice tonal music, but a great deal of music comes out of that lineage; an understanding of these basics are often necessary (or at the very least, useful) before branching out.
You see this sort of thing in all disciplines. I might find an "Introduction to computer science for normal people" that explains big-O notation, or teaches some basic Python, or what have you. Someone might well say "This isn't 'computer science,' but instead 'jargon and programming.'" This person might be right, of course, but for "non-computer scientists and normal people," the distinction is not so clear.
It never claims to be "a comprehensive guide to all things musical" or "a theory of all music," but it certainly qualifies as music theory.
Schoenberg's classic 1910 Theory of Harmony is a shining example of this. It's pretty much a practical guide for composition, and follows a structure strikingly similar to that of this document.
Unfortunately quite a lot has happened in music since 1910, and if you're trying to write music for the 2010s Harmonielehre and 'theory' of this kind won't just confuse you, it will actively mislead you.
The problem is that it teaches you nothing about the importance of performance expression, or the many different ways modes get used and abused in pop/rock/electronica, or how to create arrangements that capture and keep listener attention.
Pop has become a massive historical experiment in perceptual psychology. The most popular bands can literally fill a stadium - something common practice music has never done.
While that doesn't mean pop is better in some absolute sense, it does suggest it's doing something right for many listeners.
If your training is too rigidly classical it actively stops you being able to hear and understand what that right thing is, because you're too busy concentrating on a small subset of the many details in the music.
> While that doesn't mean pop is better in some absolute sense, it does suggest it's doing something right for many listeners.
Not Saying you're necessarily wrong, but you can't say just that without pondering that question : is it due to discoveries in music composition, or is it due to efficiently applying marketing to it ?
I don't know if it's the same everywhere in the world, but here in france, if you turn on the radio and zap through channels, you will hear the same song up to 10 times a day. Then you turn on TV on night and see those same groups as guests on TV show. Then you read in local newspaper than they will play in your town. I can see how it could produce the effect you describe.
Just like other fields, people actually do advance in our understanding and figure out what was wrong in the old theories. The music world has just done a very poor job of disseminating the updated understanding. That's probably because academic music institutions are too often about cultural preservation rather than about furthering our understanding.
It is not a "scientific theory", as, say, Thomas Kuhn might have used the term.
"Music theory" uses the word "theory" as the colloquial antonym of "practice".
As in the adage, "In theory, theory and practice are the same; in practice, they aren't".
Music practice means strumming an axe, blowing a horn, banging a drum or tickling ivories, and so on, whereas music theory is ... any study related to how to do these things, away from the instruments.
Thank you! I've long been suspicious of so-called music theory for exactly the reasons you outline. I always wanted to learn more about music and why it "works" as you say, so I assumed what I wanted to learn was music theory, but then when I tried to learn it it didn't seem to explain any of the things I was looking for. I'll have to check out that book.
The reasons he mentions are bogus -- simply his bias against a term in common use ("music theory") , only because "theory" is used with a different meaning in academic contexts.
That said, there's nothing to be suspicious of in music theory, and what's in TFA is not "so called music theory", it's actual music theory, the way every composer, musician, etc in the western world knows as such.
That it doesn't explain other aspects of music (psychological, physical etc) does not make it any less "music theory", nor does it make those other things "music theory".
The reason I complain about the term is exactly because of the post above yours: people actually do think they are going to learn explanations about the nature music and they don't get that.
That's equivocation. Nearly everything in this document is widely considered to be part of music theory.
Isn't that how language works though? If everyone calls this music theory aside from a small minority of people, then it is music theory. "Music Theory" as a term is a study on it's own, it's not "the theory of music" and you can't really use the terms interchangeably like that.
That's not really how language works in specialist fields though. For example "theory" and "proof" mean different things in science than they do to the general public (which is part of the reason why the general public misunderstand science so much). Or, for a more relevant example, the problems with how the term "hacker" is misunderstood.
The content of these cheat sheets describes what a music major learns in the first semester or two of music theory classes. But there are people who get PhD's in music theory. What do you think they study for all those years? It's not this.
Saying this is music theory is like saying arithmetic is math. It's not wrong, exactly, but it's leaving out a lot. People spend the first 12 years or more of their math education learning the notation, learning formulas, at least partly because you need to know that stuff in order to do any real math (we'll leave the discussion of whether this is the optimal pedagogy for another day, shall we?). You could say, "but people googling math want to understand why 2+2=4," but if you don't know that 2+2=4, there's not much point in trying to learn why. You could also say that what people learned in high school is what most people call math, but we all know that what people learn in high school math doesn't have much to do with what real mathematicians do.
"Real music theory" uses the contents of these cheat sheets (and many, many other things) to describe pieces of music and to try to understand things like: why did this composer choose the notes and rhythms they did? What can we use to justify the subjective observation that a composer or time period had a unified music style? What are the assumptions of musical language that govern musical composition without necessarily being known to the composers? Why does this collection of notes have meaning? What is that meaning? What does the content of this music tell us about how it should be performed?
The best of my music theory classes tried to keep a clear line from what we were learning to the kinds of questions above. The worst classes we spent a lot of time doing worksheets with the musical equivalent of times tables and algebraic equations, ad nauseam.
I'd also like to note that the things that appear under the aegis of introductory music theory are a strange hybrid of techniques, reflecting the multiple purposes of music theory for theorists, musicologists, composers, and practitioners. So you get things that don't help much with analysis, like species counterpoint (probably a useful exercise for composers, and maybe for musicologists since it is really a historical curiosity, but not really useful for anyone else) or realising figured bass (really only necessary if you're going to be performing baroque music in period style on a keyboard instrument).
You could again say similar things about high school math of course.
If you want to see a small sample of what music theorists find interesting nowadays, just look a the latest issues of some of the major journals to get an idea. For example:
Journal of Music Theory: https://www.dukeupress.edu/Journal-of-Music-Theory/
Music Theory Spectrum: http://mts.oxfordjournals.org/content/current
Perspectives of New Music: http://www.perspectivesofnewmusic.org/
19th-Century Music: http://www.jstor.org/action/showPublication?journalCode=19th...
Journal of the American Musicological Society: http://www.jstor.org/action/showPublication?journalCode=jame...
There is so much cultural baggage and assumption in the notation-focused "music theory" that is not present in mathematics. When we talk about numbers of things in math, there's no doubt we're describing something objective about reality external to culture. There indeed exists two apples or four apples. The concept of "four notes" is rarely objectively valid because almost everything in music is subjective.
"Music theory" basics are much more analogous to the elementary-school versions of linguistic grammar. And most elementary teachers' understanding of grammar is actually full of claims that are wrong, even though there's something to the gist of it. When we go to "English" class, we expect to learn about English and don't think our lessons apply to all languages. We should similarly not teach one particular language of music and call the lessons "music" without qualification. We should further recognize that grade-school definitions of nouns and verbs do not all hold up under scrutiny.
When "music theory" of the sort here is taught well, it is about as valid and useful as grade-school pedantic, prescriptivist, grammar — the sort that treats minority dialects as "bad grammar". Insisting on music theory being this notation-jargon from classical Europe is like saying that African-American dialects have poor grammar, when actually there are careful and consistent implicit rules in those dialects that sometimes carry useful meaning that standard American English doesn't even have a way to achieve.
First, I definitely didn't intend the parallels with math to extend any further than the problems of perception with regard to how they are taught versus how they are practiced by scholars. Music theory is an art-related discipline and very much culturally inflected.
And this makes sense. Most music theory (in the West at least?) does focus on Western classical music, in large part because Western music has a literate tradition (see Taruskin) that most other musical traditions lack, which allows us to treat the compositions themselves as texts/objects more easily than other musics.
Even within Western music, we tend to use style- (read culture-) specific analytical tools. It doesn't make sense to use harmonic analysis for Stravinsky, and it doesn't make sense to look for twelve-tone rows in Mozart. In general we use a combination of language that composers used and thought with (so for Mozart, think keys and counterpoint) and techniques that arose from observing the style after the fact (in this case, for instance, sonata form, or Schenkerian analysis).
All of these techniques are culturally biased because, as you've pointed out several times, music is psychological, and therefore rooted in culture. Meanwhile, it makes sense to analyze, for instance, Indian classical music using rhythmic modes.
So, coming around to your analogy with elementary school grammar education, I think you're right that there is a prescriptivist parallel here -- learning that parallel fifths are not allowed, or that the second theme in a sonata always modulates to the dominant, or even that there always is a second theme in sonata, all of these do not accurately describe all music, or even all Western music of the common practice period. They are artifacts of the particular techniques being used. The original description of the sonata came into being around the same time as prescriptivist grammar (and has had a great deal of improvement since then -- read Rosen if you haven't already). Species counterpoint and Bach-style chorale harmonizing came about to describe specific styles, and to be used as exercises for composition students in the 18th-19th Centuries. The fact that those two things in particular (which I think are the most grievous examples of what you're talking about) are still included in music theory education is possibly counterproductive, especially since they are treated as sets of rules, rather than as historical examples of the composition pedagogy that the Western classical composers themselves were subjected to. Teaching Fux as anything other than "this is how Mozart and Beethoven learned to write counterpoint" is silly.
So that's the prescriptivist parts. However, where we disagree is that I think there's still a lot here that's useful for descriptive purposes. It's difficult to talk about classical music within its cultural-intellectual context, which I think is necessary, without these tools. You can argue that any interval can be dissonant with the right timbre, but if those timbres are rarely used in the repertoire you're describing, it's not much use is it? The 18th and 19th Century composers thought about dissonance a certain way, and if you're analyzing their work as art objects (cultural objects) rather than physical objects, you have to at least take that into account.
Music notation just seems really really suboptimal for actually understanding music (music software uses totally different notations/interfaces for a reason), and all music theory seems obsessed with it.
Meanwhile, music theorists are "obsessed" with notation only insofar as the music they study is written using that notation. You seem to have skipped my previous comments -- music theory, even at this basic level, has little to do with notation. You read it as notation obsessed only because you're not thoroughly enough steeped in the notation. Reading and writing music notation is as natural to a musician as writing in English is to you. It would be strange and counterproductive to insist on using nontraditional notation when every musician who plays the repertoire you're studying already reads the standard notation, and all the repertoire you're studying is written in it.
When I was in school it seemed like most of the theory PhDs would pick a composer to focus on, but there are other ways to go than just that. Certainly, the sorts of questions I listed (asked in much more specific ways) are part of analytical inquiry, but a lot of theory papers are descriptive rather than explanatory.
Edit: I was performance major, but took classes from some pretty great music theorists. A few examples of graduate-level classes I took: the string quartets of Bartok; the music of Stravinsky; the symphony in the 19th Century. They tended to be focused on an individual composer or repertoire. Obviously scholarship is done on a much more granular level than that.
Not to say don't read them of course; you can read what you like, just that tab is what you'll be using I would have thought.
It's good to keep the limitations of tabs in mind. The're really useful, but they don't represent music nearly half as much as conventional music notation. They represent finger movements instead.
I don't think its possible to reproduce a piece from only tabs (without having heard it) while standard notation makes sight reading unnecessarily hard.
I took a quick screenshot to show an example. I think here you can tell very easily what fingerings to play, what the note duration is, and when you should sustain notes over others. The difference between slurs, slides and whammy bar bends (The V symbol you see next to notes like in meas 3), muting notes is an x, yadda, yadda. I'll stop going on about tabs now.
Tabs are physical movement instructions. With a lot of training, some people can process this into a limited mental representation of how the music sounds.
If you think about it, it's quite analog to the difference between vector and bitmap images.
I think it's a great way to begin learning guitar without needing to take a lot of time to learn how to read sheet music first, as that really scares away a lot of new players, or people who are considering learning guitar. Notation for rhythm, slurs, accents, are all pretty clear and can be learned very easily. Unless there's more that I'm not understanding about the differences between the two, I'd like to learn what it is.
There's one last benefit that really makes me prefer digital tabs over conventional notation. There are a lot of songs/riffs/etc that are very dependent on the effects being used. This is more a benefit of software than tabs, because you could do this with any instrument or notation, but support for it is more common in guitar software. Being able to add effects, and mark things such as the rhythm of a wah-pedal can be very helpful as well. An example I can remember is Searching by Joe Satriani. He rocks a whammy pedal back and forth while playing an arpeggio, and I had no idea how to mimic that sound until I saw both the notes written out, and the whammy bends on the same track as well.
edit: I still think it's useful to learn theory, tabs or not. But I don't think sheet music and theory need to go hand-in-hand anymore.
Instead, my more moderate view is that at the very least, new players should be informed of what the most common notation systems are like, and what they are used for. We can argue all day, but it's often someone else who decides how they want to notate something. Different genres have their own preferences, and there are even regional variations. I played with a bandleader who had moved up from the South, and had to re-write her book because nobody in this region can read Nashville number charts.
I play in a jazz band, and the guitarist and I would both be helpless if we couldn't read standard notation -- dots and chord symbols. But I would add that it's a musical genre where the music is pretty forgiving of the player deciding their own fingerings on the fly.
If something is tabbed inefficiently, that's a problem with the author of the tabs, not the format. I'd say incorrect tablature is similar to incorrect notation. Just because someone can notate music incorrectly doesn't mean that sheet music is a poor format.
The fact that tabs imply a certain fingering is a larger benefit than an issue. Many riffs are only realistically playable with one specific fingering, and a tab can help you figure this out much more quickly than you could with your ear or notation alone. Especially when it comes to deciphering whether something is using techniques that can produce the same notes, but different sounds or ease of playing. Like sweeping as opposed to tapping, or songs written in alternate tunings.
Very nifty and fun though.
Music Theory For Computer Musicians.
For some actually useful music theory, I can recommend the goldmine that is Ethan Hein's blog: http://www.ethanhein.com/wp/category/music/music-theory/
Listen to Glass, Reich, and Riley - and you hear the deconstruction of symphonic structure.
Listen to Beethoven's symphonies and you hear the struggle of form from Mozart's classical era construction to what would become Beethoven's pure romanticism.
Listen to the interplay of an Alberti Bass and melody in Mozart's Piano Sonatas, and you hear the beauty in the evolution of counterpoint as written by Bach, Scarlatti, and their band of powdered wigs.
Listen to Bach and Scarlatti, and you hear the echoes of Gregorian Chant and the Diabolus in Musica (and why Black Sabbath sounds like Black Sabbath.)
Those who forget the past are doomed to be Miley Cyrus.
No, you hear Koyaanisqatsi, etc.
And this is exactly why you should never try to understand a popular genre by crossreferencing its stylings against some other style or genre.
Because other people hear other things - many, many other things - which perhaps you're not aware of.
But this particular combination is like saying, "Listen to Billy Joel and you hear piano." ;) House and techno really are direct lineage from the minimalists in many ways. This is not a blind cross-reference. Any artist learns and borrows from what has come before. Some borrow more heavily than others. (As an aside, check out the 2006 album "Reich Remixed" for some really cool interpretations... )
Listen to Portrait of Tracy (or any great harmonic jazz) and you hear the same open chord structures of Impressionist works like Debussy's Preludes or Ravel's Valse Nobles.
Listen to the impressionists and you go many places...
Ravel and Debussy's piano music is barely one step removed from jazz. Makes sense, because the early jazz greats lived and played around the same time. There's a famous picture of Ravel at a birthday party when he was in his 50s, with George Gershwin standing beside him. The early 1900s was an amazing time in music... classical was mixing with early jazz was mixing with vaudeville was mixing with the first stirrings of delta blues was mixing with gospel was mixing with african folks songs...
(I can do this all night... ;)
Seriously, I make techno and am intensely interested in music theory. You might as well complain about mathematical cheat sheets containing arithmetic, geometry, and other outdated concepts that were cooked up by ancient Greeks wrapped in sheets.
Some of my favorites:
Steve Reich - Music for 18 Musicians & New York Counterpoint
Phillip Glass - North Star
Morton Subotnick - A Triumph of Reason
Iannis Xenakis - Pleiades, Musique Concrete 1959
For one thing, a lot of what one learns studying Common Practice music theory most definitely is applicable to modern styles. Things like dominant function, for example, aren't going anywhere.
That said, I agree with the point that is implied by your post, namely, that "music theory" as the term is usually used is actually a description of a specific period of music (Common Practice) and it is a mistake to view modern popular music as some kind of degenerate case of it. I suggest that people who are interested in learning a theory that applies to more recent music take a look at "What to Listen For in Rock" by theorist Ken Stephenson.
I also don't think the link you sent is going to make things much clearer for a beginner. I think that Desi Serna's guitar theory lessons in podcast form actually do a great job of explaining the basics, even if the guitar isn't one's primary instrument.
With a foundation in classical music theory, you can go beyond what anyone is doing in popular music today. I strongly believe that (for example) Beethoven's 5th, from a compositional perspective, has more rhetorical power than any music produced in the last century. I think this is largely due to popular music being very simple structurally. Where is the counterpoint? Where are the modulations? All we get is simple chord progressions repeated ad nauseum. Imagine how much farther we could go if we combined the lyrical and textural variety of popular music with the compositional depth of classical music! I salivate at the thought of an electronic or metal musician delving into this territory...
: Phish is one of the few bands I know of who actually focus on this stuff. Some of their pieces even include bona-fide fugues. I'm not the biggest fan, and it's a simple example, but I love listening to the motifs and variations in "Stash": https://www.youtube.com/watch?v=8OfQCAj2Ppg
In the sound design, the rhythms, and the production, where they never trouble the hearing of anyone who has been trained to believe that musical structures are defined almost entirely by pitch patterns.
Even the idea that music exists to 'express rhetorical ideas' is... actually quite odd, outside of classical training, anyway.
I happen to like fugues very, very much. (The fugue in BWV 542 is a favourite - http://www.youtube.com/watch?v=g6Kul3JzKI0.)
But the idea that music should aim for that always? Uh, nope.
An ideal string (or any oscillator) when disturbed (e.g. plucked) will tend to vibrate at a fundamental frequency of x Hz as well as modes of 2x, 3x, 4x, etc. These higher frequencies at integer multiples of the fundamental frequency are called harmonic partials. This is a physical phenomena unrelated to music and human hearing.
But the basic elements of harmony come from the fact that our auditory system seems to be "tuned" to identify harmonic partials.
If we start with a fundamental frequency x Hz (let's call it C), the first partial is 2x Hz, and it is another C an octave above (multiplying or dividing a pitch by a power of 2 will give you the same pitch in another octave).
The next partial is 3x Hz, and it sounds like a G. This is the interval called a perfect fifth, and is the strongest, most stable sounding interval (other than the octave). The next partial is 4x Hz, which is just another C, two octaves above the C we started with.
The next partial is 5x Hz, which sounds like an E. This is a major third, which is another strong and stable interval which is ubiquitous in most music.
Also, I believe instruments with arbitrary pitch (violin, voice) tend to naturally drift closer to just intonation.
Barbershop quartet music (and other a capella music) is a great place to hear just intonation. The consonant barbershop seventh chord was a relevation to me when I first learned of it. It's really close to the dissonant dominant 7th interval, but serves a very different purpose harmonically. The minor seventh is also a different interval. Thus there are actually 3 seventh intervals, all of which are approximated in ET by a single note. This blog post has a good summary:
1. Studying the history of Western music theory doesn't give you insight into any music, as you claim. It gives you insight into Western music. Check out music from another part of the world with a completely different notion of tuning, different scales, etc, and your music theory background isn't going to help very much. The only thing that is truly universal is the overtone series, because that's based on physics.
2. I think we could come up with plenty of structurally complex music from recent idioms, particularly jazz and jazz-influenced music. I would say that a bigger difference between something like, I dunno, Steely Dan, and Beethoven's Fifth, is length. Popular musicians don't seem to attempt such longer pieces. But for me personally, longer != more powerful. For that matter, more complex != more powerful, but I happen to share your desire for what we're calling "compositional depth", whatever that may be...
(EDIT: I just noticed that you said outside of Western music. Yes, that may be correct. Many systems of music in the world are very different from our own. But I think most people writing music today are writing with Western ears in mind. After all, we've been conditioned to understand this kind of music for hundreds of years!)
As for your second point, I think what I latch on to in classical music more than anything is the use of motif, and Beethoven's 5th of course epitomizes this. Don't get me wrong — I love popular music, and I listen to it more than anything — but most of the "top 100" songs in any popular music ranking feature wandering, improvised music more than any systemic use of motif to make a rhetorical point. And that's not a bad thing! I love Stairway to Heaven. But it just "sounds good" — it doesn't really develop its musical material.
Compare to something like this, where every single musical detail is repeated and developed across all the voices. It's so intricate. I've never heard this level of motivic development in popular music, and I've been looking for a few years now.
I am sorry if this is not making any sense, I am having beers.
I would say that the V7 gets it's power from the flatted fifth interval, aka the tritone, aka the most dissonant interval this side of a minor second. And like you say, it can be understood in terms of voice leading, e.g.the 7th (the "leading tone"!) "wants" to resolve up to the tonic.
It's interesting that you mentioned motif because I think that fits well with what I was saying about the length of the pieces. Seems to me that one isn't going to have much room to develop motifs unless writing in an extended form. But for me personally, this doesn't seem like a good requirement for a piece to be satisfying in the way that I think we are talking about. If you are seeking that kind of intricacy from modern music, have you checked out Bela Fleck & the Flecktones? Also, have you explored Zappa at all?
I don't think you need a long piece to develop motif. Look at something like "Vocalise", or, heck, any of Bach's Well-Tempered Klavier.
One of my teachers used to stress the original meaning of the word "sublime". I think that's what's missing in modern music. A feeling of awe that leaves you speechless.
Zappa's been on my to-do list for a while, I'll have to give him a listen soon!
Your book recommendation looks quite interesting too, thank you. I'm not sure if Ethan Hein's blog is a great starting place for a beginner, but it's some of the best "theorizing" around recorded music that I know of.
"The blues is based around a very different set of harmonic expectations than the ones underlying classical music. In the blues, major and minor tonality are freely intermingled. Dominant seventh chords can function as tonics. Tritones need not resolve."
Although the blues uses devices not commonly found in classical music, the language being used to discuss it is conventional, main stream music theory: "major", "minor", "tonality", "tritone", "dominant", ... No surprises!
Someone looking for basic music theory will not get into this at all.
Secondly, parallel major and minor does occur in classical music. So do dominant sevenths functioning as tonics: at least secondary tonics.
Moreover the people who came up with the blues tradition (and jazz) were not completely isolated from hearing classical music.
Lastly, there is orchestral music that doesn't consist of "powdered wig" scales conforming to cycle of fifths progressions. Let's see what comes to mind: Moussorgsky's "Night on Bald Mountain", or Ravel's Boléro, ...
Many of the most important jazz composers and musicians were classically trained and were intimate with the type of music theory we're talking about here. Thelonius Monk could reel off Chopin and Rachmaninoff etudes from memory. "Take the A Train" and many other tunes we associate with Ellington were written by Billy Strayhorn, who's main interest was classical music, but found that the classical music establishment at the time would not accept a black composer or musician. Jazz was the only genre in which he was allowed to work. (Ellington/Strayhorn and Monk are considered the most important composers in Jazz, and their initial training was in European classical music.)
Jazz is a development of Western classical music, and knows it. In fact, it's a rather miraculous revival of the improvisatory tradition that was central to European art music until it died out with the rise of symphonic music in the 19th century. If you listen to some contemporary jazz pianists, for example, Marcus Roberts, there's no mistaking the strong influence of European classical music.
only of Western classical music?
I found the PDF using Google: https://www.google.com/#q=Ravenspiral+Guide+to+Music+Theory+... (Scripd.com is annoying, like a PDF download scam)
Especially of interest.