Music Theory for Beginners | Hacker News Reader

Music Theory for Beginners

whitakerblackall.com

382 pointsr11t107 comments

I teach Music Theory (and piano) for a living-- this is an excellent introduction to the most practical concepts.

I was somewhat disappointed that the OP showed us a C Major scale without really explaining what a "major scale" is-- a collection of whole and half steps-- especially since they used a keyboard as an example, which is laid out in exactly the right pattern for teaching the major scale. (Notice that the black and white notes are arranged so that you skip some keys-- whole steps-- but sometimes you can't: half steps). I always teach how to build scales based on this pattern- WWHWWWH. Using this pattern, you can build any major scale beginning on any arbitrary note-- including notes that are sharped or flatted, which is neat. From here, you can figure out all of the scales, and thus all of the keys.

The advantage of learning in this fashion is that you can tackle intervals first, which are the distances between notes. (Note that major and minor intervals are named as such because they fit into our major or minor scales). Since a chord is simply collection of intervals, you end up with a more powerful understanding of them by learning which intervals (and which scale degrees) build which chords.

All the same, I really think the more "practical" approach here is really interesting, because you can start writing music earlier, albeit mostly in C Major.

Cool link, it really gives me insight as a fellow music educator.

I'm also a music theorist and educator. I'm interested in your perspective on whether it is a good idea to try to introduce students to the acoustic/mathematical derivation of the scale. To provide context for non-technical readers, the physical basis of harmonic intervals is integer ratios of frequencies, and European tempered tuning systems create scales and chords as a pragmatic adjustment of mathematically pure tuning to the necessity of using a finite number of predetermined pitches for instruments such as the piano.

I am still unsure as to whether the deeper understanding of scales, chords, keys, tuning, and temperament is something I should push to make students study and understand. Many students have a negative reaction to even the simplest math, but other students get a lot of benefit from understanding exactly how and why a given set of pitches fit together to form chords and scales. In the context of group instruction, deciding how much time to devote to this material is a dilemma for me.

My guess is that it would lose and scare all of the many people for whom mathematics aren't a native language. Do it for mathematically minded people, I'd say with at least a A level in sciences, but avoid it for "normal" people.

There might be a non-mathy way to show that something fishy happens with Pythagorean scales, similar to the post, with well chosen computer-generated sounds; but this would mainly interest people with a couple years of musical practice.

> To provide context for non-technical readers,

I love the fact that I'm a "non-technical" reader in this discussion!

>whether it is a good idea to try to introduce students to the acoustic/mathematical derivation of the scale

I did this when I was teaching my roommate about theory, but he has a degree in math, so it seemed like the logical approach.

That said, teaching theory is incredibly good practice, so I like to do it whenever possible, and in my experience, the best time to explain the mathematical foundations of music is when they start to ask questions about it. It's like the matrix - if they're not ready for it, it's just too much.

I think it would be worth doing with older students as a supplement to the curriculum. One of the bad things about my "major scale-centric" approach is that I never explain why a major scale is WWHWWWH, which is actually a barrier to some students, who are either curious or who need more context for their information.

I teach mostly middle-school and high-school kids, and we barely have enough time to get through what I have, so I skip it. I wish I didn't have to.

Do you ever tell them something like, "There's a bunch of cool stuff you can learn about this, if you go to the web site, or look for _____ on Wikipedia?"

I think it's very helpful to work back to the math, if the students are capable of understanding it. You can start with the familiar white-piano-keys scale and build forward, exactly like the article shows. Eventually, though, it's important to understand the math and how the different tempers were derived.

Instead of math maybe show pictures of sine waves and how they relate. My kids learned that in elementary school and it seemed to make sense to them. You can even demonstrate it pretty easily with long strings and a cheap strobe or the 60Hz lighting in the room.

Although I'm not a music educator, in my opinion it's better to teach scales primarily by ear, without teaching too much theory at the beginning.

I've seen something like this elsewhere on the web: teach the C major scale until the student is familiar with it, can play the scale and its chords/arpeggios on their instrument, sing it given the tonic, etc. Then play the scale starting on G. G, A, B, C, D, E, will sound "right", that is, just like the C, D, E, F, G, A. Only the seventh (F) will sound "off". So we "fix" it by raising it a halftone. You can go all thru the circle of fifths this way.

If the student wants to know the reasons behind it you can teach it, but just like in math and CS I believe it's better to teach the concrete before the abstract.

Something to note: whole and half steps are not the only available type of steps, you can also move quarter steps. It's not common in Western music (if present at all) but very common in Middle Eastern music. Maqam world (http://maqamworld.com) provides a decent index of many Middle Eastern scales, some of them utilizing quarter tones.

For instance:

http://www.maqamworld.com/maqamat/rast.html

http://www.maqamworld.com/maqamat/bayati.html

http://www.maqamworld.com/maqamat/sikah.html

For those interested, each scale is accompanies by several audio samples to hear what it sounds like.

There are many ways do divide an octave.

Steve Vai created a scale called the Xavian scale wich is dividing the octave by 10.

He used in on Deep Down Into The Pain

http://www.guitarflame.com/2008/xavian-scale-steve-vais-own-...

I'm thinking about a music application that lets you place tones in arbitrary locations on a continuous line (representing the tone space) and assign them keys on the keyboard.

Something close is

http://www.morphwiz.com/

and

http://misadigital.com/index.php?target=home&lang=en

They are both interesting because they are using touchscreen meaning that they are fretless.

Cool. I've started fretless bass, and reading about accommodations you make for playing with e.g. vocalists who run flat more often than sharp, or upper register of piano that are sharp.

Remember to check out Jaco Pastorious then!

That song is terrible (and I love Devin Townsend, the singer).

Of course it's terrible it's using the xavian scale which you are not used to.

no, it's terrible because it sounds like a bad technical exercise (music graduate here)

So does Jazz to a virgin ear. That doesn't mean it is.

Jazz sounds awful. There's a reason pop music sticks to the four chords of victory - they sound great!

1. "Not sure if serious"

2. Jazz is barely a genre anymore there's so many different sub-genre's and movements within it that actually using the term how you did is disingenuous.

3. You did the same as above with about the same effect for "pop music". Seeing as you addressed harmony, you'll actually find that there are lots of common harmonic (chord) progressions that are shared between the two idioms. They reflect each other more than they are different to each other. If you really wanted to make the point you were trying to make I'd suggest looking for some form of obscure ethnic music (Pakistani throat singing or Indonesian Gamelan perhaps) that has not really had much chance to mix with western music and absorb its paradigms.

To the virgin ear, yes.

Virgin? http://www.last.fm/user/superjoe30

According to this website I listen to 60 tracks every day.

60 Jazz tracks? That's what I mean with virgin ear.

You are not used to listen to Jazz so it's more likely to sound horrible to you since it's often rather complex.

Why do you think that parents of the 68' generation hated Beatles despite it being what we consider pop culture today.

You need to understand this in context rather than in absolute terms.

Makes sense except for one point: Why would a person purposefully subject themselves to a musical genre that sounds bad? You said yourself, to the virgin ear, jazz sounds bad. That means that everyone who likes jazz music at one point thought that it was terrible music yet listened to it anyway.

That is up to the individual.

Many people as they start playing instruments they start developing a more and more sophisticated sense of harmony.

It's not different than code looking like nonsense to the noob.

This is where culture comes in. Jazz used to be pop-music, people grew up with it.

Context history culture sophistication at any given subject.

Jazz sounds awful.

I can understand styles of music sounding awful, but what does it mean for a whole genre of music to sound awful? How does that even make sense?

Just to be clear, do you think this (Desafinado) sounds awful?: http://www.youtube.com/watch?v=So718wk426c

Crazy talk.

This song isn't actively bad. I wouldn't mind it in the background. But as far as I can tell, it doesn't really utilize "jazzy" chords either. It's just kind of gentle and peaceful and doesn't ask for too much attention. I wouldn't use this as a good example of Jazz music.

What I'm referring to as what sounds awful are songs that try to use "creative" chords that are really just dissonant or don't belong together and "advanced" notes that are really just out of key. As far as I can tell this song isn't doing that.

I think a big part of music is familiarity which is why you see the overuse of the I, V, vi, IV progression. So to me Xavian sounds like chromatic played out of tune. Nice idea though.

It's not just that; the musical intervals we tend to favour are based around natural resonances and constructive / destructive interference. Hence why a perfect fifth sounds good and a diminished fifth jars; the waveforms don't compliment each other.

I'm willing to be persuaded and don't claim to have made a large study of this but I'm yet to hear a microtonal tuning that didn't just sound off. The sounds actively work against each other because the resonances just aren't there.

(I'm aware in this that modern keyboards are even tempered and so we don't actually _quite_ have perfect intervals any more, but the differences at that level are far smaller.)

Don't be afraid to be right. I did study music theory and I can confirm that the intervals as we know them are just a way to modelize the natural physical relationships between the waves we hear. It is a way to remeber where to put your finger on a violin to make the two string sound good together in a given harmonic context.

One can alway declare to prefer microtonal or whatever invention, but the level interference (or harmony) between pitched sounds can be determined rationaly. This, for once, is not placable under cultural relativism. That's why it is probable that quater tones in Indian or Iranian music are not really tones, and are more like little bends to the natural scale.

(This fact do not please avant-gardists, because it means there is roughly nothing new to invent in this field, but reality is not supposed to always be pleasant, right?)

By the way, I couldn't read the OP (blocked), sorry if my contrib is not related enough.

And I guess also why they don't really use chord progressions like we do in the west no?

Hey, why stick to octaves? The Bohlen-Pierce scale divides the tritave in 13 (a tritave interval is a 3:1 pitch ratio).

http://www.youtube.com/watch?v=60SYLdMYvcE – check out the keyboards!

I agree with you re: whole-steps and half-steps. When you teach "what makes a scale major?" in reference to the scales whole and half step pattern, it is then much easier to introduce minor, and scale modes (Ionian, Dorian, Phrygian). Basic theory taught in this way is really not that hard (however, I majored in music in school). If you introduce intervals, then you don't have to say "forget about B diminished. You won't miss it". You can say "B-dimished triad has a darker, more moody sound because it is made up of two-minor thirds. Or a Phrygian mode has an "eastern" sound because its scale starts with a half step.

That said, a lot of work went into the tutorial, and it is certainly well done.

>I was somewhat disappointed that the OP showed us a C Major scale without really explaining what a "major scale" is-- a collection of whole and half steps...

I agree. I find it very frustrating that Western music breaks the twelve notes into two classes: the "naturals" (ABCDEFG), and "accidentals" (A# C# D# F# G#, and enharmonic equivalents). Playing guitar, I have come across people explaining barre chords -- a single fingering for a type of chord (e.g., major, minor) that you can shift up or down the fingerboard -- as "you can play any chord with this: E, F, G, A, etc.", and ignoring almost half of the possible chords. I'm convinced that the naming of notes to simplify playing in the key of C major or the relative A minor has inhibited players from gaining a real understanding of intervals.

To wit: when I play piano, I play in C. When I play guitar, I don't think about what key I'm in. I play in whatever fingering is easiest and what sounds best at the time.

> To wit: when I play piano, I play in C. When I play guitar, I don't think about what key I'm in. I play in whatever fingering is easiest and what sounds best at the time.

I know what you mean, but I think that's significantly a keyboard-based hazard. I play the trumpet (mostly; I can do a very little on a few others and trying to improve) and I've frequently ended up jamming away in odd keys, switching between them as required. F# major is a relatively common key for me, I just hear the intervals and the fingers move quite automatically, even though trumpet harmonics are arranged around C major (well, concert Bb). I'm sure it's much the same on other wind instruments.

Sax also favors the C major scale [].
Back in the early 20th century, sax salespeople would take advantage of this to sell the sax as an "easy to play" instrument. You can hang a saxophone from your neck and in 5 minutes you are playing the C major scale, Twinkle Twinkle Little Star, whatever.
Compare with the trumpet or the violin, where just playing your first major scale in tune scale in tune takes weeks of practice.

[] Actually, sax is a transposing instrument. But it does favor whatever scale you read as C major when you play it.

OK, there's two separate things here :-)

Trumpet fingering is easiest in C, F or G majors (as read, concert Bb, Eb and F). The actual blowing is quite physical and needs a good bit of practice to build strength; that is easiest in C, and the lowest fifth of that too.

But.... There's only three keys, they always operate in the same sequence, so once you've learnt that fingerings flow quite easily, and the harmonics are good, useful intervals. Perfect fifth, perfect fourth, major third, minor third. That gives the five core open harmonics over a core range of two octaves once you use the valves. Hence, once you've got yourself going a bit, while some keys are easier than others the instrument's structure lends itself nicely to switching keys at will without major issues. It makes it a nice instrument for improvisation.

The key-agnostic fretboard is a big part of the reason I enjoy playing guitar.

It's not a perfect tool for the application at hand because of the necessity of separating the second and third strings by a major third instead of a perfect fifth, which would confuse the issue.

However, I think it'd be more convenient to have a graphical representation of the major scale's construction on which a whole step is always clearly a whole step.

"separating the second and third strings by a major third instead of a perfect fifth"

The other strings on a guitar are separated by a fourth, not fifth (perfect or otherwise).

Depends on which way you're counting.

No, it depends on the distance between the notes, which in the standard guitar tuning is a fourth (except between G3 and B4, as mentioned). You can take the lower note an octave up or the higher an octave down to make a fifth, but that changes the interval.

While guitarists, by necessity, have a loose approach to finding the right notes for a chord, and will often use an inversion to get them all (or at least the harmonically important ones, like the third) on the fretboard in a reasonable way, that doesn't change the meaning of fourth and fifth. It's a bit pedantic, sure, and the notes have the same harmonic meaning (sort of, though inversions do feel different sometimes), but when you lay out the standard tuning of a guitar out on a piano and ask someone the distance, it is a fourth. You have to jump through some hoops to convince them to tell you that the relationship between the G to the D below it is a "perfect fifth".

I'll also point out that the post I was responding to had already established which way he was counting by describing the relationship between the G and B strings (which, if we're counting the other direction would be a flat 6th; and, as a musician of twenty years I had to do mental somersaults to make my brain think of it that way). One way or another the description of standard guitar tuning was incorrect.

See what you made me do? I had to go all pedantic and stuff, and I hate doing that.

I am an idiot.

It's a good intro, and music theory is one of those things that's quite hard to introduce well.

I'm a music educator, of a sort; this is a project of mine, build around interactive drills & concepts (click free resources if curious): http://emusictheory.com

...but I've held off for a long time on writing a real online course, because, well, it's hard. The concepts don't always seem logical in isolation, the names of concepts sometimes overlap in weird ways (er, major 7th interval or major 7th chord?), and the general approach -- to lay down all the groundwork first, and only then get into anything remotely practical -- is deadly, deadly boring.

So I'm very much in favor of taking a practical approach, and trying to give the student something actual musical-sounding they can produce at the end of every mini-lesson... but if this were easy to do, I'd have it up on the site already. :)

A friend of mine here in Tokyo owns a small music company and recently launched a series of games to help with music training. They are flash-based, but I have been quite impressed with them and have enjoyed them quite a bit! He is using a freemium model, and you can try out the games on his website without even registering. (Free registration gives you progress tracking, and subscription gives you access to all levels and games.) For anyone interested in music training, I highly recommend them!

http://trainer.thetamusic.com/

Really good stuff! Bug report: after I created an account, I was given a "Registration successful. You are now logged in." flash message in the middle of a "Cookies Required" page. It seems to have logged me in correctly, though. http://i.imgur.com/KMBPQ.png

Thank you for the bug report! I have passed it on.

Three things

1. Send him this presentation: http://fury.com/2010/02/jesse-shells-mindblowing-talk-on-the...

2. Tell him to do it for the iphone and ipad where people can also practice on the ipad.

3. Set up achievement levels

Khan Academy for music education.

>Tell him to do it for the iphone and ipad

in Flash?? Can't be done, you know that.

Thank you very much for the feedback! I have sent it to my friend via email to make sure that he does not miss it.

I recently had a short-term stay at a place which had a piano. It seemed like a waste to let it just sit there, so I did a bit o' googling and found this site: http://www.pianobychords.com/

The information on music theory is similar to the post - but it also shows you how to play a few common songs. If you follow the fingering guide and play the same chords with both hands it sounds damn great! I thought only the guitar had that "pick it up, learn a couple of chords and you're good to go..." attitude!

One of the songs on the site was "Let It Be". I remembered that that song was in the Axis Of Awesome song "Four Chords" http://www.youtube.com/watch?v=qHBVnMf2t7w - now I know how to play hundreds of party-friendly songs on the piano. Damn satisfying for an outlay of just a few hours practice!

> I thought only the guitar had that "pick it up, learn a couple of chords and you're good to go..." attitude!

Ralph Towner calls the guitar a "portable piano".

For those curious what a “portable piano” would be like, see the keytar (guitar with keys) – http://en.wikipedia.org/wiki/Keytar.

Fascinating read, but definitely not for beginners, at least for people like me, who have difficulty naming the notes (I have to go through "doe a deer..." each time, there are seven of them, right?)

My total music illiteracy really annoys me. However, whenever I try to pick up some knowledge I got held back by lots of questions that the usual music student (or teacher for that matter) has never thought about and no answer can be given. Here are a couple:

* Why are there seven notes? Is this due to an property of the ear?

* Ditto, for the octave concept, why should it be multiples of two?

* Why are there black keys between some white keys on the piano and not between others?

Is there a book that explains questions like these?

  Why are there seven notes? Is this due to an property of the ear?

The 7 tones that make up a major scale are basically a cultural artifact of western music (which goes back to gregorian chant). Other cultures have more/fewer tones.

  Ditto, for the octave concept, why should it be multiples of two?

Can you clarify this question? Octaves result from the natural harmonic series: http://en.wikipedia.org/wiki/Harmonic_series_(music)

  Why are there black keys between some white keys on the piano and not between 
  others?

Well, IMHO this is a purely arbitrary cultural artifact resulting from the evolution of the keyboard (first in pipe organs). Since the octave is divided into 12 chromatic tones, you could in theory devise a keyboard with alternating white/black keys. However, the organ keyboard evolved in the middle ages, when chromaticism wasn't fully developed, hence, it appears the "white notes" of the keyboard appeared first, then later, the black notes added at the appropriate positions within the chromatic scale. See this, along with the accompanying picture, which clearly shows a small keyboard with the white keys only:

http://en.wikipedia.org/wiki/Pipe_organ#Keyboards

I think an octave up (down) means double (half) the frequency of the tone. The usual explanation, I think, is that the Pythagoreans who invented it found this to be the "most pleasing" ratio.

I wonder if there are user studies to back this claim.

I am also at such a low level, that part of your explanation just goes over my head, i.e. what is chromatic scale? Wikipedia says: "The chromatic scale is a musical scale with twelve equally spaced pitches, each a semitone apart. A chromatic scale is a nondiatonic scale having no tonic due to the symmetry of its equally spaced tones." Now very helpful. I thought there were 7 notes! And I don't know any other terms in that sentence (checking their Wikipedia entries doesn't help either, leads to a loop)

The chromatic scale is basically playing every key, black and white, from one C to the next. Whereas the C major scale is every white key from one C to the next.

"The chromatic scale is a musical scale with twelve equally spaced pitches, each a semitone apart. A chromatic scale is a nondiatonic scale having no tonic due to the symmetry of its equally spaced tones."

basically what this is saying is that in western music we have divided an octave (the space between a frequency and exactly double that frequency) into twelve "pitches" that we call notes. non-diatonic refers to the fact that it has no basis in any of the western minor or major scales (the two fundamental western scales) as it covers every note of the octave, thus is circular and beyond definition.

Hope that helps

"The 7 tones that make up a major scale are basically a cultural artifact of western music (which goes back to gregorian chant). Other cultures have more/fewer tones."

It's difficult to draw the line between culture and biology, but that's probably too far to the "cultural" side. There is a basis for those, which is that if you start on the base tone of C and run around the circle of fifths you'll get the white keys first: C -> G -> D -> A -> E -> B -> F#, and you get F by going down from the base tone. The importance of the fifth itself comes from the fact that the first harmonic of the base tone is one octave up, and the next harmonic is very close to an octave and a fifth with equal temprement. This seems more than coincidence.

I also find this a better explanation for why so many cultures pick this up once they are exposed to it. (Which is not to say they give up all their old harmonies but this tuning+scale has certainly gone global.) I really have a hard time imagining the mechanics of the Western Global Harmonic Imperialist Conspiracy; it seems much more likely that it so happens that people we call Westerners found this local optima first and it spread because humans in general like it, and it belongs to all humanity, not "the West", just like "perspective" and mathematics.

I once asked an ethnomusicologist if any common factors existed across all musical cultures and he said that about all he could point to was: a) some concept of a tonal center and b) the interval of the 5th remained fairly constant, despite whatever scales/tunings might exist.

So, I'd grant that much, but beyond that, I don't see much evidence for the diatonic scale as being somehow inherently inevitable. The harmonic series isn't much help, since you get to the flat-7 or flat-five before various other diatonic notes (plus, it's not particularly in tune at the higher partials).

And the circle of fifths rationale seems to be a just so story: http://en.wikipedia.org/wiki/Just-so_story (why stop at 7 notes? why not include G# or even C#? why not just C-G-D-A-E? (incidentally, a pentatonic scale) etc...?)

But this debate could go on ad infinitum, because the issue lacks empirical grounding. Which is to say, how could one falsify either the nature or culture thesis?

I answered a slightly different question than I think you think I did. You said "Well, IMHO this is a purely arbitrary cultural artifact resulting from the evolution of the keyboard (first in pipe organs). Since the octave is divided into 12 chromatic tones, you could in theory devise a keyboard with alternating white/black keys." I gave you a plausible non-arbitrary answer for why that particular pattern was chosen. Not why equal temprement is inevitable or why "7" notes in a scale are special, just why the white keys are ABCDEFG as we know them and not some other pattern. You can put more or fewer notes in your scales in stuff we still would call "Western" music without anybody caring or even noticing. (Much good Western music uses all 12 tones pretty freely.)

As for whether it's a Just So story, sometimes that's all you get. However, if it is just coincidence it's a mighty coincidence.

That's basically the questions that music theory answers. As far as I understand things, it mostly relate to frequencies and harmonic resonance. The octaves are exact multiples of the same frequency (so a higher octave is 2x the frequency of the lower octave). The seven notes all fall out from that as well, but it is more complicated to explain and I don't know things well enough to break it down in a way that would be correct and make sense. But basically they resonate with each other.

As to why the human ear finds harmonic resonance pleasing is a more difficult question to answer. Why do we find order pleasing, and chaos frustrating? Speaking generally, the human brain functions as an advanced pattern seeking machine. What we do is take in chaotic and diverse information and make sense of it in some way, piecing individual facial features together into a specific face, and so on. Information that is ordered to begin with requires less work for the brain to process, so perhaps we find it pleasing because it is easy to sort and label mentally?

The intervals of black and white keys relate to the major scale. Basically, the major scale has the property of consisting of two whole steps, one half step, three whole steps and finally one half step. So the piano is constructed based on that scale.

Again, I can't explain it much better than that, but any book on the mathematics of music and signal processing / frequencies would have more information.

But yeah, the reason why you can't answer those questions is because you don't know music theory. That's where the answer to them is. It's not that they can't be answered.

Get a list of tone frequencies and do math with them. You will see patterns, called harmonics by musicians. Doubling the frequency (octave) can be thought of as the same tone playing twice, with an even offset. Our brains can pick up on that and notice that 440Hz is the same as 880Hz (only and "octave" higher)

Interesting fact: The tones of the scale aren't exactly evenly spaced, because of math. Some instruments use true tones and are made specifically for a certain key. Other instruments that can play in any key (like guitar) are never truly in tune.

To generate a list of tone frequencies, start with A=440Hz and multiply by 2^(1/12) to get the frequency of the next higher tone or divide by 2^(1/12) to go down to the next lower tone in the chromatic scale. Notice that the octave is 12 of these intervals away, making it's frequency (2^(1/12))^12 = 2 times the initial frequency.

'Music Theory for Computer Musicians' was very helpful for me. http://www.amazon.com/Music-Theory-Computer-Musicians-Book/d...

There's also a great TV series from England called 'How Music Works' which gives more of a historical background. http://www.youtube.com/watch?v=PnbOWi6f_IM

People sometimes guffaw at this, but I can't recommend Donald Duck in Mathemagic Land enough: http://www.youtube.com/watch?v=iEVGQKwKeCc They skip over several centuries of shifting and tweaking between the triad and the modern (western) major scale, but it's a great visual answer at least to your second question.

Funtastic! On behalf of HN, I award you, sir, with the best link posting of the day award!

I recently went on a crusade to find this and show it to my children. I view it as a turning point in my development and one that influenced my life's path a great deal.

Modern western music is based on medieval church music, which in turn is based on ancient Greek music. These are two cultures that placed strong value on harmony and mathematical ratios, and it so happens that notes in ratios are harmonious to the ear. Mathematically speaking, the ratios between notes come mostly from low-order ratios in 5-limit tunings: https://secure.wikimedia.org/wikipedia/en/wiki/Limit_%28musi... .

In short, the Western scale is chosen to maximize the harmonic possibilities between different notes while having a reasonably even collection of whole-steps and half-steps between them. The black keys are the "in-between" half steps that do not appear in the C-major scale. The reason the ear likes harmony is probably due to our ears performing a Fourier transform on the incoming sound waves, and our brain blending together collections of multiples of some base frequency into one "note"--this lets us recognize the different characteristics of periodic oscillations from different physical sound sources.

Thanks for the information. I wonder if there are any "music universals", like the ones for language, i.e. universal grammar. If favoring certain tone ratios is a characteristic of the human auditory system, then there should be.

Like Chomsky's search for universal grammar, the search for music universals has been a failure. Nevertheless, there are some ideas that pop up surprisingly often. Doing a quick mental search, I believe every musical tradition I've heard that emphasizes accurate pitch, and at least one I've heard that doesn't, utilizes the pentatonic scale: https://secure.wikimedia.org/wikipedia/en/wiki/Pentatonic_sc...

> Chomsky's search for universal grammar (..) has been a failure

I don't know about Chomsky, but I took a linguistics course and the universal grammar was a major part of the course. It seems you're implying there's no such thing, what makes you think so? The impression I got from the course is that the idea of "universal grammar" is universally accepted (among linguists, of course).

http://en.wikipedia.org/wiki/X-bar_theory

Ironically I don't remember Chomsky's name coming up during the course at all.

Chomsky is the first name mentioned in that article.

Yea, but I don't remember hearing about him in the course I took in the University.

Although to be honest I probably ignored names on purpose because there were so many of them.

I wasn't aware that either of these quests for universals have been a failure. My friend did a relatively recent music thesis about universals.

I'm not in either field, but a belief in universal "deep structure" has helped me learn both language + music stuff. Even if they don't exist, I'm going to stick with what helps me :D

Well, you could say music must have rhythm, yet there's music with almost no rhythm at all. You could say music is about melody, but there's lots of examples of music with no melody. And as I hinted above, there's cultures where notes don't really have definite pitches.

I can't really think of anything that universally defines "music", other than that it's sound with an aesthetically pleasing structure.

Interesting question. I think there are some. Does N hz "sound like" N*2 hz and N/2 hz across cultures? I expect the answer is yes, but I don't really know.

Have a look at http://www.youtube.com/watch?v=A13_QGMtlRE. I think Bobby McFerrin would say that there indeed are music universals.

It does. You can view any 2*N Hz signal as a N Hz signal with a doubled period. So two such signals will keep "in phase", and when you mix them it can compose a new coherent sound.

The "counter-proofs" to music universals is often just presenting an example of music from somewhere that doesn't match the universal in question.

Counter-example don't disprove trends, though, and there are certainly trends (I think "universals" is just not quite the right word).

One of the music theory things it took me a while to understand is why different major keys matter. In an idealized world, one can start a scale on any frequency and move up in whole and half steps (WWHWWWH) and have a scale. So why talk about the "key of G" vs the "key of C" if all that denotes is the frequency of the note we start on (which can be shifted up or down arbitrarily to suit the range of the instrument or vocalist)? The answer lies the physics of frequencies. The notes are not exactly the same from key to key because the whole and half steps are not exactly the same width. A perfect "fifth" (e.g., C & G played together) from a frequency perspective (meaning the two frequencies that resonate together creating a harmonic one octave above the lower) has a frequency ratio of 3/2 meaning the G is 1.5x the frequency of the C. The octave has a ratio of 2 (the high C is twice the frequency of the C below it). G is 7 half steps above C and the octave is 12 half steps. So if we walk our way up the piano in fifths, after 84 half steps, we would have a note (3/2)^12 = 129.75x the original frequency. But if we do the same on the octaves, we get 2^7 = 128x the original frequency, so the note we need to make all the major fifths sound right is different from the note we need to make the octaves sound right. The two are diverging slightly. So the result is that we can tune an instrument perfectly in one key only or we can tune it in a compromise of all the keys which sounds okay over a short range but sounds worse as we try to cover a wider range. If you're interested, there's lots of good reading on the subject (google "well-tempered" or "meantone").

EDIT: I realized I assumed a key concept in there. When two notes are played together, a third is heard (the "beat" frequency). If f1 and f2 are the frequencies of the notes being played, f2 - f1 = the beat freq. An octave sounds nice because the beat disappears (2f - f = f, so the beat is the same as the lower note of the octave). Other "pleasant" chord combinations are ones in which the beat does not clash with the first two note (e.g., is an octave of one of the notes).

If you're really interested in this, I highly recommend checking out the book How Equal Temperament Ruined Harmony (and Why You Should Care) by Ross Duffin.

Almost every instrument nowdays is tuned in equal temperament. Tuning matters most for old keyboard music, as in, pre-Beethoven.

The reason keys are important is because many instruments have different sound qualities for different notes. Keys close to E minor or G major allow guitarists to get that "twangy" open string sound. You can get a richer sound tuning up, or a thinner "heavy metal" sound tuning down. Keys close to B-flat allow brass players to use more basic tones on their instruments. All singers have certain sound qualities that are only available on certain notes. "Every Breath You Take", for example, would sound different even a semitone off, because Sting's transition from his creepy baritone to his high-pitched whine happens at a very specific part of his range, and the creepy quality of his voice contrasted with the high-pitched pleas for love is one of the most important qualities of the song.

But, yeah, temperament nowdays is almost irrelevant.

You'll find that listening to music in a single key for extended periods of time can become extremely tiring. Most (not all people) need fresh tonality, or they get bored. (Obviously all of this depends on what kind/style of music you are listening to, etc., but I would wager that even if you switched from "classical" music to "pop" music and stayed in the same key, most people would find it aurally tiring).

This is great. Can anyone recommend a "DAW (Digital Audio Workstation)" for Windows? Preferably with at least a free trial version. Thanks.

Ableton Live

One really appealing thing about Ableton, if you're just getting into music, is that the UI is simple, slick, and makes sense. The other software has way too much visuals and useless UI pieces. Ableton is direct and to the point. I'm not a musician and have never used "real" hardware, so all that visual overhead in the other programs is just noise.

Reaper: http://reaper.fm/ is excellent, very cheap ($40) and has an unlimited trial. Unlimited both in time and scope, you get the full software. I use it, works great.

Reason

Reason is great, but it's not a DAW; it's a synth package. For recording, you'll want to look at Reason's companion product Record.

I personally use FL Studio/Sibelius (FLS trial won't let you save your song in an editable format, but you can export in ogg/wav/midi/mp3). It depends on what you want to do, for music production Pro Tools/Logic Pro are a must (though it's more about the instrument library and external hardware quality).

Consider looking at the See also section for a list of DAWs: http://en.wikipedia.org/wiki/Digital_Audio_Workstation#See_a...

And also one for Linux that actually works. :(

I've heard good things about Ardour http://ardour.org/ especially and also Renoise http://www.renoise.com/ but I haven't tried them personally.

If you're a programmer, you might be more interested in Pure Data (http://puredata.info/) or cSound (http://csound.sourceforge.net/). Both are free.

There's also Renoise (http://www.renoise.com/) which is inspired by old school mod trackers. There's a free demo, and the full version is really cheap.

In addition to (and duplicating some of) the other recommendations:

Sony ACID (I use ACID Pro extensively, free trial, free lite version)

Ableton Live

FL Studio

energyXT (Linux and Mac versions available)

Other stuff to check out: console.jp, Audiomulch

Don't overlook Audacity. I'm surprised no one has mentioned it:

http://audacity.sourceforge.net/

Free/open source, for Windows, OS X, and Linux.

Overall I'm not a fan, but I come from a background in more complex/full-featured DAW's like Logic and ProTools. I also find the UI lacking. That said, it's a great way to get off the ground when starting out with digital audio.

If anybody wants to learn some music theory and Haskell at the same time, I can warmly recommend this:

http://cs.lth.se/english/course/edan40_functional_programmin...

I hope the author turns this into a series, introducing additional theory. When I was first learning basic music theory, it was either all text or text along with notation. I took lesson on snare drum when I was younger, so I can read rhythms fine but never bothered to learn to read the pitches correctly. When I started playing guitar and piano, having something with embedded content and "piano roll" images would have helped immensely.

"To write a simple melody in ‘C’" has to be the singe most important sentence in the whole text.

If you liked the Axis of Awesome’s four-chord medley, you’ll love the Pachelbel Rant: http://www.youtube.com/watch?v=JdxkVQy7QLM

on a similar note (and because there's some great links being posted here), this video by walter lewin covers the physics of sound and how it relates to music, it could be good secondary material for someone learning about music theory:

http://mitworld.mit.edu/video/168

what's great is that it's a serious physics lecture, but designed for kids, and there's plenty of funky experiments within the one hour.

If you want to go beyond the basics, I found this book invaluable:

http://www.maths.abdn.ac.uk/~bensondj/html/maths-music.html

I really love the idea behind this article, but I didn't like the execution. I was confused and intimidated after the "scales" section (and that's the first part).

Also, I don't know what the difference between a key, note and a few other words mean.

Trying to be constructive, I hope the article gets edited because I'm genuinely interested in learning these things.

It's only somewhat related, but This Week's Finds in Mathematical Physics #234 discusses some of the math behind music theory. It's a nice article if you're familiar with basic group theory. http://math.ucr.edu/home/baez/week234.html

This is so white! lol I can relate because it's how I first approached music, but most mature musicians in the Western world begin with rhythm, yet there is no mention of rhythm in this article.

Rhythm is our soul, get some soul, crackers!

I would call this article "Songwriting for Beginners" as there is very little discussion of music theory in it.

This is cool, but I am kind of disappointed that you put the chords into inversions without explaining what you were doing.

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