[icarus_drowning]

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.

[hasenj]

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.

[ThomPete]

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-...

[topynate]

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!

[bmurphy]

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

[ThomPete]

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

[te_chris]

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

[ThomPete]

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

[mmaunder]

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.

[eftpotrm]

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.)

[gbog]

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.

[ThomPete]

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

[hasenj]

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.

[ThomPete]

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.

[gtani]

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.

[ThomPete]

Remember to check out Jaco Pastorious then!

[mycroftiv]

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.

[alexophile]

>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.

[fab13n]

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.

[icarus_drowning]

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.

[nitrogen]

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?"

[nandemo]

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.

[kbutler]

> To provide context for non-technical readers,

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

[zwieback]

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.

[defroost]

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.

[presidentender]

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.

[SwellJoe]

"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).

[pessimizer]

Depends on which way you're counting.

[SwellJoe]

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.

[nollidge]

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.

[presidentender]

I am an idiot.

[zck]

>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.

[eftpotrm]

> 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.

[hernan7]

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.

[eftpotrm]

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.

[jtheory]

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. :)