Okay, it occurred to me that I would probably have regular recourse to a couple more music-theoretical ideas, so I should just go ahead and get them out of the way now.
Relative and parallel minor
I mentioned in my last post that the natural-minor scale is a permutation of the major scale -- the major scale begun on the sixth scale degree and wrapped around on itself. That means that for any given major key -- C, E, B-flat -- there is a minor key that uses all the same notes. On the piano, the C-major scale uses all white keys; so does the natural A-minor scale. The E-major scale uses black keys at F-sharp, G-sharp, C-sharp, and D-sharp; so does the natural C#-minor scale. Etc.
If you read the section on whole and half-steps carefully, you will have noticed that the minor scale that shares all its notes with a given major scale begins a minor third down from the first note of the major scale. A is a minor third down from C; C# is a minor third down from E. The minor scale that shares all its notes with a given major scale is called the relative minor of the major scale; the major scale, naturally, is the relative major of the minor.
But of course, you can build a minor scale on any note, just as you can build a major scale on any note. You just have to make sure to follow the pattern of whole and half-steps we established last time:
WHWWHWW
So you can build a minor scale that starts on C or E, too. But those scales will use different notes than the major scales starting on the same notes and, perforce, different notes than the major scales' relative minors, too. On the piano, the minor scale built on C uses black keys at E-flat, A-flat, and B-flat; the minor scale built on E uses only one black key -- at F#. What are the relative majors of C-minor and E-minor? Count up a minor third from the first note of each scale (C and E); answer below.
The minor scale that begins on the same note as a given major scale is called the parallel minor. The major scale that begins on the same note as a minor scale is, of course, the parallel major.
Chords
I want to say at least a little about harmony (chords). As I mentioned in my first post on music theory, a chord is a set of notes played simultaneously. Any set of notes can constitute a chord, but in classical music of the classical period (not the pleonasm it seems, pending some better term than “classical music”), and in the vast majority of pop music, the chords that predominate are what used to be called “common chords” -- the major and minor triads. Technically, any chord with three notes is a triad, but musicians generally use the word to denote three-note chords constructed from stacked thirds.
By “stacked thirds” I mean that the triad’s second note is a third above its first note, and its third note is a third above its second note. If you were paying attention to my discussion of intervals, however, you’ll recall that a third can be either major or minor, i.e., it spans either four or three half-steps. Two types of thirds give you four types of stacked-third triads, named as follows:
major third on major third: augmented triad
minor third on major third: major triad
major third on minor third: minor triad
minor third on minor third: diminished triad
Of these four types of triad, however, the major and the minor are by far the most common. If you’ve ever sat down to learn a couple chords on the guitar, you were probably learning to play major triads, with possibly a few minor triads thrown in. If you can play “Heart and Soul” on the piano, you can play a few major triads. Etc.
Qualitatively, major triads partake of the brightness of the major scale; minor triads partake of the melancholy or ominousness of the minor scale. If you know any pop songs that have a kind of spooky or gloomy feel to them, they probably feature a lot of minor triads.
There are seven notes in the major scale, so there are seven natural triads in any major key. (For instance, the natural triad built on the first scale degree would consist of the notes 1, 3, and 5; the triad built on the third scale degree would consist of the notes 3, 5, and 7.) Of the seven natural triads in a major key, three are major triads, three are minor triads, and one is a diminished triad.
The three natural major triads are the ones built on the 1st, 4th, and 5th scale degrees. The triad built on the first scale degree is known as the tonic, and it’s kind of the “home base” for the key: most pop songs that are written in a single key probably start on the tonic, and almost all of them end on the tonic. The chords built on the 4th and 5th scale degrees are called the subdominant and dominant, respectively. As their names imply, they are very closely related to the tonic. If you’ve ever heard the term “three-chord pop song”, the three chords in question are the tonic, dominant, and subdominant.
The natural triads built on the 2nd, 3rd, and 6th scale degrees are minor triads. That means that a major triad built on one of those scale degrees perforce takes you into a different key (or at least into a different mode).
Finally, I’ll just mention that the next most common chords after the major and minor triads also consist of stacked thirds; it’s just that the stacks keep getting higher. A seventh chord, for instance, consists of a triad with another third stacked on top of it. (The second note of the chord is a third above the first note; the third note is a fifth above the first note; and the fourth note is a seventh above the first note, hence the chord’s name.) A ninth chord consists of a seventh with another third stacked on top of it. Etc. Sevenths are very common: in any given key, the seventh chord built on the fifth scale degree -- the dominant seventh -- is almost as common as the natural major chords. Again, if you’ve ever fooled around with the basic chord shapes on a guitar, you probably learned a couple dominant sevenths.
Answer key: the relative major of C minor is E-flat major; the relative major of E minor is G major.
Showing posts with label Music theory. Show all posts
Showing posts with label Music theory. Show all posts
Wednesday, August 8, 2007
Monday, July 23, 2007
Music primer, part two
Half-steps and whole steps
As I mentioned in my last post, the major scale has seven notes in it: if you start on middle C and play up the keyboard, you'll play a total of seven notes before you reach the next C. As I also mentioned in my last post, you will also skip five black keys.
Each of those black keys lies between two white keys. But obviously, if you have five black keys distributed among seven white keys, there are a few white keys that don't have black keys between them. The relationship between adjacent white keys that aren't separated by a black key is different from the relationship between adjacent white keys that are. Adjacent white keys separated by a black key are a whole step apart. Adjacent white keys that aren't separated by a black key are a half-step apart.
The difference between the vibrational frequencies of notes a whole step apart is greater than the difference between the vibrational frequencies of notes a half-step apart. As you might imagine, there is a sense in which the distance between notes a whole step apart is twice that of notes a half-step apart. But it's a rather technical sense that I don't want to get into here. (If you're interested in reading more on the subject, you might start with this Wikipedia entry.)
The relationship between whole steps and half-steps is easier to see on the neck of a guitar than on the keys of a piano. The metal frets embedded in the guitar neck mark off consecutive half-steps. To play the melodic interval of a whole step on the guitar, you have to jump across two frets; one fret will take you only a half-step away.
Finally, the distance between a white key on a piano and the black key next to it is a half-step. So you can see that the octave (eight-note span) from C to C -- on a keyboard or on a guitar -- is actually divided into 12 half-steps. On the keyboard, most of those half-steps are between white keys and black keys, but two of them -- from E to F and from B to C -- are between white keys. (There are in fact good mathematical reasons that Western music divides the octave into 12 equal half-steps.)
The major scale revisited
Armed with the notion of half-steps and whole steps, we can make a little better sense of the notion of a major key.
Play up the major scale from middle C to the C above it (all white notes). There's a black key between C and D, so the first step of the scale is a whole step. Same with D to E. But there's no black key between E and F, so that's a half-step (can you hear the difference?). Whole step to G, whole step to A, whole step to B -- then a half-step back to C. So the pattern of whole and half-steps that gives you a major scale is
WWHWWWH.
That's why you need black keys if you start your major scale on any note other than C. Start on D. Your first whole step takes you to E. But E to F is only a half-step, so your second whole step takes you to F-sharp. Then comes a half-step: G. A, B, no problem -- but now you've found the other white-note half-step, B to C. So your next note has to be C-sharp, not C. And a last half-step will bring us back to do.
Make sense?
The same procedure, of course, applies to the neck of the guitar. You can start your scale on any fret you want. The next note will be two frets (a whole step) up. The one after that will be two more frets up. But the one after that (the first half-step) will be only one fret up. Etc.
The procedure works in exactly the same way no matter what fret you begin on. That's why pop guitarists tend to be less clear on the theoretical differences between keys than pianists: changing key on the guitar is just a matter of starting the same pattern on a different fret; each key on the piano has its own distinctive pattern.
Intervals revisited
The concept of whole and half-steps also lets me clarify some distinctions I elided in my last post. I mentioned that in any given major scale (I hope that the principle of the major scale is now clear enough to you that I can stop using C major as a reference point; C is, after all, just one of 12 major scales, none of which should, in principle, be privileged over any other), the distance from 1 to 6 is a sixth. The distance from 3 to the 1 above it is also a sixth. But they're not the same sixth. The sixth from 1 to 6 is a major sixth; that means there are nine half-steps from 1 to 6. But there are only eight half-steps from 3 to 1, making it a minor sixth. Here's the mapping of total half-steps spanned to intervals:
1: minor second
2: major second
3: minor third
4: major third
5: perfect fourth
6: augmented fourth/diminished fifth
7: perfect fifth
8: minor sixth
9: major sixth
10: minor seventh
11: major seventh
The interval of the diminished fifth (6 half-steps) is commonly called the tritone, or less commonly, the diabolus in musica. For a long time, it was considered a gross dissonance, to be avoided. In the 20th century, it was to some extent rehabilitated, but melodies that emphasize tritones can still sound sharp and spiky to the modern ear.
Other scales
So the major scale goes WWHWWWH. But you could, if you wanted, make your own scale out of some random sequence of whole and half-steps -- WHHWWHHW, or whatever. Twentieth-century jazz and classical composers experimented widely with the whole-tone scale (WWWWWW) and the octatonic scale (WHWHWHWH), but by far the most common scale other than the major is, unsurprisingly, the minor.
The minor scale
The basic minor-scale pattern is WHWWHWW. (It has variants, but I'm not going to get into them.) The distinctive thing about it is that the interval from 1 to 3 is not a major third; it's a minor third, the interval between "dead" and "and" in the schoolyard incantation "pray for the dead, and the dead will pray for you". Music written in minor keys tends to have a more melancholy, or brooding, or ominous, or menacing feel than music written in major keys: recall Nigel Tufnel's sage observation that D minor is "the saddest of all keys." Play any peppy tune you know on the keyboard with the third scale degree knocked down a half-step, and it will come out much less peppy*. The Christmas hymn "O Come, O Come, Emmanuel" spends a lot of time in a minor key -- as does Britney Spears's "Oops I Did It Again". Both songs occasionally slip into major keys, however, for reasons that I hope will come clear in the next section.
The modes
Take a look at the minor-scale pattern of whole and half-steps. The minor scale, like the major scale, starts over again at the octave. So two octaves of the minor scale will look like this:
WHWWHWWWHWWHWW
Trace out the eight-note pattern beginning on the third scale degree of the minor scale instead of the first. That is, knock off the first two and the last five letters:
WWHWWWH
Look familiar? Yes! It's the major scale! The minor scale is just the major scale begun on a different scale degree and wrapped around on itself. The converse is also true: the minor scale is the major scale begun on a different scale degree and wrapped around on itself.
Another way to say the same thing is, if you play an A on the piano, and play up the next seven white keys, you will have played the minor scale. (The white keys give you the major scale only if you start on C; they give you the minor scale only if you start on A.)
Note that starting the major scale on a different scale degree and wrapping it around will not give you the whole-tone or the octatonic scales: they have fundamentally different patterns (the whole-tone scale has no half-steps at all, so of course it can't give you the major scale). But if there are seven notes in the major scale, there must, perforce, be seven different "wraparound" scales (2 to 2, 3 to 3, 4 to 4, etc.). These wraparound scales are called modes. Two of them -- 1 to 1 and 6 to 6 -- are our familiar major and minor scales. Of the remaining five, three have minor thirds between 1 and 3, and two have major thirds between 1 and 3. The ones with minor thirds partake of the minor-scale melancholy; but the ones with major thirds have distinctive flavors all their own, and it's on those two that I will concentrate in this blog.
The two major-third modes (other than the major scale) are the lydian and the mixolydian. These are the scales that arise when you start on F and G, respectively, and play up the next seven white keys. They are also the modes that follow the following permutations of the major-scale sequence of whole and half-steps:
lydian: WWWHWWH
mixolydian: WWHWWHW
Each scale differs from the major scale in only one respect. The lydian mode has a raised fourth degree relative to the major scale. That is, in the lydian mode, 4 is a half-step higher than the 4 of the major scale. This makes the interval between 1 and 4 a tritone, which gives lydian melodies a piquant sound. The mixolydian mode has a lowered seventh degree relative to the major scale, a similarly fateful alteration. In the major scale, you'll recall, 7 is only a half-step below 1. That close proximity gives the 7 a feeling of kind of leaning toward the 1. It's hard to describe but very easy to hear -- it's the sense in which it instinctively brings us back to do. Widening that interval removes that leaning feeling, which drastically changes the color of the scale.
Because all the modes consist of the major scale wrapped around on itself, it requires a certain amount of effort on the part of the composer to keep modal melodies from simply drifting back into the major: our ears, conditioned by so much major-key music (and possibly predisposed by evolutionary adaptations), tend to pull as back to the familiar (or perhaps the instinctive).
Okay, I think that's gonna do it. I may want to say more about harmony at some later point, but then again, I may not. The distinction between different keys may be as much of a harmonic distinction as I'm going to need to make.
* I'm sure that the popular Boston band the Dresden Dolls has some tunes in minor keys. I don't really know their music, but years ago, when Amanda Palmer was still busking in Harvard Square as the 12-foot bride, I saw her play some of her songs, solo, and without makeup or carved eyebrows, at the original Zeitgeist Gallery on Broadway in Cambridge. After she'd played about four or five songs in a row in minor keys, I yelled, "Play something in a major key!" She thought for a minute and said, "Hm, I don't think I've written anything in a major key since I was 17," and I said, "Back when you could still believe in major keys."
As I mentioned in my last post, the major scale has seven notes in it: if you start on middle C and play up the keyboard, you'll play a total of seven notes before you reach the next C. As I also mentioned in my last post, you will also skip five black keys.
Each of those black keys lies between two white keys. But obviously, if you have five black keys distributed among seven white keys, there are a few white keys that don't have black keys between them. The relationship between adjacent white keys that aren't separated by a black key is different from the relationship between adjacent white keys that are. Adjacent white keys separated by a black key are a whole step apart. Adjacent white keys that aren't separated by a black key are a half-step apart.
The difference between the vibrational frequencies of notes a whole step apart is greater than the difference between the vibrational frequencies of notes a half-step apart. As you might imagine, there is a sense in which the distance between notes a whole step apart is twice that of notes a half-step apart. But it's a rather technical sense that I don't want to get into here. (If you're interested in reading more on the subject, you might start with this Wikipedia entry.)
The relationship between whole steps and half-steps is easier to see on the neck of a guitar than on the keys of a piano. The metal frets embedded in the guitar neck mark off consecutive half-steps. To play the melodic interval of a whole step on the guitar, you have to jump across two frets; one fret will take you only a half-step away.
Finally, the distance between a white key on a piano and the black key next to it is a half-step. So you can see that the octave (eight-note span) from C to C -- on a keyboard or on a guitar -- is actually divided into 12 half-steps. On the keyboard, most of those half-steps are between white keys and black keys, but two of them -- from E to F and from B to C -- are between white keys. (There are in fact good mathematical reasons that Western music divides the octave into 12 equal half-steps.)
The major scale revisited
Armed with the notion of half-steps and whole steps, we can make a little better sense of the notion of a major key.
Play up the major scale from middle C to the C above it (all white notes). There's a black key between C and D, so the first step of the scale is a whole step. Same with D to E. But there's no black key between E and F, so that's a half-step (can you hear the difference?). Whole step to G, whole step to A, whole step to B -- then a half-step back to C. So the pattern of whole and half-steps that gives you a major scale is
WWHWWWH.
That's why you need black keys if you start your major scale on any note other than C. Start on D. Your first whole step takes you to E. But E to F is only a half-step, so your second whole step takes you to F-sharp. Then comes a half-step: G. A, B, no problem -- but now you've found the other white-note half-step, B to C. So your next note has to be C-sharp, not C. And a last half-step will bring us back to do.
Make sense?
The same procedure, of course, applies to the neck of the guitar. You can start your scale on any fret you want. The next note will be two frets (a whole step) up. The one after that will be two more frets up. But the one after that (the first half-step) will be only one fret up. Etc.
The procedure works in exactly the same way no matter what fret you begin on. That's why pop guitarists tend to be less clear on the theoretical differences between keys than pianists: changing key on the guitar is just a matter of starting the same pattern on a different fret; each key on the piano has its own distinctive pattern.
Intervals revisited
The concept of whole and half-steps also lets me clarify some distinctions I elided in my last post. I mentioned that in any given major scale (I hope that the principle of the major scale is now clear enough to you that I can stop using C major as a reference point; C is, after all, just one of 12 major scales, none of which should, in principle, be privileged over any other), the distance from 1 to 6 is a sixth. The distance from 3 to the 1 above it is also a sixth. But they're not the same sixth. The sixth from 1 to 6 is a major sixth; that means there are nine half-steps from 1 to 6. But there are only eight half-steps from 3 to 1, making it a minor sixth. Here's the mapping of total half-steps spanned to intervals:
1: minor second
2: major second
3: minor third
4: major third
5: perfect fourth
6: augmented fourth/diminished fifth
7: perfect fifth
8: minor sixth
9: major sixth
10: minor seventh
11: major seventh
The interval of the diminished fifth (6 half-steps) is commonly called the tritone, or less commonly, the diabolus in musica. For a long time, it was considered a gross dissonance, to be avoided. In the 20th century, it was to some extent rehabilitated, but melodies that emphasize tritones can still sound sharp and spiky to the modern ear.
Other scales
So the major scale goes WWHWWWH. But you could, if you wanted, make your own scale out of some random sequence of whole and half-steps -- WHHWWHHW, or whatever. Twentieth-century jazz and classical composers experimented widely with the whole-tone scale (WWWWWW) and the octatonic scale (WHWHWHWH), but by far the most common scale other than the major is, unsurprisingly, the minor.
The minor scale
The basic minor-scale pattern is WHWWHWW. (It has variants, but I'm not going to get into them.) The distinctive thing about it is that the interval from 1 to 3 is not a major third; it's a minor third, the interval between "dead" and "and" in the schoolyard incantation "pray for the dead, and the dead will pray for you". Music written in minor keys tends to have a more melancholy, or brooding, or ominous, or menacing feel than music written in major keys: recall Nigel Tufnel's sage observation that D minor is "the saddest of all keys." Play any peppy tune you know on the keyboard with the third scale degree knocked down a half-step, and it will come out much less peppy*. The Christmas hymn "O Come, O Come, Emmanuel" spends a lot of time in a minor key -- as does Britney Spears's "Oops I Did It Again". Both songs occasionally slip into major keys, however, for reasons that I hope will come clear in the next section.
The modes
Take a look at the minor-scale pattern of whole and half-steps. The minor scale, like the major scale, starts over again at the octave. So two octaves of the minor scale will look like this:
WHWWHWWWHWWHWW
Trace out the eight-note pattern beginning on the third scale degree of the minor scale instead of the first. That is, knock off the first two and the last five letters:
WWHWWWH
Look familiar? Yes! It's the major scale! The minor scale is just the major scale begun on a different scale degree and wrapped around on itself. The converse is also true: the minor scale is the major scale begun on a different scale degree and wrapped around on itself.
Another way to say the same thing is, if you play an A on the piano, and play up the next seven white keys, you will have played the minor scale. (The white keys give you the major scale only if you start on C; they give you the minor scale only if you start on A.)
Note that starting the major scale on a different scale degree and wrapping it around will not give you the whole-tone or the octatonic scales: they have fundamentally different patterns (the whole-tone scale has no half-steps at all, so of course it can't give you the major scale). But if there are seven notes in the major scale, there must, perforce, be seven different "wraparound" scales (2 to 2, 3 to 3, 4 to 4, etc.). These wraparound scales are called modes. Two of them -- 1 to 1 and 6 to 6 -- are our familiar major and minor scales. Of the remaining five, three have minor thirds between 1 and 3, and two have major thirds between 1 and 3. The ones with minor thirds partake of the minor-scale melancholy; but the ones with major thirds have distinctive flavors all their own, and it's on those two that I will concentrate in this blog.
The two major-third modes (other than the major scale) are the lydian and the mixolydian. These are the scales that arise when you start on F and G, respectively, and play up the next seven white keys. They are also the modes that follow the following permutations of the major-scale sequence of whole and half-steps:
lydian: WWWHWWH
mixolydian: WWHWWHW
Each scale differs from the major scale in only one respect. The lydian mode has a raised fourth degree relative to the major scale. That is, in the lydian mode, 4 is a half-step higher than the 4 of the major scale. This makes the interval between 1 and 4 a tritone, which gives lydian melodies a piquant sound. The mixolydian mode has a lowered seventh degree relative to the major scale, a similarly fateful alteration. In the major scale, you'll recall, 7 is only a half-step below 1. That close proximity gives the 7 a feeling of kind of leaning toward the 1. It's hard to describe but very easy to hear -- it's the sense in which it instinctively brings us back to do. Widening that interval removes that leaning feeling, which drastically changes the color of the scale.
Because all the modes consist of the major scale wrapped around on itself, it requires a certain amount of effort on the part of the composer to keep modal melodies from simply drifting back into the major: our ears, conditioned by so much major-key music (and possibly predisposed by evolutionary adaptations), tend to pull as back to the familiar (or perhaps the instinctive).
Okay, I think that's gonna do it. I may want to say more about harmony at some later point, but then again, I may not. The distinction between different keys may be as much of a harmonic distinction as I'm going to need to make.
* I'm sure that the popular Boston band the Dresden Dolls has some tunes in minor keys. I don't really know their music, but years ago, when Amanda Palmer was still busking in Harvard Square as the 12-foot bride, I saw her play some of her songs, solo, and without makeup or carved eyebrows, at the original Zeitgeist Gallery on Broadway in Cambridge. After she'd played about four or five songs in a row in minor keys, I yelled, "Play something in a major key!" She thought for a minute and said, "Hm, I don't think I've written anything in a major key since I was 17," and I said, "Back when you could still believe in major keys."
Monday, July 9, 2007
Music primer, part one
Before I make any music-themed posts on this blog, I want to explain a few technical terms that I expect I'll occasionally want to invoke. They're not difficult, but some readers may be unfamiliar with them or have only a vague notion of what they mean. I assume a passing familiarity with the layout of the piano keyboard. If you don't have a keyboard handy and find any of the descriptions below difficult to visualize (or "auralize"), try playing with the little Flash keyboard here. (If you don't have Macromedia Flash installed, there's also a Java piano here.)
The major scale
Most people, I think, know how to find middle C on a keyboard and know that, if you play the next seven white keys in sequence, up the keyboard, you'll spell out the do re mi scale familiar from The Sound of Music ("Do, a deer, a female deer, re, a drop of golden sun," etc.). The last note in that eight-note sequence is another C -- not middle C, but the C an octave (a span of eight notes) above middle C. That is, the do re mi scale -- a.k.a. the major scale -- has only seven notes in it; with the eighth note, you're starting the scale over again, only higher ("that will bring us back to do").
In this blog, I will refer to the notes of the major scale by number. So do is 1, re is 2, mi is 3, etc. Ti ("a drink with jam and bread") is 7, which brings us back to do, or 1.
If you play middle C, and then play the next four white keys, up the keyboard, in sequence, you'll get to G, or 5. But if you play middle C and then play the next three white keys down the keyboard, you'll also get to G, or 5. For every 1, there's a 5 above and a 5 below. There's also a 4 above and a 4 below, etc. And for every 5, there's a 1 below and a 1 above. Etc., etc.
Intervals
An interval is the distance between two notes. We call the distance from 1 to the 5 above it a fifth: the total number of white keys you have to press to get from middle C to the G above it is five. The distance from 1 to the 5 below it, however, is a fourth: the total number of white keys you have to press to get from middle C to the G below it is four. Conversely, the interval from 1 to the 4 above it is a fourth, while the interval from 1 to the 4 below it is a fifth. The interval from 1 to 6 is a sixth, from 1 to 3 is a third, etc.
What's the interval from 5 to the 3 above it (from G to E)? Well, if middle C is 1, how many white keys do you have to press to get from the 5 below middle C (G) to the 3 above it (E)? If you can't figure the answer out in your head, try actually pressing the keys, and then check your answer against the one at the end of this post.
Key
It so happens that the first line of the Christmas carol "Joy to the World" traces out the major scale -- from 1 back down to the 1 below it. Sing it to yourself: "Joy to the world, the Lord is come." You sing the word "joy" on 1, "world" on 5, "lord" on 3, and "come" on 1 again. If you play the eight white keys from the C above middle C back down to middle C in the right rhythm, you'll play the opening line of "Joy to the World."
But let's say that, instead of starting on a C, you start on the next white key above C -- i.e., D. Now, if you just play down the white keys, the tune will sound completely wrong. In order to make it sound right, you'll have to throw in some black keys -- specifically, at "to" and "lord".
If, instead, you started playing "Joy to the World" on E, you'd need four black keys to make it sound right, and if you started on B, you'd need five!
There's a fundamental principle here, one that I've found is not intuitive for nonmusicians. Of everything I've said on this page, it's the most important thing to remember (if you don't know it already): no two major scales use the same notes. If you start your major scale on C, you can use all white keys -- but that's not true for scales begun on any other note. If you start your scale on G or F, you need only one black key -- but it's not the same black key. That is, if you play "Joy to the World" starting on F, you'll need a black key at "the" -- B-flat; but if you play "Joy to the World" starting on G, you'll need your black key at "to" -- F-sharp. (Try it.)
So, a few definitions:
a melody is a set of notes played in sequence;
a chord is a set of notes played simultaneously;
music written in a particular key is music all of whose melodies and chords use the notes of a single scale.
If you play a piece that's entirely in the key of C on the piano, you'll use all white keys. If you play a piece that's entirely in the key of G, you'll use one black key: F-sharp. If you play a piece that's entirely in the key of F, you'll use one black key, but not the same black key: B-flat. Etc., etc.
If you play middle C, then play the next six notes up the keyboard (stopping just shy of the next C), you will have played seven notes total: each of those notes determines a unique major scale, so each of those notes determines a unique major key. You will also, however, have left out five black notes. Each of those notes also determines a unique major key. So there are 12 major keys total.
An experienced musician can tell from a handful of notes what key a particular piece is in. Indeed, she can tell from only three notes what key a piece is in, if they're the right three notes. For instance, there are seven different major keys that contain the note C: C, D-flat, E-flat, F, G, A-flat, and B-flat. But five of those -- the ones with "flat" in their names, plus F -- contain the note B-flat instead of the note B. So if a melody begins on C and moves to a B (not a B-flat), it is in one of only two possible keys: C or G. The C and G scales, in turn, differ by only one note: the C scale contains an F, but the G scale contains an F-sharp. So if a melody contains only three notes, and they're C, B, and F, then the melody must be in the key of C. (Note that, by contrast, if the melody contains the notes B, C, D, E, G, and A, it could be in either C or G.)
This post has taken me a lot longer to write than I anticipated, because I'm trying to be both accurate and accessible. I'll be back with more Music Theory 101 in the coming days.
Answer key: a sixth
The major scale
Most people, I think, know how to find middle C on a keyboard and know that, if you play the next seven white keys in sequence, up the keyboard, you'll spell out the do re mi scale familiar from The Sound of Music ("Do, a deer, a female deer, re, a drop of golden sun," etc.). The last note in that eight-note sequence is another C -- not middle C, but the C an octave (a span of eight notes) above middle C. That is, the do re mi scale -- a.k.a. the major scale -- has only seven notes in it; with the eighth note, you're starting the scale over again, only higher ("that will bring us back to do").
In this blog, I will refer to the notes of the major scale by number. So do is 1, re is 2, mi is 3, etc. Ti ("a drink with jam and bread") is 7, which brings us back to do, or 1.
If you play middle C, and then play the next four white keys, up the keyboard, in sequence, you'll get to G, or 5. But if you play middle C and then play the next three white keys down the keyboard, you'll also get to G, or 5. For every 1, there's a 5 above and a 5 below. There's also a 4 above and a 4 below, etc. And for every 5, there's a 1 below and a 1 above. Etc., etc.
Intervals
An interval is the distance between two notes. We call the distance from 1 to the 5 above it a fifth: the total number of white keys you have to press to get from middle C to the G above it is five. The distance from 1 to the 5 below it, however, is a fourth: the total number of white keys you have to press to get from middle C to the G below it is four. Conversely, the interval from 1 to the 4 above it is a fourth, while the interval from 1 to the 4 below it is a fifth. The interval from 1 to 6 is a sixth, from 1 to 3 is a third, etc.
What's the interval from 5 to the 3 above it (from G to E)? Well, if middle C is 1, how many white keys do you have to press to get from the 5 below middle C (G) to the 3 above it (E)? If you can't figure the answer out in your head, try actually pressing the keys, and then check your answer against the one at the end of this post.
Key
It so happens that the first line of the Christmas carol "Joy to the World" traces out the major scale -- from 1 back down to the 1 below it. Sing it to yourself: "Joy to the world, the Lord is come." You sing the word "joy" on 1, "world" on 5, "lord" on 3, and "come" on 1 again. If you play the eight white keys from the C above middle C back down to middle C in the right rhythm, you'll play the opening line of "Joy to the World."
But let's say that, instead of starting on a C, you start on the next white key above C -- i.e., D. Now, if you just play down the white keys, the tune will sound completely wrong. In order to make it sound right, you'll have to throw in some black keys -- specifically, at "to" and "lord".
If, instead, you started playing "Joy to the World" on E, you'd need four black keys to make it sound right, and if you started on B, you'd need five!
There's a fundamental principle here, one that I've found is not intuitive for nonmusicians. Of everything I've said on this page, it's the most important thing to remember (if you don't know it already): no two major scales use the same notes. If you start your major scale on C, you can use all white keys -- but that's not true for scales begun on any other note. If you start your scale on G or F, you need only one black key -- but it's not the same black key. That is, if you play "Joy to the World" starting on F, you'll need a black key at "the" -- B-flat; but if you play "Joy to the World" starting on G, you'll need your black key at "to" -- F-sharp. (Try it.)
So, a few definitions:
a melody is a set of notes played in sequence;
a chord is a set of notes played simultaneously;
music written in a particular key is music all of whose melodies and chords use the notes of a single scale.
If you play a piece that's entirely in the key of C on the piano, you'll use all white keys. If you play a piece that's entirely in the key of G, you'll use one black key: F-sharp. If you play a piece that's entirely in the key of F, you'll use one black key, but not the same black key: B-flat. Etc., etc.
If you play middle C, then play the next six notes up the keyboard (stopping just shy of the next C), you will have played seven notes total: each of those notes determines a unique major scale, so each of those notes determines a unique major key. You will also, however, have left out five black notes. Each of those notes also determines a unique major key. So there are 12 major keys total.
An experienced musician can tell from a handful of notes what key a particular piece is in. Indeed, she can tell from only three notes what key a piece is in, if they're the right three notes. For instance, there are seven different major keys that contain the note C: C, D-flat, E-flat, F, G, A-flat, and B-flat. But five of those -- the ones with "flat" in their names, plus F -- contain the note B-flat instead of the note B. So if a melody begins on C and moves to a B (not a B-flat), it is in one of only two possible keys: C or G. The C and G scales, in turn, differ by only one note: the C scale contains an F, but the G scale contains an F-sharp. So if a melody contains only three notes, and they're C, B, and F, then the melody must be in the key of C. (Note that, by contrast, if the melody contains the notes B, C, D, E, G, and A, it could be in either C or G.)
This post has taken me a lot longer to write than I anticipated, because I'm trying to be both accurate and accessible. I'll be back with more Music Theory 101 in the coming days.
Answer key: a sixth
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