by Mark Shrime, Princeton Kindred Spirit '96
The Staves and the Clefs
In a cappella singing, you'll encounter two major clefs (a third is sometimes used, but I'll get to that): the treble clef and the bass clef (see figures 1.1 and 1.2). Most generally, sopranos and altos sing off treble clef; tenors and basses off bass clef. The clef determines the characteristics of the set of five lines and four spaces known as the staff. See figures 1.3 and 1.4 for each clef in relation to its staff, and for middle C's position on each staff.
I don't want to spend too much time on this topic, but to mention the one exception: tenors will sometimes sing off a tenor clef (figure 1.5). The 8 below this clef signifies that the note sung is actually an octave below the note written.
Other than that, if you remember where middle C is located in relation to each staff, the rest will come with practice.
Key Signatures
No work on music theory would be complete without the inclusion of the much maligned Circle of Fifths. Let me present it first and then go on to explain its usefulness:
Notice that each column in figure 1.7 begins in C major (A minor). This key has no sharps or flats--on a piano, if you play strictly in C majory, you'll use no black keys. As you add sharps, you move clockwise on the Circle of Fifths; add flats (or remove sharps), and you'll move counterclockwise.
Why is it called a Circle of Fifths? Because B is a fifth above E, which is a fifth above A, which is a fifth above D, which is a fifth above G, which is a fifth above C, which is a fifth above F, which is a fifth above Bb, and so on. (If this is confusing, that's OK. We'll talk about this later). By the way, because of the limitations of writing this on the computer, "B-flat" will be represented "Bb," etc.
Do you have to memorize this? No. (All the music teachers in the world disagree with me, but...). You don't have to memorize it, but it's definitely helpful to do so.
For much of this section, we will confine ourselves to the key of C major. Realize, however, that all of this can be generalized to any key in which you want to write.
Time Signature
Let me briefly mention what you may already know. A time signature basically sets the beat of the music and is written like a fraction without the dividing line. The numerator is the number of beats; the denominator, the length of each beat. So, a piece in 3/4 has three quarter notes per measure. 6/8 denotes a piece with six eighth notes per measure; 4/4 is four quarter notes, and is also the most common time signature. Hence, it is designated with a C.
Scales
Remember playing or singing scales? Remember not doing it? They come back to haunt... :-)
In C-major, the scale, by definition, goes from C to C:
C D E F G A B C
Or:
In any key, there are always eight notes in a scale: what makes, say, G different from C is where the scale starts and ends (on G) and the fact that, in G major, F is sharped.
Each note in the scale is called a scale degree. So, in C, C is 1 (or 8), D is 2, E is 3, etc. And the interval between the first and last C's is called an octave.
Also, because I'll use these terms interchangeably with the scale degree numbers, I'll explain them now: 1 is called tonic (or root). 3 is median. 5 is the dominant. 4 is the subdominant (makes sense, huh?). 2 is the submedian. 6 is the supermedian (which, to me, makes no sense). And 7 is the leading tone. Tonic, root, dominant, and subdominant are the most useful terms to know.
Intervals
The following section is best learned by ear, as well as by sight. So, if your browser can't play MIDI, I'd suggest printing this out and plunking it on a piano.
In an octave, there are twelve intervals (thirteen if you count unison and octave as separate). They are:
which sounds like this.
which sounds like this.
which sounds like this.
which sounds like this.
which sounds like this.
which sounds like this.
which sounds like this.
which sounds like this.
which sounds like this.
which sounds like this.
which sounds like this.
which sounds like this.
which sounds like this.
There have been arguments throughout the course of music history about the consonance (loosely translated: "nice-sounding-ness") and dissonance (loosely: "yuckiness") of each interval. I don't want to discourage historical and/or musicological inquiry, but: unison/octave, the perfect 5th, and the perfect 4th are the most consonant intervals. The minor 2nd and major 7th are the most dissonant. If you don't believe that, go back and replay the examples above.
Finally: Each interval is technically defined by the number of half-steps between the notes: unison has zero, m2 has 1, M2 has 2, m3 has 3, M3 has 4, etc.
Chords (The Basics)
This is what vocal arranging is all about.
A chord, most strictly defined, is a collection of at least three distinct notes which, when sounded together, make up one audiological entity (no, this won't be on the quiz). This definition is bent constantly, however, and the line between a chord and random-collection-of-notes is very blurry.
There are an infinite number of chords--and an entire class could be devoted to their nomenclature (if you play guitar, you've probably had to hassle with that). Let's not.
The triads we're most interested in (a three-note chord is called a triad) are: major, minor, augmented and diminished.
Major: A major triad is composed of a major third followed by a minor third. A C-major chord, then, is C-E-G, or:
.
which sounds like this.
Minor: A Minor chord consists of a minor third followed by a major third. C minor, then, is C-Eb-G, or:
,
which sounds like this.
Augmented: An augmented chord is a major third followed by a second major third. C augmented, then, is C-E-G#, or:
,
which sounds like this.
Diminished: A diminished triad is composed of a minor third followed by another minor third. C-diminished, then, is C-Eb-Gb, or:
,
which sounds like this.
In terms of nomeclature: C major = C; C minor = c or Cm; C augmented = C(aug) or C+; C diminished = C(dim) or C°
Allow me to make one final note: the C-Eb-Gb triad is exactly that... a diminished triad. A diminished chord, technically, adds another minor third to the top, making it C-Eb-Gb-Bbb:
,
which sounds like this.
This, by the way, is a very useful chord, to be discussed in later sections.
Chords in the Scale
There are only three major chords in a major key. Three chords are minor and one is diminished. In the key of C, then:
1 2 3 4 5 6 7 C d e F G a b°
(If you write out each chord, with the key signature of C in mind, you should be able to figure out why this is the case).
Notice that 1, 4, and 5 are major. These are important scale degrees. This, also, gives me an opportunity to introduce some more nomenclature: whereas scale degrees are denoted by Arabic numerals, chords are named by the corresponding Roman numerals. So, to flesh out the above diagram:
1 2 3 4 5 6 7 C d e F G a b° I ii iii IV V vi vii°
Chord Progressions
Ah, rules. Yes, much of music theory is learning the rules. Take heart, though--learn these rules so you can know how to break them. Even more encouraging: you already know many of the rules behind basic music theory. Don't believe me? OK.
What if I played this? Without even having to be told, you know the next note is this. Similarly, what if I played this? Feel unresolved? You want to hear this, instead. That final chord gives resolution to the passage.
Now, let me put names and notes to what you just heard.
The 7th scale degree is called the leading tone for the simple reason that it leads to the tonic. This is what you heard in the first example. Because V (the chord) contains the leading tone (write it out), V leads to I. This is called a cadence (Latin: closure, end), and V-I is the second strongest cadence you can play. In terms of notation, this is:
Notice the B to C resolution--the leading tone to tonic resolution. That's what your ear is hearing.
What you heard in example 2 is I-IV-V-I-V-I. The chord progression I-IV-V-1 is a simple, basic progression around which a lot can be built. It sounds like this, and once I've played it, I've firmly established myself in the key of the tonic (in this case, C). Useful, huh?
In addition, nearly every song can be broken down into I, IV, and V. Take this little ditty for example.
Louie, Louie (or one of many other songs) is simply I-I-I-IV-IV-V-V-IV-IV ad nauseam.
Why are I, IV, and V so important? Remember they're the only major chords in a major scale. Also, among them, they contain all eight notes in the scale. So, any melody can, technically, be harmonized by those three chords, provided the melody stays in the same key.
The V7 Chord
V-I is a strong cadence, but not the strongest. The V7 chord (pronounced five-seven or dominant seven), in place of plain, garden-variety V, strengthens the cadence. Here's V-I, and here's V7-1.
On paper, in the key of C, V7 is G-B-D-F, or:
Just as B always resolves up to C, F always resolves (in this context) down to E. If you'll look at a piano, you'll notice that these are the two half-steps in the C major scale. OK, so what are you hearing? This:
The arrows mark the resolutions.
Technical note: This chord is called V7 because it contains a minor seventh (from G to F) and is based on the dominant scale degree. It is not called this because it contains the 7th scale degree in the key of C. Regular old V has that.
Substitutions
Songs would get boring if all they contained was I, IV, and V. But they don't. I can be substituted for by iii and sometimes vi; IV by ii; and V by vii(dim) and I in second inversion.
The only way to convince yourself of this is to play these chords out on a piano.
Inversions
Technically, a C-major chord is C-E-G, from the bottom up. E-G-C still is C-major, but it's the first inversion thereof. G-C-E is the second inversion.
Simply put, root position is so called because the tonic (or root) is the lowest (bass) note--this is, loosely, the zero-th inversion. First inversion has the third scale degree in the bass, and second inversion, the fifth. The order of all the other notes above the bass note does not matter.
Other cadences
The plagal cadence: IV-I. Also called the Amen cadence because every hymn's Amen is this chord progression. It sounds like this.
The surprise (or deceptive) cadence: I told you that vi can substitute for I. Doing so after, say, V7 will surprise the listeners (who were expecting I)--and will allow you not to put as much finality on the passage as a V7-I cadence would. Here's I-IV-V7-I-V7-vi.