Music Theory Basics
Music is the art of sound. From an objective standpoint, there is no good music or bad music, no happy music or sad music. However, music can be subjectively evaluated. Is it pleasing to listen to? Does it inspire the ideas and emotions the composer/performer sought to communicate? Thus, there are good musicians and bad ones. Good ones understand that sound has objective properties, knows how to manipulate these properties, and puts this knowledge into action. The composer must know way more than I can cover here. The performer must be able to play his instrument with the desired technique.
Music is based upon 4 main properties of sound: rhythm, harmony, melody, and timbre. It is impossible to isolate any one element in a complete vacuum.
Contents
Rhythm
Rhythm is a pattern of sound over time. This can be a single note sustained infinitely, a drum beat, dynamic accents in a melody, etc. The vast majority of compositions seek to establish some sense of order in rhythm. Thus, most songs are locked to a specific tempo and time signature. Tempo establishes how many regular intervals of time (or beats) should occur within a certain period of time, usually a minute. A common tempo is 120 beats per minute (bpm). This means there are 120 equal intervals of time per minute. Each beat will contain the standard minumum of controlled sound. For example, a drummer may play one stroke per beat, or a guitarist may strum a chord once per beat. Of course, doing the same thing every beat is boring. Master musicians know how to play "around" the beat, "off-beat", across several beats, or even subdivide a beat. But the point is that tempo provides a framework in time to create order - the listener does not feel lost, and a band or orchestra consisting of numerous instruments can simultize their playing to create a unified whole.
Time signatures describe the number of beats per measure, where each measure is basically a musical idea, although this is a very loose concept. Most modern music is 4/4. That's 4 beats per measure with each beat represented by a 1/4 note. A guitarist may play each chord for one measure, strumming each beat. A drummer may play a repeating pattern every measure, with at least one stroke per beat.
The time signature often suggests a certain meter, which is a repeating pattern of accents. Consider a common drum pattern in 4/4 - boom ssss taah ssss boom ssss taah ssss. The musical idea repeats every 4 beats, with accents on both the 1st and 3rd beats but the 3rd being a bit stronger (> x ^ x). (x is a normal hit, > is an accent, and ^ is a strong accent.) Here's a similar pattern in 3/4 - boom ssss taah boom ssss taah (> x ^). The musical idea repeats every 3 beats. We could play the first pattern in 3/4 or the 2nd in 4/4, but the pattern won't fit neatly inside each measure, appearing more complex than it actually is.
pattern 1
4/4 |> x ^ x|> x ^ x|> x ^ x| - same every measure
3/4 |> x ^|x > x|^ x >|x ^ x| - different every measure
pattern 2
3/4 |> x ^|> x ^|> x ^|> x ^| - same every measure
4/4 |> x ^ >|x ^ > x|^ > x ^| - different every measure
The meter isn't necessarily confined to 1 measure - it may last 2 or even more measures. The point is that the meter and time signature typically have a relationship where things fit neatly and logically, allowing the musician to more easily understand the music.
Harmony
Harmony is the pattern of how frequencies interact. Most natural sounds are relatively noisy - they contain a random selection of frequencies. The true definition of noise is sound with equal distribution of all audible frequencies. Consider an untuned radio or TV, which produces white noise - you cannot "zero-in" on any particular frequency, although your brain may try. Noise is chaos, and all true noise is undifferentiatable from other true noise, regardless of its source.
Conversely, a sine wave represents a single specific frequency. Again, this is more easily understood by our minds - we can recognize it easily and even recreate it vocally. Most instruments are designed to sound such distinct frequencies, called pitches, which correspond to certain notes. Harmony is concerned mostly with the interaction of multiple notes - 2 or more notes combine to form a unique waveform, which we can perceive.
Note: popular instruments do not create a pure, single frequency, but a multitude of frequencies (and noise) when trying to sound a note. However the lowest frequency produced is called the fundamental frequency and usually the strongest. The additional frequencies are "overtones" of the fundamental frequency. This is discussed further in timbre below.
When different notes are combined, they produce different waveforms. Two different notes played simultaneously is known as an interval. Three or more is known as a chord. Some intervals and chords are perceived as being more harmonic than others. This is driven by the ratio of the fundamental frequencies involved. We have already mentioned that a 4th interval is 4/3 higher than the base frequency. A 5th interval is 3/2 the base frequency. Basically, the simpler the ratio between the frequencies can be represented, the more harmonic the two notes are. The simplest ratio is an octave - which contains 2x (2/1) the original pitch.
Rather than deal with everything in absolute frequencies, note names are used to keep things from becoming complicated. Because the octave is so harmonic, it is treated harmonically equivalent. Once the octave is reached, the note names repeat, and for harmonic purposes they are treated identically. For instance, there is an "A" note at 110 HZ and another "A" at 220 HZ. Also, you have "E" at 165 HZ, and an "E" at 330 HZ. The 110-165 HZ A-E fifth interval is harmonically equivalent to the 220-330 HZ A-E fifth interval (both contain intervals with 3:2 ratios). Thus, for purely harmonic reasons, absolute frequency is not important. Only the relative frequency of one note to others is important. Between 110 HZ and 220 HZ, you have the notes A, B, C, D, E, F, and G. Between 220 HZ and 440 HZ, you have A, B, C, D, E, F, and G again. Obviously, even if the note names are the same, they will sound differently since they relate to different fundamental frequencies. However, harmonically, A is A and B is B, regardless of which octave it actually belongs to.
While the frequency spectrum is infinite, for harmonic reasons, it is dividied into octaves (n frequency to 2n frequency, like 110 HZ - 220 HZ). There are only 12 possible notes in one octave (A, A♯, B, C, C♯, D, D♯, E, F, F♯, G, G♯) although you may see them named differently (See sharps and flats below. And the most common scales only use 7 of those notes (C Major: C, D, E, F, G, A, B). This does not mean the composer/performer is strictly limited to those fundamental frequencies. It is simply used to provide a simplifying framework to build upon, like tempo. Later we will explore why Western music uses the 12 tones per octave and discuss common intervals, chords, and progressions.
Another topic for the composer is arrangement. Arrangement describes applying some musical idea into a selection of instruments. For example, if you were arranging a piece for flute, piano, and bass, you would likely have the flute play the melody, the piano playing chords, and the bass usually playing the root note of the chords. Naturally, melody is usually given a higher-pitch than the other instruments, and the root note of chords is usually played in the lowest-frequencies. We could come up with different arrangements that are harmonically equivalent; however, they would likely be less enjoyable to listen to.
Melody
Melody is very similar to harmony, but more concerned with sequences of single notes over time than with the combination of multiple notes. Again, it is very difficult to conceptualize harmony and melody as completely separate entities. Melodies are the lines to our favorite songs we sing - a melody can tend in a particular direction, finding resolution, and having its own rhythm (meter, accents). It doesn't require harmony, although harmony often gives it its context.
Again, melody can get insanely complex...so what's our simple framework? Really, it's the same frameworks as harmony and rhythm. We take a subset of all possible frequencies and give them note names, and restrict them to 12 possibilities, with only 7 being "active" for a particular key or scale. Note duration is restricted to a common set, based around beats. The big divergence from harmony is that pitch between octaves has signfigance. So, for example, if we take a common A minor ascending scale starting at A2 (110 HZ) as our melody; our last note should be A3 (220 HZ). Here is the example melody: A2, B2, C3, D3, E3, F3, G3, A3. This makes sure each note has an ascending pitch compared to the prior note's pitch. Similarly, A2, B3, C4, D5, E6, F7, G8, A9 is not the same melody, despite having all the same note names. It will sound much different to the listener.
The melody stands out from the harmony by having louder volume or by being played in higher pitches. It typically has a less uniform or more complex rhythm than the rhythm accompaniment (consider a vocal melody compared to a drum beat).
Timbre
Timbre is the quality of a particular sound. It is why a horn sounds like a horn and a violin a violin, even when playing the same notes. Musical instruments tend to focus on sounding particular frequencies, but not necessarily. For example, drums are not designed to focus as much on frequency as the general sound they create. Some instruments are noisier than others. Some have more overtones than others. Some can have a soft attack or even swell slowly louder until reaching full volume, while others might have a very noticeable, percussive attack. Some may sustain forever (synth). Some may decay immediately (sitar).
Timbre factors mainly into arrangement choices more than fundamental composition; however, at some level, composition is determined by timbre, and timbre determines what we actually hear and how it is percieved. For example, a melody designed for flute cannot be played on drums, and a drum beat cannot be played on flute. It may technically be possible, but it will lose its meaning. Similarly, each instrument has a range. A composer desiring the use of a certain instrument for a certain part will compose that part within the range of the instrument.
Applied to Guitar
Guitar is such a popular instrument because of its extreme versatility. It can be percussive and rhythmic (funk playing). It can play rich harmonies, with up to 6 simultaneous notes. It has a large range, able to play most melodies. There are a wide range of techniques to embellish traditional playing. The angle you hold the pick and where you pick the strings can affect the tone. The type of pick you use. Finger picking. And then there are loads of different effects, such as compression, volume pedals, wah pedals, distortion, delay, reverb, modulation, pitch shifting, and synth filters, that expand even further upon this. Guitar fits into band contexts as well as being sufficient for solo compositions. It can perform the work of many different instruments, reducing the size of bands, allowing such bands to play smaller and different shows.
Do Re Mi Fa So La Ti Do
We all know the sound of the common major scale: Do Re Mi Fa So La Ti Do. Really it's like a short little melody. But where did it come from? Why are the frequencies chosen what they are? These are really, really big questions. It involves some serious music history, psychoacoustics, math, and conscious design. I feel they are important to answer, but it's still too early. For now, we need to understand simply that it works. If we sing Do Re Mi Fa So La Ti, we feel the tension. Where's that final Do? Similarly, if we just sing Do Re Mi, we want to keep going to the Fa; then it feels ok to end. The tension is at least partially resolved. We can also end on the So.
The major scale and most Western music is built around a tonic or root note. Melodies tend to start or end on this note. It is the gravitational center of the musical world. Our minds are drawn towards it.
In our scale, Do is unison or octave, a 1:1 or 2:1 ratio with our root or tonic note. Fa and So are the 4th and 5th intervals with the tonic note - the most harmonic intervals other than the octave (4:3 and 3:2).
The Chromatic Scale
The chromatic scale, or 12 tone scale, is basically made by dividing the frequency range that is covered by an octave into 12 equal pieces (on a logarithmic scale). Each dividing point is a note on the scale. Since the octave note already occurs as the root note, we are left with 12 distinct note values (A, A♯, B, C, C♯, D, D♯, E, F, F♯, G, G♯). Notice that there is no B♯ or E♯. This has nothing to do with frequency - it is a convention in note naming. E - F spans the same frequency range as A - A♯.
| Note Name | A2 | A♯2 | B2 | C3 | C♯3 | D3 | D♯3 | E3 | F3 | F♯3 | G3 | G♯3 | A3 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Frequency in HZ | 110.000 | 116.541 | 123.471 | 130.813 | 138.591 | 146.832 | 155.563 | 164.814 | 174.614 | 184.997 | 195.998 | 207.652 | 220.000 |
| % higher than last pitch (freq - last)/last * 100 |
5.946 | 5.946 | 5.946 | 5.946 | 5.946 | 5.946 | 5.946 | 5.946 | 5.946 | 5.946 | 5.946 | 5.946 |
Semi-tones and Whole-tones
The "distance" from one note to the next in the chromatic scale is called a semi-tone or half-tone. So A - A♯ or E - F is one semi-tone. A whole-tone is 2 semi-tones. So A - B is a whole-tone, just as A - A♯ and A♯ - B are two semi-tones.
Sometimes whole-tones are called whole steps and semi-tones are called half steps.
Sharps and Flats
♯ or '#' means sharp. ♭ or 'b' means flat. These terms indicate the named note is raised or lowered one semi-tone. Multiple sharps and flats can be used. For example, A♭♭ is 2 semi-tones below A. A♭♭ corresponds to the same frequency as G. Similarly, G♯ is the same frequency as A♭, and B♯ is the same frequency as C. For our purposes, we are unlikely to deal with double (or more) sharps or flats. But it's important to understand what they are to remove some of the mystique from them.
We can even represent the entire chromatic scale in terms of a single note, using flats and sharps:
| A | A♯ | B | C | C♯ | D | D♯ | E | F | F♯ | G | G♯ |
| D♭♭♭♭♭ | D♭♭♭♭ | D♭♭♭ | D♭♭ | D♭ | D | D♯ | D♯♯ | D♯♯♯ | D♯♯♯♯ | D♯♯♯♯♯ | D♯♯♯♯♯♯ |
The Major Scale
The major scale is composed of the following whole/half step pattern: (w w h w w w h). So we start on the root note. We add +1 whole step to get the 2nd note, another +1 whole step for the 3rd note, +1 half step for the 4th, +1 whole step for 5th, +1 whole step for 6th, and +1 whole step for the 7th. Another +1 half step gets us to the octave of the root note (the octave is the 8th note in the common 7 note scales). Again, that's 2 whole steps, 1 half step, 3 whole steps, and another half step. Below is the chromatic scale starting on C, then the C Major scale. The h's represent half steps (semi-tones) and the w's represent whole steps. The chromatic scale consists of 12 semi-tones.
Chromatic |-h|-h|-h|-h|-h|-h|-h|-h|-h|-h|-h|-h| Scale C C# D D# E F F# G G# A A# B C Major |--w--|--w--|-h|--w--|--w--|--w--|-h| Scale C D E F G A B C
Notice how C Major has no sharp/flat notes. Again, this is just a naming convention to simplify things. C Major is usually the first key learned on any instrument. On a piano, it represents the white keys (no black keys). Some instruments are designed around C Major. Guitar, unlike piano, is very key-neutral. It is equally simple to play in C Major as any other key.
One octave of a piano from C to C is a great visualization of the key of C Major, showing clearly where the whole and half steps are:
| whole | whole | whole | ||||||||||
| C |
C♯ |
D |
D♯ |
E |
F |
F♯ |
G |
G♯ |
A |
A♯ |
B |
C |
| whole | half | whole | half | |||||||||
Each major scale has the same quality as every other. C Major will sound like C♯ Major will sound like A Major; they just start on different notes. It doesn't matter that C Major has no sharps or flats while C# Major is all sharps (C♯ D♯ E♯ F♯ G♯ A♯ B♯) and A Major has 3 sharps (A B C♯ D E F♯ G♯). What matters is the whole-tone/semi-tone relationships between notes:
|--w--|--w--|-h|--w--|--w--|--w--|-h| C D E F G A B C C# D# E# F# G# A# B# C# A B C# D E F# G# A
This explains why there is a half step between B/C and E/F unlike all the other notes which are separated by a whole step. Labeling them this way causes the key of C major to have no flats/sharps.
Analysis of the Major Scale
Notice how the major scale is really just a whole, whole, half sequence, then a single whole tone, then another whole, whole, half sequence. (w w h) w (w w h). The (w w h) sequence is called a tetrachord (actually has 4 notes), and is historically very important in the development of music. It is our Do Re Mi Fa melody from above.
Notice also how we say Do Re Mi Fa So La Ti Do, and not Do Ti La So Fa Mi Re Do. In other words, by default, we are singing the ascending version of the scale. Whether we sing it ascending or descending doesn't change the fact that these notes form the major scale. However, it does reveal a bit about the scale itself. When we sing the scale, we encounter two semi-tones. Semi-tones, by nature are the most dissonant (non-harmonic) two notes in the 12 tone scale. Notice the location of the semi-tones in the major scale. There is one between the third and fourth note in the scale, and one between the seventh and the octave. If we are singing the scale ascending, that means our seventh note will be the most dissonant and create the most tension. Remember that our tonic note is like gravity - we find the most release there. So not only is the seventh note the most dissonant note in comparison to the tonic, it is also the tonic's neighbor in the scale, and will occur directly before reaching the tonic note in the ascending scale. The seventh is often called the leading tone because it leads into the tonic.
The other semi-tone occurs between the 3rd and 4th notes. Since the 4th is quite harmonic, it makes sense that there is a semi-tone here - you can sense the resolution from the 3rd. The 5th is arguably even more harmonic than the 4th, but if we were to lead into it with a semi-tone, then our 4th would be sharp, and we would no longer have the harmonic 4th note. Also, we don't want the 5th to have a greater resolution than the root/tonic note.
We will find the major scale creates some interesting methods of tension and resolution in chord progressions later on.
Homework
Go listen to some music, trying to identify with each of the four basic elements of music above. Listen to a song while only focusing on one of the following: the melody, the drum-beat, the bass line, and accompanying chords. Sing Do Re Mi Fa So La Ti Do. Try to stop on random notes in the scale and sense the relative tension or release of tension created.
DO NOT start trying to memorize that the key of A has 3 sharps. It will not do you any good at this point. The only thing you should memorize from this is the layout of the major scale - whole whole half whole whole whole half.