Difference between revisions of "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 understand his instrument and play with purpose and direction.

While music is technically the art of all sound, we tend to prefer music that feels logical and harmonious. Rhythm, harmony, melody, and timbre are the basic building blocks of music, providing structure and a framework that allows consistent emotional communication through music.

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. The time signature consists of a pair of numbers with a slash dividing them. The top number is the number of beats per measure, and the bottom number defines what type of note corresponds to 1 beat. Most modern music is 4/4. That's 4 beats per measure with each beat represented by a quarter note. 13/8 would indicate 13 beats per measure with an eighth note lasting 1 beat. 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 (> - ^ -). (- 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 (> - ^). 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 |> - ^ -|> - ^ -|> - ^ -| - same every measure
3/4 |> - ^|- > -|^ - >|- ^ -| - different every measure

    pattern 2
3/4 |> - ^|> - ^|> - ^|> - ^| - same every measure
4/4 |> - ^ >|- ^ > -|^ > - ^| - 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 instruments are designed to sound distinct frequencies, called pitches, which correspond to certain notes. Rather than deal with everything in absolute frequencies, note names are used to keep things from becoming complicated. 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.

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. In common Western music, there are only 12 possible notes in one octave. And most music only uses 7 of those notes in any particular musical idea. Such limited sets of notes are known as scales, which drives the harmonic possibilities. This does not mean the composer/performer is strictly limited to those fundamental frequencies. It is simply used to provide an easily-understood framework to build upon, like tempo. Later we will explore why Western music uses the 12 tones per octave.

Harmony describes both the interactions of multiple simultaneous notes (chords) as well as the sequence of different chords, which is called a chord progression. Harmony often becomes synonymous with the chords that an accompaniment instrument plays, but it's important to realize this is only a part of harmony. The interaction of all the instruments, including those playing melody as well as accompaniment, is what truly forms harmony. But while melody is concerned with every note, harmony is only concerned with larger chord changes. While a melody may have quite a few different notes per measure, generally there is only one or two perceived chords per measure. We could consider harmony slower than melody, or at least requiring greater time for our minds to perceive it.

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 significance. 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. Ranges of notes grouped by pitch are called registers.

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 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).

Some have more overtones than others. Overtones are frequencies above the fundamental at an integer multiple of the fundamental (2x, 3x, 4x ...). Like harmony, the fundamental and overtones combine to make a distinct waveform; however, since the overtone frequencies are extremely harmonic, they are often perceived as a single pitch - the pitch of the fundamental frequency. Thus, we call these overtones part of the instrument's timbre, worrying only about the fundamental frequency for harmonic and melodic purposes.

Another topic for the composer is arrangement. Arrangement describes applying some musical idea into a selection of instruments. Each instrument has a range of notes it is capable of playing, as well as their individual timbres. A composer desiring the use of a certain instrument for a certain part will compose that part within the range of the instrument. 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.

Applied to Guitar

Guitar is such a popular instrument because of its extreme versatility. It can be percussive and rhythmic. This applies not simply to strummed chords, but melodic playing and riffing as well. Picked notes have a strong attack. But even further, the guitar is not limited to playing notes - muted strums, slapping the strings, and even knocking on the guitar body all produce sounds that can be used in rhythmic contexts.

It can play rich harmonies, with up to 6 simultaneous notes. Within just one tuning, it can play nearly every conceivable chord. Don't believe me? See the chord fingerings page.

It has a large range, able to play most melodies. Melodies can be played with a variety of different expression - legato, staccato, bent notes. The guitar also has a fairly large dynamic range, and is capable of going from faint whimpers to strong accents quickly. It can also be played quickly, due to its fretted nature and multiple strings. Various techniques such as sweep picking and tapping can create jaw-dropping speed.

And it has a large variety of possible timbres. Various techniques can 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, or if you use your fingers. And then there are loads of different effects, such as compression, wah pedals, distortion, delay, reverb, modulation, pitch shifting, and synth filters, that expand even further upon this.

To truly master the guitar, you must understand the 4 basic elements of music above and know how to manipulate them through the guitar. 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.

Most Western music is based around a 12-tone selection of notes (or scale) - that is 12 distinct pitches within a frequency range of one octave. The 13th pitch is double the frequency of the first note, starting a new octave. The pitches are equidistant (on a logarithmic scale) from each other, making them "neutral" in and of themselves.

This matches the frets on the fretboard. The 12th fret is the same note as the open string, just an octave higher. Notice the 12th fret is exactly the middle of the string. All the frets between the nut and 12th fret are spaced such that each fret is ~5.946% higher-pitched than the previous fret.

These pitches are named using the letters A-G. You may notice that is only 7 letters - the other 5 can be expressed using sharp or flat symbols next to some of the letter names, covered below. It is customary to define the "A" note to a specific frequency, with the standard being A = 440 Hz. This determines the pitches of the other notes, given that they are all equidistant within an octave. Certain compositions may call for aligning the notes to different frequencies (A = 442 Hz); however, this will not change the relative pitch between notes, which is our primary concern in terms of the art of music. Whether a melody is played with A = 440 Hz or A = 442 Hz will have the same emotional impact on the listener.

Semi-tones and Whole-tones

In terms of melody, playing one tone then another is called movement - it is as if the pitch moved rather than being two distinct, unrelated pitches. The proximity between two notes in the 12-tone scale is called the distance between them. The distance between two consecutive notes is called a semi-tone (also called a half-tone or half-step). A whole-tone (also called a whole-step) is the distance of 2 semi-tones.

In general, the named notes are 1 whole-step in distance from each other. A is a whole-step from B, C is a whole-step from D, etc. The only two exceptions are B to C and E to F, which are defined as half-steps. This changes nothing about how they work - it just presents a simple naming convention for the keys of A Minor and C Major to avoid using sharps and flats.

The Chromatic Scale

The chromatic scale is the ordered set of the 12-tones:

Again, we see whole steps between most of the named notes (jumping the ♯ and ♭ notes), except B-C and E-F.

Sharps and Flats

♯ or '#' means sharp. ♭ or 'b' means flat. These terms indicate the named note is raised or lowered one semi-tone, respectively. Looking back at the chromatic scale above, we now see that either a sharped version of the note below or the flatted version of the note above fills in the gaps between the notes without such symbols.

Multiple sharps and flats can be used, and there are special symbols for double sharp and double flat . For example, A is 2 semi-tones below A. A corresponds to the same pitch as G. Similarly, G♯ is the same pitch as A♭, and B♯ is the same pitch 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 12-tone 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

If there's ever any ambiguity whether a note name means its normal version as in the chromatic scale, or a flatted or sharped version, the ♮ symbol can be used to indicate the neither sharped or flatted version. This comes in handy when we are using a key that doesn't have a natural note but we want to play the natural note. For instance, the key of C♯ contains (C♯ D♯ E♯ F♯ G♯ A♯ B♯). If I said, "play an A," this might mean play the A♯ from the scale, but if I said, "play A♮", you would know exactly what note to play.

Enharmonic Notes

Two notes are enharmonic if they have the same pitch but are spelled differently. For example, B and C♭ are enharmonic, as are B♯ and C. As noted above, notes can have multiple sharp/flat symbols, which gives us a wide variety of enharmonic notes.

• C = D = E = G♭
• C = B♯ = A♯ = G♯

A scale is a set of notes, ordered from lowest to highest pitch, typically spanning one octave. This provides a framework for melodies, as well as harmony. The most common scales are the 7-note major and minor scales, which is why we refer to note that is 2x the pitch of another note as the octave - it is the 8th note in the sequence. Scales often imply tonality - melodies and harmonies seem attracted to a certain note in the scale (usually the first note), called the tonic note.

The chromatic scale featured above is a special scale - it features all 12 tones that most instruments are capable of sounding, and each note is the same distance from its neighboring notes. This means it has poor tonality - the relationship between any note and the others is the same for every note of the scale. No note sounds unique, with little or no attraction to any particular note.

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).

Whole/Half Step Pattern

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

Every unique scale has its own w/h pattern that is largely responsible for its sound and tonality.

C Major and Keys

A key is a scale assigned to certain notes. The key of C Major uses the note C as the first note of the major scale.

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:

Other Major Keys

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{s} 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.

• Go listen to some music, trying to identify with each of the four basic elements of music: rhythm, harmony, melody, and timbre.
• Listen to a song while only focusing on one of the following: the melody, the drum-beat, the bass line, and accompanying chords.
• Know that the pitch 2x any pitch is its octave.
• Know that Western music is based upon the 12-tone scale - 12 equal divisions within one octave (excluding the octave itself).
• Know that the 12-tone scale is laid out as each fret on each string on the guitar, with the 12th fret being an octave of each open string.
• Be sure to know what half and whole steps are.
• Be sure to know that sharps and flats (♯ and ♭) raise or lower the pitch of the indicated note by a half-step.
• 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 start to memorize at this point is the layout of the major scale - whole whole half whole whole whole half.

• Music Theory - Diatonic Chord Progressions
• Music Theory - Minor Keys
• Modes
• Exotic Scales