Introduction to Music Theory

Musical keys start on a named note and go up following a pattern. •••

Music theory is a system for organizing how we think and work with music. It gives us vocabulary for working together with others and for documenting music. The structures (and rules) of western music theory do limit us musically, but all endeavors are encouraged by having rules to work with.

Western music has been very successful because it works within a flexible set of structures from which many kinds of music can be written that speak to many many parts of the human experience across many cultures.

However, systems of music theory other than western music also exist. They enable types of music that can be substantially different. They will share some aspects with western music theory, but they are a different set of rules.

Some statements in this theory introduction aren't always or strictly true, but the general information is close enough for introductory purposes.

Scales and Names

Every musical key has 7 notes that go up from the first note. The 8th note following it sounds similar to the first one although it is higher. It is an octave up.

That 8th note also has the same name as the 1st because the notes going up (or going down) repeat in a cycle. All these notes together are called a scale. A scale is a set of notes that all sound good together.

The notes have multiple sets of names, each used for different purposes.

The most commonly used set of names is fixed to pitch. (The pitch is the vibration frequency of the note.) These note names use alphabet letters A - G. In a quirk of history, the most common, most simple scale starts with C. It goes C D E F G A B (and back to) C.

There is a singable set of names which (going up) are Do Re Mi Fa Sol La Ti (and back to) Do. With these names, the first note in a scale is always called Do, regardless what pitch it starts with.

There is numbered names starting at 1 for the first note of the scale, and usually these are represented by Roman numerals - so I II III IV V VI VII (and back to) I. (These names are very commonly used with chords.)

Scales and Keys

The notes of the scale starting with C are the notes of the key of C. The musical key defines the set of notes in it, and the scale is those notes played in a sequence together.

The musical key of C (major) is played on a piano with all the white bars you press to play notes. These bars are also called keys, although they are piano keys and are not the musical keys just mentioned. Note, however, that there also are black piano keys. The black piano keys play notes that are not in the musical key of C major.

However, if you play ALL of the notes in sequence (both black and white keys) you get a different kind of scale. It is called a chromatic scale. It has no designated starting or end note. (Within an octave range there are 12 unique notes in this scale.)

The scales that have letter names (like C major) have a pattern of skipping some of the notes in the chromatic scale, simply because the ones that are played are ones that sound best together. You can observe on the piano that on the white keys the pattern goes skip skip step skip skip skip step (back to the octave note).

Adjacent notes are called half steps and when you skip one note, that is called a whole step. On a guitar each fret is a half step.

If you were to start your scale on a different letter note name, you would play the same pattern of skips and steps, but to do that you would need to make use of some black keys instead of white keys.

The notes that are black keys on the piano are given names related to their nearest white key. So the black key above/after C is called C sharp (C#). Since the note name of the white key above it is called D, that same black key note can also be called D flat (D♭ or sometimes written as Db). So, this black key is called C# or D♭ depending on the context. ••• This dual naming pattern continues for all the other black key notes, so they all have two names. In any one musical key, the choice of the names that are used is either just sharp names or only flat names and is by established convention.

This naming of notes by letter with sharps and flats is a confusing aspect of music. Unfortunately, therefore, it also is an impediment to many people.

I believe this system is part of an abstraction that was developed historically to fit more notes on a page of sheet music. I am unconvinced the abstraction is a holistic benefit, but there it is. It is a matter that requires patience and practice to learn.

Keys other than C major have either some sharps or flats in them.

Major and Minor

The spacing of notes from each other is called an interval. (In general these have a somewhat complicated set of historically-established names.)

The most important interval in a major scale is between the I and III notes. The interval sound of these notes gives the scale a musically happy feel. It is called a major interval, and this one is 4 half-steps.

However, if this interval is instead made 3 half-steps it is called a minor interval. It changes the scale to give it what many people consider to be a pensive or sad feel. This new scale is called a minor scale, and the musical key is called a minor key.

Chords

Chords are notes that are usually played all together and which sound especially good together. They also have patterns in the way they are formed. The most common chord is called a major chord. It is a note, the note 4 half steps above, and the note 3 half-steps above that. A major chord can be played in any (major) key starting with the I or IV or V note.

If starting with the I note it is called the I chord. Play also the III and V notes. Using the singing names, this is Do Mi Sol.
If starting with the IV note it is called the IV chord. Play also the VI and I notes. This is Fa La Do.
If starting with the V note it is called the V chord. Play also the VII and II notes. This is Sol Ti Re.

Playing these notes on the piano as described and with one hand, you could keep the same hand shape and move the hand to the notes you want to play.

However, the order of notes in chords can be rearranged as long as the same names are played all together. The bottom note can be leap-frogged over and made the highest note (in the octave above). (This is called a first inversion.) Likewise the second note could also be moved up an octave. (This is called the chord’s second inversion.)

Chord inversions are done at will and for convenience. They also give the chord a slightly different flavor.

The way to play these three chords on the piano with a minimum of hand repositioning is by inversions. For instance play the basic I chord, then the IV chord first inversion, then the V chord second inversion down an octave. (This is difficult to describe clearly, but is easily shown at a piano.) The hand will stay in place and only stretch slightly up and down for the IV and V chords.
On a guitar, inversions are also used to minimize hand movement along the neck. This is done by being built in to the standard chord shapes.
From the I chord, the IV and V chords only change two notes. They each share a note with the I chord, and this connects them closely to the I chord.

It turns out that by using the I, the IV and the V chords you can accompany most songs. The chords flow very naturally together in that sequence. This is called a chord progression. The V chord is noted to “want” to go back to the I chord. And the I chord has a very “home” feel in the key.

A chord’s I - III interval can be changed to a minor interval. It will then be a minor chord. For minor chords the pattern is a note, the note 3 half steps above, and the note 4 half-steps above that. The I - V interval is the same for major and minor chords; it is only the III note's interval that changes.

Some minor chords occur naturally in major keys. When a chord is minor, this is indicated by writing the number for it with lowercase letters. The vi, ii and iii chords are all minor in a major scale. Their likeliness of being used is in that order.

The next most useful chord is the one starting at the VI note (the vi chord). Adding this chord covers the accompaniment needs of almost all songs.

Of course chords can be played from all the notes in the scale. The other chords are used more rarely. They can add interest, but usually we can do without them.

Optional: Why these notes?

These things are basics of western music theory.

However, why are there these notes? Why does a chromatic scale have 12 notes, and not some other count of notes? It is because (though it may not be obvious) these notes are built into all sounds.

All note sounds are built up from a fundamental (lowest) pure tone and harmonics of this tone. Harmonics are multiples of the fundamental. Their composition (their strengths) is what gives a sound its distinctive characteristics. And, these harmonics play the notes of western scales.

These can be demonstrated with a stringed instrument such as a cello. The note of a string can be played to make the fundamental. If touched in the middle (1/2 its length) and played, it makes an octave sound (2x the frequency of the fundamental). If touched 1/3 along it length and played (3x pitch), it makes the V note sound. 1/5 its length (5x) makes the III note, 9x: the II note, 11x: the IV note, 13x: the VI. And so forth. (Other non-prime multiples repeat lower notes.)

So, the physical frequency of notes in a scale have ratios related to the first note. This enables the pitches to match very well with each other and is pleasing to our ears. And especially, the ratios of pitches in major chords have simple ratios to each other that are very pleasing.

People also discovered these pitches have a common factor between them - the 12th root of 2. That is, if you go up a scale of pitches increasing the pitch by this factor, you will pass through the notes that come from the harmonics (with some extra note steps between). This is the chromatic scale, and it has all its notes going up by this common factor (equal temperament). ••• Therefore, out of the chromatic scale we can make the patterns of named scales and named chords starting at any note we choose.

This is the great advantage of equal temperament tuning - that by using it you can change keys and everything still sounds good. However, there are other tunings that are optimized to specific keys. They can sound much better for the optimized keys, but then keys not optimized sound horrible!

All modern pianos and keyboards use equal temperament tuning because of its advantages. But for any one key they don't sound the best possible because with equal temperment, all keys are carefully just slightly out of tune. That is, the ratios of the notes played are not quite perfect.

Instruments that have direct control of pitch (e.g. the human voice, bowed string instruments) can be played to make the sound of the music optimally sweet. However, the level of control this requires takes great skill.