Music theory

What is music?

The definition of music itself is elusive. We want to be general enough to include a wide range of styles and cultures and approaches, yet not so wide that the term "music" can mean anything, and therefore, nothing. Here are some attempts: Music is a series of tones; sound organized by humans; art-and-science; an abstract communication language; an emotional expression of the soul; made up of the elements of melody, harmony, rhythm and timbre; the created order of nature; culturally-defined psychological expression in sound.

We can pursue that last definition a bit more: culturally-defined psychological expression in sound. In Western culture, there are certain combinations of sound that have implied "meaning," though the meaning is abstract. When the musician sets up expectation and then fulfills it, the result is satisfying (though perhaps not creative). When the musician sets up expectation and then does not fulfill it, the result is humorous, or confusing, or in some other way draws attention to itself. Let’s try an experiment to see if music has some sort of meaning (purely cultural, you understand). What do each of these options "say?"

(click here to listen) File:Example 01-01.mid

What is Music Theory?

Music theory is merely a system of describing, notating and communicating about musical phenomena, nothing more. It is not "a theory" like Einstein's theory of relativity. It DOES NOT describe how music should work or what makes music work. It only describes a system or a framework by which composers, musicians, educators and laymen can communicate and understand Western Music. While there are certain, advanced elements to music theory (such as tuning and the overtone series) which have a "universal" application due to being based on the physics of vibration, the more common elements of music theory that are taught in universities apply mostly to European-based, related or influenced music and are cumbersome and often useless when trying to discuss and understand, say, Carnatic Indian Classical music or Indonesian Gamelan music.

The Chromatic Scale

Traditional western music is based on a 12 pitch system, known as the chromatic scale. Many Western instruments allow the instrumentalist to play each of these notes - for example the piano, guitar, trumpet, flute and many others. Some instruments, the harmonica or Scottish bagpipes, to name a few only contain a collection of notes in one key. We call these diatonic instruments - it's very difficult to play in the "wrong" key with a diatonic instrument, whereas a chromatic instrument can play in any key.

The chromatic scale contains all the "useful" notes that we need to make any Western music, in any key. The notes, starting from C (the white note left of a pair of black notes), are given below. The notes that fall on the black keys have two names, for a good reason, which will be explained later.

C, C#/Db, D, D#/Eb, E, F, F#/Gb, G, G#/Ab, A, A#/Bb, B, C, ...

As C has already been listed, it is a repeated note and not counted as an additional note, however it is important to remember that the scale begins to repeat at this point.

It may appear that 17 notes have been listed, but this list actually only contains 12 notes. The notes with a slash between them are “enharmonic”, meaning they represent the same sound with two different names. For example C# (C sharp) and Db (D flat) are actually the same pitch (sound) with different names. To see this, these notes both get played on the left black key of any pair on a piano.

From the twelve notes of this chromatic system the majority of western music has emerged. Just about every western scale and chord, and many non-western scales and chords, including Indian classical music and Japanese diatonic music, are based on these twelve notes.

Other Notes

There are enharmonic notes other than the ones listed here, these are as follows: Cbb(Bb), Cb(B), Cx(D), Dbb(C), Dx(E), Ebb(D), E#(F), Ex(F#), Fbb(Eb), Fb(E), Fx(G), Gbb(F), Gx(A), Abb(G), Ax(B), Bbb(A), B#(C), Bx(C#)

The symbol "x" means "Double Sharp", the symbol "bb" means "Double Flat".

The Octave

In music, independently of culture, there is a fundamental similarity between certain notes which we call the octave. The name comes from the fact that Western musical scales use 7 notes, so the eighth note is a repeat of the first one "in a different place".

What we actually mean when we say that these two distinct pitches are the same note is that they have the same tonal character, or colour. That's why there are many notes on a piano keyboard called C, and why the keys are laid out in a repeating pattern. The two pitches are the same kind of note, found in different places.

The Intervals of the Chromatic Scale

Basic Intervals

An interval is the musical distance between two pitches. The octave discussed above is an interval, it's the smallest distance between two different pitches with a common note.

Within a span of an octave there are in fact 12 unique intervals - we usually think of two as being the "same" if they differ by an octave, in the same way as two notes that differ by an octave are regarded the same.

These intervals are listed in order, beginning at the Unison and progressing up to the Octave. Note that the noun in the name refers to the position held by that note in the order dictated by the musical scale being used, while the adjective tells us how large the interval is compared to the "standard" interval of that size.

Unison: No difference. Two of the same note at the same pitch.

Minor Second: Difference of one semitone. This is seldom used, except in modal music, jazz or metal.

Major Second: Difference of two semitones. This is the first interval of the major and minor scales...

Minor Third(3), Major Third(4), Perfect Fourth(5), Augmented Fourth/Diminished Fifth/Tritone(6), Perfect Fifth(7), Minor Sixth(8), Major Sixth(9), Minor Seventh(10 - this interval is usually called dominant as opposed to minor), Major Seventh(11), and the Octave(12).

The naming conventions come from the following set of rules, which you don't need to learn, but are useful to know about at least.

• When we refer to an interval by number ("second") we usually mean the standard interval, which is major or perfect.
• The unison and octave, as well as fourth and fifth, are perfect.
• Second, third, sixth and seventh are major.
• A minor interval is smaller than its major counterpart by a semitone.
• An augmented interval is larger than its perfect/major counterpart by a semitone.
• A diminished interval is smaller than its perfect/minor counterpart by a semitone.

So for example, a minor second is a semitone compared to two semitones for the major second (see the first list above), while a diminished second is zero semitones, and agrees with the unison interval in terms of size.

We can name these intevals (except the unison, which has many notations) in a universal way, consisting of the following

[Modifying Symbol][Number],

where the symbol denotes one of diminished(°), perfect(P), augmented(+), major(M) or minor(m), and the number corresponds to the name of the interval - so 2 for second, 6 for sixth etc. Note that perfect and major notations are optional, and that diminished and augmented may be notated respectively "dim" and "aug".

These intervals are closely tied to the structure of the chromatic scale - any two adjacent notes in the scale (forgetting names just now) differ by a semitone. We can then get any interval, knowing its size, by starting on the desired note and walking, one note at a time, up the notes until we count the size of the interval. So for instance the dominant 7th of D is 10 notes up on a keyboard, or a guitar fretboard, from D, and is a C.

Compound Intervals

There is a system of naming notes past the octave, used commonly in jazz but also to an extent in modern classical and pop music, called compound intervals. These are "essentially the same" as the basic intervals, but expanded by an octave (12 semitones remember). Our naming and notational conventions carry over, but we add seven to the note number. The commonly used intervals are the odd ones (which used to be even) but we can use any interval we desire.

For example, a minor sixth (8 semitones) goes up an octave to become a minor thirteenth (now 20 semitones). Where we notate it before at m6, we now notate with m13.

Major Scale

The chromatic scale and all of the intervals contained with the chromatic scale provide a means of describing any pitch in traditional, written Western music. This generality, however, is not necessary nor helpful in many musical situations. To simplify, one often chooses to limit one's musical context to a reduced set of pitches within the chromatic scale. A very common simplification of the chromatic scale is the Major scale. In fact, the Major scale is so common in most genres of Western music that, unless otherwise specified, it is the assumed form of the scale being used.

The Major scale employs only eight of the twelve notes in the chromatic scale, since it omits the tritone and the four minor interval notes. The scale is composed of the root of the scale (unison), the Major 2nd, the Major 3rd, the Perfect 4th, the Perfect 5th, the Major 6th, and Major 7th, and the octave. It is this pattern of intervals that gives the Major scale its unique sound and it is what differentiates the Major scale from other scales (such as the Minor scale).

As an example, if we choose C to be the root, the Major scale would be C, D, E, F, G, A, B, C w:Major_scale Listen ^source

Another way to describe the Major scale is to describe the "steps" between each note of the scale. Using this language, the distance from one note to the next in a chromatic scale is defined to be a "half step". By extension, a "whole step" is equal to an interval equal to two "half steps", or two notes on the chromatic scale. Another common description is to use the words "tone" instead of "whole step" and "semitone" rather than "half step". Expressed in terms of "half steps" (H) and "whole steps" (W), the Major scale can be described as WWHWWWH. It can also be expressed by using (T) for "tone" and (s) for "semitone". These ways of describing the Major scale are completely equivalent to using the interval names as employed earlier.

One creates a Major scale by first choosing a certain pitch as the starting point, or "root". Because it started on "C", the C Major scale was shown as an example above. Other major scales can be created by starting on other notes and then by following the pattern of WWHWWWH from that root. Any note from the chromatic scale can be used as the root of a Major scale.

Some major scales are redundant in the sense that they sound the same as their enharmonic counterparts (e.g. Gb-major sounds the same as F#-major). Some redundancies are more common while others are not. Generally, if one has to go beyond the use of single sharps or flats, then one has created a redundant scale which can be more simply expressed (e.g. Gbb-major: Gbb, Abb, Bbb, Cbb, Dbb, Ebb, Fb, Gbb is redundant compared to F-major: F, G, A, Bb, C, D, E, F).

Minor Scale

The minor scale is derived from the sixth mode of the major scale, (the aeolian mode). Like the Major scale, the Minor scale employs only 8 notes from the chromatic scale. The Minor scale is generally differentiated from the Major scale by the pitch of the third note of the scale -- the Minor scale employs the minor 3rd while the Major scale employs the major 3rd. The rest of the notes in the Minor scale vary depending upon which "flavor" of minor scale being used. There are generally three permutations of the 'minor scale', which are described below:

The 'Natural' Minor

This is exactly the same as the aeolian mode, and can be represented by the pattern WHWWHWW (where W represents whole-steps and H half-steps). The descending melodic minor scale also follows this pattern. With A as the root the scale is formed thus.

A B C D E F G (A')

The Harmonic Minor

For the purposes of musical composition, from (approximately) the late 1500s, the harmonic minor scale came into use in order to produce more satisfying chord progressions (in order to better emphasize a stronger dominant-tonic relationship). It is the same as the 'natural' minor scale, but the seventh degree is raised by one half step, and can be represented thus, WHWWH(W+H)H. Note the large Whole+Half Step (3 semitone) jump between the 6th and 7th note of the scale.

When A is the root, the scale runs

A B C D E F G# (A')

It is in some ways an amalgamation of the final two steps of the major scale and the aeolian mode, giving the seventh degree a inevitable 'drive' towards the root (this raised seventh is known as the leading-note). When writing works in harmony (i.e. in two or more parts), most composers prefer not to use this scale in the outer (more prominent) voices (melody and bass), writing for solo voice or melody instrument due to the awkwardness of the leap between the sixth and seventh degrees (an interval of an augmented second). For this purpose the melodic minor scale is often employed:

The Melodic Minor

Due to the above mentioned 'unattractiveness' to the ear of the harmonic minor scale, the melodic minor is used foremost in harmonic writing, in the most prominent, outer parts i.e. the melody line (usually the soprano in four part writing) and the bass. It has two forms, ascending and descending, which are used respectively according to rise and fall of the melody. In traditional theory and practice, the descending scale is the same as the aeolian mode, and can be expressed thus WWHWWHW, or where the root is A:

A' G F E D C B (A)

The ascending scale is close to the aeolian mode, but the sixth and seventh degrees are raised, giving the pattern WHWWWWH, i.e. where the root of the scale is A:

A B C D E F# G# (A')

In contemporary styles of music, such as jazz, the ascending version of the melodic minor scale is used exclusively.

w:Minor_scale

Modes

Modes are different scales produced using any tone in a scale pattern as a starting point. For example: let us begin with the diatonic major scale in the key of C. In the key of C, the notes we have available are C,D,E,F,G,A,and B. Without altering any of those notes try sounding a scale beginning with D. We come up with D,E,F,G,A,B, and C. This is a totally different mode. If we start with the E note we come up with E,F,G,A,B,C, and D. In this way we can create a total of seven different modes. When we use C as the first note (tonic) the mode is called Ionian. When the tonic is D the mode created is called Dorian. If the tonic is E we build the Phrygian mode. With F as the tonic the mode is called Lydian. When G is the tonic the mode is called Mixolydian. When we use A as the tonic we have the mode called Aolian. And finally, the last mode is called Locrian and the tonic is B. The natural minor scale is actually the Aolian mode while the Major scale is the Ionian mode. These are the two most popular modes. The aolian mode is called the relative minor to the Ionian mode, which in turn is called the relative major to the aolian mode.

Mode	Tonic relative to major scale	White note	Interval sequence
Ionian	I	C	T-T-s-T-T-T-s
Dorian	II	D	T-s-T-T-T-s-T
Phrygian	III	E	s-T-T-T-s-T-T
Lydian	IV	F	T-T-T-s-T-T-s
Mixolydian	V	G	T-T-s-T-T-s-T
Aeolian	VI	A	T-s-T-T-s-T-T
Locrian	VII	B	s-T-T-s-T-T-T

While all of these modes have the same repeating pattern of WWHWWWH, each mode has slightly different intervals. For example, in Dorian mode the steps are WHWWWHW.

We can also create seven modes using the melodic minor pattern and seven more using the harmonic minor pattern. Many of these modes can be found in different folk and classical musics of the world as well as in jazz.

Chords

Chords: three or more notes sounded at the same time. They are named based on the intervals they contain relative to the root. The convention for naming the intervals is based on the major scale. For example 1, 3, 5 means the chord contains the root, the third note of the major scale and the fifth note of the major scale. 1, b3, 5 means the chord contains the root, a flat third and a fifth.

Some chord formulas for triads are as follows:

Chord type	Formula	Example in C
Major Chord	1 3 5	C E G
Minor Chord	1 b3 5	C Eb G
Diminished Chord	1 b3 b5	C Eb Gb
Augmented Chord	1 3 #5	C E G#
Major b5 Chord	1 3 b5	C E Gb
Minor #5 Chord	1 b3 #5	C Eb G#

Some Examples of Chord Formulae for 7th Chords

Chord type	Formula	Example in C
Major 7th	1 3 5 7	C E G B
Dominant 7th	1 3 5 b7	C E G Bb
Minor 7th	1 b3 5 b7	C Eb G Bb
Minor Major 7th	1 b3 5 7	C Eb G B
Half-Diminished 7th	1 b3 b5 b7	C Eb Gb Bb
Fully-Diminished 7th	1 b3 b5 bb7	C Eb Gb Bbb

w:Chord_(music)

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