Subdivision of the octave

The mind perceives pitch to be continuously variable - there are no "quanta" of pitch - but in music, out of the infinite possible pitches that could be chosen from the pitch continuum, only a limited number are used.

Usually each octave is subdivided into a small number of steps and each of these is repeated in every octave. In almost all musical cultures notes separated by an octave are regarded as somehow equivalent, so that, for the sake of consistency and simplicity, divisions in any one octave are repeated in all others. Scales in which different notes are used in different octaves, or where octaves are not found at all, are rare.

By choosing a limited number of notes the ear is given a structure that is simple enough to be understandable and whose notes are spaced apart enough to be easily heard as different. Ideally within any octave, each note is perceived to be fundamentally different from every other note - each note has a unique identity. When that identity is unique enough it allows for each note's pitch to be varied with vibrato and other decorative techniques without losing its identity and becoming confused with other notes.

The pitches used in purely melodic musics - such as classical Arabic and Indian are generally more flexible and complex than those used in the tonal harmonic music of common practice classical and popular music. Within any one scale we will often find more than seven notes and the distance between consecutive steps can be very small.

But we also find in melodic music the frequent use of both the pentatonic scale - Celtic and Asian songs, and the seven note diatonic scale - Native American and African songs. These common scales often sound very different to how they do in tonal harmonic music, through generic forms of decoration and pitch variation.

On this site I will be examining in detail only those scales which are suitable for use in tonal harmonic music.

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What is a scale ?

What is it that differentiates a "scale" from simply just a "collection of notes" ?

A scale should constitute a unified collection of notes - a selection which is in some sense complete and to which any addition is heard to be extraneous.

The scale should also fulfil the functions demanded of it. There are at least three principle functions we may want a scale to fulfil:

  1. to serve as a melodic resource
  2. to serve as a harmonic resource
  3. to be tonally effective
It may fulfil any or all of these three functions - depending on its intended use.
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The scale as a melodic resource

For a scale to be heard to be successful as a melodic resource it should be reasonably smooth and even, without sudden gaps which sound as if a note has been omitted, or sudden concentrations of notes which sound as if an extraneous note has been added.

One of the most important measures of the completeness of a scale is whether or not it can be classed as as a proper mode or not.

A mode (scale) is considered to be proper when all intervals of an interval class are not smaller than those of lower interval classes. This means that if we start on any note in the scale and move up four notes the interval traversed should be larger (or the same size as) any other interval made up from traversing three notes.

The propriety of a scale is a significant factor of scales which are recognised to be melodically smooth.

Another important measure is consistency of the size of intervals for each pitch class in the scale. The diatonic scale, for instance, has just two types of second - a major and a minor second, while the harmonic minor scale has three types of second - major, minor and augmented. This makes the diatonic scale melodically smoother than the harmonic minor.

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The scale as a harmonic resource

In any harmonic music which uses major and minor triads, a suitable scale must be a resource not just for melody (notes in isolation) but for major and minor triads.

If we take major and minor triads to be the fundamental building blocks of our harmonic system then this means that if any note is not part of any major or minor triad then it is serving no harmonic purpose. It is therefore extraneous to the harmonic function of the scale, and so cannot be considered to be a unified member of that scale.

An example of such a "scale" is: c, d, e, f, g, gsharp, a. Here the gsharp is part of no triad, and so cannot be considered be a unified member of the scale.

The other requirement for a harmonic scale is that it should not contain any notes that allow for both a major and a minor triad to be built on the same root. This is because in any such scale one of these two possible thirds will always be heard as superfluous addition.

For example, in the "scale" c, d, e, f, g, aflat, a, b either the aflat or the a is entirely superfluous to the harmonic requirements of the scale.

This requirement forbids the use of any chromatic semitones in a fully unified scale.

Remarkably enough, out of all possible scales there are only five prime scales, in which every single note is a member of at least one major or minor triad and which contain no chromatic semitones. All of these scales contain seven notes.

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The five prime scales

The prime scales are those scales in which every note is a member of at least one major or minor triad, but which contain no chromatic semitones.

Each of the prime scales is best considered as a set of seven different scales or modes. Each mode of the prime scales contains the same notes but has a different "home" note or tonic.

Both the major scale and the natural minor scale are drawn from the same prime scale, and that prime scale is the diatonic scale. The difference between the major scale and the natural minor is their "home" or tonic note. If we take the notes c, d, e, f, g, a, b and treat c as the home note then we are using the scale of c major. If, however we take a as our home note then we are using the scale of a natural minor.

Indeed we can construct seven different scales from the diatonic scale by choosing each note as the home note. These seven scales are known as the seven diatonic modes. If we use the c major scale above, then the modes of it are as follows:

Tonic note Name of mode
f f Lydian
c c Ionian (or major)
g g Mixolydian
d d Dorian
a a Aeolian (or natural minor)
e e Phrygian
b b Locrian

As I've stated above there are five prime scales. Many of them do not have conventional names, so I have had to use the following descriptive terms.

The five prime scales are:

  1. the diatonic
  2. the harmonic minor
  3. the harmonic major
  4. the melodic
  5. the double harmonic
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Tonal harmonic scales

There is one final requirement for a scale that is to be used as a resource for tonal harmonic music. Not only must it be a suitable resource for melody and triads but it must also be able to support a tonic triad. That is, it must have a chord which serves as a chord of rest and completion, as the tonal centre against which all the other triads are measured and towards which all gravitate.

Within each of the prime scales only one or, at most, two triads are actually capable of functioning as tonics.

So although any of the modes of the prime scales are suitable in a melodic music, in a tonal-harmonic music only one or, at most, two modes of each of the prime scales are suitable.

The diatonic scale, for instance, has only two triads which are perceived to be totally at rest, resolved and final. In the scale c, d, e, f, g, a, b these triads are C major and a minor.

This means that there are only two tonally effective scales to be taken from the diatonic prime - the major scale and the natural minor (or aeolian) scale.

In total there are eight tonal harmonic scales. I will examine in detail each of these scales under the prime scales from which they are derived:

The diatonic scales
The major scale
The aeolian mode
The harmonic minor scale
The harmonic major scale
The melodic scales
The (ascending) melodic minor scale
The (descending) melodic major scale
The double harmonic scales
The double harmonic major scale
The double harmonic minor scale

For an overview of effective cadential progressions in each of these tonal scales go to The Cadence Page.