Chromatic scale

Play every key on the piano in a row, white and black, from one C to the next. Each key is a semitone above the last, and in twelve equal steps the octave closes. That is the chromatic scale:

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It is the succession of twelve consecutive semitones, the octave divided into twelve semitones (Med 1996, ch. XXXI). The thirteenth note repeats the first, which is why the scale is said to have twelve different notes. It is the scale that uses every possible sound between a note and its octave, in the tempered system.

Diatonic notes and chromatic notes

Of the twelve notes, seven are diatonic, those of the scale you start from, and five are chromatic, those placed between them. In the same way, the twelve semitones divide into seven diatonic ones, between notes of different names, and five chromatic ones, between notes of the same name (Med 1996, ch. XXXI).

The word comes from the Greek chroma, colour. Med explains the image: the diatonic notes are the base of the key, and the chromatic notes are elements of colouring (Med 1996, ch. XXXI). A melody in C major that passes through an F sharp has not changed key; it has taken on a colour.

One scale, or many?

Here the books part ways, and the disagreement teaches a good deal.

For Lacerda, the chromatic scale, unlike the diatonic ones, gives rise to no key. There is no chromatic scale "on E" or "on A flat": there is only one, going up or down, and it begins and ends on any note (Lacerda 1966, ch. XXVII). Indeed, the twelve keys are always the same, wherever you start.

For Med, in the tempered system there is apparently only one chromatic scale, but combining the chromatic notes in different ways gives a great number of scales, which differ in spelling and each have their own harmonic meaning (Med 1996, ch. XXXI). The sound of the twelve keys is the same; the name of each key changes with the key the scale is in.

Both are right about different things. Lacerda speaks of the sound, which is one. Med speaks of the spelling, and the spelling says where each chromatic note comes from.

The practical rule: sharps up, flats down

The commonest spelling is Lacerda's. With no key signature, the ascending scale sharpens the natural notes and the descending scale flattens them (Lacerda 1966, ch. XXVII). Blatter gives the same rule (Blatter 2007, part 2, art. 8). Going up, as above; coming down:

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The logic is one of direction. A sharp suggests a note that wants to rise, a flat a note that wants to fall, and the spelling follows the motion of the line.

Under a key signature

With a key signature the idea stays the same: going up, each note rises a chromatic semitone; coming down, it falls. But the sign depends on what the key signature has already put on the note (Lacerda 1966, ch. XXVII):

Note in the key signature	Going up becomes	Coming down becomes
natural	sharp	flat
sharp	double sharp	natural
flat	natural	double flat

Blatter sums it up by saying the conventions are the same, but the key signature takes priority (Blatter 2007, part 2, art. 8). An ascending chromatic scale in E flat major:

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The key signature's E flat rises to E natural, the F natural rises to F sharp, and so on. Between G and A flat, and between D and E flat, there is nothing to add: they are already semitones.

Med's chromatic scales

Med describes several ways of spelling a key's chromatic scale (Med 1996, ch. XXXI). The two most useful to know are these.

The classical chromatic scale. The chromatic notes must belong to the closely related keys. In C major, going up, every degree is raised except the sixth, and the seventh is lowered instead: not A sharp but B flat, the fourth degree of F major. Coming down, every degree is lowered except the fifth, and the fourth is raised instead: not G flat but F sharp, the leading tone of G major (Med 1996, ch. XXXI).

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The exceptions fall exactly on F and B, the two notes whose combination so often gives rise to exceptions, and they have a harmonic reason: B flat and F sharp are notes C major really does use when it leans towards F major or G major.

The current chromatic scale. The chromatic notes need not belong to the related keys. Going up, every degree is raised; coming down, every degree is lowered (Med 1996, ch. XXXI). In practice it is Lacerda's and Blatter's rule, seen from inside a key.

Med also records an enharmonic chromatic scale, giving both spellings for each chromatic note, which appeared in the twentieth century, and an atonal chromatic scale, with no key signature or key, which uses no E sharp, F flat, B sharp or C flat (Med 1996, ch. XXXI).

Why spelling matters

On the piano C sharp and D flat are the same key, and writing one or the other looks like a matter of taste. It is not. The spelling says where the note is going: a C sharp wants to rise to D, a D flat wants to fall to C. It also says which key the colour comes from. And for anyone singing or playing an instrument with free tuning, the two notes are not even quite the same pitch.

What comes next

The chromatic scale is the extreme case of the symmetric scales: a single interval repeated, a single transposition. And its notes, used with judgement, are the material of chromatic chords and secondary dominants, which borrow colour from neighbouring keys without leaving the key.