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What is a scale?

A scale is an ordered series of stepwise notes, arranged by pitch within an octave. You start from a note, the tonic, which serves as an anchor and gives its name to the whole, and you climb note after note until you land on that same note an octave higher. The reference scale, the one on which everything else is built, is the major scale.

What separates one note from the next is a gap, either a whole step or a half step. In Western music, the only half steps between natural notes are found between E and F, and between B and C; everywhere else the gap between two natural notes is a whole step. It is these whole steps and half steps, placed in a precise order, that give each scale its particular colour.

The major scale and its model, C major

The major scale always follows the same sequence of intervals, whatever the starting note: a whole step, a whole step, a half step, a whole step, a whole step, a whole step, a half step. The two half steps always fall in the same places, between the third and fourth degrees, then between the seventh and eighth degrees. The seventh degree, a half step below the tonic, is called the leading tone: it draws the ear towards the resting note.

The simplest model is C major, made up of the notes C, D, E, F, G, A, B, with no accidentals in the key signature. On a piano keyboard, it is played only on the white keys, which makes the formula visible at a glance: the half steps E-F and B-C correspond exactly to the two places where there is no black key between two white ones.

Building a major scale step by step: the E flat major example

C major is easy because it needs no accidentals, but the method has to work from any tonic. Let's take a less obvious example, E flat, and work through the calculation degree by degree to see exactly where the flats fall and why.

Two rules apply at the same time. First, strictly follow the major formula, a whole step, a whole step, a half step, a whole step, a whole step, a whole step, a half step, starting from the tonic. Second, move the letter names forward one letter at a time, without skipping or repeating any: after E comes F, never an E that is still altered, nor G directly. It is this second rule that decides whether an accidental is spelled as a sharp or a flat.

Let's work through the seven degrees. 1st degree, the tonic: E flat. A whole step up, 2nd degree: F, no accidental, the gap E flat-F is indeed a whole step. Another whole step, 3rd degree: G, also no accidental. A half step, 4th degree: the letter after G is A; a half step above G lands exactly on A flat, never on G sharp, since the note name has to move forward one letter. A whole step, 5th degree: after A comes B; a whole step above A flat gives B flat. A whole step, 6th degree: after B comes C; a whole step above B flat lands back on C, no accidental. A whole step, 7th degree: after C comes D; a whole step above C gives D, no accidental. A half step, back to the tonic: after D comes E; a half step above D gives E flat, exactly the starting note.

The resulting scale is E flat, F, G, A flat, B flat, C, D. Three flats appear, E flat, A flat and B flat, exactly the three flats of the E flat major key signature. That is no coincidence: a key signature is never more than a note-by-note summary of the calculation we have just worked through by hand.

The natural minor scale and A minor

The natural minor scale follows a different sequence of intervals: a whole step, a half step, a whole step, a whole step, a half step, a whole step, a whole step. The model example is A minor, made up of the notes A, B, C, D, E, F, G, with no accidentals in the key signature, and also playable only on the white keys of the piano. The tonic has changed, but the notes used are exactly the same as those of C major.

The contrast in colour between the two modes is immediately audible: the major is perceived as cheerful, open and bright, while the minor sounds melancholic, dark and closed. What creates this melancholic colour is the third note of the scale, the third, lowered by a half step compared to the major. It is this single degree, more than anything else, that tips a scale from bright to dark.

Relative major, relative minor and key

A minor has exactly the same notes as C major and the same key signature, only the tonic differs: A minor is said to be the relative minor of C major. A major key and its relative minor therefore always share the same key signature, that is the same accidentals. To find the relative minor, you go down a minor third, that is a whole step and a half or three half steps, below the major tonic; this note corresponds to the sixth degree of the major scale.

The tonic and the mode give the key its name: a tonic F in minor mode is the key of F minor. This is how a scale is linked to a precise key signature. B minor, the relative minor of D major, carries two sharps in its key signature; C minor, the relative minor of E flat major, carries three flats. Knowing the relative major of a minor scale therefore lets you find its number of accidentals directly.

Why three minor scales? The birth of the harmonic and melodic forms

In the natural minor scale, the seventh degree sits a whole step below the tonic, not a half step as in major. This note therefore does not act as a leading tone: played just before the tonic, it does not pull towards it with the same urgency, and the cadence, that moment when the music seems to close in on itself, sounds softer than in major. It is in fact called the subtonic, not the leading tone, precisely because it lacks that pulling function. The natural minor scale also carries another name, inherited from older modal theory: it is the Aeolian mode, one of seven ways of organising a scale of natural notes depending on the chosen starting note.

Historically, this lack of a leading tone was felt well before the modern theory of major and minor scales was fixed. As early as the modal music of the late Middle Ages and the Renaissance, composers had grown used to raising certain sung notes near cadences, a practice known as musica ficta, precisely to manufacture, case by case, a leading tone that did not exist in the original mode. This habit of adding a leading tone note by note on the dominant, rather than writing it into the key signature, is generally seen as one of the gateways to the major-minor tonal system that came to dominate over the course of the 17th century. When the theory of the minor scale settled during the Baroque era, this practice was formalised under the name harmonic minor scale: the seventh degree is raised by a half step to give it exactly the leading-tone role it plays in major, which notably allows the building of a major dominant chord, and therefore a cadence as firm as in a major key. Without this alteration, the chord built on the fifth degree of the natural minor stays minor too, and pulls much less strongly towards the tonic.

This fix, however, creates a new problem, a purely melodic one this time: between the sixth and seventh degree of the harmonic minor there opens a gap of a step and a half, an augmented second, a wide and angular interval, awkward to sing and to move through naturally in an ascending line. To smooth out this leap without giving up the leading tone, the sixth degree is also raised by a half step when ascending: this is the melodic minor scale. Descending, this melodic leading tone no longer serves a purpose, since the line is moving away from the tonic rather than towards it; the melodic minor therefore descends just like the natural minor. Three minor scales thus answer three different needs, which appeared at different points in the history of Western theory: the natural gives the basic colour, the oldest, inherited from the modes; the harmonic gives a solid cadence, at the cost of a more angular interval; the melodic gives a smooth ascending line, while still keeping the leading tone.

The table starts from A minor, the reference scale with no accidentals, to show exactly which notes change from one form to the next: in the formula column's shorthand, T stands for a whole step and S for a half step.

Using all three minors within a single piece, rather than picking just one

Faced with these three forms, a beginner often assumes they must pick just one to play a piece in minor, as if choosing from a menu of three competing scales. In practice it is the opposite: a single piece in minor commonly draws on all three forms depending on the moment, without ever announcing it, and without this changing the key signature shown at the start of the staff.

The most reliable habit is to spot the role of each passage rather than hunting for THE right minor scale. On a cadence, when the harmony leans on the fifth degree or a dominant chord just before returning to the tonic, the leading tone of the harmonic minor almost always shows up, even though the key signature carries no accidental there: it is an accidental, added note by note in the score, not a change of key. In a melodic line climbing towards the tonic, the sixth and seventh degrees are often raised too, following the logic of the melodic minor, to smooth the leap. Everywhere else, in passages aiming neither at a cadence nor a direct climb to the tonic, the default colour stays that of the natural minor, with no added accidental.

In other words, the three forms are not three different pieces to choose between once and for all, but a toolbox to dip into locally, phrase by phrase, chord by chord, according to what each moment of the piece calls for. It is this combined use, not the choice of a single fixed form from start to finish, that explains why so many minor-key pieces sound both dark and yet firmly resolved on their cadences.

Building any scale yourself

The strength of the formula is that it applies from any note, as shown by the E flat major example above. Take a starting note, apply the desired sequence of intervals, major or natural minor, move the letter names forward one letter at a time without skipping or repeating any, and add the accidentals, sharps or flats, needed to respect exactly each whole step and half step of the formula. You thus obtain the scale of any tonic, in the chosen mode, whether it carries zero accidentals like C major or seven like the most heavily loaded keys.

For the minor, the three forms seen above build on one another: start from the natural minor, raise the seventh degree to get the harmonic minor, and also raise the sixth degree when ascending to get the melodic minor. The safest way to check a result remains counting the whole steps and half steps one by one rather than trusting the ear alone, especially on an unusual tonic: the method never changes, only the starting note does.

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