The fugue — one subject that changes and stays itself
Six transformations to listen to. The same subject on the left every time, its transformation on the right — plus an exposition with two entries.
A fugue has a single subject, and the whole piece grows out of it. It appears alone first, then the next voice takes it over while the first one carries on — and along the way it is turned over, read backwards, stretched and compressed. It stays recognisable, although hardly any entry sounds like the one before.
None of that is a matter of feeling; it is arithmetic. Every transformation can be given as a number: the answer lies seven semitones higher, the inversion turns each interval around, the retrograde reads the notes backwards, the augmentation doubles every duration. That is why nothing on this page is claimed that has not been counted back from the sound.
Six pairs stand side by side here. The same subject on the left every time, the transformation on the right. Both can be played — with the inversion you hear at once that the melody keeps its shape and still goes the other way.
The answer
The second voice brings the same subject, every note seven semitones higher. The distances between the notes stay unchanged — that is the test: a transposition that alters even one interval is not one. You hear the same melody in a different place, and the opening of every fugue lives on exactly that.
The inversion
Every interval goes the other way: where the subject rises by a step, the inversion falls by the same step. The first note stays put, everything else folds around it. The shape of the melody stays recognisable, the direction is swapped — mirrored semitone by semitone here, which is why the picture carries accidentals the subject does not have.
The retrograde
The notes read from back to front: the last one becomes the first. This is the transformation that is hardest to hear, because the shape changes completely while every single note stays the same. On paper it is obvious at once; in sound it takes a trained ear.
The augmentation
The same notes, but every duration doubled: quavers become crotchets, and the subject needs two bars instead of one. In a fugue the augmentation usually comes towards the end, when the subject is to appear once more in full size while the other voices carry on at the original speed.
The diminution
The other direction: every duration halved, quavers become semiquavers. The subject runs twice as fast and fits into half a bar. Together with the augmentation this makes it possible to hear the same subject at two speeds at once.
The stretto
The second entry does not wait for the first to finish; here it comes after two quavers. The subject overlaps itself — and that is measured at the entry times: as long as the gap is shorter than the subject, it is a stretto. Towards the end of a fugue the entries often crowd closer and closer, and that is how the piece draws itself together.
The exposition: subject and answer
The subject starts alone in the upper voice. One bar later the answer enters below, an octave under the real transposition — and the upper voice keeps playing instead of falling silent. That countersubject is the counterpoint to the theme: it has to fit the answer without drawing attention away from it. At the end both voices rest on the same note two octaves apart.
What happens to the subject
The answer is the second voice: the same subject, every note seven semitones higher. The distances between the notes stay exactly as they were — that can be counted in the sound. This is what a real answer looks like. If a subject opens with a leap of a fifth, the old masters narrow it to a fourth so the answer stays in the key; then it is called tonal. The subject on this page begins with a step and needs no such adjustment.
The inversion turns every interval around: a step up becomes the same step down. The first note stays where it is, everything else folds over. The retrograde reads the notes from the back — the last one becomes the first. Both transformations change only the pitches, not the durations.
Augmentation and diminution do the opposite: the notes stay, every duration is doubled or halved. In the augmentation the subject takes two bars instead of one. The stretto, finally, lets the second entry begin before the first has finished — the subject overlaps itself, and the later this happens in a fugue, the closer the entries are pushed together.
What stands next to it
How two voices are led together: Counterpoint. What the distances between two notes are called: Intervals. How a phrase closes: Cadences.
Music symbols · Music notation glossary
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See AnotonaEvery note on this page is computed, not typed in — following the rule that also makes F# major spell its seventh degree E#, not F.