Related
The idea behind these devices is: write no new material — change one dimension of what you already have.
| Device | Dimension changed | Method |
|---|---|---|
| mirror (inversion) | direction | rising becomes falling and vice versa (interval widths unchanged) |
| retrograde | order in time | walk from the last note back to the first |
| augmentation | speed | double every note value (sounds half as fast) |
| diminution | speed | halve every note value (sounds twice as fast) |
All four share one property, and it is what makes them usable in polyphony:
The interval structure is unchanged. Only direction, order or speed moves — so the ear still recognises "this is the same material".
This is polyphonic economy at its extreme: write the material once and get four things that sound different yet come from one source.
Mirror: the other face of interval inversion
Mirror keeps an interval's width and reverses its direction. That is the same logic as interval inversion — both concern distance and direction — applied to a different object: one works between two notes, the other across a whole melody.
Mirroring changes the mode (a major passage may come out with a minor flavour), so individual notes often need adjusting to fit the harmony.
Retrograde: the hardest of the four
Its rule is the simplest and its execution the hardest:
When the melody runs backwards, so does the harmony.
And harmony has direction (dominant to tonic works; tonic to dominant does not). So strict retrograde often produces strange harmony, and in practice it is applied to short passages, or adjusted locally.
It is a useful reminder: the difficulty of a contrapuntal device is not only whether the notes fit, but whether the harmonic direction still makes sense.
Augmentation and diminution: changing the time scale
| Device | Effect | Typical use |
|---|---|---|
| augmentation | the material becomes slow motion while other voices flow normally | often at a close: the material appears one last time in solemn form |
| diminution | the material becomes dense and faster | often at a build-up: entries squeezed tighter for urgency |
Bach uses this pair heavily in the Goldberg Variations and the fugues, because they change the density of the music without new material.
Its relation to twelve-tone technique
The twelve-tone method Schoenberg established in the twentieth century raised these devices into a complete principle of pitch organisation. A row has four faces:
| Form | Description |
|---|---|
| prime (O) | the original row |
| inversion (I) | turned upside down |
| retrograde (R) | back to front |
| retrograde inversion (RI) | both at once |
Worth noting: this is not a twentieth-century invention but the systematisation of devices polyphony had used for centuries — and then made compulsory. The difference is obligation: in the Baroque they were available devices; in twelve-tone writing they are the organising principle.
Diagram: four transformations
Listen: the logic of mirroring in two notes
These devices act on whole melodies and their polyphonic use cannot be played here. Use interval to see the logic of mirroring: a rising third (C–E) and a falling third (C down to A) share a width and reverse the direction — mirroring, reduced to two notes.
Common misconceptions
- "Mirror and interval inversion are the same." Related logic, different objects: interval inversion acts
- "Retrograde is just copying the page backwards." Technically yes, but **the harmony runs backwards with
- "Augmentation and diminution only change speed." They change the density of the music — a structural
- "Twelve-tone technique invented these devices." The reverse: polyphony used them for centuries, and
between two notes, mirroring acts across a melody.
it**, so it is usually confined to short passages or adjusted locally.
device, not a performance instruction.
twelve-tone writing made them compulsory. :::
Listen in the library
All tracks from midicn-lib — inline badge is the license tier (C1 commercial / C2 non-commercial / C3 study only).
Sources
- 对位变形手法（倒影 / 逆行 / 扩大 / 缩小）各自的定义与保持音程结构的性质，属对位学通则
- 四种形态在十二音技法中构成"原型—倒影—逆行—逆行倒影"关系，为通行现代作曲技法表述
Used for fact-checking only; all prose is original.