Modal transformations

In a musical composition that is based on a scale, a motif is frequently transformed in various ways. It may be transposed to start at different places in the scale or it may be inverted around a pivot point in the scale. It may also be reversed to produce its retrograde, see Retrograde.

Modal transposition

A motif can be transposed within a given scale with:

\modalTranspose from-pitch to-pitch scale motif

The notes of motif are shifted within the scale by the number of scale degrees given by the interval between to-pitch and from-pitch:

diatonicScale = \relative { c' d e f g a b }
motif = \relative { c'8 d e f g a b c }

\new Staff {
  \motif
  \modalTranspose c f \diatonicScale \motif
  \modalTranspose c b, \diatonicScale \motif
}

An ascending scale of any length and with any intervals may be specified:

pentatonicScale = \relative { ges aes bes des ees }
motif = \relative { ees'8 des ges,4 <ges' bes,> <ges bes,> }

\new Staff {
  \motif
  \modalTranspose ges ees' \pentatonicScale \motif
}

When used with a chromatic scale \modalTranspose has a similar effect to \transpose, but with the ability to specify the names of the notes to be used:

chromaticScale = \relative { c' cis d dis e f fis g gis a ais b }
motif = \relative { c'8 d e f g a b c }

\new Staff {
  \motif
  \transpose c f \motif
  \modalTranspose c f \chromaticScale \motif
}

Modal inversion

A motif can be inverted within a given scale around a given pivot note and transposed in a single operation with:

\modalInversion around-pitch to-pitch scale motif

The notes of motif are placed the same number of scale degrees from the around-pitch note within the scale, but in the opposite direction, and the result is then shifted within the scale by the number of scale degrees given by the interval between to-pitch and around-pitch.

So to simply invert around a note in the scale use the same value for around-pitch and to-pitch:

octatonicScale = \relative { ees' f fis gis a b c d }
motif = \relative { c'8. ees16 fis8. a16 b8. gis16 f8. d16 }

\new Staff {
  \motif
  \modalInversion fis' fis' \octatonicScale \motif
}

To invert around a pivot between two notes in the scale, invert around one of the notes and then transpose by one scale degree. The two notes specified can be interpreted as bracketing the pivot point:

scale = \relative { c' g' }
motive = \relative { c' c g' c, }

\new Staff {
  \motive
  \modalInversion c' g' \scale \motive
}

The combined operation of inversion and retrograde produce the retrograde inversion:

octatonicScale = \relative { ees' f fis gis a b c d }
motif = \relative { c'8. ees16 fis8. a16 b8. gis16 f8. d16 }

\new Staff {
  \motif
  \retrograde \modalInversion c' c' \octatonicScale \motif
}

See also

Notation Reference: Inversion, Retrograde, Transpose.