Modes of limited transposition are musical mode

Musical mode

In the theory of Western music since the ninth century, mode generally refers to a type of scale. This usage, still the most common in recent years, reflects a tradition dating to the middle ages, itself inspired by the theory of ancient Greek music.The word encompasses several additional...

s or scales that fulfill specific criteria relating to their symmetry

Symmetric scale

In music, a symmetric scale is a music scale which equally divides the octave. The concept and term appears to have been introduced by Joseph Schillinger and further developed by Nicolas Slonimsky as part of his famous "Thesaurus of Scales and Melodic Patterns"...

 and the repetition of their interval

Interval (music)

In music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...

 groups. They were compiled by the French composer Olivier Messiaen

Olivier Messiaen

Olivier Messiaen was a French composer, organist and ornithologist, one of the major composers of the 20th century. His music is rhythmically complex ; harmonically and melodically it is based on modes of limited transposition, which he abstracted from his early compositions and improvisations...

, and published in his book La technique de mon langage musical ("The Technique of my Musical Language").
There are two complementary ways to view the modes: considering their possible transpositions, and considering the different modes contained within them.
Transposing the diatonic

Diatonic scale

In music theory, a diatonic scale is a seven note, octave-repeating musical scale comprising five whole steps and two half steps for each octave, in which the two half steps are separated from each other by either two or three whole steps...

 major scale

Major scale

In music theory, the major scale or Ionian scale is one of the diatonic scales. It is made up of seven distinct notes, plus an eighth which duplicates the first an octave higher. In solfege these notes correspond to the syllables "Do, Re, Mi, Fa, Sol, La, Ti/Si, ", the "Do" in the parenthesis at...

 up in semitones results in a different set of notes being used each time.