Mode of limited transposition Facts for Kids

Modes of limited transposition are special musical modes or scales that have a unique kind of symmetry. They were created by the French composer Olivier Messiaen. He wrote about them in his book La technique de mon langage musical (which means "The Technique of my Musical Language").

These scales are special because when you move them up or down (this is called transposing them) to different starting notes, they don't always create a completely new set of notes. For example, if you move one of these scales up a few steps, you might end up with the exact same notes you started with! This is why their transpositions are "limited."

What Makes These Scales Special?
- How Transposing Works
- How Starting Notes Work
Messiaen's Seven Modes
How These Modes Are Used
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What Makes These Scales Special?

Messiaen explained that these modes are built from "symmetrical groups" of notes. This means they have a balanced pattern. When you move them around, they quickly repeat the same notes.

There are two main ways to understand why these modes are special:

How Transposing Works

Imagine you have a regular major scale, like C major (C, D, E, F, G, A, B). If you move this scale up one semitone (half step) to D♭ major, you get a completely new set of notes (D♭, E♭, F, G♭, A♭, B♭, C). You can do this 12 times, and each time you'll get a different set of notes.

But with a mode of limited transposition, it's different. Let's look at Messiaen's "Mode 1," which is the whole tone scale. It has notes like C, D, E, F♯, G♯, A♯.

If you move it up one semitone, you get C♯, D♯, F, G, A, B. This is a new set of notes.
But if you move it up another semitone (a whole tone from the start), you get D, E, F♯, G♯, A♯, C. Look closely! This is the exact same set of notes as the original C whole-tone scale, just starting on D.

So, Mode 1 only has 2 unique transpositions. Any scale that creates 12 different sets of notes when transposed is NOT a mode of limited transposition.

How Starting Notes Work

In a regular major scale, if you start on a different note, you get a new kind of scale, called a "mode." For example, starting a C major scale on D gives you the Dorian mode. Each starting point creates a unique pattern of intervals (the spaces between notes).

However, with modes of limited transposition, this isn't the case.

For Mode 1 (the whole tone scale), the intervals are always tone, tone, tone, tone, tone, tone. No matter which note you start on, you get the exact same pattern. So, Mode 1 only has 1 mode.
Messiaen's Mode 2, also known as the diminished scale, has intervals like semitone, tone, semitone, tone, and so on. This scale can only be arranged in 2 ways by starting on different notes.

Any scale that has as many different modes as it has notes is NOT a mode of limited transposition.

Messiaen's Seven Modes

Olivier Messiaen identified seven specific modes of limited transposition. Here they are:

Mode 1: The Whole-Tone Scale

This mode is made of six groups of two notes. The space between each note is always a whole tone (two semitones).

It has 2 unique transpositions.
It has 1 unique mode (meaning it sounds the same no matter where you start).

Mode 1: The Whole-Tone Scale

Mode 2: The Octatonic Scale

This mode is divided into four groups of three notes. It alternates between a semitone and a whole tone. It's also called the octatonic or diminished scale.

It has 3 unique transpositions.
It has 2 unique modes.

Mode 2: The Octatonic Scale

Mode 3

This mode is divided into three groups of four notes. It follows a pattern of tone, semitone, semitone.

It has 4 unique transpositions.
It has 3 unique modes.

Mode 3

Mode 4

This mode has a pattern of semitone, semitone, minor third, semitone, semitone, semitone, minor third, semitone.

It has 6 unique transpositions.
It has 4 unique modes.

Mode 4

Mode 5

This mode has a pattern of semitone, major third, semitone, semitone, major third, semitone.

It has 6 unique transpositions.
It has 3 unique modes.

Mode 5

Mode 6

This mode has a pattern of tone, tone, semitone, semitone, tone, tone, semitone, semitone.

It has 6 unique transpositions.
It has 4 unique modes.

Mode 6

Mode 7

This mode has a pattern of semitone, semitone, semitone, tone, semitone, semitone, semitone, semitone, tone, semitone.

It has 6 unique transpositions.
It has 5 unique modes.

Mode 7

How These Modes Are Used

Messiaen used these special modes in his music in many ways: for melodies, harmonies, and even when combining different musical lines.

The whole-tone scale (Mode 1) and the octatonic scale (Mode 2) became quite popular in music from the early 1900s. Composers like Debussy often used the whole-tone scale, and Stravinsky frequently used the octatonic scale.

Messiaen felt that the symmetry of these modes gave them a "charm of impossibilities." This means that because they are so balanced, no single note feels like the "home" note (tonic), which creates a unique and sometimes mysterious sound.

Another composer, Tōru Takemitsu, also used Messiaen's modes a lot, especially the third mode.