Particularly interesting are the set of scales derived by French composer Olivier Messiaen called modes of limited transposition. These sets of scales bridge the gap between the chromatic scale and the diatonic scale (a fancy word for major/minor scales). The theoretical basis of the modes of limited transposition is actually very simple to understand, with the defining property of each mode being how many times it can be transposed up 1/2-step before you end up with the same set of notes with which you started.
Although they are in fact scales, Messiaen nearly always thought of his modes in terms of harmony. Going even further, he claimed to associate each mode (and each transposition of each mode) with an array of colors -- a condition known as synesthesia. He provided some very elaborate (borderline excessive) descriptions of the colors he associated with each transposition of each mode. I was hesitant to include these here since even he said that these colors are subjective (and that different people with sound-color synesthesia would have different color associations), but I ultimately decided to since they seemed so important to him.
MODE 0Messiaen never mentioned a "mode 0", but it is a good way to begin understanding the modes of limited transposition. It is simply the chromatic scale.
|Mode 0, more commonly know as the chromatic scale. If we attempt to transpose each note +1/2-step, we have the exact same set of notes. Click on image to enlarge.|
|A set of diagrams illustrating the idea of limited transposition. Green indicates that the pitch is in the mode. The shaded keys on the piano diagram as well as the bold circles indicate which note the scale begins on. Click on image to enlarge.|
|The only transposition of mode 0.|
MODE 1The 1st mode is a little bit more interesting because it can be transposed. It is commonly known as the whole-tone scale (i.e. a scale consisting of only whole steps and containing no semitones) and was used very often by the French composer Claude Debussy. As a result, Messiaen rarely used it, claiming that Debussy did everything that could be done with it.
|Modes 1.1 and 1.2, respectively.|
MODE 2The 2nd mode was frequently used by Messiaen and is used to create some of his most distinct harmonies. It is a scale which alternates between half-steps and whole-steps.
Note: The color descriptions given for each mode refer not to the individual scale, but to the harmonies that can be created using each scale (see further down for an example of some harmonies).
- Mode 2.1: Blue-violet rocks with flecks of gray, cobalt blue, Prussian blue with rays of purplish-blue, gold, ruby red, and mauve stars (dominant color is blue-violet)
- Mode 2.2: Spirals of gold and silver on a background of vertical stripes of brown and ruby red (dominant colors are gold and brown)
- Mode 2.3: Leaves of light green and prairie green with blemishes of blue, gold, and red-orange (dominant color is green)
|Modes 2.1, 2.2, and 2.3, respectively.|
MODE 3The 3rd mode was another one that was used very frequently by Messiaen. In particular, he said that he thought mode 3.2 was the best of all of his modes.
- Mode 3.1: Orange, gold, milky-white
- Mode 3.2: Horizontal stripes of colors (listed from bottom to top) dark gray, mauve, light gray, and white with hints of mauve and yellow -- with flamboyant gold letters forming unknown writing, and a number of small, thin red and blue arcs
- Mode 3.3: Large vertical stripes alternating between cobalt-blue and dark blue-green with red-orange lilies (dominant colors are blue and green)
- Mode 3.4: Orange, red, a bit of blue
|All four transpositions of mode 3. If we try and transpose mode 3.4 +1/2-step, we return to mode 3.1. Click on image to enlarge.|
|Modes 3.1, 3.2, 3.3, and 3.4, respectively.|
MODE 4Mode 4 has six transpositions and sounds significantly different than the previous modes because it is contains two minor 3rds (one between the 3rd and 4th pitches and another between the 7th and 8th pitches). It was used by Messiaen, but not as often as modes 2 and 3.
- Mode 4.1: Gray, gold, a bit of blue
- Mode 4.2: Streaks of iron-gray, pink-mauve and coppery-yellow; black and clear Prussian blue; green and purple-violet
- Mode 4.3: Yellow and violet
- Mode 4.4: Violet with white veins
- Mode 4.5: Deep violet
- Mode 4.6: Carmine red, violacious purple, mauve, gray, pink
|All six transpositions of mode 4. If we try and transpose mode 4.6 +1/2-step, we return to mode 4.1. Click on image to enlarge.|
|Modes 4.1 through 4.6, respectively.|
OTHER MODESModes 5, 6, and 7 were rarely used by Messiaen. Mode 6.1 was used in the first movement of his Trois Petites Liturgies de la Presence Divine. The first transposition of the sixth mode was used by the Hungarian composer Gyorgy Ligeti (1923-2006) in his Horn Trio. It also serves as the ostinato figure in his 4th piano etude Fanfares.
|Mode 6.1 occurs as an ostinato passed between the right and left hands in Gyorgy Ligeti's 4th piano etude Fanfares. Click on image to enlarge.|
One of the most interesting aspects of the modes is that they bridge the gap between the chromatic scale and the diatonic (major/minor) scale. If we perform the same analysis on the diatonic scales, we find that they both have twelve transpositions! Thus, going through all of the modes brings us from the chromatic scale to the set of diatonic scales.
|The same diagram for diatonic scales. After 12 transpositions (only the 1st two are shown) we arrive back where we started. Click on image to enlarge.|
HARMONIESMost of the time, Messiaen used parallel motion within the modes of limited transposition to obtain colorful, exotic harmonies.
|Parallel motion chord chains in modes 2.1, 3.1, and 4.1. The light green keys are keys within the given mode and the dark green keys are the ones that are "pressed down" to play the chord shown. Click on image to enlarge.|
|The first four chords of modes 2.1, 3.1, and 4.1, respectively (shown in the above figure).|
Note: A very good explanation of these modes (and other methods of harmonization used by Messiaen) can be found here.