Chromatic scale

The chromatic scale, also known as the twelve-tone scale, is a fundamental musical structure in Western music. It consists of twelve distinct pitches within a single octave. Every note in this scale is separated by a semitone, which is also called a half-step. This scale is significant because it acts as a superset for other musical structures. For example, it contains subsets like the diatonic scales used in many common songs.

In the most common modern tuning system, called 12-tone equal temperament, the scale functions with mathematical precision. This system ensures that the interval between any two adjacent notes is exactly the same size. Each semitone measures 100 cents, making a full octave equal to 1200 cents. Because of this equal spacing, the notes are distributed evenly across the octave. This provides a practical way to approximate pure musical intervals in every possible key.

Instruments are often categorized by how they interact with this scale. A chromatic instrument, such as the piano, is specifically designed to produce all twelve notes easily. However, other instruments can produce sounds that exist even between these twelve notes. These smaller intervals are called microtones. For instance, a violin can slide its strings to change pitch continuously. A trombone uses a moving slide to achieve similar variable pitch results.

Musical notation for the chromatic scale can vary based on context. There is no single fixed spelling for every note. Instead, the spelling often depends on the specific major or minor key signature being used. It also changes depending on whether the scale is ascending or descending. Generally, musicians use sharp signs when the scale goes up. They use flat signs when the scale goes down. To keep notation clear, writers avoid using the same scale degree more than twice in a row.

Before the 13th century, musicians used different tuning methods like the Pythagorean chromatic scale. This system was based on a series of perfect fifths centered on the note D. Unlike modern equal temperament, this scale was not perfectly symmetric. It used two different types of semitones: the Pythagorean limma and the Pythagorean apotome. Because these intervals were different sizes, the scale lacked the evenness we hear today.

Another historical method is known as 5-limit just intonation, or Ptolemy's intense chromatic scale. In this system, flats are actually higher than their enharmonic sharps. This method also introduces new notes between certain pitches, such as E and F, or B and C. Like the Pythagorean system, just intonation creates an asymmetrical scale. These historical tunings show how the mathematical understanding of pitch has evolved over many centuries.

Different cultures have also developed their own systems of fundamental notes. In ancient China, a series of twelve notes was known as the Shí-èr-lǜ. It is important to note that some scholars argue this was not a scale in the Western sense. Instead, it was a collection of fundamental notes used to construct various scales. This concept is similar to how the Western chromatic scale serves as a foundation for other musical forms.

Modern music theory often uses numbers to simplify the study of these pitches. By assigning a value of 0 to a starting note, musicians can use numbers 0 through 11 to represent the scale. This is possible because of octave equivalence, where notes repeat at regular intervals. This numerical approach is very helpful in the twelve-tone technique. In this technique, musicians use tone rows, which are specific orderings of the twelve notes. Using numbers makes it much easier to compare different musical forms and intervals.