In music theory, an enharmonic scale is "an maginarygradual progression by

quarter tone A quarter tone is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide (aurally, or logarithmically) as a semitone, which itself is half a whole tone. Quarter tones divide the octave by 50 cents each, a ...

s" or any " usicalscale proceeding by

s". The enharmonic scale uses

dieses In classical music from Western culture, a diesis ( , plural dieses ( , "difference"; Greek: δίεσις "leak" or "escape"Benson, Dave (2006). ''Music: A Mathematical Offering'', p.171. . Based on the technique of playing the aulos, where p ...

(divisions) nonexistent on most keyboards,John Wall Callcott (1833). ''A Musical Grammar in Four Parts'', p.109. James Loring. since modern standard keyboards have only

half-tone Halftone is the reprographic technique that simulates continuous-tone imagery through the use of dots, varying either in size or in spacing, thus generating a gradient-like effect.Campbell, Alastair. The Designer's Lexicon. ©2000 Chronicle, S ...

dieses. More broadly, an enharmonic scale is a scale in which (using standard notation) there is no exact equivalence between a sharpened note and the flattened note it is

enharmonic In modern musical notation and tuning, an enharmonic equivalent is a note, interval, or key signature that is equivalent to some other note, interval, or key signature but "spelled", or named differently. The enharmonic spelling of a written n ...

ally related to, such as in the quarter tone scale. As an example, F and G are equivalent in a

chromatic scale The chromatic scale (or twelve-tone scale) is a set of twelve pitches (more completely, pitch classes) used in tonal music, with notes separated by the interval of a semitone. Chromatic instruments, such as the piano, are made to produce the ...

(the same sound is spelled differently), but they are different sounds in an enharmonic scale. See:

musical tuning In music, there are two common meanings for tuning: * Tuning practice, the act of tuning an instrument or voice. * Tuning systems, the various systems of pitches used to tune an instrument, and their theoretical bases. Tuning practice Tun ...

Musical keyboard A musical keyboard is the set of adjacent depressible levers or keys on a musical instrument. Keyboards typically contain keys for playing the twelve notes of the Western musical scale, with a combination of larger, longer keys and smaller, sho ...

s which distinguish between enharmonic notes are called by some modern scholars

enharmonic keyboard An enharmonic keyboard is a musical keyboard, where enharmonically equivalent notes do not have identical pitches. A conventional keyboard has, for instance, only one key and pitch for C and D , but an enharmonic keyboard would have two different ...

s. (The

enharmonic genus In the musical system of ancient Greece, genus (Greek: γένος 'genos'' pl. γένη 'genē'' Latin: ''genus'', pl. ''genera'' "type, kind") is a term used to describe certain classes of intonations of the two movable notes within a tetracho ...

, a tetrachord with roots in early Greek music, is only loosely related to enharmonic scales.) Consider a scale constructed through

Pythagorean tuning Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2.Bruce Benward and Marilyn Nadine Saker (2003). ''Music: In Theory and Practice'', seventh edition, 2 vols. (Boston: Mc ...

. A Pythagorean scale can be constructed "upwards" by wrapping a chain of

perfect fifth In music theory, a perfect fifth is the Interval (music), musical interval corresponding to a pair of pitch (music), pitches with a frequency ratio of 3:2, or very nearly so. In classical music from Western culture, a fifth is the interval fro ...

s around an

octave In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...

, but it can also be constructed "downwards" by wrapping a chain of

perfect fourth A fourth is a musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth () is the fourth spanning five semitones (half steps, or half tones). For example, the ascending interval from C to ...

s around the same octave. By juxtaposing these two slightly different scales, it is possible to create an enharmonic scale. The following Pythagorean scale is enharmonic: In the above scale the following pairs of notes are said to be enharmonic: * C and D * D and E * F and G * G and A * A and B In this example, natural notes are sharpened by multiplying its frequency ratio by 256:243 (called a

limma The word limma or leimma (from Greek: λείμμα, ''leimma''; meaning "remnant") can refer to several different musical intervals, whose only common property is their small size. :More specifically, in Pythagorean tuning (i.e. 3-limit): :*The ori ...

), and a natural note is flattened by multiplying its ratio by 243:256. A pair of enharmonic notes are separated by a

Pythagorean comma In musical tuning, the Pythagorean comma (or ditonic comma), named after the ancient mathematician and philosopher Pythagoras, is the small interval (or comma) existing in Pythagorean tuning between two enharmonically equivalent notes such as C ...

, which is equal to 531441:524288 (about 23.46 cents).

References

External links

* {{scales Musical scales Musical tuning