Enharmonic scale
In music theory, an enharmonic scale is a very
- C (0¢),
- G (700¢).
The symbol
Bracketing tetrachords
Four of the scale notes – the
Despite the music of India and the Middle East still using similar intervals in traditional and classical scales, even the idea of the very small pitch intervals used in the enharmonic scale has lain outside the competence of musicians trained in occidental music at least since the time of the early Roman Empire.[4]
Difference in meaning of "enharmonic" between the classical-era and now
The ancient Greek meaning of enharmonic is that the scale contains at least one very narrow interval. (The spacing of each pair notes between their bracketing fixed notes is usually either approximately or exactly the same, so when there is one narrow interval in one bracket there is almost always another one inside the other bracket.)[4] Modern musical vocabulary has re-used the word "enharmonic" altered to have the most extreme possible meaning of its ancient sense, to mean two differently-named notes which happen to actually have the same pitch. In
Since an enharmonic scale uses (approximately)
Even among Hellenic musicians, enharmonic scales appear to have gone out of style around 2500 years ago, and only persisted as a perfunctory part of normal musical training; enharmonic scales seem to have been oddities even to the Greek writers in the Roman Empire, whose works on music theory we still have.[4] So the idea of such very small pitch intervals used in the enharmonic scale has lain outside of the scope of musicians' training for occidental music, despite music of India and the Middle East still using similar intervals traditional and classical scales.
Unfamiliar, variable-size quarter tones
An otherwise well regarded 19th century musicologist once wrote the rather blatantly false definition in his 1905 musical dictionary, that the enharmonic scale is
- ... "an [imaginary] gradual progression by quarter tones" or any "[musical] scale proceeding by quarter tones". — Elson (1905)[3]
However, enharmonic tuning does seem "imaginary" to many modern western musicians because of the intentional limitations placed into
The enharmonic scale was a very real tuning system that survived from pre-classical Greek music (when it seems to have been put to more use
The enharmonic scale uses dieses (divisions) which are not tuned in any pitch present on standard modern keyboards,[2] since modern, standard keyboards only have provisions for half-tone steps. The two different notations used for vocal and instrumental notes in ancient Greek musical are more tonally versitile, since they are based on quarter-tones = half-sharps, with step sizes that could be altered from a strict quarter tone step.[4] Despite the pitches being unknown to naïve occidentally-trained musicians, all the ancient Greek tuning systems only require seven distinct pitches in a completed octave, and only the four of those pitches, the two that lie between the fixed tonic and subdominant (or fourth) (relative to CMaj, the notes between C and F), and the other two movable notes between fixed dominant / fifth and the octave (between G and C′). When expressing notes with modern letter notation, it is conventional to use some elaborately sharpened or flattened version of the notes D, E, A, and B, representing not their precise pitches, but merely to follow the modern standard of giving every distinct pitch in a scale its own, separate letter.[4]
Since the ancient Greek pitch systems only require eight different notes in a completed octave, and a modern keyboard has twelve, there actually are more than enough keys on any keyboard to implement one of the several enharmonic scales, contrary to Elson's remark calling them "imaginary". The only difficulty is retuning the strings (on an acoustic piano or harpsichord) or convincing an electronic sound module (for a modern electronic keyboard) to produce the bizarre pitches required for enharmonic scale D, E, A, and B notes; the fixed notes (C, F, G, and C′) may also need comparatively slight adjustments, but in enharmonic scales they are all very nearly (or even exactly) tuned to the same relative pitches they have in the conventional modern scale.[4]
For example, in modern
), a simplified version of one of the enharmonic scales is- C (0¢),
- G (700¢).
None of the pitches used in any standard enharmonic scale would actually be rounded to the nearest 50
- C (0¢),
- G (700¢).[4]
The symbol
Note that the modern sharp (♯), flat (♭), half-sharp (), and half-flat () symbols do not (usually) represent fixed pitch changes when used to annotate ancient Greek notes, but instead only the approximate location of the actual pitches used in the Greek scale.
Although the movable notes are highly variable when a scale is devised, after the choice is made, all the notes are stuck in their respective positions until the end of a musical piece. So their use is not like modern musical forms, like the
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
Example of a modern, multi-tone enharmonic scale
As opposed to ancient Greek enharmonic scales, which only employed seven notes in an octave, modern musicians have expanded the idea of an "enharmonic scale" to include most of the pitches which ancient Greek tuning might select from to create a seven pitch octave. This gives the modern musician options for in-effect modulating between multiple different ancient Greek scales. This creates musical options that, as far as we now understand, was never possible for ancient Greeks musicians. Although note that some
Consider a scale constructed through Pythagorean tuning: A Pythagorean scale can be constructed "upwards" by wrapping a chain of perfect fifths around an octave, but it can also be constructed "downwards" by wrapping a chain of perfect fourths 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:
Note Ratio Decimal Cents Difference
(cents)C 1:1 1 0 D♭ 256:243 1.05350 90.225 23.460 C♯ 2187:2048 1.06787 113.685 D 9:8 1.125 203.910 E♭ 32:27 1.18519 294.135 23.460 D♯ 19683:16384 1.20135 317.595 E 81:64 1.26563 407.820 F 4:3 1.33333 498.045 G♭ 1024:729 1.40466 588.270 23.460 F♯ 729:512 1.42383 611.730 G 3:2 1.5 701.955 A♭ 128:81 1.58025 792.180 23.460 G♯ 6561:4096 1.60181 815.640 A 27:16 1.6875 905.865 B♭ 16:9 1.77778 996.090 23.460 A♯ 59049:32768 1.80203 1019.550 B 243:128 1.89844 1109.775 C′ 2:1 2 1200
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
References
- C. H. Ditson & Company. p. 281.. Moore cites Greek use of quarter tones until the time of Alexander the Great.
- ^ a b c d Callcott, John Wall (1833). A Musical Grammar in Four Parts. James Loring. p. 109.
- ^ a b c Elson, Louis Charles (1905). Elson's Music Dictionary. O. Ditson Company. p. 100.
- ^ a b c d e f g h i j k l m
ISBN 0-19-814975-1.
- Claudius Ptolemy (Harmonics), and Boethius.
External links
- Barbieri, Patrizio (2008). Enharmonic instruments and music, 1470–1900. Latina: Il Levante Libreria Editrice. Archived from the original on 2009-02-15. Retrieved 2008-12-17.