Enharmonic scale [segment] on C. Play Note that in this depiction C♯ and D♭ are distinct rather than equivalent as in modern notation.Enharmonic scale on C.
In music theory, an enharmonic scale is a veryancient Greek musical scale which contains four notes tuned to approximately quarter tone pitches, bracketed (as pairs) between four fixed pitches.[4] For example, in modern microtonal notation, one of the several enharmonic scales aligned with the conventional key of C major would be
The symbol in this example represents a half-sharp, or sharpening by a quartertone (50cents), although raising pitch by exactly 50cents is not at all required, nor even usual among the different Greek enharmonic tunings, which tended instead to have the movable, inner notes (here, D & E; A & B) variably spaced, with about 20~30cents between each other, and likewise spaced from their closest fixed note (for this example those are C, F, G, and C′).[4]
Bracketing tetrachords
Four of the scale notes – the tonic (C in the example), subdominant (F), dominant (G ), and octave (C′) – are all fixed: They are nearly exactly the same relative pitches in all three categories of ancient Greek scales (enharmonic, chromatic, and diatonic),[4] and in ancient Greek music, the fixed tones relative pitches were very nearly the same as the corresponding notes in the modern conventional scale. On the other hand, the four notes contained between the brackets, from the example D and E (between C and F); and A and B (between G and C′) are the two pairs of bracketed, variable notes; they can have nearly any pitch. After pitches chosen for them, if the interval between a movable note and any other note is about a quarter tone or less, the scale is called "enharmonic". The small, or "microtonal" interval can be between either of the bracketing fixed notes, or from the other movable note, inside the bracket.
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 ancient Greek music from which enharmonic scales come, the meaning of enharmonic not so extreme: It means that the notes are not actually the same, but do only differ in pitch by a very slight amount, and had a similar connotation to "microtonal" in modern musical vocabulary.
Since an enharmonic scale uses (approximately) quarter tones, or more technically dieses (divisions) which do not occur on standard modern keyboards,[2] nor were even used in the preceding western tuning systems, such as ¼comma temperament (the predominant tuning about 200years ago) or well temperament (finally went out of use as conventional tuning about 140~150years ago) the pitches and intervals in the several ancient Greek enharmonic scales are foreign to nearly any modern-trained musician, and generally outside the scope of musical competence of modern occidental musicians: People playing modern fixed-pitch instruments have no opportunity to experiment with musical scales containing these notes, since piano keyboards only have provisions for half tones, as do frets on guitars and mandolins, fingering holes on woodwinds, and valves on brass instruments. This has been the situation for more than 150years for fixed-pitch occidental instruments.
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 19thcentury musicologist once wrote the rather blatantly false definition in his 1905 musical dictionary, that the enharmonic scale is
However, enharmonic tuning does seem "imaginary" to many modern western musicians because of the intentional limitations placed into conventional tuning, and deficient musical training which only prepares modern students to deal with a single tuning system, even though many others were in use in the west in the recent past, and still more are in current use in other parts of the world. Even well-educated musicologists have little or no understanding of ancient Greek musical scales (among whom sits Elson[3]) nor even relatively recently disused tuning systems, such as the ¼comma temperament predominantly used up to the time of Bach, and the later unequal well temperaments based on it.
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[4]) into the Roman Imperial era. Although still taught as a perfunctory part of Hellenistic education, the enharmonic scale was only rarely – if ever – used during the period of 180~400CE when the Greek musical theory books which still survive were written.[5][4]
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 microtonal notation, and standard-pitch quarter tones (approximately 50¢ up = , down = ), a simplified version of one of the enharmonic scales is
None of the pitches used in any standard enharmonic scale would actually be rounded to the nearest 50¢, but the approximate positions would be within about ±20¢ of those shown. It is also not necessary for the movable pitches to all lean toward their lower-bound fixed note; a somewhat more realistic example would be
The symbol in this instance represents a half-sharp, or sharpening by a quartertone, however the actual pitches for ancient Greek music the half sharp () and double sharp () pitches were allowed to be anything between around = 30~70cents, and = 130~240cents, depending on the aesthetics of the musician creating the scale.[4]
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 blues, that use pitch bend on notes played on pitch elsewhere, and for those modern styles that use sliding pitch, at least in principle, any note might be bent during performance. As far as now known, the only form of "pitch bend" used by the ancient Greeks was in the initial tuning, with a bent pitch remaining bent until the instrument was retuned for the next piece of music.
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 enharmonically related to, such as in the quarter tone scale. As an example, F♯ and G♭ are equivalent in a chromatic scale (the same sound is spelled differently), but they are different sounds in an enharmonic scale (as well as nearly every known musical tuning except for the modern 12-tone E.T. scale). (See: musical tuning for a more complete introduction to the many non-12-tone E.T. tuning systems.)
Musical keyboards which distinguish between enharmonic notes are called by some modern scholars enharmonic keyboards, and more generically microtonal keyboards. (The enharmonic genus, a tetrachord with roots in early Greek music, is only loosely related to enharmonic scales.)
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 kitharodes were musically experimental and inventive, and sought musical novelty, so they might well have imagined alternating between different enharmonic scales. They might even accomplished it, by one musician switching between several different kitharas during a performance, with each tuned to a different, but tonally interlocking enharmonic scale.
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.
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), and a natural note is flattened by multiplying its ratio by 243 / 256 . A pair of enharmonic notes are separated by a Pythagorean comma, which is equal to 531441/524288 (about 23.46 cents).
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In music theory, the term mode or modus is used in a number of distinct senses, depending on context.
In music theory, a scale is any set of musical notes ordered by fundamental frequency or pitch. A scale ordered by increasing pitch is an ascending scale, and a scale ordered by decreasing pitch is a descending scale.
Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2. This ratio, also known as the "pure" perfect fifth, is chosen because it is one of the most consonant and easiest to tune by ear and because of importance attributed to the integer 3. As Novalis put it, "The musical proportions seem to me to be particularly correct natural proportions." Alternatively, it can be described as the tuning of the syntonic temperament in which the generator is the ratio 3:2, which is ≈ 702 cents wide.
In music theory, an interval is a difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord.
The chromatic scale is a set of twelve pitches used in tonal music, with notes separated by the interval of a semitone. Chromatic instruments, such as the piano, are made to produce the chromatic scale, while other instruments capable of continuously variable pitch, such as the trombone and violin, can also produce microtones, or notes between those available on a piano.
Microtonal or microtonality is the use in music of microtones—intervals smaller than a semitone, also called "microintervals". It may also be extended to include any music using intervals not found in the customary Western tuning of twelve equal intervals per octave. In other words, a microtone may be thought of as a note that falls "between the keys" of a piano tuned in equal temperament.
In music theory, a tetrachord is a series of four notes separated by three intervals. In traditional music theory, a tetrachord always spanned the interval of a perfect fourth, a 4:3 frequency proportion —but in modern use it means any four-note segment of a scale or tone row, not necessarily related to a particular tuning system.
In music, two written notes have enharmonic equivalence if they produce the same pitch but are notated differently. Similarly, written intervals, chords, or key signatures are considered enharmonic if they represent identical pitches that are notated differently. The term derives from Latin enharmonicus, in turn from Late Latin enarmonius, from Ancient Greek ἐναρμόνιος, from ἐν ('in') and ἁρμονία ('harmony').
In music, flat means lower in pitch. It may either be used generically, meaning any lowering of pitch, or refer to a particular size: lowering pitch by a chromatic semitone. A flat is the opposite of a sharp which raises pitch by the same amount that a flat lowers it.
In music theory, the wolf fifth is a particularly dissonant musical interval spanning seven semitones. Strictly, the term refers to an interval produced by a specific tuning system, widely used in the sixteenth and seventeenth centuries: the quarter-comma meantone temperament. More broadly, it is also used to refer to similar intervals produced by other tuning systems, including Pythagorean and most meantone temperaments.
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 and B♯, or D♭ and C♯. It is equal to the frequency ratio (1.5)12⁄27 = 531441⁄524288 ≈ 1.01364, or about 23.46 cents, roughly a quarter of a semitone (in between 75:74 and 74:73). The comma that musical temperaments often "temper" is the Pythagorean comma.
In music theory, the circle of fifths is a way of organizing pitches as a sequence of perfect fifths. Starting on a C, and using the standard system of tuning for Western music, the sequence is: C, G, D, A, E, B, F♯, C♯, G♯, D♯, A♯, E♯ (F), C. This order places the most closely related key signatures adjacent to one another. It is usually illustrated in the form of a circle.
A quarter tone is a pitch halfway between the usual notes of a chromatic scale or an interval about half as wide as a semitone, which itself is half a whole tone. Quarter tones divide the octave by 50 cents each, and have 24 different pitches.
In the musical system of ancient Greece, genus is a term used to describe certain classes of intonations of the two movable notes within a tetrachord. The tetrachordal system was inherited by the Latin medieval theory of scales and by the modal theory of Byzantine music; it may have been one source of the later theory of the jins of Arabic music. In addition, Aristoxenus calls some patterns of rhythm "genera".
In music theory, a comma is a very small interval, the difference resulting from tuning one note two different ways. Strictly speaking, there are only two kinds of comma, the syntonic comma, "the difference between a just major 3rd and four just perfect 5ths less two octaves", and the Pythagorean comma, "the difference between twelve 5ths and seven octaves". The word comma used without qualification refers to the syntonic comma, which can be defined, for instance, as the difference between an F♯ tuned using the D-based Pythagorean tuning system, and another F♯ tuned using the D-based quarter-comma meantone tuning system. Intervals separated by the ratio 81:80 are considered the same note because the 12-note Western chromatic scale does not distinguish Pythagorean intervals from 5-limit intervals in its notation. Other intervals are considered commas because of the enharmonic equivalences of a tuning system. For example, in 53TET, B♭ and A♯ are both approximated by the same interval although they are a septimal kleisma apart.
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 keys and pitches for these notes. Traditionally, such keyboards use black split keys to express both notes, but diatonic white keys may also be split.
In music, 53 equal temperament, called 53 TET, 53 EDO, or 53 ET, is the tempered scale derived by dividing the octave into 53 equal steps. Each step represents a frequency ratio of 21⁄53, or 22.6415 cents, an interval sometimes called the Holdrian comma.
In music, 19 equal temperament, called 19 TET, 19 EDO, 19-ED2 or 19 ET, is the tempered scale derived by dividing the octave into 19 equal steps. Each step represents a frequency ratio of 19√2, or 63.16 cents.
Diatonic and chromatic are terms in music theory that are used to characterize scales. The terms are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a pair, especially when applied to contrasting features of the common practice music of the period 1600–1900.
The musical system of ancient Greece evolved over a period of more than 500 years from simple scales of tetrachords, or divisions of the perfect fourth, into several complex systems encompassing tetrachords and octaves, as well as octave scales divided into seven to thirteen intervals.
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![Enharmonic scale [segment] on C. Play Note that in this depiction C# and D are distinct rather than equivalent as in modern notation. Enharmonic scale segment on C.png](http://upload.wikimedia.org/wikipedia/commons/thumb/5/58/Enharmonic_scale_segment_on_C.png/220px-Enharmonic_scale_segment_on_C.png)
(400 ¢), E 
(450 ¢), F (500 ¢),
in this example represents a half-sharp, or sharpening by a quartertone (50 cents), although raising pitch by exactly 50 cents is not at all required, nor even usual among the different Greek enharmonic tunings, which tended instead to have the movable, inner notes (here, D & E; A & B) variably spaced, with about 20~30 cents between each other, and likewise spaced from their closest fixed note (for this example those are C, F, G, and C′). [4] 
![Diesis defined in quarter-comma meantone as a diminished second ( min2nd - 1st [?] 117.1 - 76.0 [?] 41.1 cents), or an interval between two enharmonically equivalent notes (from D to C#). Play Lesser diesis (difference m2-A1).PNG](http://upload.wikimedia.org/wikipedia/commons/thumb/c/c0/Lesser_diesis_%28difference_m2-A1%29.PNG/440px-Lesser_diesis_%28difference_m2-A1%29.PNG)
