Editing Enharmonic scale (section)

== Unfamiliar, variable-size quarter tones ==
An otherwise well regarded 19th&nbsp;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 tone]]s" or any "[[scale (music)|[musical] scale]] proceeding by [[quarter tone]]s". — Elson (1905)<ref name=Elson-1905/>{{anchor|Elsons_stupid_remark_anchor}}

However, enharmonic tuning does seem "imaginary" to many modern western musicians because of the intentional limitations placed into [[12 tone equal temperament|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 music]]al scales (among whom sits Elson<ref name=Elson-1905/>) nor even relatively recently disused tuning systems, such as the [[quarter comma meantone|¼&nbsp;comma meantone temperament]] predominantly used up to the time of [[Johan Sebastian Bach|Bach]], and the later unequal [[well temperament]]s 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<ref name=ML-West-1992/>) into the [[Roman Empire|Roman Imperial era]]. Although still taught as a perfunctory part of [[Hellenistic culture|Hellenistic education]], the enharmonic scale was only rarely – if ever – used during the period of 180~400&nbsp;[[Common Era|CE]] when the Greek musical theory books which still survive were written.<ref>See the articles on [[Claudius Ptolemy]] (''Harmonics''), and [[Boethius]].</ref><ref name=ML-West-1992>
{{cite book
 |last=West |first=Martin Litchfield |author-link=Martin Litchfield West
 |year=1992
 |title=Ancient Greek Music
 |place=Oxford, UK
 |publisher=[[Oxford University Press]]
 |isbn=0-19-814975-1
}}
</ref>

The enharmonic scale uses [[diesis|dieses]] (divisions) which are not tuned in any pitch present on standard modern keyboards,<ref name=Callcott-1833/>
since modern, standard keyboards only have provisions for [[semitone|half-tone]] steps. The two different notations used for vocal and instrumental notes in [[ancient Greek Musical Notation|ancient Greek music notation]] are more tonally versatile, since they are based on quarter-tones = half-sharps, with step sizes that could be altered from a strict quarter tone step.<ref name=ML-West-1992/> Despite the pitches being unknown to naïve occidentally-trained musicians, all the [[musical system of ancient Greece|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 (music)|tonic]] and [[subdominant]] (or [[perfect fourth|fourth]]) (relative to [[C major|C{{sup|Maj}}]], the notes between {{sc|'''C'''}} and {{sc|'''F'''}}), and the other two movable notes between fixed [[Dominant (music)|dominant]] / [[perfect fifth|fifth]] and the [[octave]] (between {{sc|'''G'''}} and {{sc|'''c′'''}}). When expressing notes with modern letter notation, it is conventional to use some elaborately sharpened or flattened version of the notes {{sc|'''D'''}}, {{sc|'''E'''}}, {{sc|'''A'''}}, and {{sc|'''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.<ref name=ML-West-1992/>

Since the [[musical system of ancient Greece|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 [[#Elsons_stupid_remark_anchor|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 [[MIDI keyboard|electronic keyboard]]) to produce the bizarre pitches required for enharmonic scale {{sc|'''D'''}}, {{sc|'''E'''}}, {{sc|'''A'''}}, and {{sc|'''B'''}} notes; the fixed notes ({{sc|'''C'''}}, {{sc|'''F'''}}, {{sc|'''G'''}}, and {{sc|'''c′'''}}) may also need comparatively slight adjustments, but in enharmonic scales they are all very nearly (or even exactly) tuned to the same [[relative pitch]]es they have in the [[12 equal temperament|conventional modern scale]].<ref name=ML-West-1992/>

For example, in modern [[microtone (music)|microtonal notation]], and standard-pitch [[quarter tone]]s (approximately 50[[musical cents|&nbsp;¢]] up = {{music|t}}, down = {{music|d}}), a simplified version of one of the enharmonic scales is
: {{sc|'''C'''}} (0[[musical cents|&nbsp;¢]]), {{sc|'''D'''}}{{music|d}} (50[[musical cents|&nbsp;¢]]), {{sc|'''E'''}}{{music|bb}} (100[[musical cents|&nbsp;¢]]), {{sc|'''F'''}} (500[[musical cents|&nbsp;¢]]),
: {{sc|'''G'''}} (700[[musical cents|&nbsp;¢]]), {{sc|'''A'''}}{{music|d}} (750[[musical cents|&nbsp;¢]]), {{sc|'''B'''}}{{music|bb}} (800&nbsp;¢), {{sc|'''c′'''}} (1200[[musical cents|&nbsp;¢]]).

None of the  pitches used in any standard enharmonic scale would actually be rounded to the nearest 50[[musical cents|&nbsp;¢]], but the approximate positions would be within about ±20[[musical cents|&nbsp;¢]] 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
: {{sc|'''C'''}} (0[[musical cents|&nbsp;¢]]), {{sc|'''D'''}}{{music|##}} (380[[musical cents|&nbsp;¢]]), {{sc|'''E'''}}{{music|t}} (420[[musical cents|&nbsp;¢]]), {{sc|'''F'''}} (500[[musical cents|&nbsp;¢]]),
: {{sc|'''G'''}} (700[[musical cents|&nbsp;¢]]), {{sc|'''A'''}}{{music|##}} (970[[musical cents|&nbsp;¢]]), {{sc|'''B'''}}{{music|t}}(1130&nbsp;¢), {{sc|'''c′'''}} (1200[[musical cents|&nbsp;¢]]).<ref name=ML-West-1992/>

The symbol {{music|t}} in this instance represents a [[half-sharp]], or sharpening by a [[quartertone]], however the actual pitches for [[music of ancient Greece|ancient Greek music]] the half sharp ({{music|t}}) and double sharp ({{music|##}}) pitches were allowed to be anything between around {{music|t}} = 30~70[[musical cents|&nbsp;cents]], and {{music|##}} = 130~240[[musical cents|&nbsp;cents]], depending on the aesthetics of the musician tuning the instrument.<ref name=ML-West-1992/>

Note that the modern sharp ({{music|#}}), flat ({{music|b}}), half-sharp ({{music|t}}), and half-flat ({{music|d}}) 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 [[enharmonic]]ally related to, such as in the quarter tone scale. As an example, F{{Music|sharp}} and G{{Music|flat}} 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 equal temperament|12-tone E.T.]] scale). (''See'': [[musical tuning]] for a more complete introduction to the many non-12-tone E.T. tuning systems.)

[[Musical keyboard]]s which distinguish between enharmonic notes are called by some modern scholars [[enharmonic keyboard]]s, and more generically [[microtonal]] keyboards. (The [[enharmonic genus]], a tetrachord with roots in early Greek music, is only loosely related to enharmonic scales.)

[[Image:Lesser diesis (difference m2-A1).PNG|thumb|right|440px|Diesis defined in [[quarter-comma meantone]] as a [[diminished second]] {{nobr|( {{sub|min}}2nd − {{sup|Aug}}1st ≈ 117.1 − 76.0 ≈ 41.1 [[musical cents|cents]]),}} or an interval between two [[enharmonic|enharmonically equivalent]] notes (from D{{Music|b}} to C{{Music|#}}). {{audio|Enharmonic scale segment on C.mid|Play}}]]