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Beyond TemperamentNon-keyboard intonation in the 17th and 18th centuriesBruce Haynesİ Bruce Haynes, 2006My system is not based on any keyboard temperament; rather, it displays the sounds found on unrestricted instruments like the cello, violin, etc., that can play purely in tune...(G.P. Telemann, "Neues musicalisches System," 1743/44)"Temperaments" are closed systems designed to help make the intonation of instruments with immovable pitch (like the organ and harpsichord) convincing. But singers and players of stringed and wind instruments have no such limitations -- "temperament" is too rigid a concept to apply to them.Since keyboard temperaments have been studied and discussed for some time,1 it seems odd that the intonation of singers and orchestral instruments has had very little attention.2 It is a subject that is much harder to treat quantitatively, as it depends so much on context. Playing "in tune" is a relative and very personal affair, and no set of rules or abstractions from practice can possibly encompass its complexities, or substitute for an alert ear and a willing spirit. But certain basic assumptions of a singer or violinist in the 17th and 18th centuries concerning intonation were quite different from ours, and an understanding of them is not only useful in everyday ensemble work, but adds an unexplored expressive element to baroque and classical performances. Ultimately, using the available historical information, early musicians must work out this question for themselves.3 The second part of this article therefore presents extensive extracts from original sources on non-keyboard tuning.4Historic expedients to the tuning problemIt is a troublesome physical fact that it is not possible, either in theory or practice, to combine both pure fifths and pure major thirds in the same tuning system. A series of four pure fifths placed above each other (for instance, C-G, G-D, D-A, A-E) will produce a major third (C-E) considerably wider than pure. This is called Pythagorean tuning, a tuning commonly used in the Middle Ages; the fifths are pure, which means the thirds are large --- larger even than in equal temperament.5 A different system, meantone temperament, became common by the middle of the 15th century, in response to the need for better thirds. Meantone favors thirds: in order to get them low enough, the fifths must suffer by being tuned small.6Because of its one great advantage, practicality, equal temperament had some adherents even in the 18th century and before, but the attitude of one writer of the time was probably typical: it produced, he wrote, a "harmony extremely coarse and disagreeable."7 Sauveur in 1707 said equal temperament "...is used [only] among the least able instrumentalists, because it is simple and easy."8By contrast, the most common tuning of the time was described by a number of writers, including Telemann and Quantz, and was engagingly summarized by the singer and musical theorist Pier Francesco Tosi, who wrote in 1723:Everyone knows that there is a Semitone Major and Minor, because the Difference cannot be known [ie. played] by an Organ or Harpsichord, if the Keys of the Instrument are not split. A Tone, that gradually passes to another, is divided into nine almost imperceptible Intervals, which are called Comma's, five of which constitute the Semitone Major, and four the Minor....If one were continually to sing only to those above-mention'd Instruments [the organ and harpsichord], this Knowledge might be unnecessary; but since the time that Composers introduced the Custom of crowding the Opera's with a vast Number of Songs accompanied with Bow Instruments, it becomes so necessary, that if a Soprano was to sing D-sharp, like E-flat, a nice Ear will find he is out of Tune, because this last rises. Whoever is not satisfied in this, let him read those Authors who treat of it, and let him consult the best Performers on the Violin.9Among Quantz's many comments on tuning, he explained thatWhat led me to add another key not previously used on the flute was the difference between major and minor semitones.... The major semitone has five commas, the minor only four. For this reason, Eb must be a comma higher than D#.From our perspective in the late 20th century, we are introduced here to two rather startling concepts:1) the existence of major and minor semitones (a D# different from an Eb, for instance); and2) the possibility, therefore, that on some notes the harpsichord or organ might be tuned differently than the other members of an instrumental ensemble.A system that differentiates between half-steps, according to their harmonic function, suggests refinements unknown to our ears, which have grown accustomed to a mere twelve notes to the octave. But as far as Quantz was concerned in 1752,Appreciation of [this difference between flats and sharps] is needed by anyone who wants to develop a refined, exact and accurate ear in music.Modern players usually raise sharps and lower flats to enhance their melodic function as leading, or "tendency" tones. This practice has its roots at the beginning of the romantic period with the rise of equal temperament,10 and is the reverse of the normal practice of 17th- and 18th-century musicians, for whom leading tones were low. Our contemporary preoccupation with melody is apparently recent; a stronger harmonic orientation and more "vertical" awareness naturally tended to favor the pure major third (which is much smaller than the beating, unresonant equal-tempered one).The pure third is an interval that is both natural and very satisfying to play, and indeed most modern musicians seem to gravitate towards it, especially string players tuning to their open strings. But pure fifths are even easier and yet more tempting to tune on a stringed instrument. Since the end of the 18th century, therefore, fifths have usually won out over thirds in string intonation (cf. the Pythagorean system, with its perfect fifths and high thirds).11 Rameau in 1737, Quantz in 1752 (17/vii/4) and Sorge (1744:53) indicated that some violinists in their day were also inclined to pure fifths, but they considered this a mistake and associated it with poorer players.12 They reasoned that a violin tuned to perfect fifths would be out of tune with the harpsichord or organ, but the deeper implication was that it would also be unsuited to the general intonation system of the period. As John Hind Chesnut wrote (page 271):Modern intonation practice...is not appropriate if our goal is to play Mozart's music as he himself wanted it played. The quasi-Pythagorean "expressive" or "functional" intonation of nineteenth- and twentieth-century non-keyboard instruments is particularly foreign to the tradition in which Mozart stood.Tempering and "intoning justly"We are not dealing here with a closed tuning system based on a circle of fifths like a keyboard temperament. This says nothing about the naturals; it implies a general system but does not indicate any specific temperament.Quantz wrote...the other instruments play [the notes] in their correct ratios, whereas on the harpsichord they are merely tempered."Merely tempered" is the key phrase here. If we use both D# and Eb, G# and Ab, etc.), we will need more than twelve notes in an octave. These different enharmonics are available for the singer or violinist, who is able to adjust intonation while performing, but keyboard players (unless they have instruments with split keys) are forced to resort to complicated systems of temperament."Temperament" in this sense means "compromise," an expedient that attempts to make the best of the fact that only one note can be played when two are needed.13 It is an artifice that gives the illusion that a keyboard instrument is as well in tune as the other instruments when played by musicians with the "refined, exact and accurate ear" of Quantz's time.For non-keyboard instruments, in fact, "temperament" is not even possible. Without a fixed tuning, intonation is influenced by technical situations, subjective perceptions, even differences in dynamics.14 Players of such instruments are incapable (even if they wanted it) of the level of consistency in intonation implied by a temperament.15But although they are not bound by any closed system, it would still be useful to see how original descriptions of their tuning might be roughly fitted into a keyboard system, since they normally perform with harpsichords or organs. A keyboard temperament can also operate as a frame of reference or model, from which singers and players of instruments with flexible intonation can occasionally depart in the context of the moment. Ideally, a "synergetic" relationship will exist, in which the keyboard is first tempered as closely as possible to the physical and musical needs of the other instruments, who in their turn refer back to it for guidance.By definition, we can deduce that a tuning that distinguishes between enharmonic pairs, with sharps being a comma lower than flats, does not resemble either equal temperament or the Pythagorean system (in which sharps are higher than flats). If it is a system at all, it must be closer to either just intonation or some form of meantone.Just intonation "has always had a kind of fatal fascination for musicians because of the purity within the basic scale of the tonic, subdominant, and dominant chords, and of certain melodic intervals"16 that can be easily tuned to the open strings. Some early violin tutors indicate the use of a kind of just intonation, flexibly applied in a limited way (see Rameau 1726 and Tartini 1754:100-101).17 But just intonation is a kind of "holy grail" that is impossible to apply continuously,18 although ingenious attempts at it have been made.19 As Barbour put it,20The bulk of the violinists [in c1730] were probably still accustomed to the just thirds and greatly flattened fifths of meantone temperament.The line between just and meantone need not, of course, be strictly drawn on instruments whose tuning is not fixed.21 Some string players begin with open strings tuned to somewhat narrow fifths and tune intervals purely to the open strings. Wind players, too, tend to adjust long notes purely. Of any consistent system, this tuning most resembles "1/4-comma" meantone ("meantone" in its strictest sense), in which thirds are pure (as in just intonation) and fifths are smaller than pure by 1/4 of the syntonic comma.But the difference between enharmonic pairs in 1/4-comma meantone is much greater than that specified by early sources (41 cents as opposed to 22).22 The consistent use of 1/4-comma meantone is not, therefore, what they describe. Georg Muffat (1698) even warned violinists to resist the temptation to play leading notes too low (sic).Tosi said that "A Tone...is divided into nine...Intervals, which are called Comma's, five of which constitute the Semitone Major, and four the Minor." (The "comma" referred to here is just under 22 cents wide.)23 An example of a major semitone would be C-Db, a minor would be C-C#. Since the first is five commas and the second four, the difference between them is one comma.An octave, as Francesco Geminiani wrote in 1751, can be divided "...into 12 Semitones, that is, 7 of the greater and 5 of the lesser." Since the seven "greater" or major semitones each contain five commas and the five "lesser" have four, the octave will consist of a total of 55 commas, or parts. The 55-part octave, as the sources quoted in Part 2 show, was a familiar concept in the 17th and 18th centuries.24 It corresponds to a temperament known now as "1/6-comma meantone."25
Written SourcesThe term "meantone" was not used in the 18th century; in fact, like many commonly accepted assumptions, musicians were so unconscious of alternatives to a system that included major and minor semitones, that it had no name at all.26Among the more interesting descriptions of non-keyboard tuning are those by Telemann and Quantz. Sorge (1748:61) said that Telemann's tuning system "cannot be applied to a keyboard instrument, but it may be rather convenient for the fiddle and certain wind instruments, and is the easiest for singers." Chesnut has pointed out that Mozart also apparently distinguished the small and large half steps of a meantone temperament similar to 1/6-comma.27 Major and minor semitones were discussed as late as 1813.28In his 1707 Méthode (206), Sauveur classes instruments according to their ability to alter their intonation: the voice and violin are in a class in which accurate intonation depends entirely on the ear, while the keyboards are in one where no control is possible during playing. The woodwinds fall in an intermediate class, and are among instruments...on which the pitch is governed by projections, tone-holes or touchpieces, but that can be nevertheless corrected by a sensitive ear.29A number of woodwind fingering charts from the end of the 17th to the end of the 18th century confirm the use of higher pitches for flats and lower for synonymous sharps, although the exact difference is not specified. Recorder charts are the most informative, since that instrument's inflexible blowing technique requires alternate fingerings for correcting intonation. Among the many fingering charts that appeared for the recorder from 1630 to 1795, the earliest often choose only one of the two enharmonic pairs.30 By 1700, complete chromatic charts began to appear that distinguished most pairs, especially the d#/eb1. The most interesting charts were those by Johann Christian Schickhardt (c1720), which distinguished g#/ab2,31 and Thomas Stanesby Jr. (c1732), that distinguished every chromatic note.32To a lesser extent, traverso charts also offer useful information; Quantz's additional key indicates that tuning corrections were more limited on the traverso than on the double-reed instruments (to which such keys were never added).33Although embouchure adjustments make the oboe's intonation relatively flexible, most oboe charts indicate alternate fingerings for some sharps and flats, from the earliest existing chart (Bismantova, 1688)34 to at least 1816 (Whitely).35 The synonymous pairs that are given the most alternate fingerings are the "left-hand" notes G#/Ab and A#/Bb. The development of double holes on the oboe and recorder has an obvious application for "intoning" enharmonic pairs. On both instruments they affect the most ambiguous pair, G#-Ab.36Bassoon fingering charts also distinguished enharmonic pairs.37 Towards the end of the century, however, keys began to be added whose purpose may have partially been to obscure these distinctions.38Regular vs. irregular temperamentsAs Telemann wrote of his tuning system (1743/44), "It establishes a continuous proportional equality between intervals..." This implies something similar to a standard "regular" meantone temperament, defined by Barbour as one "in which all the fifths save one are the same size."39An interesting attribute of "regular" meantones is the ease with which standard transpositions can be made, since intervals are identical in strategic keys. This would explain how German composers like Bach and Telemann were able to function in meantone while using Chorton and Cammerton simultaneously.40 "Transposing" instruments were a part of life for German musicians at this time. Parts for transposing instruments were notated in different keys than the majority of the parts, because they were "pitched" differently (being tuned to Chorton/Cammerton). The "d'amore" instruments and the violino piccolo also had transposed parts.41Obviously, however notes are notated or fingered, they should be at the same frequency for all the instruments of an ensemble. But the differences in key among transposing instruments were always either a major second or a minor third. Since in a regular meantone, parallel scales a major second or minor third apart would normally be inflected identically,42 their notes would have corresponded closely.43 Meantone tuning will therefore work with transposing instruments, as long as the keyboard instruments in such music are tuned in regular (rather than irregular) temperaments.44A model based on a regular temperament is relatively simple and easy to remember.45 Let us take 1/6-comma meantone as an example. Since most musicians nowadays use a Korg or similar tuning machine, the following table shows where its notes are placed in relation to equal temperament.46C +5 centsC# -8 Db +14D +1D# -11 Eb +10E -2F +7F# -6 Gb +16G +3G# -10 Ab +12A 0A# -13 Bb +9B -4C +5As flattened notes become more distant from C, they become gradually higher, whereas sharpened notes become lower. The note Bb, for instance, is 9c higher than in equal temperament, Eb 10c, Ab 12c, etc. Going in the other direction, F# is 6c low, C# 8c, G# 10c, D# 11c, etc.47Although a regular temperament might have been useful for the keyboard instruments, it is unlikely that other instrumentalists and singers adhered strictly to it, since the thirds and fifths would not have been completely pure. Irregular meantone systems, which favor selected keys at the expense of others, were no doubt also used together with non-keyboard instruments.48 There are clear expressive advantages to these tunings, in which modulations are more colorful.But no system, regular or irregular, could possibly have been applied rigidly on the flexibly-pitched instruments. The regular 55-part octave was no more than a convenient theoretical framework, and it can be used to advantage by present-day musicians with either a similarly tuned keyboard instrument or one tuned in an irregular temperament such as the well-known "Werckmeister III" or "Tempérament ordinaire."Reconciling the keyboard to the other instrumentsDiscussing intonation, Hubert LeBlanc (p.55) commented thatThe divine artistry of Mr Blavet consists in adjusting [the tuning of his] flute by his manner of blowing. But students of the harpsichord praise the instrument for its intonation, not perceiving that it is in fact never truly in tune.It is natural to refer to the keyboard instrument when intonation questions arise in an ensemble, since it is the only instrument with a fixed pitch. But fixed pitch has the defect of its virtue: when the music changes and demands tuning modifications, the keyboard cannot adapt as the other instruments can. It is a case of the immovable object and the irresistible force. There isn't much sense, for instance, in tuning the G# of a flute to a harpsichord with an Ab.A number of sources (among them Sauveur, Tosi, Quantz, Telemann, Tartini, Sorge, and Mozart) accepted the fact that keyboards used different systems of tuning than other instruments.49 There are suggestions as to how the problem was solved. Huygens, Rameau (1726) and Sorge (1744:53, 1758), all assumed that the melody instruments should conform to the keyboard. On the other hand, Rameau (1737), Rousseau (1743) and de Béthizey considered it self-evident that (except for unison notes and final tonics) singers purposely ignored the temperament of the accompanying instruments. Quantz (17/vi/20) proposed a more diplomatic solution in which the fixed-pitch instrument also adapted to the other instruments.In larger settings such as orchestras, a keyboard instrument is considerably less audible than the treble melody instruments. In the case of the harpsichord, the sound dies away quickly, while pure intervals are sustained by the other treble and bass instruments. De Béthizey and Quantz [16/7] suggest that singers and other players would thus do better to adjust to the violins and oboes rather than the harpsichord (cf. also Tosi).50 The problem is more acute for the other bass instruments, since they usually play in unison with a harpsichord or organ.51 There are a number of possible solutions.The idea of a harpsichord or organ with split keys was mentioned by Tosi and Quantz, and evidently used by Handel.52 With both D#/Eb and G#/Ab, the keyboard would have good major triads as far as B and Ab major, making it possible to venture into tonalities with as many as four sharps or flats and still keep the thirds relatively pure.53 For continuo playing, therefore, split keys clearly have a use.54Barbour (1951:191) suggests that, when key changes were limited, it was a historic practice to retune unsplit keyboard accidentals during a program. It takes about as long to change a D# to an Eb on a harpsichord as to tune a section of violins.55Another solution is to use two harpsichords, one tuned (for instance) to sharps and the other to flats. Alternately, one two-manual harpsichord can be used in this way.56Where frequent choices between enharmonics are necessary (ie., when a wide range of keys cannot be avoided), another approach is suggested by several sources. Quantz's "good temperament which allows either [synonymous flat/sharp] to be endurable" and Telemann's enharmonic pairs that are "blended together" on keyboard instruments (1767) imply either the use of an irregular meantone or the splitting of the difference between the two or three troublemaking accidentals within the framework of a regular meantone system.57 The latter compromise (which is necessarily rather colorless in character) might look on a Korg tuner like this:C +5 centsC# -8D +1D#/Eb 0E -2F +7F# -6G +3G#/Ab +1A 0Bb +9B -4C +5This scale is based on 1/6th-comma meantone; C#, F# and Bb plus all the diatonic notes are left in their normal places (see previous table), and the difference between the two ambiguous flat/sharps is split.Some practical considerationsQuantz gave some advice on practicing intonation in 17/vii/8. He advised (as did Leopold Mozart) the use of a monochord to players of melodic instruments.58The best manner of escape from [poor intonation] is the monochord, on which one can clearly learn the intervals. Every singer and instrumentalist should become familiar with its use. They would thereby learn to recognize minor semitones much earlier as well as the fact that notes marked with a flat must be a comma higher than those with a sharp in front of them. Without these insights one is obliged to depend entirely on the ear, which can however deceive one at times. Knowledge of the monochord is required especially of players of the violin and other stringed instruments, on which one cannot use the placement of the fingers as an exact guide, as one can on wind instruments.In our time, we can add that we have all grown up in a prevailing atmosphere of approximate equal temperament, making the help of a reference beyond our ears even more necessary. There is a "black box" on the market that functions much like a monochord; it is designed to play in any temperament the user wishes.59A player using meantone as a model is theoretically expected to have alternate flats and sharps available for every note, but in practice, some accidentals are rarely used, since 18th-century music usually stays within the bounds of keys with four flats and sharps. One seldom has to play the notes E#, Fb, Gb, B#, Cb, etc. There are, then, three sets of enharmonic pairs that are usually ambiguous and need attention: Ab/G#, Eb/D#, and Db/C#.60 The other notes (C, D, E, F, F#, G, A, Bb, B) are normally always in the same place.The less adaptable to different tonalities a temperament needs to be, the purer and richer it can be. Just intonation, the theoretical ideal, is practical in only one key; equal temperament works in all of them. When planning concert programs, therefore, the choice of tonalities relates directly to the choice of keyboard temperament, and vice-versa.ConclusionIt is hopefully clear by now why the concept of major and minor semitones is fundamental to 18th-century tuning practice, why it can cause problems between the keyboard and the other instruments, and how it logically leads to intonation models that resemble various temperaments known nowadays as "meantone." A closed system is artificial when applied to strings, winds and voices, but it can help players and singers understand how to work with the "immovable object," a keyboard instrument with its fixed pitch, as well as provide them with a frame of reference with which to build a more expressive and "harmonious" structure of intervals.6162