Pythagorean and éxpressive-function' intonation

C.5. The Italian maniera smorfiosa of violinists and singers inflessioni di voci che fanno 1 cantanti quan- inflections of the voice that singers make do da un tuono passano ad un altro qualun- when they pass from one note to any another que in una gradazione quasi impercettibile, si through almost imperceptible gradations, by nell’aumento che nella diminuzione dell’ acu- both raising and lowering the note — those to e del grave è appunto l’enarmonico, mal- are what we call enharmony, even if they grado che talora essi stessi lo ignorino. I vio- themselves may be unaware of the fact. Violinisti fissano il dito su di una corda, e quindi linists do the same thing when they place the 157 ion indicated above — made a great impression on the audience; the same source adds that even the famous sopranist Giovanni Battista Velluti (1781-1861), active on the 5.113 stage up to 1830, used the same kind of“grace”: Slide or portamento. |...] On the violin it is simply produced by sliding up the finger in close contact with the string, during an even-drawn bow. [...] The portamento, or carriage ofthe voice, as the Italians term it, is an easy mode of sliding from strisciandolo sulla medesima fino ad un altro finger on a string and then slide it up to antuono fanno lo stesso. other note on the same string. one tone to another. Hence second-rate singers find it a convenient method of en- This fashion then extended until it was even identified with a definite name: the “maniera smorfiosa” (i.e. the “mincing” style) of the Italians. In a letter published in the Allgemeine musikalische Zeitung in 1811, Antonio Salieri confirms that it was adopted even by singers, and condemned it roundly: discretion, it adds much to the force of expression; and in Madame Caradori, it was a countering those notes which lie at remote and awkward distances. In some voices it is so fixed by habit, that two bars cannot be sung without it. [...] When used with grace both tender and agreeable. The violinist Paganini, the present wonder of the world, plays an entire cantabile upon one string, sliding through all the intervals with a single finger, — the effect of which is so plaintive and desolate, as to move his audience to tears. Velluti, the first For some time an effeminate and laughable manner of playing their instruments has crept in with various weak solo violinists, which the Italians call the maniera smorfiosa, stemming from an abuse of sliding the finger up and down the string. This singer-master of the age, uses this grace with incomparable beauty; in his voice it imparts a tenderness not to be described. feeble and childish mannerism has, like an infectious disease, spread to some orches- Sentimental ‘salon style’, which had also extended to the cello: “Cellists such as Alexander Batta and J.F. Mendes, who were especially popular with female Parisian audiences, were frequently castigated by ‘refined’ male listeners for their emulation of the popular tenor Giovanni Battista Rubini (1794-1854)”, whose style included “portamento ‘sobs””.''* Such an excessive use of portamento was also peculiar of the tral players and, what is most ridiculous, not merely to our courageous violinists, but also to violists and even double-bass players. Because a tolerated evil always gets worse, such a mannerism, particularly in a full orchestra, must necessarily change a harmonious body into a collection of whining children and miaowing cats. [...] From now on, it is forbidden to employ players or singers who adhere to this method either in the Court Theatres or in the Music Society of the City of Vienna. 1 Clive Brown observes that this shifting is implied by the type of fingering then in use for chromatic notes, illustrated by Leopold Mozart and described above (Section C3.1)." Nicolò Paganini (1782-1840) is also known to have still made use of it.''' About him contemporaries remembered “that enharmonic chromatic scale of many octaves, and that he was accustomed to sliding on a string, a passage described as the maniera smorfiosa of the Italians; called horrible cat-music”.''* From a contemporary witness, we also learn that the cantabile on the [fourth] string was performed by him in the same manner adopted earlier by Mestrino (Fig. C.5.1), which — contrary to the opin102 Quoted from Brown C. 1988: 18, and Zaslaw 1997: 569. “Artificial miaowing” which in 1807-08 the Allgemeine musikalische Zeitung had reprimanded in the performances of the young Spohr, and which, as early as 1805 was satirically cited in other German papers of the time as a style to be condemned (Brown C. 1999: 559, 564-5). 110 Brown C. 1999: 560; this author had already observed that even many of the fingerings by Ferdinand David (1810-73) “have a potential for portamento” (Brown 1994: 130). 11! Stowell 1992: 127 (see e.g. the glissando employed on his variazioni on Rossini’s Moses). 12 Polko 1892: 91 (“quella enarmonica scala cromatica a più ottave, e ch’egli usava scivolare su una corda, un passaggio qualificato per maniera smorfiosa degl’Italiani, chiamata un’orribile musica di gatti”). late-19th- and early-20th-century violinists, and roused Carl Flesch’s criticisms.'" This fashion is confirmed by most early-20th-century recordings and by British orchestras’ performance-style of the 1920s.''° C.6. Pythagorean and ‘expressive-functional’ intonation C.6.1. First mentions in France and Italy. Towards the middle of the 18th century the modern tonal-harmonic approach of the system had begun to impose its needs also on intonation: the power of attraction of the tonic on the leading tone and of the sixth degree on the minor 7th had for example ensured that these two semitones, from being ‘large’ (as they had been in the syntonic-meantone system) were reduced to being ‘small’. In the division of the tone the sharp therefore became sharper than the enharmonically equivalent flat. Already in the last quarter of the preceding century, Christiaan Huygens had offered us a first isolated testimony to the new tonal sensibility by declaring that he pre- I Gardiner 1832: 165. 114 Walden 1999: 192. 15 Stowell 1992: 128. 16 Philip 1994: 200-01 (a habit discouraged, or at least refined, in the late 20th century).

ferred — as a leading-tone interval used melodically — the minor semitone to the large:'!” En jouant en E majeur il est bon de faire When playing in E major it is recomles cadences E-B-E, qui ont quelque chose mended to play the cadences E-E+-E, since de plus tendre et plus plaintif, que E-D#-E they sound more tender and plaintive than quand la feinte est adjoutée au clavier. Mais E-D#-E, [which is played] when the [reladans des accords, surtout a la derniere note tive] black key [= D#] is added on the keyd’une cadence ou la basse est B, le D# vaut mieux. board. But in chords, above all in the last note of a cadence of which the bass is B, the Dt is preferable. C. Violin and woodwinds intonation commandé de fortifier un peu les diéses, en sharpen a little the sharps, by raising them, les élevant, et de radoucir dans la méme pro- and to sweeten the flats in the same proportion, by lowering them. portion les bémols, en les baissant. This obviously reflected on the major 3rd, which from being syntonic (5:4) was wid121 ened by a comma and became Pythagorean (81:64): the third of 64:81, which our moderns in la tierce de 64 à 81, que nos modernes their writings have always taken pains to ont toujours soin de réprésenter comme trésrepresent as very dissonant, is precisely that discordante, dans leurs ecrits, est précithey themselves play when they lay down sément celle qu’ils chantent eux-mémes, lorsqu’ils quittent la plume; du moins est-il The Dutch physicist had also pointed out that on common organs and harpsichords tuned with the quarter-comma (harmonic extension Eb-G#), the key of E minor, compared to that of D minor, a quelque chose de plus plaintif et de plus sounds a little more plaintive and tender, on tendre, a cause des cadences qui se font par account of the cadences that are played with ces demitons mineurs, et aussi quelque cho- these minor semitones, and also a little sad se de triste à cause de quelques consonances on account of certain consonances that bequi en deviennent un peu fausses, et de ce comea little false, and of the fact the tritone qu’on y employe le triton au lieu de la is used instead of the diminished 5th [i.e. Efausse quinte. A instead of C#-G]. 159 the pen; at the very least it is true that it is vrai que c’est celle qu’on chante communé- that which is commonly sung [...] that it is ment [...] que c’est celle que nous font en- that which we hear on the free instruments, tendre les instrumens libres, tels que le vio- such as the violin, cello, etc. when these inlon, le violoncelle, &c, lorsque ces instru- struments are in the hands of one who only mens sont entre les mains de ceux qui ne consults his own ear. Among the many virconsultent que l’oreille (Entre plusieurs vir- tuosos that I could mention, I shall here tuoses que je pourrois citer, je ne nommerai merely mention the name of Monsieur ici que M. DUPORT, pour le violoncelle, 4 DUPORT for the cello in Paris and Monsieur VACHON for the violin.) Paris, et M. VACHON pour le violon). Roussier’s remarks, however, should be regarded with some suspicion, coming as they do from a partisan (and a rather fanatical one at that) of the Pythagorean intona- Only a few years later (1698) Georg Muffat also expressed a similar opinion, complaining about the fact that violinists did not play the leading notes high enough.'"* But it is only in 1760 that we can record the first real codification of this preference. For in that year the fingerings prescribed by Delusse for the flute produce sharps that are sharper than flats.''” As regards singers and violinists, the switching of the two semitones is mentioned ten years later by Abbé Roussier. Although this practice was not generalized (and would not be for a long time) he adds: °° J'ai rencontré en ma vie plusieurs perIn my lifetime I have met many people sonnes a qui leurs maîtres, à ce que ces per- who, from what they told me, had always sonnes me disoient, leurs avoient toujours re- been recommended by their teachers to "” Huygens 1940: 74 (from the manuscript Les divers modes, post 1672). Alexander Silbiger observes that this preference seems to be manifest as early as the Renaissance, since “Vicentino presents a series of cadence formulas in which the seventh degree is raised by an enharmonic diesis (Libro III, Cap. L, fol. 66v), and introduces similar cadences in several of his enharmonic compositions (e.g., ‘Musica prisca caput’, mm. 31-32, 35-36). However, unlike modern musicians, he was not willing to sacrifice the purity of the vertical sonority caused by the raised leading tone; he solved the problem by moving the entire chord up an enharmonic diesis” (Vicentino 1990: 7). ne Haynes 1991: 359, 367 (from the Florilegium secundum, Passau, 1698). | || | N According to Sechet 1975: 10. °° Roussier 1770: 164-5. tion ‘of the ancient Greeks’. But fortunately, independent confirmation is given by Anton Bemetzrieder, music theorist of Diderot’s circle and a supporter of equal temperament, who only six years later was to observe: 122 Let us break down the barrier of our muFranchissons la barriere de nôtre musicien observateur, et examinons un peu les sician-observer [who had ideally divided the sons que les virtuoses ont introduits dans octave into 12 equal semitones] and take a look at the notes that the virtuosos have introl’octave. Le petit excès ou le demi-ton n’est plus le duced into the octave. The small excess or the semitone is no seul intervalle qui sépare la sensible de la tonique; la sixte mineure est souvent plus près longer the only interval that separates the de la quinte; la seconde n’est pas toujours éga- leading tone from the tonic; the minor 6th is lement éloignée de la tonique et de la tierce; la often closer to the 5th; the 2nd is not always quarte est tantôt plus près de la tierce, et tantôt equally distant from the tonic and the 3rd; the Ath is sometimes close to the 3rd, sometimes elle en est plus éloignée. Le virtuose hausse le “diese”, tantôt beau- more distant. '21 Roussier 1770: 213-4; Barbieri 1987a: 167. Until 1987, the official date attesting this inversion was believed to be 1797, the year in which Campagnoli published his violin method, according to Boyden 1951: 212. The forerunners of the new intonation were therefore the violinist Pierre Vachon (1731-1803) and the cellist Jean-Pierre Duport (1741-1818). '? Bemetzrieder 1776: XXIII-XXIV.

coup, et tantôt peu; il baisse plus ou moins les notes “bémols”; il joue la même note “bémol” différemment, suivant qu’elle est sixte mineure ou tonique; le même “diese” differemment, suivant qu’il est sensible, tierce majeure ou tonique: il exerce le méme empire sur les notes naturelles; le si de la seconde corde du violon, qui s’accorde avec le mi de la chanterelle, ne contente plus l’oreille sensible et exercée dans l'accord de sixte, qu’il fait avec le re de la troisième corde vuide. Sometimes the virtuoso raises the sharp more, sometimes less; he lowers the flats more or less; he plays the same flat note differently according to whether it is a minor 6th or a tonic; the same sharp differently according to whether it is a leading note, major 3rd or tonic. It is the same with the natural notes: the B of the second string on the violin, tuned to the E of the first string, no longer satisfies the sensitive and skilled ear in the chord of the 6th, made with the open D-string. The intonation described by Bemetzrieder, though clearly of a Pythagorean type, has however a strong “expressive” or “functional” component.'” For, ironically alluding to Roussíer, who unfailingly harked back to the virtues of the ancient Greeks, he adds: '** 161 new type of intonation had been Bemetzrieder, whereas Dupuy later ascribed its paternity to Roussier. As for Roussier, with the strict Pythagoreanism of the ‘new Greek’, he also criticized the tempered approach that had inspired his adversary. The polemic seemed to lose its virulence only in 1781, when Bemetzrieder left Paris to settle for good in London. "7 Around 1774-8 the switching of sharp and flat by singers was explicitly mentioned also by Jean-Jacques Rousseau, who had probably picked up echoes of the po: lemic: 126 Ceci, je le sais bien, est directement That, I know well, is completely concontraire aux calculs établis et à l’opinion trary to the calculations in use and to the commune, qui donne le nom de semi-ton common opinion, which calls a minor semimineur au passage d’une note à son dièse ou tone the passage of a note to its sharp or its à son bémol, et de semi-ton majeur au pas- flat, and a major semitone the passage of a sage d’une note au bémol supérieur ou au note to the higher flat or lower sharp. But in dièse inferieur. Mais dans ces dénomina- these namings more attention has been given tions on a eu plus d’égard à la différence du to the difference of degree than to the true Suivons pourtant l’usage, et voyons si nous pourrons, sans le secours de la Grece, traiter de la double famille des “dieses” et des “bémols”. En réduisant à sept le nombre infini des sons intermédiaires entre l’ut et le ré, et après avoir consulté l’expérience, je dis: 1°. Les trois premiers et les plus proches de Put, s’appellent forcément ré-bémols, et de- Let us therefore follow the practice, and let us see if we can — without the assistance of Greece — discuss the double family of the sharps and flats. After reducing to seven the infinite degré qu’au vrai rapport de l’intervalle, ratio of the interval, as anyone equipped comme s’en convaincra bientôt tout homme with a good ear and good faith will be immediately convinced. qui aura de l’oreille et de la bonne-foi”. Regarding Italy, Antonio Eximeno had already said the following in 177 5: number of intermediate notes between C and D, and after consulting experience, I say: 1°. The first three, those closest to C, are necessarily called D flat and require, as miquartes, à retourner à l’ut. nor 6ths or as 4ths, to return to C. 2°. Les trois derniers et les plus proches de 2°. The last three, those closest to D, are ré, s’appellent forcément ut-dièse, et deman- necessarily called C sharp and require, as dent, comme sensibles ou comme secondes, leading tones or as seconds, to rise to D. d’aller au ré. 3°. The fourth, positioned exactly half3°. Le quatrième, qui fait justement le mi- way between C and D, is called, as one prelieu entre l’ut et le ré, s’appelle, comme on fers, D flat or C sharp and can resolve on veut, ré-bémol ou ut-dièse, et va à l’ut ou au ré. either C or D. [...] Le virtuose, dans les solo, rend divi[...] The virtuoso, in his ‘solos’, renders nement ces délicieuses nuances; il n’est pas né- these delightful nuances divinely; it is not cessaire de lui en donner des avis: la nature, en necessary to give him advice: nature, having donnant des organes infiniment flexibles, en- gifted him with infinitely flexible organs, seigne tout. suggests everything to him. mandent, comme sixtes mineures ou comme The opposition between the two theorists very soon aroused one those querelles (albeit a minor one) that were so widely cherished in the 18th-century French musical scene: Vandermonde began by claiming that the first to have become aware of the Qualor la voce umana passa per un semituono dalla settima maggiore all’ottava di un tono, quasiché rinforza quella settima, e rende quel semituono alquanto minore di quello che sia sul cembalo. Al contrario qualor discende per un nuovo semituono, come spesso accade nell’espressione patetica, quasiché si rilassa, e rende quel semituono più languido, e alquanto maggiore di quello che sia sul cembalo. If the human voice should move by a semitone [a sharp] from the major seventh to the octave of a key, it strengthens that seventh a little and makes the interval somewhat smaller than what it would be on the harpsichord. If, on the contrary, it descends by a different semitone [a flat], as often happens in the expression of pathos, it relaxes a little and makes that semitone more languid and a little bigger [as an interval referred to the upper note] that it would be on the harpsichord. He adds that the keyboard instruments did not have such flexibility of intonation and were instead unsuited to rendering the new cantabile style.' In 1791 Francesco 135 Cfr. [La Borde] 1781: this small collection of Mémoires contains some Observations by Alexandre-Théophile Vandermonde (p. 39 ff., in which the discovery is attributed to Bemetzrieder), followed by Remarques de M. l'Abbé Roussier sur les Observations de M. Vandermonde (p. 42 ff, in which Roussier claims to have been the first to have drawn attention to the fact in 1770). Roussier’s claims were to be confirmed by Dupuy 1781. 126 Rousseau 1995: 464. Passage already cited in Zaslaw 1979: 54. 123 || | 127 Da Terms introduced by Chesnut 1977: 256, 271. Bemetzrieder 1776: XXVI-XXIX. See also Bemetzrieder [1808]: 6 (Pythagorean scale). 7 Eximeno 1775: 75. '8 Eximeno 1775: 79 (“lo stile che si chiama ‘cantabile””).

Galeazzi also realized, with surprise, that for violinists the leading tone-tonic semi- 2 8 ins À tone was small instead of large (in contrast with what was prescribed by the just intonation that he upheld): '”” Sfgidlaele | 5 Riguardo alla settima v’é una osservazioConcerning the seventh there is one ne in più da farsi, ed & che quando sale di more observation to be made, and it is that grado all’ottava si deve far sempre alquanto when it rises by one step to the octave it alterata, e crescente acciò grata riesca, e sodun semituono minimo, in teorica, € un semia ER 3 5 must always be made somewhat altered and disfaccia pienamente l’orecchio, del che & sharp so that it sounds pleasing and satisfymolto difficile render ragione, poiché se in ing to the ear; which is very difficult to expratica l’intervallo tra settima ed ottava è di plain, since if in practice the interval between the seventh and octave is a minimal tuono maggiore, né sO come conciliar si pos- semitone, in theory it is a major semitone, sa l’una coll’altra. nor do I know how the one can be reconciled with the other. balbf ibe || Progressioni de Quinlw per ‚gradazionv enarmoniche Safe” Mi „dol 3 7 S | 6! fl el ¢ im gl el a di à. AREA S | bd} bal pest Su hd @ | bel % = 2 . A— zE or ‘ lab múb sib fa 7’ be = | ik vt lab er æ# do_ I gol re = mi si Fr ‚fe 2 ; b du be la! He ing — designated notes by their dual enharmonic functions, implying that the flats should still be played higher than the sharps, by means of the flexible blowing techze 72: Studio per famigliarizzarsú col genere. enarmonico , nique, as already seen in Section C.3.2): °° jet OU NP PR, 1. à ane ad 2 24 = 24 z o4 5 5 2 5 2 == | i Ssebs x Wer || He à lame |; to either find fingerings to bring this about or manage by rolling the mouth-hole in or out and strenghtening and weakening the wind. = o 3 nn SOUL: ZZ IRRE aX mibbsihhfabbb = r note a little higher, or the seventh in a dominant chorda little lower etc., then he has = dob ur zum rn À iy di fap does : # | six: fase do, JohR dut cr| re Ya = mit aitof Jet laghE TE gol sih fu do > mb lab > © fy x= ur = = TR dob doll, "he = Iz: Suonv sinonimy = solb: ach fb. dhh E ©) The flute must, like the fortepiano, be tuned to equal temperament. Then if a skilled flutist here or there, where it has a good effect; e.g. wants to make a leading 2 aS = | é 3 la mv JL, S|belbelbalball 3 re oF 5 S A similar conflict between just- and Pythagorean-intonation appears again in 1824, in a document by Karl Grenser on the flute (an author that — throughout the same writ- 163 Shortly after Galeazzi’s treatise, Bartolomeo Campagnoli — a concert performer from Italy who had emigrated to Germany (1751-1827) — published his violin method, the first to prescribe a Pythagorean type of intonation explicitly.'”' Regarding the sharps and flats, only in certain cases does he allow them to be united by temperament. His comment on Examples 225 and 226 of his method is categorical (see Fig. C.6.1): *? 12 Galeazzi 1791: 122. 1 Powell 2002: 148-9. "I The first surviving version of this method “is a parallel Italian/French edition, printed in Florence sometime between 1808 and 1815” (Duffin 2007: 78). At Leipzig, however, in 1824, Breitkopf & Härtel printed the better-known edition, bearing the title Nouvelle méthode de la mécanique progressive du jeu du violon [...] op. 21. The date of the first publication of this work is disputed however. According to Montanari U. 1969: 49, “Fétis quoted from the Bachmann edition (Hannover), in French and German. Probably, the date to be accepted for the first is 1797, and 1803 for the second” (“Fétis cita l’edizione Bachmann (Hannover), in francese e tedesco. Probabilmente si deve accettare, come data della prima, il 1797, della seconda il 1803”). 15? Campagnoli Metodo: 38-9, 129 (plate). This author uses the term “temperament” in the 18th- FIGURE C.6.1. Campagnoli Metodo. See, at the top of the fingerboard, the position of the temperamento, halfway between the sharp and the enharmonically equivalent flat. It should be observed that, though the fingerboard strictly follows the Pythagorean division, some of the fingerings of N°. 226 seem still to adhere to the syntonic-type intonation of Fig. C.3.1 (L. Mozart). century sense: see for example Lirou 1785: 110 (“l'intervalle entre lab et sol#, rendu nul et identifié par le tempérament”). Serre 1763: 13 had already written that in enharmonic transitions it was necessary to unify the notes of the type G# and Ab by means of “temperament” (“le tempérament”).

[Es. 225, Temperamento] Tavola che [Ex. C. Violin and woodwinds intonation 225, Temperament] Table that rappresenta la giusta distanza e la differenza shows the correct distance and difference che si trova tra i tuoni sinonimi meccanica- that is found between the synonymous notes mente accordati sull’organo, pianoforte ed mechanically tuned on the organ, piano and arpa, misurati sulla tastiera del violino; per harp, measured on the violin fingerboard; to servirsi del temperamento bisogna porre le dita sulle corde tra le piccole linee. [...] La giusta intonazione non permette d’adottare il temperamento sul violino, che in certi casi: make use of temperament one must place the fingers on the strings between the small lines. [...] Correct intonation does not allow one to adopt temperament on the violin, ex- 1°. Per diminuire il movimento delle dita; 2°. Per soddisfare la delicatezza dell’oreccept in certain cases: 1°. To reduce the chio accompagnando gli altri stromenti; 3°. delicacy of the ear when accompanying Per facilitare l’agilità: per esempio incontrando il lab e [sol]# sulla terza corda, non bisogna ritirare il quarto dito per porre il terzo other instruments; 3°. To facilitate agility: for example, if one finds Ab and [G]# on the [cfr. Es. 226], ma si deve tenervi sopra il fourth finger and put the third [cf. Es. 226], but one must retain the fourth finger, movquarto modificandolo sino al punto che la natura dell’armonia lo richiede. movement of the fingers; 2°. To satisfy the third string, one must not withdraw the ing it up to the point where the nature of the harmony requires. We can legitimately conclude, therefore, that in his pieces for solo violin he genuinely intended to differentiate the enharmonically equivalent notes (Ex. C.6.1).'” | © N I N NHL T T | : Se” oe. © ann century — favoured the attempts to admit in practice the 7th harmonic, until then considered a ‘diabolus in musica’. Among the violinists, the first to declare that he made use of it was Giuseppe Tartini (who employed it in the form of a minor 7th), followed by Michele Stratico, also of the same school. At the same period, the composer Francesco Bianchi tells us that violinists also utilised the “septimal ratio’ (14:9) to play the Neapolitan 6th. The question is dealt with and documented in Section D.4. C.6.3. ‘Expressive’ intonation in the 19th century. Although the reference to the Pythagorean intonation become almost mandatory in the course of the new century, ”° its effective, actual practice must have been considerably conditioned by factors that we could call ‘expressive’. For example, Bernhard Romberg — in his famous method for the cello, published in 1840 with the approval of Cherubini, Spontini and other musicians — asserts that the leading tones in minor keys were pitched higher than those in major keys. After prescribing equal temperament (though only for beginners), he then adds: 17 [p. 20] Il serait également superflu d’en- [p. 20] It will be equally superfluous to seigner au commencement, à l’écolier, la différence qu’il y a entre un demi-ton produit par un dièze (#) qui hausse ou par un bémol (b) qui baisse la note naturelle. Ces distinctions ne feraient que l’embrouiller. Aussi bien il arrive souvent, comme on verteach the pupil right from the beginning the rean?] commatic interval Ab/G#. Finally let us pass on to examine the position of Wolfgang Amadeus Mozart. In the lessons he gave Thomas Attwood (1785-7) he conformed to what was contained in Leopold’s Violinschule, hence supporting the syntonic ratios of the semitones.'”* As a result Chesnut holds that modern intonation, of an expressive-functional type, “is not appropriate if our goal is to play Mozart’s music as he himself wanted it played”.'”” However, we know that Mozart travelled widely in France and Italy precisely during the years when the evidence (reported above) on the new intonation was multiplying, so probably he also applied it, even if only unconsciously. C.6.2. The ‘harmonic’ (‘septimal’) 6ths and 7ths. The natural tendency to lower the intonation of the flats was probably one of the factors that — in the course of the 18th 15 Campagnoli Fugues: 4. © Mozart W.A. 1965: 6, 8. 55 Chesnut 1977: 271. As we saw in fn. 121, when this important article appeared much of the evidence mentioned here had not yet surfaced. difference between a semitone produced by a diesis (#), which raises the natural note, and a flat (b), which lowers it. These distinctions would do nothing but confuse him. And yet it often happens — as we shall see in ra au chapitre du gout, qu’il faut, pour l’ex- the chapter “On taste” — that for expression pression, prendre, au moyen d’un dièze, une one must play, for the sharp, a note that is a note un peu plus haut, ou, au moyen d’un EXAMPLE C.6.1. Bartolomeo Campagnoli, Six fugues pour le violon seul: see the [Pythago- 165 little higher, or, for the flat a little lower, bémol, un peu plus bas que le calcul théori- than those indicated by theoretical calculaque ne l’indique; ce sont les cas où il y a tion. There are cases where theory and muconflit entre la théorie et le sentiment musical. [...] [p. 127] [...] cette teinte douce et mélancholique qui est 1’attribut du mode mineur. Il faut ajouter à cela que pour renforcer le caractère propre à ce mode, on prend la note sensible un peu plus haut que dans les tons majeurs, et la pétite septième un peu plus bas. sical feeling come into conflict. [...] [p. 127, from the chapter “On taste”] [...] this sweet and melancholy shading that constitutes the attribute of the minor mode. To this we must add that — to reinforce the specific character of this mode — the leading note is pitched a little sharper, and the minor 7th a little lower, than in the major modes. Regarding the ‘taste’ of intonation in Italy, a precious source of information is that of the Roman Filippo Natali, who in 1886 published a series of experimental results obtained with his “diapason differenziale” (“differential tuning-fork”). A first 56 See, for example: Fabricius 1832: 152; Bergerre 1833: 385; Romberg [1840]. Even in Hector Berlioz’s great treatise on instrumentation, the sharp is sharper than the enharmonically equivalent flat, as already noted by Pole 1879: 147 (about Berlioz, see also below, in the present Section). 7 Romberg [1840]: 20, 127.

example of expressive-functional intonation, for the voice, is illustrated in Ex. C62: In questa melodia troviamo lo stesso semitono più piccolo, cioé quello della settima si che ascende all’ ottava do. Nella quarta battuta in quella settima di tono si che scende alla sua quinta diminuita fa, la voce si trova sempre con il fa calante ed il si crescente, da ciò come per sorpresa, scorgiamo che le due note sensibili si fa quarta e settima di tono, che sono la radice essenziale delle modulazioni, appoggiano sempre strettamente verso i loro semitoni prossimi e naturali perché più sensibilmente avvisano l’udito del passaggio In this melody we find the same smaller semitone, i.e. that of the 7th B, which rises to the octave C. In the fourth bar in that seventh step B that descends to its diminished fifth F, the voice will always be found with a flat F and\a sharp B; from this, a little surprisingly, we detect that the two leading tones B F, the fourth and seventh steps, which are the essential root of modulations, always lean closely towards their close and natural semitones so that they may more markedly warn the ear of the immediate pasimmediato a cui tendono; mentre nella setti- sage to which to tend; while in the seventh ma battuta il si che ora é la terza della produ- bar the B, that is now the third of the base, is cente si trova in accordo colla scala tempera- found to be consonant with the tempered ta; come ancora nella decima e dodicesima Ho fatto eseguire da quattro buoni artiI had this brief passage from the second sti, e dopo ho analizzato col mio Diapason movement of Beethoven’s Quartet in C maquesto breve periodo del secondo tempo del jor, Op. 59 played by four good artists and quartetto in do, Opera 59 di Beethoven, ed then analyzed with my Diapason, and I ho rilevato i seguenti spostamenti di suoni noted the following adjustments of notes dalla scala equabile [...] In quest’esempio from the equal-tempered scale [...] In this sopra esposto, nella quarta battuta, in quella example given above, in the fourth bar, in scala discendente in re minore che tocca il that descending scale in D minor played by primo violino e la viola, si trova il do diesis the first violin and viola, there is a C sharp settima crescente, e si bemolle sesta calante; nella sesta, ottava, nona battuta quella settima re diesis crescente che tocca la viola; seventh that is sharp and a B flat sixth that is flat; in the sixth, eighth, and ninth bars that seventh D sharp that is sharp, played by the nella decima battuta quella settima diminuita viola; in the tenth bar that diminished sevfa calante, che tocca il violoncello e poi il violino nella dodicesima battuta. enth F that is flat, played by the cello and then the violin in the twelfth bar. scale; as also in the tenth and twelfth bars all battuta tutti i fa sono giusti, perché il canto ha the Fs are just, because the voice has modumodulato nel tono di fa. lated to the key of F. Quelle differenze di suoni che noi tro- These differences in notes that we find in the major scale, which is based on the viamo nella scala modo maggiore, che é basato sopra i cardini della scienza acustica, foundations of acoustic science, are obvengono avvertite in maggior copia nella served in more abundance in the minor scala modo minore, scala stabilita sopra il scale, a scale established on the sixth degree sesto grado della scala maggiore, in cui é ri- of the major scale, with a sharpening of the dotta alla tonalita alterando il sesto e settimo sixth and seventh steps of the major scale. grado. A BeisIegute. _Lantabile religioso. 8 | _ A PK Y gr Sal ve Re.gi .na ges _ 2 to Hert TO zaam En ne; + a BPH ie mater mise.ri_cor.diae a f sens .. AET Lei SIT SR e } ER .ce.do spes nostra sal.ve. — ° vita dul. Nat + tt | RS PE vita olulcedo; Re. gi-na Sales. EXAMPLE C.6.2. From unknown composer (Natali 1886: 74-5). Similar considerations apply to the stringed instruments (Ex. C.6.3): 38 Natali 1886: 74-5 (he specifies that the Salve Regina in question was by an unknown composer). Autografia F.Bini. Rome. EXAMPLE C.6.3. From Beethoven’s Quartet op. 59 (Natali 1886: 81-3).

si rinvengono sovente, e danno una grazia and they give a particular grace to the phrase. particolare alla frase. In the eighth bar the note F, which is here Nella ottava battuta la nota fa, che in the diminished seventh of the fundamental questo caso si trova come settima diminuita bass note G sharp, is flat; and again the flat C del basso fondamentale so/ diesis, é calante; returns in the tenth bar. cosi ancora nella decima battuta torna la terza When the singing artist expresses the do calante. concept of the melody with correct feeling, Quando l’artista di canto esprime con one encounters the above-described differgiusto sentimento il concetto di questa melo- ences in notes between the voice and the dia, si rinvengono le sopra descritte differen- tempered scale. ze di suoni tra la voce e la scala temperata. Moving on to melodic embellishments, Natali observes: nelle appoggiature ed anche nei mordenti, le note di passo appoggiano sopra le note reali When a good violinist wishes to express a certain grace in playing a melody, he will notice that in suspended notes, appoggiaturas and also mordents, the passing notes lean on the real notes with a very narrow incon un intervallo molto stretto; e tutti i clasterval; and all the classic melodists make fresici melodisti fanno frequente uso di questi ritardi. In Rossini s’ncontrano spesso questi motivi carezzevoli. Trascrivo poche battute che trovo nella sinfonia della Gazza ladra [Ex. C.6.4]. quent use: of these suspensions. Such caressing motifs are frequently encountered in Rossini. Here I transcribe a few bars that I found in the overture to La gazza ladra [Ex. C.6.4]. Il bravo violinista nell’eseguire una melodia, quando vuole esprimere una certa grazia, potra avvedersi che nelle note di ritardo, N) AND CANTABILE. 4 to e TD + tra Pitr7-? LP fPeps,...... ad aan Ct i u & [De Ah! non eredea mi.rer_ … -ü of! pre.sto e-atin.to ee = a N —— ° io + j e © mee + TR + 169 TS + ed a P_ Pp = © 1 Ke et — à — n me al aus, | f 3" A tang EN E Ei Pa oe ; H eo a! fe — Pac ii — d "OF ry . > I 4 yr a dl 4 ”* - re; passa — sti olpardamo _ re chungiorno solo ie: AT aesa in + un # EXAMPLE C.6.4. From Rossini’s La gazza ladra (Natali 1886: 83). . gierno Even in the notes of “gruppetti” he detected a strong gravitational attraction from the note around which they rotate (Ex. C.6.5): 139 sol du __ ro... a ch un gior:noso_lo ? . du — — ro. EXAMPLE C.6.5. From Bellini’s La Sonnambula (Natali 1886: 77-8). Ecco un altro esempio di un periodo intero dell’aria finale della Sonnambula per soprano: Ah! non credea mirarti. In questa melodia appassionata di carattere patetico, nella seconda battuta la terza minore “do” è calante; nel secondo quarto della quarta battuta quel re diesis, e quel fa, note di passo che poggiano sulla quinta mi, sono intervalli picciolissimi. Come gia rilevammo altrove le note di passo che servono di abbellimento alla frase melodica son sempre inter- Here is another example of a complete section of the final aria of La sonnambula for soprano: Ah! non credea mirarti. In this impassioned melody of a pathetic The melodic intonation that Natali presents us with — though clearly Pythagorean in approach — is therefore not easily classifiable, given that all the notes (including the diatonic) are altered according to the ‘function’ that they are required to fulfil. In character, in the second bar the minor third “C” is flat; on the second beat of the fourth bar that D sharp, and that F, passing notes any case, at least as late as the turn of the new century, the wrangle between syntonic and Pythagorean cannot have been definitively sorted out. In the second half of the that lean on the fifth E, are very small intervals. As we already noted above, the passing notes that serve to embellish the melodic line are always very narrow intervals on the note valli molto stretti sulla nota dell’accordo, e of the chord, and these passing notes are queste note di passo nelle melodie di Bellini found frequently in the melodies of Bellini century, the disagreement — or perhaps it would be better to say ‘ambivalence’ — is evident from the following: e In 1845, a flute designed by W.J. Monzani and manufactured by William Henry Potter provided split keys to allow sharps and flats to be played with different pitches (in this case, remarks Ardal Powell, the sharps are higher than the flats).'*° e In 1848 Delezenne, a supporter of just intonation, writes: “Consult some good 139 This is also confirmed by Anglas 1919: 205 (“Il semble même que des altérations plus considérables encore soient pratiquées par les meilleurs artistes, surtout dans 1’exécution des ‘trilles’ et des “gruppetti””). 0 Powell 2002:149.

amateurs who play chamber music and who claim not to confuse the sharp of one note with the flat of the following note. Ask them to play, under your very eyes, first an Af and then a Bb, for example, and you will see that some play the sharp lower than the flat and others exactly the reverse”.'”' A few years later, referring to Pythagorean intonation only, the same author writes that “some performers raise the sharps so much and lower the flats to such an extent that they are incapable of playing a bearable scale when it contains notes with sharps or flats”.'* e Around 1843-55, Hector Berlioz condemned the English concertina, still tuned in meantone temperament (with split keys for the D#/E> and G#/Ab), because this kind of intonation was “fully contrary to the practice of musicians”. He affirmed that the violinists — in solo performances, when playing the leading tones — intoned the sharps higher than those of the equal temperament, while, in the minor 7ths and 9ths, the flats were played by them lower than those of the equal temperament, so that, accompanying the violinists with the concertina, he ironically advises to exchange sharps with flats.'*° e Two French physicists, Cornu and Mercadier, in 1869 performed an experimental test and arrived at the conclusion that the Pythagorean intonation and the just-meantone — which in theory seem to rule out one another — were both in practice compatible: the former was preferred melodically, the latter harmonically.'“* e On the contrary, still in Paris and according to the tests carried out around 1870 by Georges Guéroult, the just intonation was preferred also melodically (Sec- 14 Delezenne 1848: 31 (“Adressez-vous à des amateurs distinguéz qui jouent la musique de chambre et qui disent ne pas confondre le dièse d’une note avec le bémol de la note suivante. Priezles de faire sous vos yeux successivement la# et sib, par exemple, et vous verrez que les uns font le dièse plus grave que le bémol et les autres précisément le contraire”). 14 Delezenne 1855: 14 (“quelques praticiens montent si haut les dieses et descendent si bas les bémols qu’ils sont incapables d’exécuter une gamme supportable quand elle contient quelques notes diésées ou bémolisées””). 171 tion B.5.5). Gueroult’s findings are in perfect agreement with Helmholtz’s.'* e Towards the end of the century the Reverend John A. Zahm, a professor of physics, made tests with the Hungarian violinist Ede Reményi (1828-1898), checking the performance with a harmonium tuned in just intonation: “the results arrived at were identical with those obtained by Delezenne and Helmholtz”.'*° He also observes: The good violinists and violoncellists, when unaccompanied by equally tempered instruments, execute pieces of music written for harmony, in pure intonation, is well known. This accounts for the remarkable purity and fullness of tone that characterize the playing of such artists as Remenyi, Joachim, Popper, Wilhelmj, and Ole Bull. In listening to such performances, one can always hear distinctly the Tartini, or beattones, that add such richness and volume to violin music. [...] Remenyi tells me that when he is not accompanied by a keyed instrument, he instinctively plays in pure intonation, and that he feels the difference between notes like D# and Eb, or G# and and Ab, for instance, of which equal temperament can take no account. Only starting from the new century did the neo-Pythagorean tendency begin to be widely reported: (1) see the surveys made in 1987 of certain recordings of the early 20th century;'*’ (2) also a 1937 test by the acoustician P.C. Greene, involving analyses of a total of eleven unaccompanied performances by six professional violinists, gave results statistically in agreement with the last-mentioned intonation;'** (3) in 1949 another acoustician, J.F. Nickerson, reached the same conclusions; furthermore, after measuring the sizes of the intervals in six performances of the Emperor Quartet by Haydn, he found that Pythagorean intonation was on the average also adopted in ensemble music.“ Only around the 1970s, following the Early Music revival and then only by specialist performers, ‘just-meantone’ intonation once again began to be applied. One of the first treatises to provide instructions on how to realize it, on both unfretted string instruments and equally-tempered ‘baroque’ woodwinds (by means of special fingerings), was that by Claudio Di Veroli.'” 14 Berlioz 2003: 466-8; Id. 2002: 305-11 (on the English concertina see also Section B.5.6, fn. 138). An indirect confirmation of Berlioz’s assertions is offered by a letter written by Moritz Hauptmann in 1836. Referring to the tempered tuning of the piano, he observes: “It is a matter of easy calculation, that in respect of C, C sharp is lower than D flat; but if I use C sharp as leading note, and D flat as minor ninth, my first note is far ahead of the other; consequently, it is not the slight deviation of temperament which baulks and disturbs the violinist” (but instead the rigidity of the piano’s tuning). Hauptmann concludes by noting, with some indignation, that Louis Spohr had a very different opinion: “Now I come to the temperament of the voice! Do you know that Spohr maintains, that the singer should learn intonation from a piano in equal temperament? — ! —? — —; what marks of admiration can I use?” (Hauptmann 1892: 150, Hauptmann to Hauser, Cassel, 20.2.1836). This opinion is confirmed by Spohr himself in his Violin School: “By just intonation I mean that which is according to equal temperament; for modern music no other exists”; he also adds: “If you raise D a semitone, or lower E a semitone, the two notes will coincide” (quoted in Goddard 1901-02: 64). '* Cornu & Mercadier 1869. 'S Helmholtz 1885: 325 had occasion to demonstrate experimentally that the major 3rds of the scales played by Joseph Joachim — who tuned his violin in pure 5ths — were perfectly just. This is curious, since the famous violinist — like his teacher Moritz Hauptmann — upheld the Pythagorean intonation of sharps and flats (Pole 1879: 147-9). ra Zahm 1892: 441-3 (with reference to just intonation). im Jackson 1997: 148. | 149 Greene 1937. See also Fik 1995: 91. Fik 1995: 91. The Pythagorean intonation was also confirmed in performances by Soviet violinists, according to the tests made by A.V. Rabinovitch (1932) and N.A. Garbuzov (1955) (Fik 1995: 93-4). Still towards the end of the previous century, on the contrary, when playing in a string quartet, performers preferred pure intonation: in this regard, in 1876 the Genoese music historian Cornelio Desimoni mentioned the contrast between the piano’s equal temperament and the “armonia pura del quartetto o simili stromenti ad arco” (Tarrini 1987: 59). Di Veroli 1978: 215-23.

Nonetheless, purely emotional factors and matters of habit must have once differ- C. Violin and woodwinds intonation 173 C.7. Ensemble music and ‘tempered’ intonation entiated the intonation of enharmonically equivalent keys, such as F# and G major (which in the Pythagorean system, with regard to the respective tonics, are instead In Section C.2 we saw that violin intonation was of the just or meantone type at least governed by the same relative ratios). In a test made in 1862, one that today would be until the 18th century and that that would also apply when the strings were a part of a called of the ‘double-blind’ technique, a Swiss physicist reports on the following cu- ‘concerto’ (mixed consort, i.e. band). In 1609, for example, Adriano Banchieri claims : : 15 rious experiment: to have succeeded in reconciling the different tunings of the various instrument families in a mass for four choirs performed in Verona two years earlier. Among the in- Once we asked a musician whose ear was very Sensitive to play a tune in C major; then we asked for the same tune in the key whose tonic lies between F and G natural on the piano. That completed, we asked him in what key he had just played. “In F#”, he said L’air exécuté, nous lui demandâmes dans without hesitation. We said that he had quel ton il venait de jouer. — En fat, répon- played in Gb. “No” he replied “it is too brildit-il, sans hésiter. — Nous lui dimes qu’il liant, it is F# and not Gb. Wait” he continued avait joué en sob. Non, reprit-il, c’est trop “here is Gb major”: and he played the same éclatant, c’est du fat, et non du sob. Tenez, tune without changing the tonic, but introcontinua-t-il, voici du sob majeur, et il joua ducing several modifications that gave the struments were violins, viols of various types, two harpsichords, ‘big’ organ, lutes, chitarroni, and trombones. The instructions he provided required that the individual Nous avons une fois demandé à un musicien dont la délicatesse de l’oreille est bien connue, de jouer un air en uf majeur; puis nous l’avons prié de jouer le même air en prenant pour tonique la note qui se trouve sur le piano entre le fa et le so/ naturels. le méme air, sans sortir du ton, mais en inpiece a certain sweetness, which to my ears troduisant quelques modifications qui don- seemed to bring it closer to a minor mode. nèrent de suite à l'air une certaine douceur, quelque chose qui, à mon oreille, semblait se rapprocher d’un ton mineur. violins were also automatically tempered (Fig. C.7.1). Besides, this is the practice followed by many modern early-music consorts. The situation changes radically in the 18th century, and not only for the reasons given in the preceding section (concerning ‘expressive-functional’ intonation). During this century the widening of the tonal spectrum and the proliferation (especially among Italian composers) of enharmonic transitions, led to the unification of the two semitones (large and small) around a mean value. On this subject we will return below. °° We have seen that in 1843-55 Berlioz reported that violinists, playing solo pieces, This is indirectly explained in a passage by Modeste Grétry (1789): 152 En procédant par ‘dieses’ our par ‘bémols’ les gammes ont-elles différens caractères? Oui, sans doute, puisque c’est procéder par ‘quintes’ ou par ‘quartes’. Quel musicien n’a pas remarqué que le ‘diese’ un peu forcé, et le ‘bémol’ un peu foible, contentent l’oreille, et que le contraire est insupportable? strings of the plucked and bowed instruments — violins included — be tuned in unison with the corresponding keys of the organ or harpsichord (for which he illustrates a tuning of the regular meantone type, extending from B» to G#). There is therefore no doubt, though there is no explicit confirmation to that effect, that the open Sths of the If one proceeds by sharps or by flats, do the keys have different characters? Yes, without doubt, since it is a matter of proceeding by fifths or by fourths. What musician has not noticed that a slightly sharp sharp and a slightly flat flat satisfies the ear, whereas the opposite is unbearable? Besides, these practices are justified by a deeply-rooted conviction of musicians that is already recorded around 1774 in the Traité du violon by Théodore-Jean Tarade: “Many people believe that the flats always give minor keys and the sharps major keys: this is an error”. ” 'S! Prevost 1862: 21. 152 Grétry 1789: 361. 13 Tarade c1774: 24 (“Beaucoup de personnes s’imaginent que les bémols en général donnent toujours des tons mineurs et les dièzes des tons majeurs, c’est une erreur”). intoned the sharps higher than the enharmonically equivalent flats, adding however that most of them abstained from doing so in concerted music, so as not to create clashes with other instruments. “°° This practice, however, did not necessarily lead to a IS Banchieri 1609: 51-5; Id. 1611: 97-8. For other problems, again relating to the co-existence of strings with the various families of the Baroque ‘concerto’, see Barbieri 1990c. 155 Tt is worth noting that as late as the mid 18th century only Quantz 1752: 248 was to continue to claim that wind and string instruments must genuinely perform the quarter tone even in enharmonic transitions. In passages of the type F-Ab / E-G# he in fact prescribes that the violinist should “retirer le doigt un peu sur le diése qui suit le b mol; autrement la tierce majeure [E-G#] seroit trop haute contre la partie fondamentale”. Similar instructions apply also to the transverse flute, oboe and “tous les instrumens, excepté au clavecin, où l’on ne peut pas effectuer des sous-demi tons, et lequel pour cette raison doit avoir une bonne temperature, afin qu’on puisse souffrir l’un et l’autre de ces tons”. Identical considerations were repeated in the German edition printed posthumously and near the threshold of the 19th century (Quantz 1789: 244). Romberg [1840]: 134, on the other hand, prescribes: “Relativement aux sons enharmoniques [he provides the ex. D#/Eb], je dois faire remarquer encore que, soit qu’on passe d’une note bémolisée a une diézée, ou d’une note diézée a une note bémolisée, on fera toujours mieux de laisser le doigt dans sa position que de la changer”. 156 Berlioz 2003: 468 (“T'immense majorité des musiciens s’en abstient instinctivement dans les ensembles harmoniques. D'où il résulte que les sons prétendus inconciliables par les acousticiens [i.e. sharps and flats] se concilient parfaitement dans la pratique musicale”).