Harmonia & Discordia Among the Sister Arts in the Age of Leonardo and Gaffurio
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This document discusses the relationship between music and other arts like painting during the Renaissance era, specifically during the time of Leonardo da Vinci. It notes that Leonardo viewed music and painting as "sister arts" that both rely on harmonic proportions and composition of proportional parts. The document also examines different historical perspectives on musical development and the relationship between ancient and modern musical traditions from writers in the 15th-18th centuries.
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Harmonia & Discordia Among the Sister Arts in the Age of Leonardo and Gaffurio
- 1. Harmonia & Discordia Among the Sister Arts in the Age of Leonardo
- 21. “Yet, I dare say, if one looks into it closely, our British musicians have found with great subtlety of mind those things they call the induction of proportions, and in that one thing they’ve surpassed all antiquity. But on the other hand, I’m amazed that most of them do not know what they know and what they do not know.” -Richard Pace, De fructu qui ex doctrina perciptiur (1517)
- 26. Guido’s gamut Ut queant laxis re sonare fibris Mi ra gestorum fa muli tuorum, Sol ve polluti la bii reatum, Sancte Joannes.
- 30. “certain pleasantness caused by a combining of sound.” Tinctoris, Terminorum musicae diffinitorium (Treviso, ca. 1495) “A modulation of the voice and a concord of many sounds, as is very evident in mensural music, especially when we sing in three or four concordant parts.” Niccolò Burzio, Florum libellus, 1487
- 31. “According to you, when one sings or plays a work for two voices, it is not harmony but consonance, unless as you say, it has three or four voices. This is a patent falsehood and in this you show what you know, because you ought to know that consonance is only the consideration of the interval between a low and a high note and vice versa... Harmony is the mixture of consonances and dissonances in a composition, because it is quite true that good composers exert themselves to make dissonances marvelously consonant in harmony.” -Spataro (1491, fol. E III)
- 32. “What harmony is. Harmony differs from consonance: consonance consists of two sounds, harmony of three.” Consonances divided by a “sonorous mean.” Gaffurio, De harmonia musicrum instrumentorum opus (1500)
- 33. “[Music] composes harmony from the conjunction of her proportional parts, which make their effect instantaneously, being constrained to arise and die in one or more harmonic intervals. These intervals may be said to circumscribe the proportionality of the component parts of which such harmony is composed – no differently from the linear contours of the limbs from which human beauty is generated.” Leonardo’s proporzionalità armonica
- 34. Leonardo’s proporzionalità armonica “The eye is the true intermediary between the objects and the imprensiva, which immediately transmits with the highest fidelity the true surfaces and shapes of whatever is in front of it. And from these is born the proportionality called harmony, which delights the sense with sweet concord, no differently from the proportionality made by different musical notes to the sense of hearing.”
- 36. “The poet may be regarded as equivalent to a musician who sings by himself a song composed for four choristers, singing first the soprano, then the tenor, and following with the contralto and then the bass. Such singing cannot result in that grace of harmonic proportionality which is contained within harmonic beats... Yet music, in its harmonic beat, makes its suave melodies, which are composed from varied notes. The poet is deprived of this harmonic option...and is unable to describe the harmony of music because he has not the power to say different ghins at the same time.” - Leonardo
- 37. “If attention is paid to the other arts, how much utility has accrued precisely from numbers may be easily perceived; for when you look at painting, you will discover that nothing has been done in it without numerical proportions but you will see that both the measurements of bodies and the mixtures of colors, and thus the beauties of paintings, have been determined according to numbers and symmetries, and that it is thus that the beauties of the paintings have been arranged, and that in turn it is through numbers that the art itself imitates primary nature.” -Gaffurio, De harmonia
- 39. “However, the harmonic proportionality of painting is composed simultaneously from various components, the sweetness of which may be judged instantaneously.” Leonardo
- 40. Harmonic Tempo
- 41. “Music is not to be regarded as other than the sister of painting, in as much as she is dependent on hearing, second sense behind that of sight. She composes harmony from the conjunction of her proportional parts sounded simultaneously, constrained to arise and die in one or more tempi armonici. These tempi surround the proportionality of the component parts of which such harmony is composed no differently from the linear contours of the limbs which human beauty is generated.” -Leonardo
- 49. “This is done by means of harmonic time, and it could be done by a pulse if the time of its beat were uniform; but musical time is more reliable in such a case, for by means of it it is possible to calculate the distance that an object carried by this water travels in ten or twelve of these beats of time; and by this means it is possible to make a general rule for every level canal.” -Leonardo, Paragone
- 52. “Just as the mensura of the human pulse is considered to be one tempo divided into two motions... which physicians call the systole and diastole, and musicians arsis and thesis, so have scholars of later ages ascribed the mensura of a sonorous tempo to the semibreve equal to the tempo of the pulse.” -Gaffurio, Angelicym ac divinum opus musice (1508)
- 54. “[Music] composes harmony from the conjunction of her proportional parts, which make their effect instantaneously, being constrained to arise and die in one or more harmonic intervals. These intervals may be said to circumscribe the proportionality of the component parts of which such harmony is composed – no differently from the linear contours of the limbs from which human beauty is generated.” -Leonardo, Paragone
- 55. Historiography of Music in the Renaissance
- 56. “And how strange that we find in matters of music a situation entirely different from that of the general state of the arts and letters: in the latter whatever comes closet to venerable antiquity receives most praise; in music, he who does not excel the past becomes the laughing stock of all.” -Othmar Luscinius, Musurgia seu praxis musicae (Strasbourg, 1536)
- 57. “Tapissier, Carmen, Cesaris, Not long ago so well did sing That they astonished all Paris And all who came foregathering. But still their discant held no strain Filled with such goodly melody (So folk who heard them now maintain) As Binchois sings, or Dufay. For these a newer way have found In music high and music low, Or making pleasant concord sound, In “feigning,” rests, mutatio. The English guise they wear with grace, They follow Dunstable aright, And thereby have they learned apace To make their music gay and bright.” Martin le France (early 1440s)
- 58. “God...has favored us by causing Adriano Willaert to be born in our day, in truth one of the rarest masters who has ever practices music, a new Pythagoras, as it were, who, after examining thoroughly all of music’s possibilities and finding a vast number of errors, set to work eliminating them and restoring music to the honor and dignity that it once had and rightly should have; he has shown us a reasonable way of composing any song in an elegant fashion, providing a very clear example in his own works.” -Zarlino, Le istitutione harmoniche (1558)
- 59. “Ockeghem was, as it were, the first to rediscover music, then as good as dead, just as Donatello discovered sculpture in his. And might also say that Josquin, Ockegham’s pupil, was a natural prodigy in music, just as our own Michelangelo Buonarotti has been in architecture, painting, and sculpture, for just as Josquin has yet to be surpassed in his compositions, so Michelangelo stands alone and without a peer among all who have practices his arts; both have opened the eyes of all who delight in these arts, now and in the future.” Cosimo Bartoli, Ragionamenti Accademici (1567)
- 60. “There does not exist a singe piece of music not composed within the last forty years that is regarded by the learned as worth hearing.” -Tinctoris, Liber de arte contrapuncti (1477)
Editor's Notes
- The painting shown, “A concert,” by Lorenzo Costa was created between 1485-95, a time when art and music theorists attempted to redefine our understanding of harmony and proportion in their respective disciplines. The three singers are likely performing an isorhythmic motet, a piece in which each performer sings a different text, perhaps each in a different temporal proportions. The confusing musical texture that results is perhaps why the singer in the background, likely singing the most florid contrapuntal line, stares off into the distance, allowing himself to concentrate on his own part without becoming too absorbed in the music and text delivered by the two lower voices. Yet amidst this confusion, the singers are united by harmony and time. But, how did they harmonize? How did they determine the musical pulse? These questions were central to musical theory and practice at the end of the fifteenth century, the same time Leonardo da Vinci sought to define proportional harmony in painting, while simultaneously elevating painting above her sister arts. Today I will discuss trace Leonardo’s voice in the polyphony of debate regarding harmony proportionality and harmonic tempo, comparing his views in particular with those of music theorist Franchino Gaffurio, a Milanese contemporary of Leonardo. Despite the immense amount of discord among competing voices at the end of the fifteenth century, figures like Gaffurio and Leonardo were harmonized in their humanistic motivations.
- This is the lira da braccio, Leonardo’s instrument of choice. The instrument is similar to the violin with an added d string below the low g, which provided players with a drone.
- As you can see from this woodcut, the name of the instrument - lira da braccio - is derived from how it is played. In contrast with modern string instruments, it is held down on the arm, freeing the player’s neck so that she or he can sing while playing. This woodcut shows an idealized performance in which Apollo beats Pan in a musical contest. Apollo, Orpheus, and angelic figures are often depicted playing this instrument, which illustrates the elevated states it and its players enjoyed during the fifteenth century. Leonardo was renowned for his abilities to improvise on this instrument.
- The drawing on the right shows a fantastical design for a lira da braccio by Leonardo, in which the soundboard of the instrument is constructed of a horse’s skull.
- Leonardo’s design was perhaps inspired by ornate and grotesque lire that he encountered as a musician.
- In addition to the whimsical lire, Leonardo designed other fantastic instruments which could surprise certain human limitations. For example, horns operated by bellows in order to compensate for limited human breath.
- One of the most curious designs is for the clavi-viola - a string instrument operated by a keyboard, which produces a more-or-less continuous string sound. The instrument was reproduced recently.
- Leonardo also likely designed costumes, stage machines, and scenery for pageants and proto-operas. The picture above shows his designs for stage machines for the a drama called in 1496.
- Leonardo also executed experiments in the study of acoustics. The drawings here show some of his studies in acoustics and optics, and at first glance, it is almost difficult to tell which is which.
- He also studied the Echo Volume and fading of sound Resonance Velocity of sound Physiology of voice production and a host of other properties of sound and acoustics
- It has often been said that humanism was late to reach music, and in truth, a musical “Renaissance” did not truly begin to pick up momentum until the end of the fifteenth century. Developments in Italy were further hampered because mathematics was neglected in Italian universities, thus impeding the advancement of theoretical knowledge of music, which was traditionally linked with the the other subjects of the quadrivium. T
- There are many classical sources which theoretically discuss music, and I cannot discuss them all today. The most influential, however, were those by Pythagorus and Ptolemy. PTOLEMY’s three-volume Harmonics (Harmonika), written during the mid-2nd century, constitutes the most learned and lucid exposition of music theory in antiquity, its logical, systematic comprehensiveness making it a ‘worthy counterpart’ to the Almagest (Düring). Ptolemy's basic postulate was that the two criteria of judgment or reason and empirical observation should not contradict each other. He criticized the Pythagoreans for frequently postulating theoretical relationships that do not correspond with reality.
- Pythagorus discovered in the monochord, which enables acoustic phenomena to be expressed in visual, geometric terms, a precise scientific instrument by which to measure the numerical ratios of consonances. He therefore conceived of music theory in terms of precise mathematical calculation. Unfortunately, Ptolemy’s writings were not as influential in the centuries that followed in comparison with those of Pythagorus.
- Boethius was the main transmitter classical music theory, and favored the Pythagorean system, which doubted the reliability of the ear as an instrument for judging consonance or intonation. 12 century copy of Boethius’s De institutione musica
- During the 10th and 11th centuries the Pythagorean diatonic musical system espoused by Boethius formed the essential collection of pitches imposed on the repertory of liturgical chant and subsequently became the basis of musical notation – with relatively little concern for the many incongruities that existed between the chant melodies and Boethius’s highly restricted set of pitches. Not until Guido of Arezzo (d after 1033) was Boethius candidly regrouped with philosophers rather than musical theorists; yet even Guido repeated the myth of Pythagoras and the smithy – a myth that espouses the essentially Pythagorean basis of musical thought. Although Boethius’s influence waned in the later Middle Ages as theory became more oriented toward musical practice, his work nevertheless remained an authority of ultimate appeal in musical thought throughout the later Middle Ages and even well into the early 17th century.
- Franchino Gaffurio’s treatises on music were some of the most influential works at the end of the fifteenth, and beginning of the sixteenth centuries. His three most important works were the Theorica musice, Practica musice, and De harmonia. Most musicians had heard of Boethius, but few had access to manuscript copies of his work. Gaffurio’s works not only summarized the major points of Boethius, but also other classical sources, including Ptolemy and Aristoxenes, thus making classical thought on music theory more widely available through the medium of the printing press. Furthermore, while Boethius was not a musician, Gaffurio was a singer, composer, teacher, and choirmaster of Duomo in Milan. Thus, he was able to interpret ancient wisdom in practical ways. One of his scholarly limitations was his paltry knowledge of Greek. He relied primarily on Boethius because Boethius, of course, wrote in Latin, and subsequently commissioned Latin translations of texts originally in Greek. Though his interpretations of classical texts were far from perfect, he provided a foundation on which other theorists, including Spataro, Glarean, and Zarlino, would build.
- Gaffurio’s work was even adapted by John Dygon for English musicians. IN the example above from Dygon’s manuscript Proportiones practicabiles secundum Gaffurium, he has included new musical examples in the English style. One of the most salient differences between them are in the elaborate cadential figures in Dygon’s figures.
- Interestingly, Dygon claims that some of Gaffurio’s “new” ideas had been adopted and practiced by the English for ages, and in fact, evidence shows that they probably had. This idea was echoed years later by Richard Pace, in the quote above.
- Gaffurio does not present a purely Christian vision of celestial harmony, and in one of the plates at the front of his Practica musica, he includes a rather pagan woodcut which features images of the Muses and Roman Gods, corresponding to the planets, of course, in his cosmic representation of music. The curious three-headed dog-snake which bisects the image and also represents the Pythagorean monochord, which stretches from the throne Apollo in heaven all the way down to the earth, thus making the connection between the heavenly “music of the spheres,” and the earthly music made by humans voices and instruments. The three graces next to Apollo, Angelic figures, and the presence of the four elements surrounding the earth, at the bottom of the diagram, completes the cosmic picture.
- Gaffurio and Leonardo were contemporaries who both lived in Milan at the same time, and chances are they knew each other. Emanuel Winternitz, in his book Leonardo as a Musician, suggests that not only were they personally acquainted, but that they lent each other books. He makes this suggestion without any hard evidence, however. Gaffurio and Leonardo were both embroiled in current debates about music and music theory, particularly regarding harmonic proportion and harmonic tempus - the two theoretical debates on which we will focus today.
- Pythagorus via Boethius QUICK EXPLANATION OF GREEK TUNING AND MODES BUILT ON TETRACHORDS GREEK TETRACHORDS and the importance of the fifth, fundamental ratio of 3:2, in contrast to the octave, 2:1 “ WOLF” tone, and impure thirds
- emergence of the hexachord combination of theory and practice Hucbald, who emphasized instruction by aural pedagogy tendency of musicians to develop their own systems with a new emphasis on rhetoric, such Aurelian’s 10th century treatise, Musica disciplina, or a contemporary of Aurelian,
- The Guidonian system provides Gaffurio with a platform in the concluding chapter of his Theoretica musice for a comparison of Greek tonality and Western modality, and a starting place to “cleanse the obscure and flase” of both his predecessors and his contemporaries.”
- Gaffurio’s interpretation of the Boethian modes OCTAVE AS THE PRIMARY DIVISION
- The major advancement is in the transformation of the third. EXAMPLE OF THE SYNTOIC COMMA IN VIDEO Pythagorean major third, 81 / 64, differs from the true harmonic major third, 5 / 4, by a small amount, 81 / 80, known as the syntonic comma. The Pythagorean minor third, 32 / 27, differs from the true harmonic minor third, 6 / 5, by exactly the same amount. The same holds true for major and minor sixths. But, since many music theorists calculated the third according to the Pythagorean system, which does not contain true harmonic major thirds, music tended to avoid thirds, and as a result music did not contain true “harmony” or chords, even if compositions contained many voices and occasional chords resulted from various horizontal overlap of contrapuntal lines. There are occasional compound “consonances,” but no true vertical harmonies. This is similar to works of visual art which appear to contain true linear perspective before it had been explained by concisely by Alberti. But, composers at the end of the fifteenth century begin to make a distinction between “consonances” and “harmonies,” and eventually begin to favor the later.
- Spataro’s definition puts into technical terms a concept that had theretofore been treated rather generally. But whereas Spataro was not specific about the placement of dissonance, Tinctoris is. THe sharpest dissonances are reserved for cadences, the ends of sections. At this points, the outer voices, which must expand to the octave, are governed by the behavior of the other voices, which ordinarily refrain from touching a third or sixth in the final chord.
- Gaffurio does not have a word for a chord as we know it in the modern sense, but the concept certainly exists for him. This is similar to Leonardo’s “proportionalità armonica.” A proportionality is a technical mathematical term which was explained by many, including Boethius. A proportion consists of two terms, but a proportionality consists of three. Simple proportions can become proportionalities when divided by an arithmetic, geometric, or harmonic mean. The terms are in harmonic proportion if the greatest is to the least as the difference between the beast and the mean is to the difference between the mean and the least.
- Here are other sketches for Leonardo’s experiments in optics and acoustics. The differences are almost indiscernible.
- He praises music in comparison with poetry, because of harmony Here, he refers specifically to polyphonic music.
- Though, Leonardo would probably be pleased to know what Gaffurio thought of painting, despite his own pejorative remarks about music.
- Thomas Brachert ‘s study of the Last Supper is one of several that has attempted to find musical proportions in Leonardo’s paintings.
- Leonardo’s main condemnation of music, and consequently his preference for painting, is temporality. Music must be understood in time, where as a painting can be judged instantly.
- Leonardo acknowledges that harmonic proportions are common to both music and painting, but then goes on to stress their main difference - the dimension of time. This point becomes central to his argument, and he states several times that music dies immediately after it is created. In truth, this is a significant problem to the study of music. Until the age of recording, there is simply no way to determine how music sounded. Most music, after all, is not notated, and even when notation does exist, it is often an inadequate semiotic system to convey much meaning at all. Even in modern scores of popular music, one must rely on knowledge of music to interpret rhythms accurately, not to mention infinitely subtle melodic ornaments, dynamic effects, changes in timbre, and the list goes on. The problem with determining tempo in fifteenth century scores was a particular problem, and to understand this, we need to take a quick trot back to the 12th century to examine the birth of rhythmic notation.
- Rhythmic notation was only really essentially when composers and performers became interested in polyphonic music. The example above is from one of the earliest sources for polyphonic music, the Magnus liber organi of music composed at Notre Dame. The source dates from the 12th century though the music is likely older. In this notation, there are three different voices singing simultaneously, creating a polyphonic texture. However, the notational system is unable to denote wide variances in rhythm, and as a result, music from this time was performed in 1 of 6 rhythmic “modes,” or patterns, which are analogous almost to Latin American “claves.” We call this the “Ars antigua”
- In the period that follows, the Ars nova, rhythmic notation advances beyond the limits of the rhythmic modes. However, rhythmic values were not fixed, and instead were determined relatively based upon what came before or after it. The emergence of proto-time signatures also emerges, allowing composers more freedom to create polyphonic music. Composers, particularly ones like Machaut, pictured here, would often include subtle musical-rhetorical games based upon changes in rhythmic proportion. A favorite compositional device of these composers is to change time proportionally at different points in the composition, or even to instruct singers to sing music backwards. There is often wide disagreement among modern musicians and scholars as to how to interpret this complex “mensural notation.”
- Quickly after “mensural” notation develops and notation advances, compositional possibilities explode, and composers begin to fetishize notation as an art until itself. In a brief period known as the “Ars subtillior,” notation became an art object until itself, as in the example above from the famous Chantilly Codex, in which a love song is written in the shape of a heart.
- Brunelleschi’s Dome and Musical Proportion:Nuper rosarum flores, Guillaume Dufay (139?-1474) Though not an “Ars subtilior” composition, Guillaume Dufay’s motet “Nuper rosarum flores,” composed for the consecration of the Florence Cathedral, still follows in the tradition of exploiting complex mensural proportions.
- The temporal proportions of each of the four voices is 6:4:2:3, the same ratio, based upon the a biblical passage from the book of Kings which gives the dimensions of the Temple of Solomon as 60 x 40 x 20 x 30 cubits At the end of the fifteenth century, composers sought to do away with the complex mensural notation which dominated music up to that point, which brings us back to Leonardo.
- New interests in studies of the human body, including investigations by Leonardo himself, let many musicians and theorists to use the human pulse as the basis for determining basic temporal proportions. Leonardo thought the human heart beat was too variable, and sought to find other scientific means to determine musical tempi.
- How fast is a musical beat for Leonardo? In Codex Arundel, one hour is said to contain 1080 tempi, based on human respiration, making one tempo equal to 3.33 seconds, or 18 per minute, or 54 semibreves in Renaissance rhythmic notation.
- Musicians at the time kept the pulse by tapping their feet or hands, as one theorist, Giorgio Anselmi wrote, “the mensura is near enough to a moderate tempo in which the singer, not much accelerating the song or extending the note-lengths, stamps the front part of the foot, keeping the feel still, or claps on hand to the other or the back of the student as regularly as possible. Not surprisingly, this is exactly how Gaffurio pictures himself in his own treatise, tapping the back of his youngest student. The older students are reliable enough musicians that they can keep time by tapping on hand on top of the other.
- Gaffurio and his contemporaries preferred to use the human heart beat, though there was disagreement about whether or not they should measure the interval between the diastole and systole, or whether the beat comprises both the diastole and systole. Gaffurio took the later view.
- This is a view echoed by Tinctoris, “the possibilities of our music have been so marvelously increased that there appears to be a new art, if I may so call it, whose fount and origin is helf to be among the English, of whom Dunstable stood forth as chief.”
- Josquin becomes the hero in the 16th century Thus, over the course of the fifteenth and sixteenth centuries, each generation seems to create its own musical hero, either a contemporary composer or one whose feats were still vivid enough to be remembered. In 1581, Galileli explains that polyphonic music is no older than 150 years, he admits that he can provide no authority for music that old. For him, the oldest music to exist is that which Petrucci printed at the beginning of the 16th century.
- A more fruitful way of treating the evidence may be to suggest that a new era came into being through the expose of music and musicians to a new set of prevailing aesthetic and philosophical impulses, combined with a new set of social and technological conditions and with steady developments in the autonomous aspects of musical technique. THere is no reason to claim that this was a “better” age than its predecessor, yet it does appear to have been new in sufficient measure to warrant a separate historical identity, in part carrying forward certain tendencies of the Middles Ages, in part breaking with them. The refinement of these perceptions, together with the creation of new knowledge on which they may be based, is a major task of further research.”