Harmonia & Discordia Among the Sister Arts

in the Age of Leonardo

Leonardo the Musician

Ancients and Moderns

Competing Classical Systems

“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)

Harmonic Proportions

Guido’s gamut

Ut queant laxis    re sonare fibris Mi ra gestorum    fa muli tuorum, Sol ve polluti        la bii reatum, 

Sancte Joannes.

“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

“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)

“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)

“[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

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.”

“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

“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

“However, the harmonic proportionality of painting is composed simultaneously from various components, the sweetness of which may be judged instantaneously.”

Leonardo

Harmonic Tempo

“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

“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

“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)

“[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

Historiography of Music in the Renaissance

“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)

“Tapissier, Carmen, Cesaris,Not long ago so well did singThat they astonished all ParisAnd all who came foregathering.But still their discant held no strainFilled with such goodly melody(So folk who heard them now maintain)As Binchois sings, or Dufay.

For these a newer way have foundIn 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 apaceTo make their music gay and bright.”

Martin le France (early 1440s)

“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)

“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)

“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)