Handout: Juxta artem conficiendi: Notating and Performing Polyphony in Solmization Society for Music Theory, 40 th Annual Meeting Arlington, VA Nov. 2, 2017) Adam Knight Gilbert akgilber@usc.edu Ex. 1: Deductiones Ex. 2: Octaves and Solmization 1
Ex. 3: Dufay, Le serviteur with solmization (mm. 28-33) If anyone were to say to me, Tinctoris, I ask of you of what tone is the song, Le serviteur?, I would reply generally of the first irregular tone, since the tenor, the principal part of this song, is of this type tone. If, however, he would ask specifically of what tone is the supremum or contratenor, I would reply specifically that the former and the latter are also of the second irregular tone [hypodorian]. 1 The classification of the contratenor in mode 2 is surprising, since its range is exactly that of the tenor, and even the distribution of the notes within the range is very similar. The most notable difference is its final note, g. Only if this note is taken as the modal final and the range and scale are considered in relation to this note, can this voice be said to be in mode 2. This might be an extreme consequence of Tinctoris's adherence to the omnis cantus definition. 2 Ex. 4: Rules for Counterpoint Anonymous, Regulae cantandi contrapunctum Note that over every ut, the unison is ut, the third mi, the fifth sol or ut, the sixth la or re, the octave fa or ut, the 10th la or re, the 12th sol or ut, the 13th la or re, and the 15th fa. Note that over every re, the unison re, the third fa, the fifth la or re, the sixth mi, the octave sol or re, the 10 th fa, the 12 th la or re, the 13 th mi, the 15 th sol, etc. Note that over every mi, the unison is mi, the third is sol or ut, the fifth mi, the sixth fa or ut, the octave la or mi, the 10 th sol or ut, the 12 th mi, the 13 th fa, the 15 th la. Note that over every fa, the unison is fa, the third la or re, the fifth fa or ut, the sixth sol or re, the octave fa, the 10 th la or re, the 12 th fa, the 13 th sol. Note that over every sol the unison is sol or ut, the third mi, the fifth sol or re, the sixth la or mi, the octave sol or ut, the 10 th mi, the 12 th sol. Note that over every la, the unison is la or re, the third fa or ut, the fifth la or mi, the sixth fa, the octave la or re, the 10 th fa, the 12 th la. The rule stated above is general and should serve the entire hand. 3 1 Johannes Tinctoris, Concerning the Nature and Propriety of Tones (De Natura Et Proprietate Tonorum), trans. Albert Seay (Colorado Springs: Colorado College Music Press, 1976), 24-25. Tinctoris designation of the mode as irregular stems from the fact that the mode of Le serviteur is in transposed to C, a step lower than regular mode 1. 2 Frans Wiering, The Language of the Modes, (2015), 52. 3 Christian Meyer, Tractatus De Cantu figurativo et de contrapuncto (c. 1430-1520) (American Institute of Musicology, 1997), 50-51. 2
Example 5: Juxta artem conficiendi, Counterpoint Notated in Solmization 4 5a: Example of Simple Counterpoint "simplex est note contra notam in eadem specie, cuiuscumque signi formatio ut sic, ponendo tenorum ut re mi fa sol la, discantus iungitur simul in octav ut sic: sol fa sol la fa sol, contratenor iungitur simul in unison ut sic: sol re sol fa re ut;" simple counterpoint is note against note of the same type, as is formed like this: assuming that the when the Tenor is like this: ut re mi fa sol la, the discant joins in at the same time at the octave like this: sol la fa sol la sol, and the contratenor joins at the same time at the unison like this: sol re sol fa re ut. Cantus Sol Fa Sol La Fa Sol Tenor Ut Re Mi Fa Sol La Contra Sol Re Sol Fa Re Ut Ex. 5b: Example of Florid Counterpoint, Leaps and Neighboring Tones cum enim aliquis tenor sic formatur: ut re ut fa fa mi fa sol mi la sol fa sol sol, tunc discantus potest simul iungi in octava ut sic: fa mi fa sol sol la sol mi fa fa fa re mi mi, tunc contratenor iungitur istis vocibus cum tenore in unisono: sol re sol fa [fa] sol fa re mi ut sol la re re et caetera. when someone forms the tenor like this: ut re ut fa fa mi fa sol mi la sol fa sol sol, it can be joined by the discantus at the octave like this: fa mi fa sol sol la sol mi fa fa fa re mi mi, and the contratenor can join its voice with the tenor in unison: sol re sol fa [fa] sol fa re mi ut sol la re re, etc." Cantus fa mi fa sol sol la sol mi fa fa fa re mi mi Tenor ut re ut fa fa mi fa sol mi la sol fa sol sol Contra sol re sol fa fa sol fa re mi ut sol la re re 4 Christian Meyer CSM 41, 98-100. 3
Ex. 5c: Florid Counterpoint Si tenor formatur sub huiusmodi forma: ut mi sol la sol mi ut, ita quod variatur penes ascensum et descensum, discantus ponet simul iungi in octava in ista forma tenens unisono: fa fa fa fa fa fa fa. Contratenor vero iungitur tenori in unisono ut sic: ut ut ut fa ut ut ut. Example for the fourth [rule]. If the tenor is formed in this manner: ut mi sol la sol mi ut, in such a way that it varies in ascent and descent, the discant shall join in the same time at the octave, formed by holding a unison like this: ut ut ut ut ut ut. The contratenor will however join the tenor at the unison like this: ut ut ut fa ut ut ut. Cantus fa fa fa fa fa fa fa Tenor ut mi sol la sol mi ut Contra ut ut ut fa ut ut ut Ex. 5d: Decimae with Solmization Si tenor sic formatur tenens simul processum in unisono, ut sic: ut ut ut ut ut ut ut, discantus iungitur simul in octava, ut sic: ut mi fa ut fa fa. Contratenor vero iungitur tenori in unisono ut sic: sol mi ut re mi ut ut. An example of another form. If the tenor is formed by holding the same procedure in unison, like this: ut ut ut ut ut ut, the discant joins at the same time at the octave. like this: ut mi fa mi ut fa fa. The contratenor however joins the tenor in unison like this: sol mi ut e mi ut ut. Cantus ut mi fa mi ut fa fa Tenor ut ut ut ut ut ut ut Contra sol mi ut re mi ut ut 4
Ex. 6a: Kyrie, Ockeghem Missa Quinti toni (mm. 1-4) Ex. 6b: Hidden Imitation and Retrograde in Kyrie, Missa quinti toni (mm. 8-13) Ex 6c: Scala peccatoris in Agnus, Missa Quinti toni 5
Ex. 7a: Chaminata ( Passamezzo antico in dur ) Ex. 7b: Chaminata ( Passamezzo antico in molle ) Ex. 8: Faburden and Solmization 6
Ex. 9: Elision and Mutation in Isaac, Pleni, Missa Quant j ay au cuer (mm. 79-85) Ex. 10: Motives Expressed as Solmization 7