Emilio de’ Cavalieri’s mysterious enharmonic passage

Emilio de’ Cavalieri’s surviving music sources:

• The monody Godi turba mortal and the ballo O che nuovo miracolo are in: 1591, Intermedii et concerti, fatti per la Commedia rappresentata in Firenze nelle nozze del serenissimo Don Ferdinando Medici, e Madama Christiana di Loreno, gran duchi di Toscana. The print was made by Cristofano Malvezzi, after the task was delegated to him by Cavalieri. Modern edition available on imslp.
• Lamentations and Responsories for the Holy week: a complete set of Lessons for the holy week, a set of Responsories, an incomplete set of other Lessons and alternative sections for the incomplete set. Undated manuscript: O. 31, biblioteca Vallicelliana, Rome. Free modern edition available on imslp.
• Rappresentatione di Anima e di Corpo, Rome 1600. Print available on imslp.

Nicola Vicentino's treatise:

Nicola Vicentino, L'antica musica ridotta alla prattica moderna (Rome, 1555) [imslp]

Footnotes:

1 [01:28] “Aria di Fiorenze” / “Il Ballo del Gran Duca” / “Ballo di Palazzo” and more. See Groves, “Cavalieri, Emilio de’”, Claude V. Palisca [link].

2 [01:53] For more information about the Lamentations, see in Elam Rotem’s edition from 2014 [imslp].

3 [02:40] Mercore, 2nd lesson, incomplete set of Lamentations. See no. 20a in Rotem’s edition [imslp],

4 [05:52] Cavalieri commissioned an organ with each tone divided into 10 parts(!). Kirkendale, Warren. Emilio de' Cavalieri "Gentiluomo Romano": His Life and Letters, His Role as Superintendent of All the Arts at the Medici Court, and His musical Compositions. Florence: Leo S.Olschki, 2001, p. 134, 157. Such a division of the tone is greater than this of Vicentino’s, and greater than what is needed to execute his Lamentation’s enharmonic passage.

5 [17:17] Using exclusively just consonances to construct all musically relevant intervals, the diatonic semitone (also called "semitono maggiore", "mi-fa", "leading note", "Cantizans" [in a hard cadence] or "minor second") can be understood as the difference between a fourth (4:3) and a pure major third (5:4), which results in the proportion of 16:15. The chromatic semtione (also called "semitono minore", "chroma", "(chromatic) alteration" or "augmented unison") can be constructed as the difference between a major third (5:4) and a minor third (6:5), which is 25:24. These two semitones add up to the small tone (10:9). In the meantone temperaments, the size of these two semitones (16:15 and 25:24) are very closely approximated. In the special case of quarter-comma-meantone (where all the fifths are pure fifths (3:2) reduced by a quarter of a syntonic comma (81:80 ^ 1/4), both semitones are enlarged by a quarter of the syntonic comma. Whether musicians used the theoretical goal of Just Intonation or were just playing and singing with meantone keyboard instruments, the sizes of the diatonic and the chromatic semitone would have followed this principle. Roughly speaking you could sum it up like this: the diatonic semitone is like three fifths of a tone, the chromatic semitone is like two fifths of a tone. Therefore: the difference between the diatonic and the chromatic semitone is like half the size of the chromatic semitone.

6 [07:56] Vicentino differentiated between small and large diesis (diesis minore and diesis maggiore), the large one being the size of the chromatic semitone and therefore contains two small diesis. The diesis referred to in the video are all small ones (diesis minore).

7 [08:40] These adjectives are spread out all through Vicentino’s treatise. For example f. 4r, 4v, 17v.

8 [09:07] For more details please see the documentation page of Studio31 (www.projektstudio31.com) and its YouTube-Channel. We thank the institutions that granted us access to the Arciorgano [in the video referred to as "Vicentino's organ"], the Hochschule für Musik Basel and the Schola Cantorum Basiliensis.

9 [09:20] This division of the tone into five (equal or almost equal) parts is not precise enough to define the organ tuning. Vicentino describes a method of tuning his Archicembalo on f. 103v in his treatise. He doesn't give any numbers, but he instructs the tuner to start the temperament according to the "usual practice" ("la prima & seconda tastatura secondo l’uso de gl’altri stromenti con le quinte & quarte alquanto sponta- te, secondo che fanno li buoni Maestri"). Because later in the chapter he describes the major thirds to be pure, the assumption of quarter-comma-meantone makes sense. This would cover the complete lower manual with its 19 keys per octave. All the pitches that are notated with a dot are raised by a Diesis, and they are all gathered in the upper manual with its 17 keys per octave. Because the Diesis intervals that occur within the lower manual are just (128:125, for example between e flat and d sharp), we decided to tune all 'dotted' notes a just Diesis higher than their 'undotted' counterparts. Based on this interpretation of Vicentino's instructions we end up with the following model for the tuning: the lower manual consists of a chain of fifths ranging from g flat to b sharp, all tempered by a quarter of the syntonic comma. The upper manual consists of a chain of fifths ranging from g flat to a sharp as a transposition of the lower manual by the interval of 128:125 (Diesis). The organ in this recording was tuned following this model.

10 [10:17] The two recordings referred to are: Le Poème Harmonique / Vincent Dumestre: Cavalieri, Lamentations (ALPHA 2001), and Gesualdo Consort Amsterdam / Harry van der Kamp: Cavalieri, Lamentationes et Responsoria (Sony Classical 2002). There is a third recording of the piece, but it does not include the relevant passage: I Madrigalisti / Livio Picotti: Cavalieri, Lamentationes Hieremia Prophetae (TACTUS 2008).

11 [11:22] 31 October 1592, Letter to Luzzaschi (Kirkendale, 343-344).

Credits:

Created by Elam Rotem and Johannes Keller.

Soprano: Alice Borciani, organ: Johannes Keller, audio recording: Omri Abram

Special thanks to Anne Smith and the Hochschule für Musik Basel / Schola Cantorum Basiliensis.