The vocal intonation in Gioseffo Zarlino's theory

Gioseffo Zarlino (1517-1590) , Venetian musical theorist and chapel master in San Marco, revolutionized the conception of vocal harmony through a system that integrated mathematics, natural philosophy and executive practices.

His natural empty theory, exposed in Harmonic Institutions ( 1558), represents a meeting point between the Pythagorean tradition and the needs of Renaissance polyphony, offering an innovative solution in the vocal ensembles.

The scientific foundation of the Senarium  

Zarlino expanded the Tetraktis Pythagorean based on the first four natural numbers by introducing the senario (numbers 1-6), which made it possible to mathematically justify the third (5/4) and sixth (5/3) intervals as consonances.

This approach responded to a practical need: in the vocal polyphony of the sixteenth century, the thirds acquired an increasingly central structural role, despite the Pythagorean system considered to be dissonant.  

The Zarlinian natural scale is built through the following relationships: 

| Interval. | Freq ratio. |  

|————|——————–|  

| Third major | 5/4 |  

| Sixth major | 5/3 |  

| Seventh major | 15/8 |  

These values, derived from the harmonic series, guaranteed a more stable intonation in choirs, particularly in cadences and counterpoint resolutions.
Tsarlino himself observed how singers instinctively tended to these proportions, correcting the fixed temperament tools.

Vocality as an ideal model for Gioseffo Zarlino

For Zarlino, the human voice was the absolute parameter of harmonious perfection. In the Harmonic demonstrations (1571) he claimed that the song embodied the "natural" harmony, in opposition to the "artificial" instrumental tuning.

This position derived from a neo-platonic vision that saw the reflection of Mundana music in vocal music the cosmic harmony ordered by God through numerical relationships.  

The theory found practical application in the management of dissonances: Tsarlino prescribed to limit them to the weak times and to solve them on the perfect consonances (octaves, scenes) or imperfect (third, sexte), according to a system that anticipated the tonal hierarchy.

Its rules for the three -part counterpoint defined as "perfect harmony" demanded the formation of complete triads (fundamental, third, fifth), vertically structuring the polyphonic fabric.

Comparison with instrumental tuning  

While Tsarlino accepted the mesotonic temperament for the keyboard tools (which reduced the scenes of 1/4 of harmony paragraph), insisted on the purity of the intervals in singing.
This dualism reflected the distinction between:

- Artificial music : based on acoustic compromises to allow modulation

- Natural music: based on innate mathematical laws in the human voice

's research , a pupil of Zarlino, however showed the practical limitations of the natural system in modulating contexts, opening the way to the equilial temperaments.
However, recent musicological studies (Zanoncelli, 2017) highlight how the Zarlinian theory remains optimal for the modal vocal repertoire.

Inheritance and contemporary studies  

The rediscovery of Zarlinian theories in the twentieth century influenced:  

• Historically informed executive practice (e.g. vocal ensembles such as the Tallis Scholars )

• The development of micro -sympliers (Benoît Mandelbrot cited Zarlino in his studies on fractal structures in music)  

• Psycho -acoustic research on the perception of consonance (Terhardt, 1984)  

A study from 2015 (Bodrato-Ermacora) experimented experimentally that professional choirs tend spontaneously to the natural intervals described by Tsarlino, with maximum waste of 2-3 percent compared to theoretical relationships.

This confirms the Zarlinian intuition on the instinctiveness of the natural vocal emptying.

Tsarlino's approach to vocal intonation represents a unique synthesis between philosophical speculation and music practice.
Although exceeded by the advent of the shade and equilial temperaments, its system maintains valid:

- in vocal education, as a model for ear training  

- in the contemporary choral composition of modal inspiration  

- as a bridge between acoustics and musical perception  

The recent critical editions of the Zarlinian works (Levi Foundation, 2017) and the international conferences dedicated to him testify to the topicality of a thought that was able to reconcile scientific rigor and artistic sensitivity.

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