<\/a><\/p>\n \u00a0 \u00a0 \u00a0Benedetti\u2019s puzzles have reinforced the modern view that Just tuning is impossible in practice\u2014that the theory of pure intervals was not transferable to the real world of musical sound even though the ratios were set forth so unanimously by theorists of the Renaissance. It is true that Zarlino, perhaps the most conspicuous champion of Just tuning, had to endure criticism from colleagues at the time. But even Vincenzo Galilei, Zarlino\u2019s \u201cmost outspoken and severest critic,\u201dFn30<\/a><\/sub><\/span> in 1589 had to admit that, in practice, singers do use pure intervals rather than tempered ones:<\/p>\n \u2026 truly, voices sing musical intervals in their true and perfect ratio, whereas most artificial musical instruments play them more or less distantly from their true form.Fn31<\/a><\/sub><\/span><\/p>\n \u00a0 \u00a0 \u00a0Among modern critics, Palisca and others implicitly or explicitly call for some form of temperament as the only solution. As Palisca says:<\/p>\n \u00a0 \u00a0 \u00a0In [Benedetti\u2019s] examples, the performance will continue on an even keel only if the true intervals of the senario<\/em> recommended by Zarlino are abandoned through judicious adjustments by the singers. A system of temperament thus becomes a necessity.<\/p>\n \u00a0 \u00a0 \u00a0The solution to the problem is obviously equal semitones and tones, or what is called equal temperament.Fn32<\/a><\/sub><\/span><\/p>\n \u00a0 \u00a0 \u00a0Without endorsing temperament, other critics simply discount the utility of Just intonation, as in Blackwood\u2019s comments cited in the Introduction above,Fn33<\/a><\/sub><\/span>and Mark Lindley\u2019s characterization of Zarlino\u2019s flexible Just system based on the senario<\/em> as \u201cmetaphysically inspired nonsense.\u201dFn34<\/a><\/sub><\/span><\/p>\n \u00a0 \u00a0 \u00a0The fact is, the evidence suggests that Renaissance singers did try to follow the precepts of Just intonation, using simple ratios for both melodic and harmonic intervals wherever possible, and since they did not seem to migrate in pitch as would have been inevitable with strict adherence to Just ratios, it behooves us, I believe, to try to figure out what they did. As I hope I have shown, it is possible in problematic passages, and even in Benedetti\u2019s puzzles, to devise solutions that follow principles of Just tuning but that modify only one or two pure intervals, rather than the entire system, as does temperament. This is a compromise, certainly, but I don\u2019t believe it invalidates the whole concept of Just intonation nor necessitates the total replacement of Just tuning with some form of temperament.\u00a0 Moreover, most Renaissance choral works do not contain many tuning problems, if any at all, and thus allow the singers to pursue a goal of Just intonation without the kind of severe difficulty encountered in the Benedetti examples.<\/p>\n \u00a0 \u00a0 \u00a0As a demonstration of this, I have chosen part of a piece apparently composed around the time Benedetti was writing to Rore\u2014the end of the first part of the Tallis Lamentations (see Ex. 6)\u2014and have annotated an untexted score with the notes as they appear, and changes as necessary. The sound examples include an electronic performance to demonstrate the Just ratios under controlled circumstances, a recording by the Hilliard Ensemble (Thomas Tallis: Lamentations of Jeremiah<\/em>, ECM 1341 833 308-2 (1987), trk 1 excerpt), used with the kind permission of ECM Records, and lastly, for comparison, an electronic version in equal temperament. While there are one or two notes in the human performance that may not be absolutely perfect (I\u2019m thinking in particular of the top part in mm. 132-34), it still illustrates, overall, that the ideals of Just intonation can be achieved in practice with stunning effect.<\/p>\n Hilliard Ensemble<\/strong><\/p>\n\n\n\n
\n Example 6. Thomas Tallis, Lamentations of Jeremiah<\/em> (end of the 1st part)<\/strong><\/td>\n<\/tr>\n \n \n