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I am a bit confused by this phrase in a text by Italian scholar Benedetti, talking about intervals in music. He writes:

Cum praeterea Ludovicus Folianus aperte monstrarit (etiam si id a diatonico sintono Ptolomei desumpserit) reperiri duos tonos...

I admit I do not really understand the use of the passive infinitive reperiri here and how it combines with the accusative that follows. My gut feeling is that the phrase has a meaning along the lines of:

Moreover, as Lodovico Fogliano has clearly pointed out (even if he borrowed it from the sytonic diatonic of Ptolemy) there are two tones...

But that has no passive sense. Does anyone have an insight into this?

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If you replace "exist" with other viable conversions like "come upon" or "discover" it makes sense. Even better, a phrase like "described in rigorous detail" helps further to enhance a sense on the writing.

In this situation, depending on context, the writer / orator may be implying

  1. two tones have been come upon, regardless of how many exist

  2. two tones have been discovered thus far, and have been formally dilated as important

  3. two tones have been catalogued as the ones that are exhaustive

Since he's talking about Just tuning, with one tone (the major) having a 9:8 (sesquioctavum), while the minor tone has a 10:9 ratio (sesquinonum), I'm guessing this is an exhaustive list of precisely two things that exist in a theoretic human construction. I think the tuning that Fogliano is talking about is Ptolemy's intense diatonic scale (it could be something similar hwv), a scale that contemporaries like Zarlino revered, and which was mathematically fully elaborated. It's something that exists in nature, but also needed to be "discovered" and systematized/developed by people as a concept.

Moreover, as Lodovico Fogliano clearly pointed out (even if he has taken it from the diatonic tone [system] of Ptolemy) two tones to be established/discovered, the major (9/8) and minor (10/9)..."

Honestly, I have no idea what Benedetti is talking about when he brings up the 65 ratio and 64 rat semitones though. The sesquifourth has something to do with ditone 81/64 ratio. The sesquiquinth is a mystery.

Moreover, as Lodovico Fogliano clearly pointed out (even if he has taken it from the diatonic tone [system] of Ptolemy) two tones to be established/discovered, a major (9/8) and minor (10/9) (that is, a sesquioctave, and a sesquinone) -, and three semitones - a major, a minor [average], and a smallest ["minimum"] (that is, the 65th which is major; the sixty-fourth, that is, the smallest ["minimum"]; and average, as .27 to .25 which proportion is called the proud bipartite twenty-fifth) -, and when he knows that the consonant semitone is the sesquiquinth, the ditone the sesquifourth...[blah blah blah about hexachords]; to the knowledge of all the simple consonances, he put his last hand.

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  • Thanks for the detailed comment! I think this makes sense, as with the previous comment. Regarding the other ratios, I believe Beneditti is using "sesqui" in the sense of "one more unit than the whole". So "sesquiquintumdecimum" for the "minimal semitone" is "one more unit than 15", i.e. 16/15 and so on. With that logic, all of the ratios make sense...25/24 for sesquivigesimumquartum, and so on... Apr 30, 2023 at 11:02
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In English, we often say "are found" to mean "there exist", as in "52 species of gastropod are found in Virginia." This phrasing casts the fact epistemologically, suggesting that perhaps more gastropods exist in Virginia beyond the 52 that people have found so far. More often, though, I've seen "are found" written to suggest the fruit of a complete search: "four prime numbers are found in the range of 1 to 10".

I haven't come across reperiri used in Latin for this meaning before, but I'm not well read, so I offer this interpretation as an educated guess.

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  • I had thought along these lines as well. That makes sense! Thank you for the response. Apr 30, 2023 at 11:03

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