Dialogue on Ancient and Modern Music

Galilei's Dialogue.

Zarlino's opinion refuted by the Author in chapter 16 of the second book of the Harmonic Institutions.

Zarlino in the second book of the Harmonic Institutions, at chapter 39.

Having understood in detail which numbers contain each of the first sixteen intervals shown, and for what reason; we can now come to discuss the names of the proportions: The mathematical ratios (like 2:1 for an octave) that define musical intervals. that contain them, what they consist of, which are their more or less distant or near parts, and by how much one exceeds or is exceeded by the other. By means of these principles, I will come to clarify the doubts proposed; and to follow the proposed order, we will look at all these details (before any other interval) in the minor and major Semitone: The smallest interval in Western music, roughly half of a whole tone.. Because I desire to be understood by you with the greatest ease I can manage, it is necessary first to know the proper position of the major and minor tones: Whole steps in a scale. according to the common opinion of the practical and theoretical musicians of our times, who claim that what is sung today in the Diatonic genus: The standard musical scale consisting of two whole tones and one semitone. is original: "Syntono di Tolomeo" Ptolemy’s Syntonic; and in what order they proceed through each octave, even for those with a flat: The "b molle" or soft B, which lowers a note by a semitone.. This understanding will be given to you by the examples that follow below, in which the notes are marked according to the mind of Ptolemy himself. Nor can they be tuned in any other order in this species, because the inconveniences mentioned (as appears in the Distribution of Didymus: An ancient Greek music theorist who preceded Ptolemy.) would become even more manifest. The nature, then, of Ptolemy’s Syntonic Diatonic is to proceed from low to high in each of its tetrachords: A scale of four notes spanning the interval of a fourth. by a Sesquiquindecima: The ratio 16:15, representing a major semitone., a Sesquiottaua: The ratio 9:8, representing a major tone., and a Sesquinona: The ratio 10:9, representing a minor tone.. To be better understood by modern practitioners, we will say that in each tetrachord it proceeds from low to high by a major semitone, a major tone, and a minor tone; and conversely from high to low by a minor tone, a major tone, and a major semitone. Such is the Genus in which one composes, sings, and plays today, according to the pleasure of the Reverend Master Gioseffo Zarlino. In refuting his opinion, we will establish (to satisfy your first request, as I promised) the beginning of this our Discourse.

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Musical notation showing a series of chromatic notes with flats and sharps (diesis), each labeled as "Minor Semitone" (Semit. min.).

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The flat never has the minor semitone in the low range, nor does the sharp (X) have it in the high range.

I must warn you at this point that I do not mean for there to be any other intervals in the Syntonic than the pure Diatonic ones, and the others called Chromatic by modern contrapuntists: Composers of counterpoint, the art of combining different melodic lines.. It can be seen, according to the examples of modern practice shown, that the major semitone is marked on different strings (notes), while the minor stays on the same string with some added sign. From this it necessarily follows that the flat never has the minor semitone in the low range, just as the sharp never has it in the high; and the opposite happens to the major, which is exactly the opposite of what occurs in the very ancient Ditonic Diatonic: The Pythagorean tuning system used in antiquity, based strictly on ratios of 3 and 2.. Coming now to reason about the quality and size of the intervals, I say that among the various ones commonly considered by practical and theoretical musicians today, two among them are dissonant...