Extended-diatonic interval names: Difference between revisions

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In Part 3, Zarlino writes that the Unison, Fourth, Fifth and Octave (and, by extension, 11th, 12th, 15th, 18th, 19th and 22nd) are considered perfect consonances, and that Thirds and Sixths (and, by extension, 10ths, 13ths, 17ths and 20ths) are considered imperfect consonances, after Aristotle. Seconds, Sevenths (and, by extension, 9ths, 14ths, 16ths and 21sts) are considered dissonances. He adds that the imperfect consonances come in two types, 'maggiore' and 'minore', where, for each interval class, the minor is the smaller interval, and the major, the larger, defining therefore, the ditone and essachord as the major Third and Sixth respectively, and the semiditone and minor essachord as the minor Third and Sixth. The major and minor Seconds are then equated to the tone and semitone. Here we begin to see today's interval names.

He adds further,<blockquote>Et la Quarta è di tre sorti cioè la Diatessaron consonanza; il Tritono, che è una compositione di tre Tuoni; & la Semidiatessaron, che è una compositione di un Tuono, & di due Semituoni; i quali intervalli ne i loro estremi sono dissonanti. Questo istosso si potrebbe etiandio dire della Quinta, della Ottava, & della replicate, le quali si lassano per non andare in lungo.</blockquote>defining the two 'extremely dissonant' other types of Fourth as the ''Tritono'', consisting of three tones, and the ''Semidiatessaron'', consisting of a tone and two semitones, and suggesting that similar could be said of the Fifth and Octave, and their (octave) replicates, but will not be, in order that he does not go on too much. These two dissonant fourths correspond to today's augmented and diminished fourth. If the definitions Zarlino alludes to for the fifth, octave and replicates were completed, they would define today's augmented and diminished fifth and octave, augmented unison, and other octave replicates.

He adds further,<blockquote>''Et la Quarta è di tre sorti cioè la Diatessaron consonanza; il Tritono, che è una compositione di tre Tuoni; & la Semidiatessaron, che è una compositione di un Tuono, & di due Semituoni; i quali intervalli ne i loro estremi sono dissonanti. Questo istosso si potrebbe etiandio dire della Quinta, della Ottava, & della replicate, le quali si lassano per non andare in lungo.''</blockquote>defining the two 'extremely dissonant' other types of Fourth as the ''Tritono'', consisting of three tones, and the ''Semidiatessaron'', consisting of a tone and two semitones, and suggesting that similar could be said of the Fifth and Octave, and their (octave) replicates, but will not be, in order that he does not go on too much. These two dissonant fourths correspond to today's augmented and diminished fourth. If the definitions Zarlino alludes to for the fifth, octave and replicates were completed, they would define today's augmented and diminished fifth and octave, augmented unison, and other octave replicates.

In the 1691 ''Lettre de Monsieur Huygens à l'Auteur [Henri Basnage de Beauval] touchant le Cycle Harmonique,'' theorist Christiaan Huygens gave names and ratios to common intervals and mapped them to [[31edo|31-tET]], which very closely approximates 1/4-comma Meantone. Translated from French, 3/2 was labelled a Fifth, 4/3 a Fourth, 5/4 a major Third, 6/5 and minor Third, 5/3 a major Sixth and 8/5 a minor Sixth, we can see that these names and definitions match those of Zarlino.

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 In Part 3, Zarlino writes that the Unison, Fourth, Fifth and Octave (and, by extension, 11th, 12th, 15th, 18th, 19th and 22nd) are considered perfect consonances, and that Thirds and Sixths (and, by extension, 10ths, 13ths, 17ths and 20ths) are considered imperfect consonances, after Aristotle. Seconds, Sevenths (and, by extension, 9ths, 14ths, 16ths and 21sts) are considered dissonances. He adds that the imperfect consonances come in two types, 'maggiore' and 'minore', where, for each interval class, the minor is the smaller interval, and the major, the larger, defining therefore, the ditone and essachord as the major Third and Sixth respectively, and the semiditone and minor essachord as the minor Third and Sixth. The major and minor Seconds are then equated to the tone and semitone. Here we begin to see today's interval names.
-He adds further,<blockquote>Et la Quarta è di tre sorti cioè la Diatessaron consonanza; il Tritono, che è una compositione di tre Tuoni; & la Semidiatessaron, che è una compositione di un Tuono, & di due Semituoni; i quali intervalli ne i loro estremi sono dissonanti. Questo istosso si potrebbe etiandio dire della Quinta, della Ottava, & della replicate, le quali si lassano per non andare in lungo.</blockquote>defining the two 'extremely dissonant' other types of Fourth as the ''Tritono'', consisting of three tones, and the ''Semidiatessaron'', consisting of a tone and two semitones, and suggesting that similar could be said of the Fifth and Octave, and their (octave) replicates, but will not be, in order that he does not go on too much. These two dissonant fourths correspond to today's augmented and diminished fourth. If the definitions Zarlino alludes to for the fifth, octave and replicates were completed, they would define today's augmented and diminished fifth and octave, augmented unison, and other octave replicates.
+He adds further,<blockquote>''Et la Quarta è di tre sorti cioè la Diatessaron consonanza; il Tritono, che è una compositione di tre Tuoni; & la Semidiatessaron, che è una compositione di un Tuono, & di due Semituoni; i quali intervalli ne i loro estremi sono dissonanti. Questo istosso si potrebbe etiandio dire della Quinta, della Ottava, & della replicate, le quali si lassano per non andare in lungo.''</blockquote>defining the two 'extremely dissonant' other types of Fourth as the ''Tritono'', consisting of three tones, and the ''Semidiatessaron'', consisting of a tone and two semitones, and suggesting that similar could be said of the Fifth and Octave, and their (octave) replicates, but will not be, in order that he does not go on too much. These two dissonant fourths correspond to today's augmented and diminished fourth. If the definitions Zarlino alludes to for the fifth, octave and replicates were completed, they would define today's augmented and diminished fifth and octave, augmented unison, and other octave replicates.
 In the 1691 ''Lettre de Monsieur Huygens à l'Auteur [Henri Basnage de Beauval] touchant le Cycle Harmonique,'' theorist Christiaan Huygens gave names and ratios to common intervals and mapped them to [[31edo|31-tET]], which very closely approximates 1/4-comma Meantone. Translated from French, 3/2 was labelled a Fifth, 4/3 a Fourth, 5/4 a major Third, 6/5 and minor Third, 5/3 a major Sixth and 8/5 a minor Sixth, we can see that these names and definitions match those of Zarlino.