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cherubini_counterpoint_and_fugue:on_double_counterpoint:inversion_at_the_tenth [2018/08/10 17:11] (current)
brian created
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 +====== On Double Counterpoint ======
 +===== First Section: Double Counterpoint in Two Parts =====
 +==== Inversion at the Tenth ====
  
 +At present, double counterpoint at the //tenth// or //third// will be discussed, commencing with the usual rule, of the two rows in figures:
 +
 +^ Counterpoint ​ |  1  |  2  |  3  |  4  |  5  |  6  |  7  |  8  |  9  |  10  |
 +^ Inversion ​ |  10  |  9  |  8  |  7  |  6  |  5  |  4  |  3  |  2  |  1  |
 +
 +By these two series, it will be seen that two //thirds// (or two //tenths//) in succession must not be made; since there will then be two //octaves// (or two //​unisons//​). Neither must two sixths in succession by employed, because their inversion would produce two //fifths//. Nor must the //fourth// and the //seventh// be employed, except as passing tones (see **I.** in Example 166a), unless the //fourth// be resolved into a //fifth// or into a //sixth// (as in **II.** in Example 166b), and the //seventh// be resolved into a //fifth// (see **III.*** in Example 166c).
 +
 +{{ :​cherubini_counterpoint_and_fugue:​ex166a-1.png?​700 |}}
 +
 +{{ :​cherubini_counterpoint_and_fugue:​ex166a.mp3 | :​cherubini_counterpoint_and_fugue:​ex166a.ogg |}}
 +
 +{{ :​cherubini_counterpoint_and_fugue:​ex166b-1.png?​700 |}}
 +
 +{{ :​cherubini_counterpoint_and_fugue:​ex166b.mp3 | :​cherubini_counterpoint_and_fugue:​ex166b.ogg |}}
 +
 +{{ :​cherubini_counterpoint_and_fugue:​ex166c-1.png?​700 |}}
 +
 +{{ :​cherubini_counterpoint_and_fugue:​ex166c.mp3 | :​cherubini_counterpoint_and_fugue:​ex166c.ogg |}}
 +
 +The //ninth// must be resolved either by the octave or by the fifth, in this manner:
 +
 +{{ :​cherubini_counterpoint_and_fugue:​ex167-1.png?​700 |}}
 +
 +{{ :​cherubini_counterpoint_and_fugue:​ex167.mp3 | :​cherubini_counterpoint_and_fugue:​ex167.ogg |}}
 +
 +From this analysis -- with consideration,​ intelligence,​ and application -- the pupil may acquire practice in this kind of double counterpoint,​ of which here is given an extended example:
 +
 +{{ :​cherubini_counterpoint_and_fugue:​ex168-1.png?​800 |}}
 +
 +{{ :​cherubini_counterpoint_and_fugue:​ex168.mp3 | :​cherubini_counterpoint_and_fugue:​ex168.ogg |}}
 +
 +This counterpoint may be inverted in several ways:
 +
 +> 1st manner: By transposing the counterpoint a //tenth// below, while the theme remains in its place
 +
 +{{ :​cherubini_counterpoint_and_fugue:​ex169a-1.png?​650 |}}
 +
 +{{ :​cherubini_counterpoint_and_fugue:​ex169a.mp3 | :​cherubini_counterpoint_and_fugue:​ex169a.ogg |}}
 +
 +> 2nd manner: By transposing the theme a //third// above, and the counterpoint an //octave// below
 +
 +{{ :​cherubini_counterpoint_and_fugue:​ex169b-1.png?​650 |}}
 +
 +{{ :​cherubini_counterpoint_and_fugue:​ex169b.mp3 | :​cherubini_counterpoint_and_fugue:​ex169b.ogg |}}
 +
 +> 3rd manner: By transposing the counterpoint a //third// below, and the theme an //octave// below
 +
 +{{ :​cherubini_counterpoint_and_fugue:​ex169c-1.png?​650 |}}
 +
 +{{ :​cherubini_counterpoint_and_fugue:​ex169c.mp3 | :​cherubini_counterpoint_and_fugue:​ex169c.ogg |}}
 +
 +> 4th manner: By transposing the counterpoint,​ and the theme, a //third// higher
 +
 +{{ :​cherubini_counterpoint_and_fugue:​ex169d-1.png?​650 |}}
 +
 +{{ :​cherubini_counterpoint_and_fugue:​ex169d.mp3 | :​cherubini_counterpoint_and_fugue:​ex169d.ogg |}}
 +
 +In all the inversions and transpositions of this example, it will be perhaps necessary to add some accidentals,​ either to the theme, or to the counterpoint;​ and, sometimes, even a third part, in order to render the whole more correct: at the same time, nothing has been indicated of this, seeing that a counterpoint can be constructed in such a manner, as there need be no such alterations,​ nor any additional parts. The short examples set forth above have only been given to show in how many ways a double counterpoint at the tenth may be inverted. This counterpoint is one of those most used, as well as that at the octave.
  • cherubini_counterpoint_and_fugue/on_double_counterpoint/inversion_at_the_tenth.txt
  • Last modified: 2018/08/10 17:11
  • by brian