====== 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 |}}

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{{ :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 |}}

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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 |}}

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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 |}}

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> 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 |}}

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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.