cherubini_counterpoint_and_fugue:on_double_counterpoint:inversion_at_the_ninth [Bondari Wiki]

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====== On Double Counterpoint ======
===== First Section: Double Counterpoint in Two Parts =====
==== Inversion at the Ninth ====

When the inversion of a counterpoint takes place at the ninth, either in the higher, or the lower part, the counterpoint takes the name of //double in the ninth (or second)//. The combinations of this kind of counterpoint are attained by the method already employed for that at the octave, which consists in placing one against the other two series of figures, each series of which should be limited by the figure indicated by the denomination of the counterpoint; that is to say, each series in the counterpoint at the octave being composed of eight figures, and in the counterpoint at the //ninth// -- which is here in question -- each series should be composed of nine figures; for that at the //eleventh//, eleven; and so on, with the rest. This explanation is given here, in order not to be obliged hereafter to speak again of it, when discussing the kinds of counterpoint which follow.

These are the series of figures, therefore, which belong to double counterpoint in the ninth:

^ Counterpoint  |  1  |  2  |  3  |  4  |  5  |  6  |  7  |  8  |  9  |
^ Inversion  |  9  |  8  |  7  |  6  |  5  |  4  |  3  |  2  |  1  |

By this demonstration, it is seen that the //unison// changes into a //ninth//; the //second// into an //octave//, and so forth. The //fifth// forms here the principal interval; it merits particular attention, whether in preparing or saving, not only dissonant intervals, but even those which become so by inversion. The discord of the //fourth// resolves into the //third//; the discord of the //seventh// resolves into the //sixth//, //etc//. These are the proper means for combining a double counterpoint at the //ninth//, which should be confined within the range of a ninth, for the same reasons that the octave should not exceed the limits of the octave.

> Examples taken from Marpurg

{{ :cherubini_counterpoint_and_fugue:ex163a-1.png?800 |}}

{{ :cherubini_counterpoint_and_fugue:ex163a.mp3 | :cherubini_counterpoint_and_fugue:ex163.ogg |}}

{{ :cherubini_counterpoint_and_fugue:ex163b-1.png?800 |}}

{{ :cherubini_counterpoint_and_fugue:ex163b.mp3 | :cherubini_counterpoint_and_fugue:ex163b.ogg |}}

By transposing the theme an octave higher, and the counterpoint a note lower, the double counterpoint at the //second// will be obtained.

{{ :cherubini_counterpoint_and_fugue:ex164-1.png?400 |}}

{{ :cherubini_counterpoint_and_fugue:ex164.mp3 | :cherubini_counterpoint_and_fugue:ex164.ogg |}}

By transposing the theme to the second above, and the counterpoint to an octave below, the following inversion will be obtained, to which accidentals must be added, on account of the change of key.

{{ :cherubini_counterpoint_and_fugue:ex165a-1.png?800 |}}

{{ :cherubini_counterpoint_and_fugue:ex165a.mp3 | :cherubini_counterpoint_and_fugue:ex165a.ogg |}}

> Other examples

{{ :cherubini_counterpoint_and_fugue:ex165b-1.png?800 |}}

{{ :cherubini_counterpoint_and_fugue:ex165b.mp3 | :cherubini_counterpoint_and_fugue:ex165b.ogg |}}

{{ :cherubini_counterpoint_and_fugue:ex165c-1.png?800 |}}

{{ :cherubini_counterpoint_and_fugue:ex165c.mp3 | :cherubini_counterpoint_and_fugue:ex165c.ogg |}}

Among double counterpoints, that of the ninth is one of the most limited, one of the most ungracious to treat, and one of the least used; when it is adopted, it should only be employed during very few bars.