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

These are the two rows of figures which should be compared together for obtaining the inversions of double counterpoint at the //twelfth//:

^ Counterpoint  |  1  |  2  |  3  |  4  |  5  |  6  |  7  |  8  |  9  |  10  |  11  |  12  |
^ Inversion  |  12  |  11  |  10  |  9  |  8  |  7  |  6  |  5  |  4  |  3  |  2  |  1  |

It will be seen that the //unison// or //octave// changes, in counterpoint of this kind, into a //twelfth//, the //second// into an //eleventh//, //etc//.

The //sixth//, which by inversion becomes a //seventh//, should be prepared either in the upper part, or the lower; and the bass should then descend one note or degree.

> Examples from Marpurg

{{ :cherubini_counterpoint_and_fugue:ex173a-1.png?650 |}}

{{ :cherubini_counterpoint_and_fugue:ex173a.mp3 | :cherubini_counterpoint_and_fugue:ex173a.ogg |}}

{{ :cherubini_counterpoint_and_fugue:ex173b-1.png?650 |}}

{{ :cherubini_counterpoint_and_fugue:ex173b.mp3 | :cherubini_counterpoint_and_fugue:ex173b.ogg |}}

This is an extended example of double counterpoint at the //twelfth//:

{{ :cherubini_counterpoint_and_fugue:ex174a-1.png?800 |}}

{{ :cherubini_counterpoint_and_fugue:ex174a.mp3 | :cherubini_counterpoint_and_fugue:ex174a.ogg |}}

> 1st manner of inverting: Transpose the counterpoint a //fourth// below, while the theme remains in its place

{{ :cherubini_counterpoint_and_fugue:ex174b-1.png?650 |}}

{{ :cherubini_counterpoint_and_fugue:ex174b.mp3 | :cherubini_counterpoint_and_fugue:ex174b.ogg |}}

> 2nd manner of inverting: Transpose the theme a //twelfth// below, while the counterpoint remains in its place

{{ :cherubini_counterpoint_and_fugue:ex174c-1.png?650 |}}

{{ :cherubini_counterpoint_and_fugue:ex174c.mp3 | :cherubini_counterpoint_and_fugue:ex174c.ogg |}}

> 3rd manner of inverting: Transpose the theme an //octave// below, and the counterpoint a //fifth// below

{{ :cherubini_counterpoint_and_fugue:ex174d-1.png?650 |}}

{{ :cherubini_counterpoint_and_fugue:ex174d.mp3 | :cherubini_counterpoint_and_fugue:ex174d.ogg |}}

> 4th manner of inverting: Transpose the theme a //fifth// above, and the counterpoint an //octave// below

{{ :cherubini_counterpoint_and_fugue:ex174e-1.png?650 |}}

{{ :cherubini_counterpoint_and_fugue:ex174e.mp3 | :cherubini_counterpoint_and_fugue:ex174e.ogg |}}

This counterpoint is one of the most used, and one of the most fertile in resources.