Counterpoint applied in the invention, fugue, canon and other polyphonic forms : an exhaustive treatise on the structural and formal details of the polyphonic or contrapuntal forms of music, for the use of general and special students of music . *i) Theme A is shifted up, past its fellow, a 12th; Theme B remains whereit was. *2) Such modifications as this (/changed to f% by the accidental) are oftenabsolutely necessary, and are to be freely employed, with discretion, in favor of bettermodulatory agreement. Their use is entirely legitimate, inasmuch as the two forms(the Original and the Inventi
Counterpoint applied in the invention, fugue, canon and other polyphonic forms : an exhaustive treatise on the structural and formal details of the polyphonic or contrapuntal forms of music, for the use of general and special students of music . *i) Theme A is shifted up, past its fellow, a 12th; Theme B remains whereit was. *2) Such modifications as this (/changed to f% by the accidental) are oftenabsolutely necessary, and are to be freely employed, with discretion, in favor of bettermodulatory agreement. Their use is entirely legitimate, inasmuch as the two forms(the Original and the Invention) never appear together. The change, however, mayonly affect the accidental, — never the letter. An apparently new result is obtained by moving the other Themedown, past its fellow, a 12th. But this, or any other movement of bothparts together, equivalent to the 12th, represents simply a transpositionof the Inverted form. Thus : B). (a) Inversion in 12th (affecting Th I Th. #_- y rijL Th. f X X (b) Inversion in the 12th (affecting both Themes). (#). 171. The invention of a Double-subject (or any two-voice sentence)which may thus submit to Inversion in the 12 th — or any other intervalexcepting the 8ve — is so largely a matter of incessant experiment, tonefor tone, that scarcely any valid rules can be given. At the same time,there is a certain device for each separate species of Double-counter-point, which systematizes and simplifies the formation to some extent. Par. 171. ARTIFICIAL DO UBLE-COUNTERPOINT. 271 The device for Double-counterpoint in the 12 th consists in the frequent use of the interval of a 3rd {or 10th) in the Original form ; for thisinterval, when inverted in the 12th, results again in a 3rd; for example: Ex. I becomes, when • ainverted in ~3 3 3 3 Hs * * « the 12th: v#—7$\—7* *— 1 This point, and others, are illustrated in the following: 1. The Orig. Cpt. u n m Th. B. mm Th. A. jz FT*+H-Hrjj±l} ft J j J-4-l
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