User:Unque/On Voice Leading: Difference between revisions

Line 37:

Another common usage of mediation is to create a form of resolution by contrary motion wherein the two voices move by the same interval in opposite directions.

Consider two pitches separated by a tension such as [[13/10]]. When moving by contrary motion, the harmonic target would be a consonance such as [[3/2]]. However, if the two pitches are to move by unequal distances to the target, such as [[15/14]] and [[14/13]], the stronger pull created by the shorter of the two steps makes one of the voices necessarily more prominent. The closer in size the two steps are, the more this effect is mitigated, and the closer the two voices come to standing on equal ground with one another; thus, it follows that the optimal step size for this voice leading is [[15/13]] split into two equal parts.

Consider two pitches separated by a tension such as [[13/10]]. When moving by contrary motion, the harmonic target would be a consonance such as [[3/2]]. However, if the two pitches are to move by unequal distances to the target, such as [[15/14]] and [[14/13]], the stronger pull created by the shorter of the two steps makes one of the voices necessarily more prominent. The closer in size the two steps are, the more this effect is mitigated, and the closer the two voices come to standing on equal ground with one another; thus, it follows that the optimal step size for this voice leading is [[15/13]] split into two equal parts. If desired, the voices may require further subdivisions to reach the consonance; for instance, if an intermediary is desired between the 13/10 and 3/2 dyads, then 15/13 may be divided into four parts, or further into six, etc.

Now consider the tension that is precisely half of [[4/3]], and assume that one wants to resolve to a perfect 4/3 via contrary motion. Using the above method, one can see that the optimal step for voice leading by contrary motion is half of that half, or one quarter of 4/3.

Now consider the tension that is precisely half of [[4/3]], and assume that one wants to resolve to a perfect 4/3 via contrary motion. Using the above method, one can see that the optimal step for voice leading by contrary motion is half of that half, or one quarter of 4/3. This sense of dividing divisions may occur as many times as one pleases; if one wants the precise semi-[[3/1|tritave]] to be used as the main consonance and the semi-semi-tritave or quarter tritave to be the main tension, then the step size which follows from it is the semi-semi-semi tritave, or one eighth of a tritave.

== On Common Denominators ==

@@ Line 37: / Line 37: @@
 Another common usage of mediation is to create a form of resolution by contrary motion wherein the two voices move by the same interval in opposite directions.
-Consider two pitches separated by a tension such as [[13/10]].  When moving by contrary motion, the harmonic target would be a consonance such as [[3/2]].  However, if the two pitches are to move by unequal distances to the target, such as [[15/14]] and [[14/13]], the stronger pull created by the shorter of the two steps makes one of the voices necessarily more prominent.  The closer in size the two steps are, the more this effect is mitigated, and the closer the two voices come to standing on equal ground with one another; thus, it follows that the optimal step size for this voice leading is [[15/13]] split into two equal parts.
+Consider two pitches separated by a tension such as [[13/10]].  When moving by contrary motion, the harmonic target would be a consonance such as [[3/2]].  However, if the two pitches are to move by unequal distances to the target, such as [[15/14]] and [[14/13]], the stronger pull created by the shorter of the two steps makes one of the voices necessarily more prominent.  The closer in size the two steps are, the more this effect is mitigated, and the closer the two voices come to standing on equal ground with one another; thus, it follows that the optimal step size for this voice leading is [[15/13]] split into two equal parts.  If desired, the voices may require further subdivisions to reach the consonance; for instance, if an intermediary is desired between the 13/10 and 3/2 dyads, then 15/13 may be divided into four parts, or further into six, etc.
-Now consider the tension that is precisely half of [[4/3]], and assume that one wants to resolve to a perfect 4/3 via contrary motion.  Using the above method, one can see that the optimal step for voice leading by contrary motion is half of that half, or one quarter of 4/3.
+Now consider the tension that is precisely half of [[4/3]], and assume that one wants to resolve to a perfect 4/3 via contrary motion.  Using the above method, one can see that the optimal step for voice leading by contrary motion is half of that half, or one quarter of 4/3.  This sense of dividing divisions may occur as many times as one pleases; if one wants the precise semi-[[3/1|tritave]] to be used as the main consonance and the semi-semi-tritave or quarter tritave to be the main tension, then the step size which follows from it is the semi-semi-semi tritave, or one eighth of a tritave.
 == On Common Denominators ==