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--- cherubini_counterpoint_and_fugue:two_part_counterpoint:second_order [2018/06/14 15:29] – created brian
+++ cherubini_counterpoint_and_fugue:two_part_counterpoint:second_order [2020/01/28 21:08] (current) – brian
@@ Line 3: / Line 3: @@
 ==== Rule 9 ====
-In this order of counterpoint, two minims ((half notes)) should be placed over every semibreve ((whole note)) of the //cantus firmus//, except for the last bar, where a semibreve ((whole note)) should always be put against a semibreve ((whole note)).
+In this order ((species)) of counterpoint, two minims ((half notes)) should be placed over every semibreve ((whole note)) of the //cantus firmus//, except for the last bar, where a semibreve ((whole note)) should always be put against a semibreve ((whole note)).
 The first part of the bar which is occupied by a minim ((half note)), is called the //accented part of the bar//; and the second part occupied equally by another minim ((half note)), is called the //unaccented part of the bar//.
@@ Line 13: / Line 13: @@
 ==== Rule 10 ====
-The //accented// part of the bar
+The //accented// part of the bar should be in concord ((consonance)); although there are cases, where this may allow for variation, -- that is to say, by employing a discord ((dissonance)) at the accented part of the bar; but this can only be in certain dilemmas, either that the melody shall not be too disjunct, or to avoid other objectionable points.
+The //unaccented// part of the bar may consist of a concord ((consonance)), or else of a discord ((dissonance)), provided this latter be introduced between two concords ((consonances)), and that the movement of the melody be conjunct. In such a case, this discord ((dissonance)) is called a **passing tone**.
+{{ :cherubini_counterpoint_and_fugue:ex032-1.png?400 |}}
+{{ :cherubini_counterpoint_and_fugue:ex032.mp3 | :cherubini_counterpoint_and_fugue:ex032.ogg |}}
+==== Rule 11 ====
+The accented parts of the bar are not in this order subjected to Rule 4; provided, however, that the infraction of that rule be corrected in the unaccented part, -- by which is meant: Firstly, that the unaccented parts shall strike another concord ((consonance)). Secondly, that from the accented part of the bar to the unaccented, the procedure shall be by an interval of //more than a third//. Thirdly, that in proceeding from the accented to the unaccented part, it shall be by contrary movement.
+//Demonstrations// -- It shall now be seen, whether, in fulfilling the prescribed conditions, several consecutive ((parallel)) fifths might be saved.
+> Fault (parallel fifths) according to Rule 4:--
+{{ :cherubini_counterpoint_and_fugue:ex033-1.png?400 |}}
+{{ :cherubini_counterpoint_and_fugue:ex033.mp3 | :cherubini_counterpoint_and_fugue:ex033.ogg |}}
+By observing the conditions of Rule 11, the melody can only be arranged thus:--
+{{ :cherubini_counterpoint_and_fugue:ex034-1.png?400 |}}
+{{ :cherubini_counterpoint_and_fugue:ex034.mp3 | :cherubini_counterpoint_and_fugue:ex034.ogg |}}
+For it is prohibited to be written thus:--
+{{ :cherubini_counterpoint_and_fugue:ex035-1.png?400 |}}
+{{ :cherubini_counterpoint_and_fugue:ex035.mp3 | :cherubini_counterpoint_and_fugue:ex035.ogg |}}
+It follows, then, from these two methods, that the fifths are not saved; firstly, because in Example 34, the unison which occurs on the unaccented parts of the bars, cannot, on account of its nullity, either mitigate, or destroy, the effect of the fifth which precedes it, nor of that which follows it; secondly, because in Example 35, the interval of a third which intervenes between the accented and unaccented part of the bar, is too insignificant to work the desired effect.
+There is a method by which several consecutive ((parallel)) fifths may be saved; thus:--
+{{ :cherubini_counterpoint_and_fugue:ex036-1.png?400 |}}
+{{ :cherubini_counterpoint_and_fugue:ex036.mp3 | :cherubini_counterpoint_and_fugue:ex036.ogg |}}
+But this method is harsh and bold, inasmuch as between the first unaccented part and the second accented part, there occurs a movement prohibited by Rule 6. This expedient, therefore, is available to save two consecutive ((parallel)) fifths only, and not more; and even then, it must be in cases where the melody and the harmony violate no rule.
+It may now be examined, whether, under favor of the precribed conditions, several successive octaves can be saved.
+> Fault (parallel octaves) according to Rule 4:--
+{{ :cherubini_counterpoint_and_fugue:ex037-1.png?400 |}}
+{{ :cherubini_counterpoint_and_fugue:ex037.mp3 | :cherubini_counterpoint_and_fugue:ex037.ogg |}}
+By observing Rule 11, these means may //not// be employed:--
+{{ :cherubini_counterpoint_and_fugue:ex038-1.png?400 |}}
+{{ :cherubini_counterpoint_and_fugue:ex038.mp3 | :cherubini_counterpoint_and_fugue:ex038.ogg |}}
+All the conditions are fulfilled by this method, and the octaves are saved, at least according to the rule:--
+{{ :cherubini_counterpoint_and_fugue:ex039-1.png?400 |}}
+{{ :cherubini_counterpoint_and_fugue:ex039.mp3 | :cherubini_counterpoint_and_fugue:ex039.ogg |}}
+But even this method is not exempt from reproach, since, in order to save several octaves, two fifths are introduced in the two unaccented parts which succeed each other; and although whatever occurs in the unaccented part of a bar is not regarded with extreme rigour, yet the two fifths are not the less perceptible to the ear.
+The following examples are better, because they offer no such objectionable point, and because they do not redeem one fault by other:--
+{{ :cherubini_counterpoint_and_fugue:ex040-1.png?800 |}}
+{{ :cherubini_counterpoint_and_fugue:ex040.mp3 | :cherubini_counterpoint_and_fugue:ex040.ogg |}}
+Notwithstanding, it is to be observed, that this method of saving either two fifths or two octaves, was regarded by the ancient authors, as a reprehensible license, in two-part counterpoint. I am of the same opinion; and I think that two accented parts succeeding each other in fifth or in octave, whatever may be the intervening note placed on the unaccented part, the impression produced by the two fifths or two octaves is not destroyed; unless indeed the movement may be very slow, in which case each portion being taken for an entire bar, the unaccented parts may be computed by feeling, as so many accented ones. This reasoning, however, is specious, and should not pass into a law.
+It is to be concluded, then, that the present rule must be applied only to composition in more than two parts; or else to employ it in this order but very rarely, and as a means of eluding some perplexing point.
+These remarks and demonstrations upon the subject of two fifths and two octaves, have been set down, not so much for the sake of proving by example that they may be saved in a stated manner, as to show the little force of this rule, which I look upon as having been added to the severe rules of the ancient classical authors. Notwithstanding its want of force, however, it may occasionally be of some use.
+==== Rule 12 ====
+In counterpoint of the present order, it is permitted to have a single chord in each bar, or to introduce two. Accordingly, when a single chord is taken, each minim ((half note)) must mark a different concord ((consonance)), but both must belong to the same chord.
+{{ :cherubini_counterpoint_and_fugue:ex041-1.png?400 |}}
+{{ :cherubini_counterpoint_and_fugue:ex041.mp3 | :cherubini_counterpoint_and_fugue:ex041.ogg |}}
+And when two chords are taken, the accented parts of the bar will be occupied by a concord ((consonance)) belonging to one chord, and the unaccented part will, in its turn, consist of another concord ((consonance)) belonging to a different chord:--
+{{ :cherubini_counterpoint_and_fugue:ex042-1.png?400 |}}
+{{ :cherubini_counterpoint_and_fugue:ex042.mp3 | :cherubini_counterpoint_and_fugue:ex042.ogg |}}
+==== Rule 13 ====
+With two notes against one, it is easier entirely to avoid the false relation of tritone, and this facility arises from the power to divide the bar into two different chords.
+{{ :cherubini_counterpoint_and_fugue:ex043-1.png?400 |}}
+{{ :cherubini_counterpoint_and_fugue:ex043.mp3 | :cherubini_counterpoint_and_fugue:ex043.ogg |}}
+The first-inversion chord placed between the common chords of E and F suffices to destroy the effect of the false relation. The following example offers a similar method for its avoidance:--
+{{ :cherubini_counterpoint_and_fugue:ex044-1.png?400 |}}
+{{ :cherubini_counterpoint_and_fugue:ex044.mp3 | :cherubini_counterpoint_and_fugue:ex044.ogg |}}
+==== Rule 14 ====
+In this order of counterpoint, whether the //cantus firmus// occur in the upper part, or the lower, a minim rest ((half rest)) instead of a note may be placed in the accented part of the first bar, provided the unaccented part is a perfect concord ((consonance)):--
+{{ :cherubini_counterpoint_and_fugue:ex045-1.png?800 |}}
+{{ :cherubini_counterpoint_and_fugue:ex045.mp3 | :cherubini_counterpoint_and_fugue:ex045.ogg |}}
+This method is more elegant than if the two parts commenced at the same time.
+==== Rule 15 ====
+In the first order ((first species)), the disjunct movement of a minor sixth is permitted; in the second order ((second species)), it should be employed only when the parts, by the nature and pitch of the //cantus firmus//, approach each other too nearly, and that there would be a difficulty in preserving their mutual distance otherwise than by this movement. It is likewise permitted in similar cases, as in the first order ((first species)), to cross the parts -- that is to say, to let one part pass above or below the other.
+All the other movement, permitted in the first order ((first species)), are retained in the present order.
+> **Observation** -- The leap of a minor sixth is here in a measure prohibited, because this interval being more difficult of intonation than all the other permitted intervals, particularly in ascending, it becomes still more so in this order, where notes of the smallest value occur, which leaves less time for preparing the intonation than notes of greater value.
+==== Rule 16 ====
+When the //cantus firmus// lies in the lower part, and that it terminates, descending, from the second of the key and the tonic (D to C in the key of C), the counterpoint at the penultimate bar should be (if possible) a fifth in the accented part, and a major sixth in the unaccented part of the bar:--
+{{ :cherubini_counterpoint_and_fugue:ex046-1.png?400 |}}
+{{ :cherubini_counterpoint_and_fugue:ex046.mp3 | :cherubini_counterpoint_and_fugue:ex046.ogg |}}
+And when the //cantus firmus// lies in the upper part, the counterpoint should be (if possible) a fifth in the accented, and a third in the unaccented part of the bar:--
+{{ :cherubini_counterpoint_and_fugue:ex047-1.png?400 |}}
+{{ :cherubini_counterpoint_and_fugue:ex047.mp3 | :cherubini_counterpoint_and_fugue:ex047.ogg |}}
+This rule forms a sequel to what was said respecting the last two bars of a //cantus firmus// in the observations which conclude the portion that treats of counterpoint of the first order ((As in, the cadence formulae near the end of Rule 8.)).
+> **Observation** -- All the other rules of the first order ((first species)) which may be necessary to the present order, are retained here in all their rigour. It is therefore useless to re-cite them, as the pupil can refer to and consult them, or see by the experience he has already gained, the cases in which these rules serve to guide him.
+Here follows the example of a lesson in the second order ((second species)), that the pupil may perceive, at one view, how he is to proceed:--
+{{ :cherubini_counterpoint_and_fugue:ex048a-1.png?800 |}}
+{{ :cherubini_counterpoint_and_fugue:ex048a.mp3 | :cherubini_counterpoint_and_fugue:ex048a.ogg |}}
+{{ :cherubini_counterpoint_and_fugue:ex048b-1.png?800 |}}
+{{ :cherubini_counterpoint_and_fugue:ex048b.mp3 | :cherubini_counterpoint_and_fugue:ex048b.ogg |}}
+Note in Example 48a, at the passage marked with an asterisk, that instead of placing the discord ((dissonance)) in the unaccented part of the bar, according to Rule 10, it is placed in the accented portion. As I have asserted that this method may be employed, I have introduced it here, expressly, for the sake of giving an example. I might have contrived differently; but, by putting the discord ((dissonance)) in the accented part of the bar, I obtain a more free and elegant melody; and this is one of the objects which may justify this infringement of the rule. In the course of studying, the pupil will meet with other cases in which this method may be employed. Upon going through these examples, it will be seen how the counterpoint should proceed, to be in conformity with all the rules, and to have the melody easy, as well as in the style which suits with this kind of composition.