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====== Chapter 1 ====== 
===== Of Counterpoint, in the Composition of 2 Parts =====

====== !!! IN PROGRESS !!!======

Counterpoint is divided into **simple** and **figurative**. The former is a kind of composition in two or more parts, wherein the notes in the different parts are of the same value, and is called //plain// or simple from being note against note in concords ((consonances)) only. We may choose the subject either from our own fancy or from a church tune; in the latter case the subject is called in Italian //canto fermo// ((Hereafter referred to as //cantus firmus//.)).

In figurative counterpoint the notes in the different parts may be of different value, and concords ((consonances)) intermixed with discords ((dissonances)). When the //cantus firmus// or subject is placed in the lower parts, it is called in Italian //contrapunto sopra il soggetto//, and if in the upper parts, //contrapunto sotto il soggetto//.

Before we proceed, the following general rules in composition will be necessary to be observed with regard to the different motions in music: the regular, contrary, and oblique.

1. The **contrary** and **oblique** may be used in any progression; but the **similar**, only when we proceed from a perfect concord ((consonance)) to an imperfect, or from an imperfect to an imperfect: in this sense only the 8<sup>th</sup> and 5<sup>th</sup> are deemed perfect concords ((consonances)), but the 3<sup>rd</sup> and 6<sup>th</sup> imperfect.

The reason why the similar motion in the progression from a perfect and imperfect concord ((consonance)) to a perfect is not allowed is to avoid the wrong progression of successive fifths and eighths ((parallel fifths and octaves)), whether open or hidden; the last may be discovered by the intermediate notes contained within the spaces, as may be seen in the following example.

{{ :fux_gradus_ad_parnassum:ch01-ex01.png?300 |}}

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2. We must avoid proceeding to an octave or unison by a skip, that is when the lower part ascends one degree and the upper descends by a skip, though it be in contrary motion.

{{ :fux_gradus_ad_parnassum:ch01-ex02.png?300 |}}

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3. An imperfect concord ((consonance)) is to be used preferably to a perfect, as the former is more harmonious than the latter.

4. The notes must be comfortable to the nature of the key.

5. The inharmonic relation in **Mi** against **Fa** is to be avoided as much as possible.

6. Regularity, variety, and good melody must continually be kept in view.

==== First Counterpoint ====

Now we proceed to the composition of plain counterpoint in two parts only. The principal points to be observed in this kind of composition are as follow:

a. Every note of the //cantus firmus// must have its particular concord ((consonance)). If it is in the lower part, the intervals must be taken upwards, and if in the upper part, then the intervals must be reckoned downwards. ((If the //cantus firmus// is in the lower voice, then write the counterpoint above, and //vice versa//.))

b. We must begin and end with a perfect concord ((consonance)).

c. If the //cantus firmus// is in the lower part, the last note but one requires the greater sixth, and if in the upper part, the lesser third. See the following example in D (La - Sol - Re).


{{ :fux_gradus_ad_parnassum:ch01-ex03.png?300 |}}

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==== Second Counterpoint ====

This is the kind of composition where two notes are set against one; it is used therefore in binary measure consisting of two equal parts: the first whereof is accented, and the other unaccented. Here the first minim ((half note)) is to be a concord ((consonance)), and the second may be either a concord ((consonance)) or discord ((dissonance)). The discord ((dissonance)) therefore only is used in a gradual transition from concord ((consonance)) to concord ((consonance)); but in skips the concord ((consonance)) only can have place ((can occur)).


{{ :fux_gradus_ad_parnassum:ch01-ex04.png?300 |}}

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**First Rule:** If the //cantus firmus// is in the lower part, the two notes in the last bar but one must have a fifth for its first note and a greater sixth for its second note. But if in the upper part, then the first note requires a fifth and the other a lesser third.

**Second Rule:** Skips of thirds in a similar motion following one another must be avoided, as it would occasion a forbidden progression of fifths and octaves. See Ex. 1 - Greater skips as those of a fourth, fifth, and sixth are allowed, as it would not offend the ear so much. See Ex. 2.

{{ :fux_gradus_ad_parnassum:ch01-ex05.png?300 |}}

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** Third Rule:** When the //cantus firmus// is in the upper part, a minim rest ((half-note rest)) is to be placed at the beginning of the counterpoint instead of the first note.

** Fourth Rule:** If the parts should meet so close together as not to leave sufficient room for the notes to move in the contrary way, then in such case a skip of a sixth or octave is allowed to be used.

{{ :fux_gradus_ad_parnassum:ch01-ex06a.png?300 |}}

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{{ :fux_gradus_ad_parnassum:ch01-ex06b.png?300 |}}

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In triple time ((triple meter)), when one note is set against three, the middle-most note bay be a discord ((dissonance)), provided it be in a gradual progression.

{{ :fux_gradus_ad_parnassum:ch01-ex07.png?300 |}}

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==== Third Counterpoint ====

Third-species counterpoint is a kind of composition where four crotchets ((quarter notes)) are set against one semibreve ((whole note)). Here it must be observed, that when five crotchets ((quarter notes)) follow one another gradually either rising or falling, the first, third, and fifth note are to be concords ((consonances)), and the second and fourth discords ((dissonances)). See Ex. 1. But this is not always the case, as sometimes the second and fourth note may be concords ((consonances)), and the third a discord (dissonance)) by way of filling up the space of a third. See Ex. 2. To explain which more fully we will reduce those examples to their original form (Ex. 3) which will show them to be regular transitions.