Counterpoint Study 4: 1:1 Ratio (Part 2)

Counterpoint Study Lesson 4: 1:1 Ratio (Part 2)

In the last lesson, we have studied at least 5 basic rules of strict counterpoint. In this lesson, we will further study more rules in strict counterpoint. 

Rule No. 6
Horizontal leap which forms at least diminished 5th interval is better approached (preceded and succeeded) by notes which lie inside the interval.

You may notice that this rule is more like a suggestion since it uses the word 'better'. However, in strict counterpoint, rule number 6 is regarded as strong suggestion (because there are contrapuntal works which violates this particular rule, for instance, Bach's Invention Number 4). In the example below, the first leap, which forms a major 7th interval, is preceded and succeeded respectively by note C and A, which lie inside the leap. In the second leap, it is preceded by note B and is succeeded by note F, which both lie inside the minor 6th interval.

Rule No. 7
Seventh (7th) interval, and its inversion, second (2nd) interval, must be resolved (or succeeded) by a step note.

The rule number 7 states that any 7th or 2nd intervals must be resolved by step notes. This rule exists because, as I stated in the first lesson about interval, that 7th and 2nd intervals are categorized as dissonant intervals. Dissonant intervals have the characteristic of being unstable, therefore they are relatively not so good to hear in a long time. Hence, they must be resolved by step notes. In 7th interval, a step note may form 6th or octave intervals horizontally, whereas in 2nd interval, a step note may form unison or 3rd intervals horizontally.

Rule No. 8
Do not use major seventh (M7) chord.

This is simply because M7 chord was not known nor used in the Baroque era.

Rule No. 9
Avoid using any diminished chord.

If diminished chord appears, then eventually, it will cause problems, mainly in the counterpoint which ratio is more than 1:1.

Rule No. 10
Three or more consecutive horizontal leaps on the same direction is forbidden.

This rule forbids the existence of three or more consecutive horizontal leaps on the same direction. In other words, there should not exist three or more leaps on melodic intervals appear consecutively on the same direction. The example below shows the violation of rule number 10. On the first bar, there are 3 consecutive upward leaps. On the second bar, there are 3 consecutive downward leaps. On the third bar, the upward leaps is interrupted by an upward step. Finally, on the last bar, the downward leaps is resolved by an upward leap. In conclusion, the first and the second bars violate the rule number 10, whereas the remaining bars do not.

Exercise
Try to compose counterpoint part for the cantus firmus below by using all the given rules. Notice that because the CF is written in clef F, the CP must be written in clef G. If you notice, the first four bar is the same with the last exercise in the previous lesson. Thus, you are allowed to use your own answer of the previous exercise. I will put my answer on the next update.

Below is my composition for the counterpoint part of the exercise above,

Counterpoint Study 3: 1:1 Ratio (Part 1)

Counterpoint Study Lesson 3: 1:1 Ratio (Part 1)

Assuming that we know basic harmony, now we should move on to the real lesson of counterpoint. The simplest type of counterpoint is 1:1 ratio. Ratio is defined as horizontal relation between two vertical notes. In the famous book Gradus Ad Parnassum by Johann Fux, ratio can be associated with species. 1:1 ratio means that one particular note is compared with another note with the same value, hence, 1:1 ratio simply means note against note.

There are many rules in counterpoint. These rules make counterpoint sometimes perceived as 'one of the most difficult subject in music theory'. Composing a contrapuntal music should consider these rules. Because our start point in studying counterpoint is from scratch, the type of counterpoint that we are going to study is strict counterpoint. All contrapuntal music that will appear or given in this lesson are subject to these rules. By studying strict counterpoint, I hope we can make a contrapuntal music using the same way Baroque composers composed theirs. In this lesson, I will introduce several rules in 1:1 ratio of counterpoint.

Rule No. 1
Good counterpoint is a counterpoint which has good harmonic structure.

The first rule states that good counterpoints must have good harmonic structures.  In more simple words, good harmonic structure in counterpoint means that the chords in counterpoint must be properly defined. It means that every essential notes (CF and its CP) must form a chord. In two notes counterpoint, chord not always be formed by a triad. Two distinct notes (one represents CF and the other represents CP) can be regarded as a chord. The chord may appear in various positions: root, first inversion, or second inversion.

Rule No. 2
Sometimes use dominant 7th chord.

This rule is more like a suggestion rather than a necessity. To make it clearly, dominant 7th is a major triad chord with an additional minor seventh. Dominant 7th chord is sometimes used as a resolution chord, because of its tendency to change to tonic chord. Since leading tone has also the same tendency, dominant 7th chord sometimes appears together with it.

Rule No. 3
Use 3rd and 6th intervals as frequent as possible.

Rule number 3 is a strong suggestion. It could even be regarded as weak necessity. In most good contrapuntal works, 3rd and 6th intervals appear more often rather than other intervals. The extensive use of these intervals may caused by their characteristic of being consonant. Nevertheless, other consonant intervals (any kind of perfect intervals) do not get the same rule.

Rule No. 4
Octave interval may be used, but not too frequent. If it appears, it should be approached by contrary motion.

As I was saying that consonant intervals other than 3rd and 6th do not have the same rule like rule number 3. Therefore, rule number 4 is the one the consequences which apply to particular perfect interval. I believe that rule number 4 is a self explanatory. The application of rule number 4 can be seen in the picture below.

As you may notice that an octave interval appears on the third bar. The motion from second bar to third bar forms a contrary. Thus, the appearance of octave interval follows the rule number 4.

Rule No. 5
Perfect 5th interval may be used, but not too frequent. If it appears, it should be approached by contrary motion.

Rule number 5 is identical with rule number 4 except that it applies for perfect 5th rather than octave. The picture below shows an example of the application of rule number 5.

In this example, the appearance of perfect 5th in the fourth bar is approached by contrary motion which is formed from third bar to fourth bar.

Exercise
Try to compose counterpoint part for the cantus firmus below by using all the given rules. Notice that because the CF is written in clef F, the CP must be written in clef G. I will post my composition of this exercise on the next update.

Here is my composition for the above exercise. If you find my composition violates any counterpoint rules, please do not hesitate to elaborate. 

Counterpoint Study 2: Motion

Counterpoint Study Lesson 2: Motion

Some rules in counterpoint consider the motion of the notes. Motion is defined as how the notes are arranged horizontally. In counterpoint, the main melody is called as cantus firmus (or CF), whereas its counterpoint is simply called counter point (or CP). The notes arrangement between CF and CP form motion. These motions also referred to as contrapuntal motion. There are four basic type of contrapuntal motion:

1. Parallel, characterized by motion which has the same interval (CF and CP move within the same intervals). 
2. Similar, characterized by motion which has the same direction but has different interval (CF and CP move in the same direction but within different intervals).
3. Contrary, characterized by different direction between CF and CP.
4. Oblique, characterized by no change in pitch (in one melodic line), whereas the other goes up or down.

Below is the example of each contrapuntal motions, along with their respective intervals.

Analysis: Assume that clef G is the CF and clef F is the CP. On the first bar, the interval doesn't change, thus its a parallel motion. On the second bar, CF's and CP's melodic lines go on the same direction (down) but the intervals change, hence its a similar motion. On the next bar, CF's melodic lines go up whereas CP's melodic lines go down, hence its a contrary motion. Last, on the fourth bar, CF's melodic lines are on the same pitch whereas CP's melodic lines go down, hence its an oblique motion.

Counterpoint Study 1: Interval

Counterpoint Study Lesson 1: Interval

Counterpoint is one of the fundamentals in musical composition. It is very important in composing structured music. Counterpoint was widely used and developed in Baroque era. One of the pioneers in counterpoint music was Johann Sebastian Bach. Counterpoint music can be identified by its complex-structured polyphony. In Baroque music, counterpoint can be found in many forms, such as fugue, sarabande, gavotte, minuet, gigue, even in toccata.

I've been interested in studying everything related to musical composition. Recently, I joined an online class held by IMI (Indrapraja Music Institute), taught by its founder (and also my friend) Mr. Diecky K. Indrapraja himself, to increase my knowledge in composition. This online counterpoint class is very interesting. I study along with two other students who are currently studying music in various universities. This page, and other next pages titled "Counterpoint Study", will be my notes while studying this particular subject.

The word "counterpoint" originates from Latin words, contra punctus. In musical terms, these words mean point against point. A point here is associated with a musical note. Therefore, counterpoint generally discusses how to create a note which counters another note.

Because counterpoint discusses about relations between notes, one particular subject in musical theory must be understand before our study going further. The particular subject is interval. Interval measures the differences between two notes. To understand intervals, I will give a simple example. The most simple scale which can be played on a piano is C major scale. As we know, C major scale consists of 7 notes (8 notes if includes C'), which are C, D, E, F, G, A, and B (and C'). The relations among these notes form intervals. Basic intervals in C major scale is shown below.

The table above shows intervals in C major scale. As you can see, it is very simple. You can easily identify these basic intervals by using only white keys on a piano. I say 'basic' because the table above only shows intervals which are formed by white keys. What about the intervals of black keys in C major scale? For instance, what is the interval between C and E♭? To answer this, see the table below, which shows more general intervals in C major scale. 

By referring to the table above, the answer of previous question is minor third (m3). There are several terms in interval which are common in music theory. Those are: 

1. Consonant: intervals which are categorized as consonant is third and sixth. These intervals can be identified by their sound characteristics: stable, pleasant, good to hear. Hence, because of the characteristic of unison and octave, these intervals are also categorized as consonant.
2. Dissonant: second and seventh are dissonant intervals because of their characteristic: unstable, tend to change.
3. Perfect: fourth and fifth are clearly perfect intervals
4. Tritone: tritone intervals are characterized by their 'unpleasant' sound, which is very unstable. This is caused by three adjacent whole tones.

To understand more about interval, on the picture below, I've made several examples of intervals in different scales. 

Here is my analysis of the exercise: on the first bar, the first note (bottom note) is G. The first note to the second note (upper note) forms a fifth interval. But, since the D got a sharp signature, the fifth interval is augmented. Hence, augmented fifth (A5). On the second bar, the first note (E♭) forms a seventh interval with the second note (D). But, since the D got a flat signature, the interval becomes minor seventh (m7). On the next bar, the note B forms a sixth interval with G. But, what type of sixth? On a B major scale, major sixth is formed between B and G♯. Because G♭ is 2 semitones lower than G♯, the interval on the third bar is diminished sixth (d6). Next, the first note on the last bar is A♭. A♭ to C forms a major third. Since the C got a sharp signature, the interval becomes augmented third (A3). 

The next lesson is about motion in counterpoint. If anyone has any question about this interval lesson, please put your question on comment.

Soundcloud: Random Thoughts

Yes, this is my first post after my last post a long time ago. By the way, I just want to tell you that I've just created my Soundcloud account. I've uploaded my first recording since I moved to Jakarta.

Many weeks ago, after office time, I played random sound on my office's piano, a Yamaha DGX650. This digital piano has the capability to record what I play and save it into my USB memory stick. Thus, I started to play random music. When I say random music, I mean it was just a kind of improvisation. You can hear the result on this Soundcloud link. I simply titled it "Random Thoughts 1". I hope you'll enjoy it, and don't forget to subscribe my channel.