Category: counterpoint

Articles and ideas that focus on counterpoint.

  • What’s counterpoint in music? who what when where & why

    During my undergraduate work, counterpoint happened to be one of my favorite topics in music theory (Who am I kidding? I liked them all!). I was a teacher’s assistant and graded many counterpoint exercises. What I saw was if students grasped the principles of counterpoint, they were more successful when we got to four-part writing, other composition techniques, and analysis.

    Counterpoint is a horizontally layered approach to writing music. The music is based on a primary voice (line or melody). Other voices are added but are written with the intervallic relationship with the primary voice dictating what notes the other voices may use. The voices have independent melodic contours and rhythms.

    There’s a lot that can be said about counterpoint, but here’s a quick round up of the main points.


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    Who created counterpoint?

    No one person created counterpoint. As with most theoretical writings, the music comes first then the theory. There’s certainly a who’s who list of theorists and composers who used counterpoint ideas in their music and/or explored writing down the principles of counterpoint. Instead of just listing a bunch of names, I thought it might be more interesting to list the names and influential works only if I could find an English translation for sale. It may be – dare I say – fun to read these works.

    Early Influential theorists who wrote about counterpoint

    • Prosdocimus de Beldemandis – Contrapunctus: Counterpoint: found a copy on AbeBooks. The translator is Jan W. Herlinger.
    • Gioseffo Zarlino – The Art of Counterpoint: found a version published by W.W. Norton on AbeBooks.
    • Johannes Tinctoris – The Art of Counterpoint (Liber De Arte Contrapuncti): found a copy on AbeBooks
    • Johann Joseph Fux – Gradus Ad Parnassum: found basically everywhere!

    All the masters learned counterpoint!

    Though these composers didn’t create counterpoint, they certainly treated it seriously and reaped the benefits of its development. Basically every composer you’ve heard of learned counterpoint in some manner. Haydn, Mozart, Beethoven and many of the biggest names in classical music had extensive training in counterpoint. By the time these composers came around, counterpoint was pretty well established not only in music but theoretical and pedagogical writings.

    Here is an example of where counterpoint went in the hands of Bach. He wrote this Fugue about 400 years after the first mention of contrapunctus in writings.

    What is counterpoint?

    At a fundamental level, counterpoint is simply considering the sonic relationships between two or more notes. Going a little deeper, counterpoint consists of two or more melodic lines that are interrelated to each other while rhythms and melodic contours are independent. Counterpoint is a sub-field of polyphony – polyphony being two or more independent musical lines. Counterpoint, whether Western classical, folk, or another tradition, is a more careful consideration of how each pitch relates vertically and horizontally. It is also the consideration that each line is a melody unto itself and fits in a woven texture with the whole. This is a slightly different angle than polyphony at large. Polyphony is more general in it’s definition of simply simultaneous voices.

    What counterpoint isn’t

    This could be a long list but let’s just go with, counterpoint is not monophony, homophony, or heterophony. Monophony is just a single line of music – think solo voice or violin. Homophony is where there is a melody that is supported by chords – think most pop songs. Heterophony is the simultaneous performance of the same melodic line by different instruments or voices. Counterpoint’s definition does not fit any of those.

    When did counterpoint start?

    Counterpoint, like other movements in the arts, is a continuum, not a one time event. Precursors to what is now considered counterpoint were in full swing toward the end of the Medieval period and many pieces were counterpoint in all but name. There are key texts that help us place when the concept of counterpoint began to become more concrete. The word contrapunctus is seen in a number of writing since the 1300s. But authorship among these earliest of writings is debated. By 1412 the Italian theorist Prosdocimus de Beldemandis wrote a Treatis of Counterpoint which clearly showed the development of the theory. At this point counterpoint was no longer only concerned with “note against note” but melodic line against melodic line.

    The 15th century ushered in a golden age of polyphony (counterpoint), with Guillaume Dufay (1400–1474), Josquin des Prez (c. 1450–1521), and Giovanni Pierluigi da Palestrina (c. 1525–1594) just to name a few. Johannes Tinctoris (c. 1435 – 1511) wrote Liber De Arte Contrapuncti which went into intervals, consonance and dissonance, and their usage. In this book he put down strict rules for introducing dissonances, limiting them to unstressed beats and syncopations – all of which contributed to the codification of counterpoint.

    Though many theorists wrote about counterpoint during the 1600s, it wasn’t until Johann Joseph Fux wrote Gradus ad Parnassum in 1725 that counterpoint had it’s “official” text book. This became the definitive pedagogical work for counterpoint. Though there are plenty of counterpoint text books available today, 300 years later, Gradus ad Parnassum continues to provide a clear way for students to learn this method of composition.

    Where did counterpoint start?

    Primarily in France and Italy. Counterpoint grabbed hold at the end of the musical period called Ars Nova (late 1300s and 1400s) which is the commonly accepted transition between the music of the Middle Ages and the Renaissance periods in Europe.

    Why learn counterpoint

    Counterpoint is an important piece of musical knowledge and understanding

    In Alfred Mann’s translation of Gradus ad Parnassum, the monumental work by Johann Joseph Fux, he begins by says, “The Study of Counterpoint might be compared to the study of perspective. Bother we important developments in Renaissance art. Both reflect the rise of three-dimensional thought.” Counterpoint is the rise of three-dimensional thought. Before counterpoint was in common use or written down into a system, a medieval composer conceived of music as two-dimensional – strictly note against note. This means medieval composers viewed their craft note to note moment by moment. Whereas later polyphonic composers of the renaissance period began to judge an entire melody against another entire melody. The three dimensions of counterpoint are the vertical and horizontal relationships, and time (rhythm). More importantly, it’s the long-range horizontal composition of entire melodic lines while keeping in mind how they relate to the other lines in the piece of music at the scale of the entire piece.

    After about 1300, the word counterpoint started to emerge. And by 1412 the music and theoretical writing on counterpoint we well underway. Part of what makes counterpoint so important for all types of musicians is how it codified an important shift in Western music. As art “discovered” perspective, music “discovered” a new awareness of the distance of time.

    Counterpoint became a teaching tool with Fux’s influential book. It is a great way to learn about intervals, voice leading, consonance, dissonance, how to control multiple lines of music, melodic shaping, and more! Typically, a student of music must learn counterpoint and harmony. In order to understand how the underlying principles of harmony were determined and used, one must understand the counterpoint.

    For composers, counterpoint teaches discipline and care all the while showing students that there are many “right” answers and when in doubt to use their ears.

    For performers, understanding counterpoint helps bring out the subtilties in music from the renaissance on. Knowing more about the whys and how’s of interweaving musical lines can help performers make musical decisions that enhance the performance.

  • The rules of counterpoint: cantus firmus through 5th species

    For a more detailed look at each species of counterpoint refer to the related articles below. This article is intended to be a reference and summary of the main “rules” of counterpoint.

    In general there are five elements to be aware of and control when writing traditional counterpoint: 1) lines move predominately by stepwise motion, 2) horizontal and vertical intervals between the pitches, 3) conventional penultimate and ending measures, 4) rhythmic values, and 5) intervallic repetitions.

    Inside each of those five elements are many pieces to consider. If you learn how to control those five counterpoint elements, you are on your way to writing solid counterpoint.


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    Rules for writing your own cantus firmus

    Something to keep in mind when working on any aspect of counterpoint is that this is music that originated from singing and was codified with the voice in mind. This means that certain rules were born because counterpoint began as vocal music rather than instrumental.

    1. Avoid exceeding the range of an octave.
    2. Avoid outlining a tritone, minor 7th, or major 7th.
    3. Avoid having to much motion going up or down.
      1. A good rule of thumb is to not have more than four notes moving in the same direction.
    4. Do not leap to a tritone, minor 7th, major 7th, or any interval greater than an octave.
    5. Should have only one note that is the highest pitch (do not repeat the highest pitch). This is the climax.
    6. Should move predominately by stepwise motion.
      1. Avoid more than two leaps in a row.
    Cantus firmus rules

    1st Species Counterpoint Rules

    1st species takes some principle rules of writing a cantus firmus and extends them. The primary difference is that you now have vertical intervals to worry about. In order to follow along you must know what intervals are considered consonant and which ones are dissonant.

    Consonances and dissonances in 1st species counterpoint

    Perfect ConsonancesImperfect ConsonancesDissonances
    unison (P1)minor 3rd (m3)minor 2nd (m2)
    perfect 5th (P5)major 3rd (M3)major 2nd (M2)
    octave (P8)minor 6th (m6)perfect 4th (p4)
    major 6th (M6)tritone (TT), augmented 4th (A4), diminished 5th (d5)
    minor 10th (m10)minor 7th (m7)
    major 10th (M10)major 7th (M7)
    minor 9th (m9)
    major 9th (M9)

    The three horizontal motions

    Contrary motion is where the voices move it opposite directions. This is the type of motion you should use the most.

    Contrary motion in counterpoint

    Direct motion is where the voices move by the same interval in the same direction.

    Direct motion in counterpoint

    Oblique motion is where one voice stays the same and the other moves.

    Oblique Motion in countepoint

    1st species rules

    1. Only use consonant intervals but strive to use more imperfect intervals than perfect.
    2. Strive to use more contrary motion than direct or oblique.
    3. perfect intervals can move to another perfect by contrary or oblique (not direct)
    4. perfect intervals can move to imperfect by any motion.
    5. Imperfect intervals can move to perfect by contrary or oblique (not direct)
    6. Imperfect intervals can move to imperfect by any motion.
    7. Do not let the interval between the voices exceed a major 10th.
    8. Try to limit voice crossings.
    9. Do not leap by a major 6th or dissonant intervals.
    10. Do not leap into an octave or unison even in contrary motion.
    11. Do not leap by an interval greater than an octave.
    12. Do not outline a tritone.
    13. Avoid repetitions.

    1st Species Counterpoint Example

    1st species counterpoint example
    Example from Johann Joseph Fux’s Gradus ad Parnassum

    2nd Species Counterpoint Rules

    From now on, I’ll be referring to the intervals and motion that was introduced in 1st species. The biggest changes are the use of two notes in the counterpoint for every note in the cantus firmus and the inclusion of dissonant intervals.

    • The downbeat is always consonant.
    • The upbeat (the second half of the measure) may be consonant.
    • If the upbeat is dissonant, the notes before and after must be approached and left by stepwise motion. This will result in either neighbor tones or passing tones. See example below.
    stepwise dissonance in counterpoint
    • If the weak beat (upbeat) moves by skip, the interval must be consonant.
    • If the cantus firmus is in the lower voice, then the final two measures must have the following interval sequence: P5 — M6 — P8.
    • If the cantus firmus is in the upper voice, then the final two measures must have the following interval sequence: P5 — m3 — P1.
    • Do not write a series of measures where the downbeats are P5, P8, or P1.
    • Don’t separate the voices by more than a 10th.
    • Be careful with voice crossings (allowed but don’t do it too often).
    • Prefer contrary motion over direct or oblique.
    • No dissonant leaps.
    • No leaps larger than an octave.

    2nd species counterpoint example

    There are always little issues you can disagree about when it comes to evaluating an exercise, but I like to remind anyone working towards learning counterpoint that it is just an exercise. The goal is to learn. So, correct the big mistakes, but more importantly understand the deeper reasons the rules exist in the first place. Remember that the rules came after the music, not the other way around!

    2nd species counterpoint example
    From Johann Joseph Fux’s Gradus ad Parnassum

    3rd Species Counterpoint Rules

    The species of counterpoint is now four notes in the counterpoint against one note in the cantus firmus. Most of the same rules from the previous species of counterpoint should be observed. The full article is here: 3rd Species Counterpoint.

    • Start with a consonance.
    • If five quarter notes are going up or going down the following rules apply:
      • The 1st note must be consonant.
      • The 2nd note can be dissonant or consonant.
      • The 3rd note must be consonant unless all the other beats in the 5-note series are consonant.
      • The 4th note can be dissonant if the 5th note is consonant.
    • You can leap away from a dissonance if you then resolve it in the opposite direction by step. This is called “cambiata”.
    Third species counterpoint cambiata example
    • The next to last measure:
      • If the cantus firmus is in the lower part, then the 2nd to last interval must be a major 6th that then moves by contrary motion to the octave.
      • If the cantus firmus is in the upper part, then the 2nd to last interval must be a minor 3rd that resolves to a unison (can also be a minor 10th to an octave).
    • It’s suggested to continue to use more contrary motion.
    • It’s suggested to try not to write “too many” notes going in the same direction. How many is too many? Fux wrote up to nine notes going in the same direction, but use your ear.

    4th Species Counterpoint Rules

    This species changes things up rhythmically by tying half notes over the bar line. For the full article go here: 4th Species Counterpoint.

    • The first measure of the counterpoint begins with a half rest.
    • The upbeat (2nd half of the measure) must be consonant.
    • The downbeat (1st half of the measure) can be consonant or dissonant.
    • Dissonant intervals are resolved by moving down by stepwise motion to a consonant interval.
    • When a ligature (tied note) is not possible, you can write a couple of half notes to get out of the situation.
    • Be careful to avoid repetitions.
    • The 2nd to last measure:
      • If the cantus firmus is in the lower voice, you should have a 7th resolve to a 6th that then moves to the final interval of an octave.
      • If the cantus firmus is in the upper voice, you should have a 2nd resolve to a 3rd that then moves to the final interval of a unison.
    4th species counterpoint example.

    5th Species Counterpoint Rules

    This species can also be called “florid counterpoint” because you are free to use a combination of any of the previous species. At this point you are getting a lot closer to actual composition. In this species Fux says, you are looking for melodic lines with liveliness of movement, and beauty and variety of form.

    There are no specific rules to this counterpoint that are different than the rules already explained in the previous species. This is simply where you put them all together! Something to keep in mind though is that the counterpoint should always be viewed through the lens of a vocal melody – it should be singable.

    5th species counterpoint from Fux.
    From Johann Joseph Fux’s Gradus ad Parnassum
  • 4th Species Counterpoint – the art of tension and release

    You may not have known it but 4th species counterpoint is a clear articulation of that push and pull of tonal music. Western tonal music developed dissonance consonance relationships that helps give “direction” to the music. Typically, compositions utilize building up tension with dissonance which is then relieved by resolving to a consonance in very particular ways. 4th species counterpoint is a written out teaching of that very principle.

    Where the previous species of counterpoint controlled intervals and motion, 4th species introduces suspension (though not technically suspensions as we would find in pieces with more than two voices). In a 4th species counterpoint exercise you will get two melodic lines and chains of “suspensions.” By itself, 4th species can be pretty restrictive but it is the foundational layer that some of the most powerful music is built upon. I’m not saying that 4th species counterpoint “invented” tension and release or dissonant and consonant movement, but it is a systematic way to understand that relationship on a note to note level. Furthermore, these principles can be used in a wide variety of ways and genres.

    4th Species Counterpoint Rules

    • Consonant intervals are minor 3rd, major 3rd, perfect 5th, minor 6th, major 6th, perfect 8th (octave), minor 10th, major 10th.
    • Dissonant intervals are any interval not listed as a consonance.
    • The upbeat must always be consonant.
    • The downbeat can be consonant or dissonant.
    • Dissonances are resolved by descending stepwise to a consonance.
    • When a tied note (ligature) is not possible it is allowed to write plain half-notes to get out of the situation.
    • Avoid repetitions.

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    The resolution of dissonances

    The way Johann Joseph Fux in his 1725 work, The Gradus ad Parnassum, describes how to view the dissonance in a way that we still hear these combinations of intervals.

    “…The notes held over and, as it were, bound with fetters, are nothing but retardations of the notes following, and thereafter proceed as if brought from servitude into freedom.”

    What a poetic way to think about the relationships between the notes.

    Dissonances are easy to handle in this species because all dissonances resolve by descending stepwise to a consonance.

    When the cantus firmus is in the lower voice, 2nds resolve to unisons, 4ths resolve to 3rds, 7ths resolve to 6ths, and 9ths resolve to octaves.

    When the cantus firmus is in the upper voice, you can have a 2nd resolve to a 3rd, a 4th to a 5th, and a 9th to a 10th. Refrain from using the 7th to an octave.

    The First Measure

    To begin these exercises, place a half rest and then begin with a consonance.

    Penultimate Measure in 4th Species

    7th resolves to a 6th if CF is in the lower voice then up to the octave. If CF is in the upper voice one should conclude with a 2nd to 3rd then up to a unison.

    Counterpoint Writing Tips

    One method for writing 4th species is to write a modified 1st species exercise and then shift the notes back by a half-note. This won’t be exactly like a 1st species because you will use more similar and parallel motion as well as less variety of intervals, but it can help to think of composing a 4th species in this way.

    For example here is an example from Fux. Here is the 4th species shifted to look like a 1st species. As you can see there is a preponderance of parallel 3rds that would be unacceptable in a 1st species exercise.

    But when we shift the lower voice over to the right by a half note, it turns into an acceptable 4th species counterpoint.

    Observe the difference in interval variety when the 1st species was shifted to create a 4th species. It went from 3rds, octave, and unison to octave, 10th, 3rds, 2nds, 6ths, P5, and unison.

    When you’re in a bind

    Take the opportunity to leap when you have the chance. Typically, you can do this when you have three consonances in a row because this means you don’t have to deal with resolving a dissonance down by step.

    General shape of the counterpoint

    4th species counterpoint will typically have a distinctive leap up and work downward over the next few measures, then leap up again. This is due to having to resolve dissonances down by step and by wanting to avoid repetitions.

    Succession of fifths

    Due to the syncopation, having perfect 5ths in a row is acceptable. The reasoning according to Fux is that the syncopation breaks up the parallel sound.

    4th species from other sources

    This is a short example from Alfred Mann’s, The Study of Fugue, which of course must address elements of beginning counterpoint. It is easy to see the us of the 7-6 and 4-3 (11-10) patterns.

    Page 21

    Here is another example that is in the context of a more intricate piece by Telemann. As you can see in the first two measures we get the “counterpoint” in the lower staff. The E is tied over the bar line and resolves stepwise down to the D-sharp. When you remove some of the decoration, you get the intervals of minor 3rd to major 2nd back to minor 3rd – just as we expect in a 4th species counterpoint exercise.

    In the last two measures of the excerpt, the “counterpoint” is now in the top staff. The high B is tied over the bar line and then resolves down by step to an A-sharp. Once again, when you remove the decoration pitches in the lower staff, the remaining intervals are major 6th, minor 7th, and a minor 6th.

    The idea of 4th species is a central element in all genres of music and is a fundamental piece to tonal music – namely the concept of tension and release.

  • 3rd Species Counterpoint – (audio ex) rules and steps

    If you do not know about cantus firmus, 1st species counterpoint, or 2nd species counterpoint, check out the following articles first:

    In 3rd species counterpoint the counterpoint moves in quarter note durations against the cantus firmus in whole notes.

    Rules of 3rd Species Counterpoint

    • If 5 quarter notes are ascending or descending the following must be observed:
      • The first note must be consonant
      • The second note may be dissonant
      • The third note must be consonant
      • The fourth note may be dissonant if the fifth is consonant

    Consonant and dissonant beats

    Here is an example of having the 1st and 3rd beats consonant and the 2nd and 4th can be either consonant or dissonant. Remember perfect 4th (perfect 11ths) are considered dissonant.

    Here is an example where the 3rd beat is allowed to be dissonant as long as the other beats are consonant.

    Another acceptable consonant dissonant movement is the cambiata or “exchanged note.” This is where the 2nd beat is dissonant and then you leap away to a consonant and resolve the leap in the opposite direction.

    The next to last measure in 3rd Species Counterpoint

    If the cantus firmus is in the lower part, then the second to last note must be an interval of a Major 6th that then moves by contrary motion to the octave.

    If the cantus firmus is in the upper part, place a minor 3rd at the second to last note and resolve to a unison. Alternatively, you can use a minor 10th and resolve to the octave.

    Using sharps and flats and examples

    Sometimes it is necessary to use sharps and flats in order to avoid tritones (augmented 4th/diminished 5th). Here are some examples from Joseph Fux. Even in these examples there are issues that might be flagged as “less good” or “incorrect”. In my experience, writing counterpoint (or any composition) there is no “perfect” answer. You should try to learn the principles behind the theory or exercise but don’t be bound by them. Use your ear. And if something just sounds strange or breaks the rules, don’t fret. One of the beauties of music is that you can always write more.

    From The Study of Counterpoint trans. Alfred Mann pg. 54

    The two issues I flagged in the example above are “too many notes going in the same direction in a row” and “large repetitive leaps”. The first issue of too many notes going in the same direction also outlines a major 9th (d to e) which is dissonant. The second issue is the octave leap of c to c and back to c again. And then the leaps of a to d repeated. Typically, in counterpoint we try to avoid repeated patterns and sequences (at least for now). Is the above example “wrong”? No. There are countless ways this example could have been written, and in the end if it sounds good, it is good. Here is what this short counterpoint sounds like.

    Here is an example of using flats and sharps in the same exercise.

    From The Study of Counterpoint trans. Alfred Mann pg. 54

    Here is what this example sounds like. I love the mixing of B and B-flat.

    Lastly, here is an example where Fux accepts lots of leaps. Usually, counterpoint favors smooth voice leading – meaning steps are preferred to skips. But as you can see in the example below, there are many leaps and some are “unresolved” by stepping back in the opposite direction.

    3 species counterpoint audio example #8

    It’s easy to get wrapped up in all the rules of counterpoint, but examples like the one above shows that you can be lenient and to just enjoy writing rather than being so strict.

  • 2nd Species Counterpoint – composition for two voices

    If you don’t know what a Cantus Firmus is or what 1st species counterpoint is, please read these articles first:

    2nd species counterpoint is two notes against one. Meaning the cantus firmus is a whole note and the counterpoint consists of two half notes.

    Be sure to download a free counterpoint workbook! Click here.

    2nd species counterpoint rules

    In 2nd species counterpoint, you have to follow the rules of 1st species plus a few new rules.

    • The downbeat is always consonant
      • P1, P8, P5, P4, M3, m3, M6, m6, M10, m10
    • The upbeat may be consonant
    • The upbeat may be dissonant if it moves from the preceding note to the following note by stepwise motion
    • If the upbeat moves by skip, it must be consonant
    • Ending measures: cantus firmus in the lower voice requires a perfect 5th followed by a major 6th
    • Ending measures: cantus firmus in the upper voice requires a perfect 5th followed by a minor 3rd
    • Do not write a series of fifths or octaves on consecutive downbeats

    Books to learn counterpoint

    2 notes against 1

    In 2nd species counterpoint, the counterpoint is made of note durations half as long as the cantus firmus – i.e., counterpoint is half notes and the cantus firmus is whole notes. The first half note is the downbeat, and the second half note is the upbeat.

    The downbeat must be consonant, and the upbeat may be dissonant if it moves from the preceding note to a consonance. The only kind of dissonance allowed on the upbeat is if it is “filling in the third.”

    The first measure

    You can begin with a consonance or a half rest.

    The next to last measure and final measure

    The penultimate measure (next to last) should have a fifth followed by a major sixth when the cantus firmus is in the lower voice. If the cantus firmus is in the upper voice, there should be a fifth followed by a minor third.

    Be careful not to use F against B (fa and ti) because this is not a perfect fifth or perfect fourth, it is a tritone.

    I recommend writing the ending before beginning your counterpoint exercise.

    Beware of Parallel Fifths and Octaves

    Do not write a series of fifths or octaves on consecutive downbeats.

    Use a minor sixth or octave leap to separate the voices

    Sometimes you get in a bind and the voices are too close together. You can use the leap of a minor 6th or an octave to separate the voices.

    Steps for writing 2nd species counterpoint

    • Step 1 – write the ending two measures
    • Step 2 – write the beginning two measures
    • Step 3 – look ahead and see if there are tricky leaps in the cantus firmus
    • Step 4 – fill in the measures
    • Step 5 – make sure you did not break the rules

    As always, play and/or sing your work. This is one of the best ways to train your ear.

    Remember, counterpoint is a compositional tool. These are exercises, so don’t take them so seriously that you don’t complete the exercises. Do your best. Check your work. Move on to the next exercise. Like anything else, it takes practice.

    Continue on to 3rd Species Counterpoint here.

    Free Counterpoint Workbook!

    Practice writing counterpoint in all modes. Here is an awesome free download with cantus firmus ready for you to practice your counterpoint.

  • 1st Species Counterpoint – a foundation for two voices

    In this article you will learn how to write a 1st species counterpoint in 6 steps. I also strive to bring a deeper understanding around some of the “whys” of this practice.

    Why you should learn 1st species counterpoint

    Counterpoint is the foundation of Western music polyphony (multiple melodic lines of music). 1st species counterpoint is a great way to begin to understand and manage two voices. It is a methodical way to build a second part from a melody. Learning counterpoint is a fantastic way to hear how intervals interact vertically and how to handle melodic lines horizontally.

    Whether you are composing in a classical style or writing pop songs, counterpoint can be an incredible tool to have ready to use. Counterpoint can be used as a way to generate ideas, or work to develop a piece. I believe it offers a method to explore music creation in a way improvisation and other compositional methods may not excel at.

    Be sure to download this free counterpoint workbook!


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    Prerequisites before writing:

    What are perfect and imperfect intervals in counterpoint

    Consonance refers to the intervals between two notes that are deemed “pleasant” or consonant. Imperfect intervals are more dissonant than the perfect intervals. Dissonance typically sounds harsh where as consonance sounds smooth. This has to do with how the sound waves from each pitch are interacting with each other.

    What are perfect intervals?

    In 1st species counterpoint the perfect intervals are:

    • Perfect 5th
    • Perfect 4th
    • Octave
    • Unison

    Why are these considered perfect? It has to do with the complexity of wave patterns when these intervals are sounded. For example, when a C and a G are sounded together, we get a perfect 5th – a consonance. The wave patterns of these two pitches fit into each other rather nicely – meaning their peaks and troughs match often and consistently.

    Quick acoustical physics refresher: 1 hertz = 1 vibration per second. Middle C is 261.63 hertz and the next G above middle C is 392 which lets us visualize their wave patterns interacting. In the time it takes C to complete 2 periods G has completed 3 periods and the waves line up again. This gives us a nice ratio of 2 to 3.

    What are imperfect intervals?

    Imperfect intervals create wave patterns that are more complex than the perfect intervals but not as complex as the dissonant ones. Let’s look at C and E (a major 3rd). In the time it takes C to complete 4 vibrations or periods, the E has completed 5. This makes sense because the E is higher in pitch and has a higher frequency which means it moves faster than the C.

    In 1st species counterpoint the imperfect intervals are:

    • minor 3rd
    • major 3rd
    • minor 6th
    • major 6th

    What are dissonant intervals?

    Dissonant wave patterns do not fit so nicely. When C and F# are sounded together we get a tritone (augmented 4th) and it sounds rather harsh. This time the C must complete 12 periods and the F# will complete 17 in the same amount of time and then they line up again. This generates a lot more clashing and takes longer for the pitches to sync up than it does for the C and G combination. In this case we get the ratio of 12 to 17 – a much more complex number than 2/3.

    Hopefully, that short break down helps you imagine why we perceive certain intervals as consonant and dissonant. In classical counterpoint, you should employ more imperfect consonances than perfect. Dissonant intervals are forbidden. If you write too many perfect consonances in a row the music will sound empty, and you will most likely be breaking some rule of counterpoint.

    In 1st species counterpoint the dissonant intervals are:

    • minor 2nd
    • major 2nd
    • tritone (augmented 4th/diminished 5th)
    • minor 7th
    • major 7th

    The three motions of counterpoint – oblique, contrary, and direct.

    There are three types of motion you must understand: direct, contrary, oblique. Each motion has it’s own set of rules. When I talk about motion in 1st species counterpoint, it’s referring to moving from one interval to the next interval.

    Contrary motion in 1st species counterpoint

    Contrary motion is the type of movement you should strive to use the most. With contrary motion you can move from the following types of intervals:

    • perfect consonance to a perfect consonance
    • perfect consonance to an imperfect consonance
    • imperfect consonance to a perfect consonance
    • imperfect consonance to an imperfect consonance

    As you can see from the example, contrary motion is where the two notes move in opposite directions.

    Direct motion in 1st species counterpoint

    When using direct motion, you will have to use care not to move too many times in one direction. Here are the allowed and prohibited movements you can make in direct motion.

    Allowed

    • perfect consonance to an imperfect consonance
    • imperfect consonance to imperfect consonance

    Prohibited

    • perfect consonance to perfect consonance
    • imperfect consonance to perfect consonance

    In the example the notes are both moving in the same direction, either up or down. Direct motion does not specify that the notes must move by the same interval (that’s called parallel motion). As long as the notes are moving in the same direction it is considered direct motion.

    Oblique motion in 1st species counterpoint

    Like contrary motion, oblique motion can move to and from any intervals. Unlike contrary motions, oblique is the type of movement you should use sparingly. The allowed motions are:

    • perfect consonance to a perfect consonance
    • perfect consonance to an imperfect consonance
    • imperfect consonance to a perfect consonance
    • imperfect consonance to an imperfect consonance

    In oblique motion, one note stays the same while the other note moves. Even though one note is remaining on the same pitch you have to watch out for dissonant intervals between the two lines.

    The four fundamental rules of counterpoint

    These rules are laid out in Joseph Fux’s book Gradus ad Parnassum:

    • First rule: From one perfect consonance to another perfect consonance, one must proceed in contrary or oblique motion.
    • Second rule: From a perfect consonance to an imperfect consonance, one may proceed in any of the three motions.
    • Third rule: From an imperfect consonance to a perfect consonance, one must proceed in contrary or oblique motion.
    • Fourth rule: From one imperfect consonance to another imperfect consonance, one may proceed in any of the three motions.
    PerfectImperfect
    PerfectContrary/ObliqueContrary/Oblique/Direct
    ImperfectContrary/ObliqueContrary/Oblique/Direct

    5 Steps to compose a 1st species counterpoint

    Even though we can lay out how to write this kind of counterpoint in just a few steps, I’d like to impress upon you that this is music not simply robotic-rote learning. You should play back what you write so you can make adjustments to give it some artistry.

    Step one – choose a cantus firmus

    Select the cantus firmus you will use for the exercise. The cantus firmus I selected is from Fux’s book. The cantus firmus is in the Phrygian mode. (You can also write your own cantus firmus. I go over how to do that here: How to write a cantus firmus.)

    I highly recommend singing (or playing) the cantus firmus to get a feel for the shape of the melody before writing the counterpoint.

    Step two – write the beginning and end

    The beginning and the end must both be perfect consonances. I love the way Alfred Mann translates Fux regarding this:

    The beginning should express perfection and the end relaxation. Since imperfect consonances specifically lack perfection, and cannot express relaxation, the beginning and end must be made up of perfect consonances.

    -Page 28 from The Study of Counterpoint from Johann Joseph Fux’s Gradus ad Parnassum, translated by Alfred Mann

    In general, it is easiest to begin and end with an octave or unison (though a perfect 5th can be used in the first measure).

    I highly recommend writing the intervals between the staves. This will help you identify errors.

    Step three – write the 2nd to last measure

    The next to last bar must be a major sixth if the cantus firmus is in the lower part. If the cantus firmus is in the upper part, then the next to last bar must have a minor third.

    In my examples above you can see that I crossed voices (this means the counterpoint went below the cantus firmus) which is fine. You calculate the interval from the lowest pitch up – d to f.

    Step four – plan your climax

    When the counterpoint is in the upper voice, your climax should be the highest note. When the counterpoint is in the lower voice, your climax should be the lowest note.

    Step five – fill in the rest

    Fill in the remaining measures but following the Four Rules of Counterpoint.

    It’s a good idea to label your motion and intervals when you are just beginning so you can more easily see what is going on in the music.

    I have filled in the rest of the measures and analyzed the intervals and the type of motion I used. Instead of presenting a “perfect” counterpoint, I wanted to show how you can improve the counterpoint. There are three things I’d like to point out at this stage:

    • Motions: not enough contrary motion (C = contrary, D = direct, O = oblique)
      • 3 contrary
      • 4 direct
      • 2 oblique
    • both voices leaping in the same direction at the same time
    • a tritone leap from f to b in the 2nd and 3rd measure

    I’d start to fix these issues by changing the counterpoint in measures 2 and 3. But like a chain reaction, most of the time when you fix one issue another pops up, so you end up doing a rewrite – like I did below.

    I’ll take the same inventory of intervals and motions and see how it comes out.

    • Motions: I have plenty of contrary motion
      • 5 contrary
      • 2 direct
      • 2 oblique
    • I still have the voices leaping at the same time in measures 3 to 4 but it is in contrary motion which is more tolerable.

    I think I’m ready to move on with this version and look for more errors.

    Step six – watch out for these rules

    The hidden perfect fifths or octaves.

    This occurs when you have a perfect interval that is then followed by an imperfect and another perfect. For example:

    The above is very poor writing because of the repetitive nature, the consistent motion (direct), and the repeated 5th.

    Outlined tritones or leaps by a tritone.

    In the 1st red box there is a leap from F to B which is a tritone. Don’t do that. In the 2nd box from the bottom F to the top B the tritone is “outlined”. The A in the middle does not break up the tritone.

    Voice crossing is acceptable

    You are allowed to have the counterpoint drop below or above the cantus firmus, just make sure it is not for too many notes.

    No skips of a major sixth

    Pretty self-explanatory…don’t do this.

    Unisons can only be used in the beginning and end

    You have to be more careful with this when the voices are crossing. Octaves are okay.

    Watch out for leaping into an octave or unison even in contrary motion.

    If you have to add an accidental to achieve a major 6th or minor 3rd at the penultimate measure, then if that note is used prior it might be good to give it an accidental as well.

    In measures 11 and 13 Fux adds raises the F to F sharp. The advice is to not only raise the F in measure 13 but in measure 11 as well.

    Continue on to 2nd Species Counterpoint!

    Free counterpoint workbook download!

  • What is Cantus Firmus Counterpoint? – how it improves any creative musician

    Yes, learning counterpoint is an old way composers have learned the basics of composition but I believe it is a skill all composers, songwriters, and producers should have in their tool belt.

    Cantus firmus literally means “fixed melody” which just means the main melodic line that all other voices will be based on. Think of it as the first layer in a multilayer music composition.

    In this article I’ll explain what the cantus firmus is and how it works but more importantly how learning the principles of writing a cantus firmus, and counterpoint, will improve your creative skills.

    Quick overview of cantus firmus

    This practice comes from at least as early as the 13th century and was primarily used in sacred chant music. Over the centuries of it’s usage, the cantus firmus has moved from the top voice to the lowest voice to finally settle in a middle voice called the “tenor” (tenor means “to hold”, as in holding the music together).

    I’d like to pause and just note that the idea of the cantus firmus as a way to organize, build, shape, and teach music has so far lasted over 700 years! That fact alone should make anyone creating musician take notice (I also strongly believe that other disciplines might be able to use some of the principles found in the cantus firmus in their approach to their own fields, but that is a topic for another article).

    As a pedagogical method, counterpoint (the cantus firmus) can stand tall because pretty much every successful and famous classical composer learned through this method at one point or another. It’s incredible that counterpoint has been a through line of success across so many geographies, individuals, times, and musical tastes. All that’s to say, this is great stuff to learn if you are interested in creating music – whether that is writing pop songs or string quartets!

    Lastly, cantus firmus forms the basis for Western music’s polyphonic writing. Other cultures also have polyphonic music that is built in entirely different ways – yet again, another topic for another article.

    Some examples of cantus firmus

    Before explaining all the “rules” that go into a cantus firmus, I’d like to point out that these rules were created after the fact. Most music theory explains music that is already written – it doesn’t necessarily predict. Music theory typically takes a look at music and tries to explain why the music works. Same goes for the rules of counterpoint.

    The music is always first. Rules and theories come after.

    – Common Knowledge

    Also, keep in mind cantus firmus and counterpoint began as vocal music. With that out of the way, let’s listen to a few examples.

    The first example is from the most famous of counterpoint books Gradus ad Parnassum by Joseph Fux.

    Another example, this time composed by me.

    You may note many things about these short lines of music, but one thing should stand out – it only has one rhythmic value!

    You should be able to hear the following characteristics of a cantus firmus:

    • it’s a melody within a fairly narrow range
    • it has virtually no rhythmic variety

    Music of the time certainly had more than one rhythmic value but rhythmic notation in Europe took a while to catch up – remember music first!

    Here is a nice two-part example from Pérotin, a French composer from the 1200s. Among many other features to notice, you may notice there is variety of rhythm.

    Why learn to write a cantus firmus?

    I already enumerated the reasons to learn counterpoint but more specifically, the cantus firmus can help in melodic writing. Many of the rules that shape a cantus firmus are still found in contemporary melodic writing. Of course, there are plenty of exceptions, I’m not saying all melodies follow the cantus firmus approach, but there are certain principles that have managed to persist. Aesthetically, what Western music deems to be a “good” melody, has some parallels with cantus firmus. This will become clearer as I show you the way a cantus firmus is composed.

    How to write a cantus firmus in 5 steps

    To compose a cantus firmus, the only prerequisite you need is to be able to place notes on a staff, know their pitch, and be aware of a few intervals. Understanding intervals is a critical skill and I highly recommend reading my interval article to get that skill under your belt.

    Step 1 – just try!

    Just try writing something that mimics the examples above. This is just to get you comfortable setting up the 8 -14 measures and getting notes on a page. I highly encourage you to always play back your work, whether that is on an instrument or by singing.

    Step 2 – the beginning and the end

    Whatever note you started on is the note you must end on. So, it’s a bit like fill in the blank. Setup your measures, place your first note, and then place your final note.

    Step 1 – the beginning and the end of our example

    Step 3 – plan your climax

    Climax in this type of writing just means the highest note. There should be only one highest pitch. Past the half-way mark of your cantus firmus (if you have 10 measures than from the 6th measure onward) and before the 3rd to last measure, make that your highest note. This is now the climax of your cantus firmus.

    For example, if you have an eight-measure melody, you can place the climax in measure 5.

    Example two, if you have an eleven-measure melody, you can place the climax in measures 6, 7, or 8.

    If you like, you can take the total number of measures and multiply by 0.7 and that should tell you pretty well where you climax should be placed. This is just a guide not an absolute! There are always exceptions.

    Number of measuresX 0.7Climax
    85.65
    96.36
    1077
    117.77
    128.48
    139.19
    149.89/10

    The placement of the climax is one of those traits that has continued until this day. Many pieces, pop or otherwise, place their climax near the end of the song, much like the placement we find in cantus firmus.

    Step 3 – place the climax in our example

    Step 4 – steps and leaps (skips)

    There are two types of motion from one note to another – steps and leaps. A step means the note is either one line or space higher or one line or space lower. A leap is anything more than an interval of a 2nd. An example helps here:

    Steps and Leaps (skips)

    Leaps are treated differently than steps. In general, if your melody leaps up by a minor sixth (8 half steps) or octave it must fall back down by a step.

    If your melody leaps down by an octave, it must move back up by step. This is one of those melodic principles that has persisted until today. Many pop melodies follow the “rule” that after leaping up or down the melody needs to move in the opposite direction by step.

    Here is a cantus firmus from Joseph Fux that shows a couple of leaps in the same direction are sometimes resolved by stepping in the opposite direction. In general, you do not want your melody continuing up or down for too long – breaking up the direction of the melody after it has moved in the same direction for three-four notes is a good rule of thumb.

    Example Cantus Firmus from Joseph Fux

    There are some intervals you must not create when you leap. The following are “forbidden”:

    • tritones (6 half steps)
    • minor 7th (10 half steps)
    • major 7th (11 half steps)
    • any interval greater than an octave (12 half steps)
    Forbidden intervals

    You should already have your first, last, and climax measures filled in, now use steps and leaps to fill in the rest of the measures to connect the notes.

    Step 4 of our example

    Step 5 – don’t outline a tritone

    Be careful to make sure your melody does not outline a tritone (augmented 4th/diminished 5th).

    hidden tritone

    Completed cantus firmus

    You have now completed your first cantus firmus! Here are the steps right next to each other:

    Draw measures then place the beginning and ending notes.
    Place the highest note past the half-way point.
    Fill in the rest of the measures with steps and leaps watch out for forbidden intervals.

    Now you can play your cantus firmus!


    I’ve written a short book for composers that explores how music is organized and the roles it can play across the globe. The book is called Formative Forces in Sound. If you are interested, it’s available on Amazon here for $0.99 www.amazon.com/formativeforcesinsound