The Counterpoint "Game" - Part 3
CANTUS FIRMUS: PART 3 - Link to Part 4
Balance, Melodic Tension, Repetition, Beginnings and Endings: This is a continuation of the two previous essays [see link one and link two], and an ongoing tutorial in the fundamentals of musical counterpoint.
BALANCE – You will recall that the word cantus firmus means “fixed song” and refers to a set melodic line, devoid of dissonant intervals and stripped of rhythmic emphasis. A cantus firmus (abbreviated CF) is used as a scaffolding for added counterpoint. As you can see above, an occasional change in the vertical direction of a cantus firmus creates musical interest, because BALANCE. Note: You should always try to sing, and play these examples on a musical instrument.
BALANCE 2 – Following a leap, particularly after a leap of a Fifth (or larger), reversal of direction creates musical interest. Again, because BALANCE.
FYI the C-Clef (Tenor Clef) in the above staff tells us that the fourth line, counted up from the bottom, is the note C, or “DO.” Thus, this example begins and ends on the note F, or “FA.”
BALANCE 3 – It has been said that unidirectional motion in a CF should be limited to five tones, but this is relative to the total length of the line. As we see here, the longer CF on the top staff tolerates a six-tone one-way motion at the end better than the shorter line underneath it.
Even when we “season” a long, unidirectional line with a few skips, it is better to break it up with brief changes in vertical direction. Because BALANCE. Play/sing and compare the bland sound of #1 with the more satisfying line #2 beneath it. Are you getting the idea?
Before going on, try to play on a piano-keyboard and listen to some of the DISSONANT MELODIC INTERVALS of a Scale: DO-TI, RE-DO’, MI-RE’, FA-TI, FA-MI’, SOL-FA’, LA-SOL’, TI-FA, and TI-LA’.
The dissonances shown above were listed among the melodic intervals declared unacceptable in the Rules for writing a cantus, remember? No melodic 7ths of any kind, and no chromatic, diminished, augmented, or compound intervals. The implications are extensive.
HIDDEN DISSONANCE – A mostly conjunct segment that happens to be bounded by the endpoints of one of these dissonant intervals also creates unresolved tension, which for now, by means of these exercises, we are disciplining ourselves to avoid. Can you hear the hidden dissonances outlined by the brackets above? The C-Clef in examples #1, 2, 3 has moved to the third, or middle line of the staff; the Alto Clef position. Play/sing these three examples, and listen for the forbidden hidden dissonances.
The strong pull of the Leading Tone (abbreviated LT), in Major or Minor, can create imbalance. As seen above, the line ascends to the 7th scale degree – the "TI" – but never completes its journey all the way to the tonic. Play and sing the line. In other words, in a CF, the LT should not be written as the “last stop,” the high point – the climax – of an ascending line.
NO REPEATS – We want all the tones of a CF to be of EQUAL duration and emphasis; no tones may stand out. Because repeating the same tone two times in succession not only gives it more emphasis than the others, but effectively doubles the duration of the sound.
The only “breve” allowed is the Final! – See Salzer & Schachter in the References below.
NO REPEATS 2 – We know not to repeat the climax note. We know that only the first and final tones occur twice. As for the rest of the “story,” NO single tone should receive more emphasis than the others – repeating any tone several times throws off the balance of the CF – See Salzer & Schachter, p. 8.
NO REPEATS 3 – In the little game of species counterpoint, and even tinier mini-game of cantus writing, there is no room for repetition of an isolated group of tones – in music we call this a motive. Play/sing the above example and listen carefully. Repetition of motives is a tool of composition; later on we will go into the application of repetition. (But not yet.)
NO SEQUENCES – For similar reasons, no sequences are permitted here, though we will deal with both repetition and sequences further down the road. Again, the repetition of recognizable groups of notes – as shown here – this is NOT permitted in a CF! See Salzer & Schachter, p. 9.
Note: A musical sequence is in some ways similar to a repeating "loop" used in popular music today, but occurring at higher or lower pitch levels with each repetition.
Beginning of Cantus Firmus – We mentioned already that the cantus must begin and end with the chosen tonic. After the initial tone, the line may proceed by step, skip, or leap (as long as we reverse direction after a big jump). To reiterate: The CF must end on the same tone with which it began.
Ending Descending – Most cantus firmi conclude with a descent to the tonic pitch. Why a descent?
Because a rising line builds up tension, and we want a cantus with a relaxed ending. No tension.
The final tonic of most historical CF is approached from above.
The penultimate tone just before the Final may be approached by step, or skip (no larger than a third), from either direction, but the final note itself may be approached only by step. While playing or singing the two lines above, notice how abrupt a leap on the end sounds. That leap to the Final tone leads us to expect the cantus to continue, because it wants to fill in the leap – because BALANCE! For that reason, the second line sounds more stable, relaxed. See Salzer and Schachter.
Incidentally, the above staves feature the “Soprano Clef,” which places Middle C or “DO” on the bottom, or first line of the staff.
Finally, we do encounter a few cantus firmi that approach the final tonic from below, for the sake of … variety! When such a CF is in a minor mode, it resorts to a raised 7th and possibly raised 6th scale degrees, to avoid that augmented 2nd interval (A2) we know is lurk lurking just below the minor tonic. This is one example of musica ficta mentioned in a previous essay.
For completeness, a subsequent essay will talk a bit about the various modes that can be used in writing a cantus firmus. But in this and the previous two parts, you already know the essentials of how to play the cantus firmus game.
Incidentally, the ending tone in modal counterpoint, is actually called THE “FINAL” (and that is no fantasy!).
So, we’ve refined some of the Rules for writing a musical line called a cantus firmus, Latin for “fixed song.” Our objective is to create a scaffolding which we will later use for learning to write musical counterpoint, a technique of adding additional melodies above and below the CF. #Counterpoint writing requires a comprehension of the same Rules used CF, for achieving Balance, pertaining to melodic dissonance (tension), change of direction, leaps, number and repetition of tones, climaxes, beginnings and endings. #CantusFirmus #MusicTheory
REFERENCE WORKS CONSULTED
Salzer, Felix and Carl Schachter. Counterpoint in Composition: The Study of Voice Leading, pp. 3-12. New York: McGraw-Hill, 1969.
Mann, Alfred. The Study of Counterpoint, from Johann Joseph Fux’s Gradus ad Parnassum. New York: Norton, 1965.
Schubert, Peter. Modal Counterpoint, Renaissance Style, First Edition, p. 18. New York: Oxford, 1999.
Jeppesen, Knud. Counterpoint: The Polyphonic Vocal Style of the Sixteenth Century. New York: Dover, 1992.
PRIMARY SOURCE OF MISCELLANEOUS CANTUS FIRMI
Gradus ad Parnassum, by Johannes Fux (reprint of original, in Latin, published in 1725). Public Domain: http://imslp.org/wiki/Gradus_ad_Parnassum_(Fux,_Johann_Joseph)
FLICKR IMAGE CREDITS, in Order of Presentation:
Balance, by Natalie Lucier: https://flic.kr/p/6HBN2C
Vintage balance scale, by Colleen Smith [mods and commercial use allowed]: https://flic.kr/p/aGSh8r
HK Harbour, by Chor lp: https://flic.kr/p/8duFKv
Eagletail Mountains Wilderness, by Bureau of Land Management [AZ?]: https://flic.kr/p/fkKUrx
Stairway to nowhere, CA, by Delaney Turner: https://flic.kr/p/aRQBqP
Arboga river, by Arvid Rudling: https://flic.kr/p/84BSQ7
Cliffs of Moher, by Stephen Carter: https://flic.kr/p/9xSAX1
Minky Whale, by William Warby: https://flic.kr/p/dtS35s
Otakuthon 2014 – Final Fantasy VII, by Pikawil: https://flic.kr/p/oCitN9