How to use this page
Section 1 is the example from the workshop video, press play to hear it above the cantus, then hear the same line dropped below. Section 2 is Stage 1 of your exercise: a strict line and its inversion with nothing marked. Find what breaks; it has one right answer. Section 3 is Stage 2: write your own line above the given cantus and put it through the same test. Most lines fail the inversion. That is expected. The point is not to get it right but to try to get it right, to hear with intention before you write.
Every example follows the rules on your rule sheets (species counterpoint after Fux): opening rest where the species asks for one, raised leading tone at the cadence (C♯ here), leaps of a 5th or more answered by a step the other way (and 4ths wherever possible), no hidden 5ths or octaves, no more than three 3rds or 6ths in a row, one high point.
1 · The worked example from the workshop
Second Species above Fux's Dorian cantus firmus. Interval figures are printed over every attack.
Original
Inverted
Dropped an octave, the circled notes are what the rules no longer allow:
- Bar 2, beat 1: a 4th
- Bar 3, beat 1: a unison in the middle
- Bar 4, beat 3: a 4th
- Bar 10, beat 1: a 4th
Nothing was wrong above. Everything circled is wrong below. That is the lesson of this workshop: a strict line and an invertible line are two different things.
2 · Stage 1, find what breaks
A strict second species line above Fux's Mixolydian cantus firmus, then the same line dropped an octave. Nothing is marked. Go through the lower version note by note and write down every note the rules no longer allow: a 4th on a downbeat, a unison in the middle, a weak-beat 4th that is not a passing tone, fifths in a row. Then reveal the key. There are 6 to find.
Buttons: Play above plays the strict line over the cantus. Play below plays the same notes dropped under it, listen for the places that go wrong. Reveal the key shows the circled answer.
Above the cantus
Below the cantus, unmarked
The key
Inverted, the circled notes fail:
- Bar 2, beat 3: a 4th
- Bar 3, beat 1: a unison in the middle
- Bar 4, beat 3: a 4th
- Bar 7, beat 3: a 4th
- Bar 11, beat 3: a 4th
- Bar 13, beat 1: a 4th
One thing in this line I want to point out, because I would rather address it than leave it sitting there. In bar 3 the line leaps onto an octave on a downbeat. That is the battuta, and it is First Species rule 22: do not leap onto a unison, a fifth or an octave on a strong beat, in any motion. Fux is relaxed about the stepwise version, where a tenth closes to an octave, and refuses the leaping one. It does not break the inversion, which is what this workshop is testing, so the line still does its job here. But if you were writing this as a finished exercise you would step onto that note instead. Worth spotting on your own line too.
3 · Stage 2, write one and try
The cantus below is given, the same Mixolydian cantus firmus, in whole notes. You do not write your own cantus; you write a counterpoint on a staff above it (the MusicXML in section 4 has the empty staff ready).
1. Copy the cantus. 2. Write strict second species above it, half rest, two halves a bar, passing tones only, F♯ on the second half of the second-to-last bar. 3. Drop your line an octave. 4. Circle every downbeat that is now a 4th or a unison, and every weak-beat 4th that is not a passing tone. 5. Open the key: the notes will differ from yours, but look for the same kinds of failure, and notice that the cadence bar fails for everyone.
Buttons: Hear the cantus plays the given line alone, so it is in your ear before you write anything. Run the drill is the audiation exercise: it plays the cantus, then counts down one cantus-length of silence in which you sing, aloud or in your head, the line you intend to write against it, then plays the Stage 1 line as a reference, then plays that line inverted. Sing first; write second; invert and check third. Most lines fail. Push anyway.
The cantus firmus (given)
4 · Bonus, the version that does invert
The worked example above keeps the ordinary second-species cadence, with the leading tone on the weak half of the second-to-last bar. That is what forces a 5th or an octave onto that downbeat, and it is why the line will not invert. I had the computer check every strict second-species line over this cantus with that cadence. Not one of them inverts.
Modern practice after Jeppesen allows a first species ending: make the second-to-last bar a single whole note. Fux himself does not — he keeps two half notes right to the end, which is why none of his second species solutions invert. C♯ then arrives on the downbeat, a 6th above E, and a 6th inverts to a 3rd. Here is a line built that way. It obeys every rule of the species above the cantus, and every rule again when you drop it an octave. Nothing is circled because nothing fails.
Original
Inverted
Try this on your own exercise once you have done Stage 2 the ordinary way. The whole-note cadence is on your Second Species rule sheet, rules 3 and 11.
5 · Files
MusicXML opens in MuseScore (free), Dorico, Sibelius or Finale, edit it, transpose it, replace the line with your own.
Workshop 13.2 - Bonus (inverted).musicxmlWorkshop 13.2 - Bonus (the line that inverts).musicxmlWorkshop 13.2 - Slide 3.musicxmlWorkshop 13.2 - Slide 4.musicxmlWorkshop 13.2 - Slide 7 (inverted, circled).musicxmlWorkshop 13.2 - Slide 7 (original, above the cantus).musicxmlWorkshop 13.2 - Slide 8 (cantus, write above it).musicxml