Workshop 13.6, Inverting at the Twelfth

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 (none, the upper voice falls F–E 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

First Species above Fux's Phrygian cantus firmus. Interval figures are printed over every attack.

Original

Inverted

Dropped a twelfth, every rule of the species still holds. This line is invertible.

2 · Stage 1, find what breaks

A strict first species line above Fux's Dorian cantus firmus, then the same line dropped a twelfth. 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. Trick question: this line survives, every 4th below is a passing tone. If you marked one, work out why it is legal.

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, every rule still holds.

3 · Stage 2, write one and try

The cantus below is given, the same Dorian 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 first species above it using 3rds, 5ths, octaves and 10ths, no sixths, and close on a 5th. 3. Drop your line a twelfth. 4. Check with 13 − n: every column should add to thirteen and contain no 7. 5. Compare with the key, fair warning: only one strict line exists here, so see how close you get.

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 · Files

MusicXML opens in MuseScore (free), Dorico, Sibelius or Finale, edit it, transpose it, replace the line with your own.