William Bathe's Method for Two Parts in One

Crispin Sexi (Jaysen Ollerenshaw), 2006

Introduction

Canon is a difficult technique in musical composition, for it involves writing a melody that works as its own accompaniment. In canon a leading voice sings the melody, and a following voice copies the same melody only a few notes after the leading voice starts, usually at a different pitch. Such composition would appear to be made an even harder task if one tries to write canon above a third voice. In his book The Skill of Song, William Bathe (1564-1614) included a cunning method for writing two-part canon to an existing plainsong or ground. Unfortunately his explanation is difficult to understand, and does not contain worked examples. Here I will attempt to better describe his method.

Step 1: Write a Ground

Write one, pinch someone else's bass line, or use an existing chant melody. Write the notes out as semibreves on the bottom voice of a score laid out in 4:4 time for three voices.

C E D C G C

Step 2: Choose a Place

Select a number from 1 to 7. Write it down. Select a direction, either up or down. Write the direction next to the number, eg "Place = 4 up". If your number is 1, don't include a direction.

Step 3: Choose a Delay

The Delay is how long the following voice of the canon waits after the leading voice of the canon starts. I recommend one semibreve the first time you do this, because it is easiest. Two or three semibreves would also work well. (I'm not going to discuss delays of fractions of semibreves here; only try that once you've had a lot of practice.) Write down the delay.

Step 4: Calculate the Course

Under every note of the ground, write down the interval from that note to the note that starts after the Delay. For example, if your Delay is 1 semibreve, and the first two semibreves of the ground are C and D, write down "2 up" under the C (since C to D is a 2nd). Unisons and leaps of an octave are treated as 1.

C to C is 1; C to D is 2up; G to F is 2dn; etc...

If your delay is 2 semibreves, or more, you skip the intervening notes. For example if the first four notes are G A E A and the delay is two semibreves, write "3 down" under the G (since G to E is a 3rd) and "1" under the A (since A to A is a unison). Continue on writing down the Course numbers until you run out of notes in the Ground. Our earlier bass line now looks as follows:

3up 2dn 2dn 5up 5dn

Step 5: Pencil in the Leading Voice

Now you need to write the leading voice of your canon. Bathe provided a complicated table for doing this, which I have deconstructed to make your job easier. Find the section below that is relevant to the Place you have selected, and use it for the duration of this composition.

Look up the first Course in the Place table. The table will give you a set of numbers (any of 1, 3, 5 & 6) that represent possible intervals that the leading voice may have with regard to the first note of the ground.

In our example, the Place is "4 up" and the first Course is "3 up". The table indicates the only choice of note for the leading voice is 5 (i.e. a 5th). Since C is the first note in the ground, the leading voice gets a G. The second Course is "2 dn", giving a choice of 1 or 6, so either E or C could be used in the leading voice in the second bar.

For every Course you have marked under the ground, pencil in your selected notes for the leading voice as semibreves. You must stay within a reasonable range for the singer or instrument, such as an octave. Any of 1, 3 or 5 may be used for the last note.

5 6 1 6 3 5

Step 6: The Observations

Now calculate the Course again as per Step 4, but this time for the leading voice.

4up, 2up, 4dn, 2up, 3dn

Bathe observes that the following conditions are undesirable:

Fix either of the above problems by selecting a different note from those allowed by the Place table, or by replacing one of the two semibreves involved at least partially by a rest.

In the example here, 4dn in the third bar is listed in the discord table. The Place table lets us use B (a 6th), but this then introduces the problem of two 2dn's in a row, which is listed in the parallel table. The Place table does not give another option for the note in bar 4, so a minim rest has been added at the start of the bar.

Initially the leading voice Course reads 4up 2up 4dn 2up 3dn.  This is modified to 4up 2dn 2dn 2up 3dn, with a minim rest in the 4th bar.

Step 7: Ornament the Leading Voice

You may now add passing notes to smooth out jumps in the melody, and otherwise ornament the leading voice. The third beat of the bar may only have notes from the Place table, and the Observations in Step 6 also apply to these. The second and fourth beats may generally have any note that is moved to or from by a tone or semitone. You may also tie a minim over into the next bar to create a suspended dissonance if it is followed by a minim a step below.

_ G | C D C | B | _ A | B A | G

Step 8: Fill in the Following Voice

Now write in the complete following voice, copying it from the first voice transposed by the Place and the Delay.

Notice that following voice will not be an exact copy of the leading voice; the notes C D E in the leading voice will become D E F in the following voice if the Place is "2 up", giving a different sequence of tones and semitones.

Now mark in accidentals, as appropriate to the mode. A sharp or flat in one voice does not need to be copied by the other voice.

At this point you might also come across a limitation of Bathe's method; the Discord tables do not reveal tritones, such as between F and B. You will have to remove any tritones that occur on the beat, either by using a flat or a sharp, or by going back and selecting another note from those allowed by the Place table. The example has B in the third bar flattened to avoid the tritone it made with F in the following voice.

The B in the 3rd bar becomes a B-flat

And Finally

Go find three musicians and get them to play your finished piece.

That's it. Using Bathe's method, you have saved yourself weeks of trouble and pain that you might have had trying to write such a complicated style of music. For your benefit he has done all the hard work of determining how the puzzle that is a canon can be put together, without you having to put thought into what the following voice is up to.

The Tables

Place: 1 (Unison)
CourseNotes
8 up1 3 5 6
7 up5
6 up1 3 6
5 up3 5
4 up1 6
3 up1 3 5
2 up6
11 3 5 6
2 dn5
3 dn1 3 6
4 dn3 5
5 dn1 6
6 dn1 3 5
7 dn6
8 dn1 3 5 6
Discord
7 up
2 up
2 dn
7 dn
Parallel
8 up
5 up
4 up
4 dn
5 dn
8 dn
Place: 2 up or 7 down
CourseNotes
8 up5
7 up1 3 6
6 up3 5
5 up1 6
4 up1 3 5
3 up6
2 up1 3 5 6
15
2 dn1 3 6
3 dn3 5
4 dn1 6
5 dn1 3 5
6 dn6
7 dn1 3 5 6
8 dn5
Discord
8 up
3 up
1
6 dn
Parallel
6 up
5 up
2 up
3 dn
4 dn
7 dn
Place: 3 up or 6 down
CourseNotes
8 up1 3 6
7 up3 5
6 up1 6
5 up1 3 5
4 up6
3 up1 3 5 6
2 up5
11 3 6
2 dn3 5
3 dn1 6
4 dn1 3 5
5 dn6
6 dn1 3 5 6
7 dn5
8 dn1 3 6
Discord
4 up
2 up
5 dn
7 dn
Parallel
7 up
6 up
3 up
2 dn
3 dn
6 dn
Place: 4 up or 5 down
CourseNotes
8 up3 5
7 up1 6
6 up1 3 5
5 up6
4 up1 3 5 6
3 up5
2 up1 3 6
13 5
2 dn1 6
3 dn1 3 5
4 dn6
5 dn1 3 5 6
6 dn5
7 dn1 3 6
8 dn3 5
Discord
5 up
3 up
4 dn
6 dn
Parallel
8 up
7 up
4 up
2 dn
5 dn
8 dn
Place: 5 up or 4 down
CourseNotes
8 up1 6
7 up1 3 5
6 up6
5 up1 3 5 6
4 up5
3 up1 3 6
2 up3 5
11 6
2 dn1 3 5
3 dn6
4 dn1 3 5 6
5 dn5
6 dn1 3 6
7 dn3 5
8 dn1 6
Discord
6 up
4 up
3 dn
5 dn
Parallel
8 up
5 up
2 up
4 dn
7 dn
8 dn
Place: 6 up or 3 down
CourseNotes
8 up1 3 5
7 up6
6 up1 3 5 6
5 up5
4 up1 3 6
3 up3 5
2 up1 6
11 3 5
2 dn6
3 dn1 3 5 6
4 dn5
5 dn1 3 6
6 dn3 5
7 dn1 6
8 dn1 3 5
Discord
7 up
5 up
2 dn
4 dn
Parallel
6 up
3 up
2 up
3 dn
6 dn
7 dn
Place: 7 up or 2 down
CourseNotes
8 up6
7 up1 3 5 6
6 up5
5 up1 3 6
4 up3 5
3 up1 6
2 up1 3 5
16
2 dn1 3 5 6
3 dn5
4 dn1 3 6
5 dn3 5
6 dn1 6
7 dn1 3 5
8 dn6
Discord
8 up
6 up
1
3 dn
Parallel
7 up
4 up
3 up
2 dn
5 dn
6 dn

Examples

10 sundry waies of 2 parts in one upon the plain song, example 1 (William Bathe): Noteworthy, Pdf, Midi.
Place = 4 down, Delay = 1 semibreve.

Benedicamus Domino (Crispin Sexi): Noteworthy, Pdf, Midi.
Place = 3 down, Delay = 1 semibreve, ground moving by minims.

Bibliography

Bathe, William, A Briefe Introduction to the Skill of Song, c. 1587, B. Rainbow (Ed), Boethius Press Limited, Kilkenny, Ireland, 1982.

Karnes, Kevin (Ed), William Bathe's Brief Introduction To The Skill Of Song (Music Theory in Britain, 15001700: Critical Editions), Ashgate Publishing, Aldershot, England, 2005.

Other Compositional Techniques

Mathematical Musick: The Contrapuntal Formula of Dr. Thomas Campion, an article by Jeff Lee.

Die Bassmethode: A system for writing a 16thC bass part.

The Eighth Part: A system for 16thC composition for eight or more parts, based on Campion's formula.


Copyright Jaysen Ollerenshaw 2006. Free use for non-profit.

Joan & Crispin's Homepage: http://aelflaed.homemail.com.au/