The Magic Table That Lets You Compose Canons Over A Cantus Firmus (1596)
The Magic Table That Lets You Compose Canons Over A Cantus Firmus (1596)
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MAIN SOURCES:
William Bathe, A Briefe Introduction to the Skill of Song (London: Thomas Este, [1596]) [imslp].
Modern ed. under the same title by Kevin Karnes (Ashgate, 2005 / Routledge, 2016).
(*Notice that Karnes interpretation of the table is different from ours)
A PDF with Bathe’s table and a transcription of his 10 canons [link]
Order a POSTER of the table here [link] (and support Early Music Sources!)
FOOTNOTES
[0:34] See our episode cantare super librum [YouTube]. Evidence for canons over a cantus firmus being also improvised can be found in several sources, among them Vicente Lusitano, Gioseffo Zarlino, Thomas Morley and Pietro Cerone. See the works of Philippe Canguilhelm, Peter Schubert, Julie Cummings, Denis Collins.
[1:24] See Kevin Karnes preface to his edition of Bathe’s treatise, where he also explains that some parts were most probably added by the publisher without the supervision of Bathe.
[1:44] See our episode Solmization and the Guidonian hand in the 16th century [YouTube].
[1:50] Karnes, p. 3.
[04:41] In our episode cantare super librum [YouTube] we showed how plainchants were used in this way when it was expected that further voices would be improvised above them.
[09:56] Bathe’s first music treatise – A Briefe Introductione to the True Art of Musicke (London, 1584) – survives only in the form of a 17th century manuscript copy (University of Aberdeen Library MS 28). See Karnes’ edition that includes a transcription of it.
[10:12] “The first kynde of vay yat is vsed to be maid, is to mak on concord for evrie not of ye plain song, quhich is called counter poynt, in quhich certain roules ar to be observed, vherof, ye first and cheifest is, yat twa perfect conncordes of on kynd sould not be maid asending or discending to gieder: as two vnisones, two fyftis, vith ye concordes of ther kyndis.” Karnes, pp. 123-4.
[15:17] The only exception is observation 6 at the unison, where it says 8 5 instead of 12. But if 8 and 5 are an octave and a fifth, together they are indeed a 12th.
[15:43] While this argument is correct, if Bathe had wanted to consistently note those intervals that can be used melodically only once, some of the numbers of observations 5 and 6 would have been different. Another possible reason for Bathe to include observation 5 (that if ignored leads to unisons or octaves between the leader and follower) is the opinion held by Zarlino (and possibly others) that unisons and octaves should be generally avoided unless absolutely necessary. See Gioseffo Zarlino, Le istitutioni harmoniche (Venice, 1558) [imslp, TMI], part III, cap. 41, p. 194 (Eng. ed.: pp.90-2).
[18:38] In some cases in Bathe’s examples, if stripped down to their skeletal versions, you can find parallel octaves between the leader and the cantus firmus. In the ornamented final pieces these are “corrected” using rests. Such rests, however, are not considered as a valid solution by authors such as Zarlino, for example. Gioseffo Zarlino, Le istitutioni harmoniche (Venice, 1558) [imslp, TMI], part III, cap. 47, p. 205 (Eng. ed.: p.113).
[19:05] Thomas Morely, A Plain and Easy Introduction to Practical Music (Londong, 1597) [imslp], p. 98.
[19:30] Karnes, p. 125 [The English in the quoted segment is slightly modernized].
[22:55] See Denis Collins, ‘Sufficient to quench the thirst of the most insaciate scholler whatsoeuer: George Waterhouse's 1,163 canons on the plainsong Miserere’, in: Canons and Canonic Techniques, 14th-16th Centuries (Peeters, 2007), pp. 407-20.
[23:25] Even if it was clear to us how the table can create the other kinds of canons that Bathe claims it can deal with (he mentions a canon for two parts without a plainsong, a canon for three parts with the third voice being below, and a canon for two parts upon two plainsongs at the same time; Karnes, p. 78) – which is not the case, still, many more tables would be needed to accommodate all the different possible kinds of canons that are found in the above mentioned canon collections.
[23:42] Morley, p. 98.
[24:05] The canon by John Bull shown on the video is from MS Vienna MUS Hs 17771 [Onb], f. 38v.
[24:22] In slightly later German repertoire one may find a few canons over a cantus firmus in organ versets. Selected examples: Samuel Scheidt – some pieces titled “canon” in Tablatura Nova; Matthias Weckmann – ‘Es ist das Heil’ (verses 4 and 5); and Johann Sebastian Bach – some variations in ‘Vom Himmel hoch, da komm ich her’.
[26:03] “Ma si dè sapere, che è impossibile in tutte queste sorti di Contrapunti doppij, & fatti con simili oblighi, di osseruar pienamente le Regole date di sopra; massimamente quando cotali oblighi crescono: essendo che non si può osseruare la bellezza, & il decoro del Contrapunto, si in quanto alla modulatione, quanto ancora intorno la inuentione, & il modo di porre le page consonanze: percioche è leuata la libertà al Compositore, che hauea nel comporre gli altri senza alcun obligo… Sono queste maniere veramente molto ingegnose, ancora che si oda alle volte qualche cosa, che sia strana da udire.” Gioseffo Zarlino, Le istitutioni harmoniche (Venice, 1558) [imslp, TMI], part III, cap. 64, p. 258 (Eng. ed.: pp.220).
[26:51] Morley, p. 115 [The English in the quoted segment is slightly modernized].
APPENDIX Ia - Surviving printed sources with canon over a cantus firmus:
APPENDIX Ib - Selected surviving manuscript sources with canon over a cantus firmus:
APPENDIX II - Features of canons over a cantus firmus in English sources VS canons that can be created using Bathe's table:
APPENDIX III - Bathe's descriptions of his observations VS what we found the numbers to indicate implicitly:
William Bathe, A Briefe Introduction to the Skill of Song (London: Thomas Este, [1596])
The first and second figures sheweth what distances (in respect of the latter notes of the course) should not come twise together, remouing one way with the latter notes, and also where in respect of the latter note of the course, a flat for a sharp, or a sharp for a flat, contrary to the order of the place should not bee.
The third & fourth sheweth what mouing one way with the place, iust so long after as the following part resteth, maketh discords.
The fift and sixt serueth wherein the distance, there should not be like mouing one way with the place iust so long after as the following part resteth, and the fift figure. Also where sharp for flat, or flat for sharp, contrary to the order of the place should not bee iust so long after as the following resteth.
Observations 1 & 2: These numbers refer to the interval between a note of the leader and the following note of the cantus firmus. Those intervals should not be repeated more than once in a row.
Observations 3 & 4: These numbers refer to forbidden melodic intervals of the leader. Ascending intervals that should be avoided are found on the top part of the table and descending ones at the bottom.
Observation 5 & 6: These numbers refer to melodic intervals of the leader (ascending and descending similar to ob. 3 & 4), that if used will lead to the following relation with the follower: a unison/octave or a fifth/fifth and octave. Using them more than once in a row will lead to parallel movement.
CREDITS
Created by Elam Rotem and Alon Schab, May 2024
Music examples by Leonardo Bartolotto (viols) and Elam Rotem (harpsichord).
Special thanks to Denis Collins, Peter Schubert, Tim Braithwaite, Sean Curtice, Loren Ludwig and Anne Smith.
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