In this article Surface Topology in Bach Canons, I: The Möbius strip the author wrote that

Canon 5 is described by Bach as a duplex, a 4: there are 4 voices singing two canons in parallel.

Could you please explain for me what is a duplex? And what is a 4?

Please help me.


  • 3
    You quoted the definition of duplex: "there are 4 voices singing two canons in parallel." – Todd Wilcox Mar 6 '17 at 5:04
  • So a 4 is also defined by 4 voices singing two canons in parallel? – Knumber10 Mar 6 '17 at 5:46
  • 1
    @Knumber10: No, a 4 simply means any four-voices piece. It could be instrumental, sung or anything and it definitely does not need to be a canon, let alone two. – guidot Mar 6 '17 at 8:31

duplex: just as in duplex apartment means there are two floors, here it means there are two voices/tracks to sing, probably a deeper one and a higher one.

a 4: in French and Italian (and probably latin ?), this is how you would say with 4 people. For instance, to play (a game, music, ...) with 4 people would translate to jouer à 4 in French. So it really just means 4 people are singing.

In the end the definition of duplex a 4 is exactly what you wrote: there are 4 voices singing two canons in parallel.

EDIT: 4 people re singing in total if it's a 4. Then if it's duplex you just group those people onto different voices.

  • In my opinion it is still to undefined, how the grouping is: duplex (canon à 4) which means we have 4 voices per canon and so 8 voices in total, or (duplex canon) à 4 (four voices grouped into two canons). – guidot Mar 6 '17 at 14:04
  • duplex a 4 would means there are 4 people singing in total. Which are then grouped onto two voices. Though the grouping is not defined, so it doesn't say it's two and two people, I guess you could still call a canon with 3 and 1 persons singing on each voice a duplex canon a 4 – Nicolas Marshall Mar 6 '17 at 14:28
  • Accepted for the the given example, difficult to generalize. I want to point out however, that 4 voices canon neither means, that someone sings at all, nor that each voice is only performed by one player/singer. – guidot Mar 6 '17 at 16:18

The phrase "duplex, a 4" is italicized, which leads me to believe it is a phrase from a different language rather than being a pair of separate terms. Looking at other places on that web page, I see there is at least one other case of italicized text in Latin ("motu recto et contrario") referring to Bach's descriptions. The phrase "duplex, a 4" could be translated from Latin as "double, from 4" or "two-fold, from 4."

When interpreted as "two canons from 4 voices," this properly matches the source text's explanation of "4 voices singing two canons in parallel."

  • Translating "a" as "by" would probably make the most sense, given the latter half of the quote. – delete me Mar 6 '17 at 8:23
  • even that, what does "from 4" mean? I mean by 4 should be understood from 4 voices right? – Knumber10 Mar 6 '17 at 8:30
  • 3
    @Knumber10 Two canons sung by four voices. Two voices for each canon, as per the following sentence at your link. "Canon simplex à 3 voci" would be one canon with three voices, as another example. Here's a visualization of a canon triplex à 6 which should help; you can clearly see three pairs of voices. – delete me Mar 6 '17 at 8:37

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