Duodenal harmony

The word duodene derives from medieval Latin duodena “a dozen, a group of twelve”, so Joyce’s “duodene of birdnotes” refers to a group or set of twelve notes. But what is the motivation behind Joyce’s use of the word?

There are several possibilities, each of which may have contributed something to the expression.

The technical meaning

The word duodene was coined by the nineteenth-century mathematician and phoneticist Alexander J. Ellis (1814-90). Ellis’s On Early English Pronunciation (London, 1869-89) was a standard phonetics text of the time, and his radical ideas on spelling involved him in work with Isaac Pitman. Duodene, however, arose from his work on musical acoustics and harmony.

In 1875 Ellis published On the Sensations of Tone as a Physiological Basis for the Theory of Music, a translation of Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik (1862), by the German physicist Hermann Helmholtz. Ellis’s translation included over 150 pages of his own annotations and comments, along with much of the text of lectures on the subject that he had read before the Royal Society in London in 1864 and 1874.

Ellis introduced the word duodene in the title of his 1874 paper to the Royal Society, “On Musical Duodenes, or the Theory of Constructing Instruments with Fixed Tones in Just or Practically Just Intonation” (Proceedings of the Royal Society of London vol. 23 (1874-5), pp. 3-31.¹ Ellis was interested in developing a theory of musical “temperament” and “its application to the theory of constructing musical instruments with an intonation practically just, without changing the fingering, and, if there are three or four performers, without change of mechanism” (p. 3). A duodene is a set of twelve notes proportionately related. A theory of duodenes could supposedly be applied to the construction of organs, harmoniums, and other instruments to give a more perfect harmonic or “just” intonation than was previously available, without necessitating the construction of complex new keyboards or manuals.

According to Ellis’s 1874 paper, “a duodene […] consists of 12 tones, forming four trines of major Thirds arranged in three quaternions of Fifths” (p. 16). He prepared complex tables of “manuals for duodenary instruments”, and some harmoniums and organs were constructed to his method.

The Academy of 11 December, 1875 contains a useful description of the duodene:

In a scheme of horizontal and vertical lines, each horizontal step to the right being a perfect third up, and each vertical step a perfect fifth. Placing anywhere on this scheme an oblong which includes three notes in a horizontal and four in a vertical line, we find within it twelve notes, which are defined as constituting the duodene of a note occupying a definite position within the oblong.

But even the Academy sounds slightly uncertain about the utility of the idea:

The practical use of this is intended to be that the actual notes can be designated without altering the ordinary notation of music, by simply writing above the line the name of the duodene employed. (p. 606)

Ellis’s theory enjoyed a short-lived celebrity. He wrote the article on the duodene for Stainer and Barrett’s influential Dictionary of Musical Terms of 1876, though the entry was edited out of later additions. Ellis’s theory was still being used into the twentieth century by enthusiasts wishing to construct musical instruments:

Duodenes…

Sir. – The following plan of a small cottage reed organ, capable of producing a duodene in just major thirds in any key, is respectfully submitted to those of your readers who are interested in the subject as a more complete method of exhibiting the superiority of just intonation over equal temperament than that given in your issue of April last under the title of “An Idea for Equal Temperament”.

William Bethell in Musical Opinion & Music Trade Review (1902) October, p. 43/2

But is it likely that Joyce was more than passingly familiar with the word? The association of the duodene with “the keys, all twinkling, linked, all harpsichording” is suggestive of Ellis’s theory of the duodene, but Joyce was more familiar with informal musical performance.

A more realistic suggestion

I am grateful to Vincent Deane for a more attractive explanation of this passage. Joyce’s description accompanies an improvised, purely instrumental performance of the popular song “Good bye Sweetheart Good bye” (“I was only vamping, man”: U 11.448). The sheet music for the song opens with two sextuplets (groups of six notes equal to four of the original note-values) in the left-hand part, making up simple broken C major chords. Duodene can therefore be regarded as referring to a barful of sextuplets. The pianist is obviously playfully enhancing the otherwise plodding accompaniment by playing sextuplets in the treble, suggestive of the soaring lark and pearling dewdrops.

This myth of male and female birdsong might explain the otherwise cryptic “bright treble answer”, as there is no question-and-answer situation in the song.

Conclusions

It seems that Joyce made use of the word duodene, from Ellis’s theory of ‘just intonation’, but that he employed it in a different context, that of the repeated sextuplets of a popular modern song. Whether he also wove in the allusion to the Chinese harmonic myth remains a moot point.

John Simpson

Search by keyword (within this site): Music Germany Songs Myths Chinese