In hydraulis by Antoine Busnois

You may remember this post of mine:

• Renaissance polyphony: the Franco-Flemish school.

This school of music flourished for two whole centuries, roughly from 1400 to 1600. Though I haven’t been posting about it lately, I continue to enjoy it.

Antoine Busnois (1430–1492) is one of the most famous composers in the second generation of the Franco-Flemish school. He’s almost up there with Johannes Ockeghem. And I just ran into a piece by him called In hydraulis. I really like it! But why did he call it that? You don’t hear many songs about hydraulics.

It turns out the lyrics are a description of Pythagorean music theory based on simple fractions and also a homage to his colleague Ockeghem: in 1467, when Busnois wrote this piece, he had recently joined Ockeghem working at the court of Burgundy. The first two words just happen to mention a ‘hydraulis’, which is an ancient kind of water organ.

According to Wikipedia,

The hydraulis is the name of a Greek instrument created by Ctesibius of Alexandria. The hydraulis has a reservoir of air which is inserted into a cistern of water. The air is pushed into the reservoir with hand pumps, and exits the reservoir as pressurized air to blow through the pipes. The reservoir is open on the bottom, allowing water to maintain the pressure on the air as the air supply fluctuates from either the pumps pushing more air in, or the pipes letting air out.

But why was Busnois writing a song about a hydraulis? Translated into English, the lyrics of In hydraulis start like this:

Once when Pythagoras was wondering
at the tones in water organs and the tonalities
of hammers, having followed with his eyes the surfaces
according to the inequalities of the weights,
he discovered the essence of music:
the proportions of epitritus and hemiola,
epogdous and duple, for they lead to
the harmony of fourth, fifth, and also
tone and octave, while they connect
the species of the monochord.

These lyrics are remarkably scholarly, and I’d like to know why. I had to look up some of these words, but it was worthwhile.

The ‘epitritus’ is a ratio of 4:3, which is called a ‘fourth’ in music. The ‘hemiola’ is a ratio of 3:2, which is a ‘fifth’. The ‘epogdous’ is a ratio of 9:8, or a ‘second’, also called an interval of a ‘tone’ since it’s approximately one step up the white keys on a piano. The ‘duple’ is obviously 2:1, or an octave. So Busnois is reviewing how some simple fractions give some of the most important intervals in music. And of course, we attribute this discovery to Pythagoras—though nobody really knows exactly what Pythagoras did.

The ‘monochord’ is a one-stringed instrument supposedly used by Pythagoras to study harmony. And there’s a popular but pretty clearly false legend that Pythagoras noticed these ratios by hitting some hammers in a blacksmith’s shop and comparing their weights! It just doesn’t work like that with hammers.

• Wikipedia, Pythagorean hammers.

The lyrics continue:

Ockeghem, you who sing before all
in the service of the King of the French,
Strengthen the practice of your generation,
examining these things on occasion in the
halls of the Duke of Burgundy in your fatherland.
Through me, Busnoys, unworthy musician
of the illustrious Count of Charolais,
may you be greeted for your merits as the
highest trope-uttering Cephas,
Farewell, true image of Orpheus.

I don’t know why he says farewell — to Ockeghem? Ockeghem hadn’t died. ‘Cephas’ is another name for the apostle Peter, ‘rock’ of the church, so Busnois seems to be saying that Ockeghem played a similar role in the Burgundian musical tradition (which is true).

Here’s a live version of In hydraulis by the group Blue Heron, with captions in Latin and English:

I know Blue Heron because they’re recording Ockeghem’s complete songs in honor of his 600th birthday. But the pungent leading-tones in this piece by Busnois—seventh tones, desperately eager to resolve to the tonic—remind me a bit more of Guillaume Dufa, from the first generation of the Franco-Flemish school, than the more smoothed-down harmonies of Ockeghem.

Busnois could also craft catchy melodies like Dufay. Indeed, he may have written L’homme arme, one of the most popular songs of the entire Renaissance!

The recording of In hydraulis at the top of this page was made by another group who specializes in this era: Pomerium. It’s better recorded and more peppy. If you like this kind of music, I urge you to check out everything by Pomerium. But this version of In hydraulis not live and it doesn’t have lyrics!

This entry was posted on Sunday, September 10th, 2023 at 10:37 am and is filed under music. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

3 Responses to In hydraulis by Antoine Busnois

  1. John Baez says:
    11 September, 2023 at 8:14 am

    This paper does a detailed analysis of the Latin lyrics of In hydraulis and claims to notice a lot of patterns in them. I’ll just quote the part about ratios.

    • David Howlett, Busnois’ motet In hydraulis: an exercse in textual reconstruction and analysis, Plainsong and Medieval Music 4 (1995), 185–191.

    Let us consider the ratios of musical theory mentioned explicitly by Busnois in the motet.

    First, sesquioctavus, sesquioctave ratio or epogdous, 9/8 : 1 or 9 : 8, widely used for reference to authors and their subjects. The eighty words of the text divide by 9 : 8 at 42 and 38, at Hec | Oggeghen. The last part, of forty-two words, divides by 9 : 8 at 22 and 20, at per | me Busnois. Of those forty-two words the first twenty-two divide by 9 : 8 at 12 and 10, at | tue propaginis, ‘your’ being Ockeghem’s, and the last twenty divide by 9 : 8 at 11 and 9, at | tuis pro mentis, ‘your’ being Ockeghem’s. The first part, of thirty-eight words, divides by epogdous at 20 and 18, at epogdoum |.

    Second, sesquitertius, sesquitertian ratio or epitrite, 4/3 : 1 or 4 : 3, by which the fourteen rhymes divide at 8 and 6, there being eight end-rhymes and six caesural rhymes. From phthongitates to phthongum inclusive there are twenty-four words, which divide by epitrite at 14 and 10, at | epitritum.

    Third, sesquialter, sesquialter ratio or hemiolus, I2: 1 or 3 : 2, by which the eighty words divide at 48 and 32, at the thirty-second word, pason. The thirty-two words divide by hemiolus at 19 and 13, at inequalitates | and hemioliam | .

    Fourth, duplus, duple ratio, 2 : 1, by which the eighty words divide at 53 and 27, at tessaron penthe concordiam |, the twenty-seventh word. After muse the fifty-third word is musicum. From phthongitates to phthongum inclusive there are twenty-four words, which divide by duple ratio at 16 and 8, at duplam |. Note also the verbs perducunt, adducunt, conducunt. From the first to the third inclusive there are fifteen words, which divide by duple ratio at 10 and 5. From perducun to pason inclusive there are ten words; from adducunt to conducunt inclusive there
    are five words.

    Let us consider fifth symmetry, the ratio 1:1, not mentioned explicitly, but exhibited. The first two stanzas occupy ten lines, one hundred syllables, and 252 letters, and the last two stanzas occupy ten lines, one hundred syllables, and 252 letters.

    Reply
  2. John Baez says:
    21 September, 2023 at 10:34 am

    Kevin Arlin wrote:

    I bet “farewell” is just being used literally, as “fare well” i.e. “good wishes”.

    It’s interesting to see hemiola used for a pitch interval because it’s quite common to use it these days to describe a rhythm in the same ratio or something similar!

    Yes, that’s interesting! And when I looked up “epitritus” (meaning a frequency ratio of 4:3) I found this:

    Epitrite. (poetry, Ancient Greek and Latin prosody) A metrical foot consisting of three long syllables and one short syllable.

    Reply
  3. Wyrd Smythe says:
    29 September, 2023 at 9:59 pm

    A song about music theory, wow, impressive! Talk about appropriate use of one’s tools!

    Reply

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