Musical Ciphers

The fancy name for this is gematria from the Hebrew, but it could also be derived from the Greek geometria. In either case it refers to assigning numerical values to letters or phrases. Here is the Wikipedia article. In music, it is the practice of associating musical notes with letters so the music, or even the notation, can contain a message. Another method used in music was number symbolism in which the number of notes can be symbolic. Guillaume Dufay offers a couple of examples of this. In his motet Vasilissa ergo gaude written to celebrate the marriage of the daughter of an Italian nobleman, Cleofa Malatesta, to the son of the Byzantine emperor Manuel II the total number of notes in the motet are 800 which in Medieval numerical symbolism means 'eternity'. The actual symbolic number is 8, but you can't write much of a piece with only eight notes! Here is the motet:

Dufay would also sometimes sign his name in the score by writing "Du" followed by the note "fa". But the great master of number and note symbolism was J. S. Bach and the most famous instance was his signing his name to the last piece in his Art of Fugue. In German, the way the notes are pronounced is different than in English. For historical reasons, Germans pronounce B flat as "B" and B natural as "H". Therefore Bach could write his name in notes: B flat, A, C, H. Here it is as it appears in the last (unfinished) piece in the Art of Fugue:

And here is that fugue, Contrapunctus XIV:

It ends abruptly, incomplete... The BACH cipher appears at the 9:38 mark in the recording. This is a triple fugue. It starts with a subject derived, as are all the subjects in the Art of Fugue, from the original theme. Then, after a substantial fugue on that theme, a new theme in eighth notes is introduced, and in this second part, the theme from the first part returns. Then, after a full cadence, the new theme, BACH is introduced and a third fugue begins. The plan would have been to then reintroduce both of the other themes, but it remains incomplete. With most pieces by great composers left incomplete, someone always steps in to complete it. The most famous example is the Requiem of Mozart, completed by his student Süssmayr. Yes, there are completions for this piece too, but the suspicion always is that no-one alive is quite qualified to complete it. So it is often, as above, left incomplete... Here is the Wikipedia article on the Art of Fugue. There are two entries of the BACH cipher that are backwards, 'cancrizans' in musical parlance. Here is one of them:

This is quite similar to another famous cipher used by Dmitri Shostakovich. Taking advantage of the fact that in German E flat is pronounced "es", he writes his own name in notes this way: D S C H. Here it is in notes:

Those intervals differ from H C A B by only one note, the last one. This theme permeates all of Shostakovich's String Quartet No. 8 and was also, appropriately, used on his tombstone:

Click to enlarge

Here are the first and second movements of the string quartet. That four note theme is presented as a fugue in the very beginning:

Going back to Bach to close, he also used number symbolism as Dufay did. On his own printed copy of the Goldberg Variations he jotted down fourteen canons based on the bass of the theme. Why fourteen? It is the number of his name: B = 2, A = 1, C = 3 and H = 8. Total = 14. This was only discovered in the 1970s! You might also recall that the Art of Fugue also has fourteen fugues? And there may be more symbolism that we haven't noticed yet. One scholar has pointed out that the Mass in B minor seems to have some interesting numbers in it. The only music in the mass that is repeated is the chorus Gratias agimus tibi from the Gloria which returns as the Dona nobis pacem to end the piece. The theme of these two sections begins with the notes D, E, F#, G, or, numbering the notes, not in the key of the movement (D major), but as if they were in C major, we get 2 3 4 5. Now this may be of no significance whatsoever, but, as a matter of fact, there are precisely 2345 measures in the mass as a whole. Hmmm. Here is that Dona nobis pacem:

Read more »

Music and Architecture

One of the things I love about blogging about music as opposed to writing a book, is that I can provide all the musical examples within the text itself--courtesy of YouTube. But for this post, the examples will not really give you an idea of the original effect. I am going to talk about several instances in which a particular piece of music is associated with a particular building.

The first dates back to March 25, 1436 and the consecration of the Cathedral of Florence, under construction since 1294. Guillaume Du Fay (ca. 1397 - 1474) was commissioned by Pope Eugene to write a motet for the occasion at which the Pope himself, temporarily exiled from Rome, officiated. The motet is "Nuper rosarum flores" (Garlands of roses), the text chosen in honor of both the city (the name means 'flowering') and the cathedral whose formal name is "Santa Maria del Fiore" (Holy Mary of the Flowers). A theory was long accepted that the very structure of the motet reflected in some way the proportions of the cathedral. Alas, this has been pretty thoroughly refuted. In fact, the structure of the motet is far more complex than that. The score is written out in a musical shorthand that requires a bit of sorting out to understand. The rhythmic proportions of the music actually refer to Pythagoras, the Greek philosopher who discovered the relationship between harmonic proportions and mathematical ratios. Du Fay is translating these proportions into durations. The idea is to represent the metaphysical harmony of the universe in sound. But there is far more than this kind of symbolism in the motet: the musical proportions also refer to the proportions of the Temple of Solomon as described in the Old Testament in the second book of Kings. The feast of dedication of the temple lasted seven plus seven days. Du Fay's motet is based on a fourteen note chant which is realized in the piece with two tenors, each singing groups of seven notes. The text is also in a poetic meter with seven syllables per line. Seven, in Christian symbolism, represents the Virgin Mary. There is more, but this should give you the sense that the music has many layers that refer symbolically to the cathedral, the city, the Virgin Mary and the Temple of Solomon! According to an earwitness to the ceremony of consecration, Giannozzo Manetti,

all the places of the Temple resounded with the sounds of harmonious symphonies as well as the concords of diverse instruments, so that it seemed not without reason that the angels and the sounds and singing of divine paradise had been sent from heaven to us on earth...

Here are two photos of the cathedral, the first of Filippo Brunelleschi's enormous dome and the second of the interior.

And now, finally, the music. "Nuper rosarum flores" by Guillaume Du Fay. Wikipedia has a good article on the piece if you want to know more.

My second example takes us to Venice, the Basilica Cattedrale Patriarcale di San Marco, known as St. Mark's Basilica. Giovanni Gabrieli was principal organist and composer there from 1585 to about 1606 when ill health began to prevent him from performing his duties. He was the master of what is known as the Venetian polychoral style and this style, with its use of multiple choirs and groups of instruments, is directly related to the cathedral itself which uniquely has two choir lofts facing one another. A third choral/instrumental group was often placed on a stage in the center, near the altar. The possibilities of spacial separation were exploited by both Giovanni himself, and his uncle Andrea before him. Here are photos of the cathedral and its interior:

Now here is a recording of a Gloria in 12 parts that was recorded (in the 1960s, I believe) in San Marco:

I think I will save my other examples for another post as this one is running rather long! I'll leave you with one more piece by Giovanni Gabrieli, who was a huge influence on later Baroque composers. This was written for and recorded in the Scuola Grande de San Rocco, the other great musical venue in Venice where he worked.

Read more »

Masterpieces of Music: Guillaume Dufay

Portrait by Jan van Eyck, possibly of Dufay

Almost exactly a hundred years after Machaut, the leading composer was Guillaume Dufay. He was born around 1397 and died in 1474, the leading figure in the Burgundian School. He grew up in Cambrai and later was employed by the Malatesta family and two popes, where he sang in the papal choir. Nowadays nearly all composers are pianists (with the occasional guitarist...), but in this period they tended to be singers and their compositions are inherently vocal as a result. Dufay is the central figure in the transition from Medieval music to the Renaissance. As Wikipedia notes, "Dufay was one of the last composers to make use of medieval techniques such as isorhythm but one of the first to use the harmonies, phrasing and expressive melodies characteristic of the early Renaissance." Here is their article on Dufay.

Looking back in music history, one thing that comes to light is that, as we move from antiquity closer and closer to our time the musicians and their music become more individual. While Machaut's texts were in the traditions of courtly love, Dufay strikes a personal note and for the first time we seem to hear the voice of a single human being. In this song, for example, he laments leaving the things he loved in Lannoys:

Adieu ces bons vins de Lannoys

Rondeau by Guillaume Dufay (1426)

 Adieu ces bons vins de Lannoys,

Farewell to the fine wines of the Laonnais,

 Adieu dames, adieu borgois

farewell ladies, farewell townsmen,

 Adieu celle que tant amoye

farewell to her I loved so much,

 Adieu toute playssante joye,

farewell to all joy and pleasure,

 Adieu tous compaignons galois.

farewell all boon companions.

Here are the Ensemble Unicorn performing the song. In their arrangement, the song is heard first on the lute, played freely, then with several instruments and finally with the voice.

Dufay wrote this as a young man, probably in response to the fact that then, as now, young ambitious musicians often had to travel far from home to further their careers. A modern analogue might be "Strawberry Fields Forever" by John Lennon:

In 1436, Dufay wrote a spectacular isorhythmic motet, Nuper Rosarum Flores, the culmination of this method of composition, for the consecration of the cathedral in Florence with its Duomo by Brunelleschi. Here is the Wikipedia article on the piece. And here is a performance:

You could write a whole book on that piece! Quite a few articles have been written about whether or not the proportions of the piece relate to the proportions of the cathedral or to the biblical passage Kings 6:1–20, which gives the dimensions of the Temple of Solomon. No real modern analogues to this one. Maybe the Dona nobis pacem from Bach's B minor mass. Or perhaps the Third Symphony of Gorecki:

Read more »