Melanie Spiller and Coloratura Consulting

Escapades in Early Music, Writing, and Editing

Music Notation Explorations: The Dasia System

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I’m obsessed with the history of music notation. I’ve got a whole shelf of books on the subject, and I’m always boring anyone whole listen and sketching on random scraps of paper and paper napkins.

Recently, I tripped over a form I hadn’t seen before, and on closer inspection, I find that it had been quietly hiding in the dark recesses of several of my own books! I’m determined to make it a secret no more, so here it is. The story of the Dasia system.

Guido D’Arezzo (990/991-after 1033) was a scholarly monk credited with creating Do-Re-Mi and putting the neumes that were being used to represent musical gestures on the staff. He’s kind of a big deal, in his own quiet way. In his Micrologia, Guido attributed the system of Daseia (that’s the plural form of Dasia) to Odo of Cluny (c878-942). Odo is credited for naming the notes after the letters in the alphabet, although he used ALL the letters, first the capitals and then the lower cases, and only found 52 notes in the scale, which was admittedly more than they thought they’d ever need at the time. Most instruments, even the organs of the time, didn’t go much further than the two octaves (or so) of a human singing voice.

The reason Guido attributed Dasia to Odo was that Dasia notation was discussed in the 9th century treatise Musica enchiriadis (occasionally attributed to French Odo of Cluny, and sometimes to Frankish Hucbald, c840-930, and also sometimes to German Abbot Hoger, d. 906). This treatise illustrated the earliest known forms of polyphony (multiple lines of melody meant to be sung simultaneously).

Unlike the systems for notating chant, which is monody (one line of melody, sung or played by all involved), Dasia was based on the tetrachord principle of Greek music theory (in its most basic form, two tetrachords—four notes each—plus a whole tone, equals an octave), and Greek symbols were used. The Dasia system is only a little bit different. (Mostly, it seems that the whole tones were piled at the top of the tetrachords. So two tetrachords plus a whole tone is an octave, but four tetrachords in a row plus two whole tones in a row at the top end are two octaves.)

The system covers a two-octave range of notes in a series of tetrachords (a tetrachord is four step-wise notes of a scale), each of which is granted one of four signs to represent the specific note. Three of the signs are based on the letter F (I didn’t find any explanation for why an F was used). The fourth sign is like the accent sign of Greek grammarians, called an acutus, and it signifies the half-step between it and the sign below it. This is just like the two pairs of white notes on the piano that don’t have black notes between them.

Here’s what it looks like on a modern five-line staff.

DasiaNotation2

In this image, modern-shaped notes are on a modern staff to give you a point of reference. I used this image (from Wikipedia) so you can understand the principles.

In the first and lowest tetrachord, the signs are turned backward; in the second tetrachord, the most commonly used notes, the signs are forward; in the third tetrachord, the signs are upside-down; and in the fourth and highest, they’re turned both upside-down and backward. A different accent sign is used in each of the tetrachords so that you knew where you were in the scale—remember, they didn’t have a staff yet. The N stood for inclinum, the I for iota, the V (it looks like a lower-case N) for versum, and the cross for iota transfixum.

This is what the music written using this system looked like.

Dasian Polyphony

This is a bit of polyphony, in roughly parallel movement. Both lines (the clumps of symbols connected by lines on the right), were meant to be sung at the same time. You can see that the gesture of “up” and “down” was understood in terms of the notes relationship to each other, but marking off how great or small the interval was took the Dasia.

The words—lyrics—are all piled up neatly on the left. The Dasian tetrachords involved are in that nice vertical dividing box, and the melody is on the right, with certain syllables at relevant points pinned to their relevant places. You had to already know the words, pretty much, in order to read this, and the two singers sang different words from each other. It’s rather probable that it took a few tries for the singers to shape it into something they liked.

It’s like a new secret language, isn’t it?

The use of Dasia symbols was brief—less than 50 years and not widespread, mostly in Italy. By Guido’s time, neumes were in common usage, and that’s what evolved into modern notation.

Sources

  • “The Notation of Polyphonic Music, 900-1600,” by Willi Apel, The Mediaeval Academy of America, 1953
  • “Music in the Middle Ages,” by Gustave Reese, W.W. Norton & Co., New York, 1940
  • “Temperament, The Idea the Solved Music’s Greatest Riddle,” Stuart Isacoff, Alfred A. Knopf, New York, 2001
  • “Music, Body, and Desire in Medieval Culture, from Hildegard of Bingen to Chaucer,” by Bruce W. Holsinger, Stanford University Press, Stanford, 2001
  • “The Notation of Medieval Music,” by Carl Parrish. Pendragon Press, New York, 1978
  • “Music in Medieval Manuscripts” by Nicolas Bell. University of Toronto Press, Toronto, 2001
  • “A History of Western Music,” by J. Peter Burkholder, Donald Jay Grout, and Claude V. Palisca. W.W. Norton & Co., New York, 2010.
  • “Medieval Music,” by Richard Hoppin. W.W. Norton & Co., New York, 1998.

 

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Written by Melanie Spiller

October 10, 2017 at 9:21 am

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