Monthly Archives: October 2017

Some Notes on Relativity

Relativity may sound like the title for an Einstein blog but it also applies well to medieval musical notation systems, specifically those that differ from the modern western tradition. In the middle ages, there were many forms of relative notation and a particularly interesting one was posted yesterday by René Zandbergen on the Voynich.ninja site.

I’ve had a passion for music all my life and if I could quintuple the length of the day, I would spend one of those extra “lifetimes” as a composer.

I’m familiar with some of the notation systems in medieval manuscripts, but there are far too many to learn them all, and some of the earlier ones haven’t yet been unraveled, even by the experts. Many of them are comprehensible, however, and old tomes contain a wealth of staffed and unstaffed music (in the sense of not having horizontal lines).

Here is an example of medieval chant music that uses a staff. Note there are only four staff lines and stems are barely visible on the rectangular notes. There are no phrasing arcs as we know them, and no bars to connect the stems but it’s still quite recognizable as western staff-notation:

For comparison, this is an unstaffed line of musical symbols in a medieval Italian manuscript (MS 30337). Note how the symbols are laid in a horizontal line with a minimum of vertical positions and do not resemble round-headed notes as we know them:

My interest in music spilled over into my research on the Voynich manuscript almost from the beginning. When you are trying to figure out if something is ciphered, it’s important to search beyond linguistics. Certainly linguistic codes can be hidden in sneaky places, like astronomical charts and musical scores, but there are also non-linguistic ciphers. Take something like the Dorabella code mentioned on Nick Pelling’s cipher blog… the originator was a composer, so if I had time to investigate it, probably the first thing I would look for is a song or some commonality with music.

I am also intrigued by some of the notation systems that resemble letters and punctuation, such as this one from MS Lat Qu 44, and was curious as to whether musical notation might have inspired some of the VMS glyph-shapes:

I didn’t discover any convincing glyph origins in medieval music, but I did learn quite a bit about notation systems.

Jotting a Note

Detail of musical notation with five staff lines, vertical bars, the key signature, and arcs for phrases. This system is well-known to musicians throughout the world, but in the middle ages, music had not yet been standardized, and numerous staffed, staffless, and relative systems existed.

In modern western systems, the staff is an anchor for denoting a specific pitch, with the key signature providing a guideline to generalized sharps and flats.

The notes themselves follow conventions for duration (quarter note, half note, etc.), additional symbols specify the number of beats per bar, and curving arcs and <> symbols indicate phrasing and volume.

You could cut apart the music with scissors and still have a pretty good idea of how each part sounds.

Not every system works this way, however.

Some notation systems are based on the pitch distance from one note to the next, rather than an absolute system anchored within a staff. Ear-trainers teach intervals such as perfect fourth, perfect fifth, major thirds, minor thirds, etc. These are the distances between two notes. If you learn them, you can read certain forms of staffless music by following the interval from one note to the next based on the shape of the symbol rather than its vertical location on a set of lines. Other symbols function as modifiers to indicate duration or tempo.

Systems like this were developed when instrument-making was primitive, and choral music was widely practiced as a form of worship or as entertainment. Relative systems were especially suitable for chants. If you’ve seen the Brother Cadfael series, you’ve heard the kind of music that was originally expressed in this kind of notation system.

You might notice in the example from MS 30337, that the symbols are rather squarish. Many of the earlier systems have this general look-and-feel. Systems with curves and lines (a phrase familiar to Voynich researchers) tended to come later, and sometimes included more symbols than their predecessors. Even so, many of them were comprised of about 15 symbols—less than typical alphabets.

Some systems included a symbol for the key of the starting note and others did not—you could choose whatever was most comfortable for the voices. In modern western notation, the entire set of notes is transposed to a different position on the staff lines to alter the key. In a relative system, only the starting symbol is changed and the rest of the notes follow from that.

From Music to Mystery Glyphs

One of the reasons relative-notation systems intrigued me is a certain “follow-along” feeling to the way VMS word-tokens are organized, with many of them being similar to those that go before them, often differing by only one or two glyphs. Torsten Timm has done some interesting work in trying to algorithmically model these characteristics of the VMS text.

There also seem to be rules about where certain glyphs can be placed in a VMS-word, a characteristic I’ve discussed in numerous blogs, and one that is integral to many relative musical notation systems.

Repetition and self-similarity are very common in VMS text, with certain patterns occurring in specific positions in a word-token. This kind of positional priority is also found in Roman numerals and relative music-notation systems. [Image credit: Beinecke 408, Beinecke Rare Book Library, Yale.]

As I see it, there is a long list of commonalities between the VMS text and relative musical notation. For example, doubled letters are uncommon in the VMS (with the exception of the “c” shapes, which are sometimes repeated up to four times in succession). Doubled notes in certain musical systems are indicated with a doubling symbol rather than actually repeating the tone-symbol. Imagine writing words like penny, brittle, bell, and missal as pen2y, brit2le, bel2, and mis2al.

Most western languages are not tonal (in the sense of a different pitch indicating a different word), but many African and Asian languages are, and writing the sounds requires extra symbols to indicate the tones. This is also done in musical systems. In staffed systems, different pitches are arranged in different locations on horizontal lines. In relative systems, the shift in tone can be indicated with an interval symbol, but can also be notated as ascending or descending (in other words, there’s more than one way to notate related concepts).

Not every musical symbol has a sound value, just as linguistic systems include symbols without sound values, like the apostrophe. While some relative-notation symbols inherently indicate the length of a tone by their shape or length, others may be modifiers (like the one just mentioned that doubles a note). Modern staffed systems also have their share of modifiers, such as symbols to indicate the quality of a sound (e.g., pizzicato or staccato).

Byzantine Musical Notation

I don’t know Byzantine notation well enough to sing it aloud. There is a long set of rules for how the symbols may be combined and it takes practice to read it, just as sight-reading modern notation takes practice, but I am familiar with some of the basic terminology, a few of the symbols (known as neumes), and the concepts of relative notation that I learned from other musical systems, which apply in the same way to Byzantine systems.

For example, there is a small bowl-like symbol that is written together with tonal symbols to prolong the beat, just as there is a symbol for doubling the beat (playing it twice rather than prolonging it). Once again, this idea could be applied to linguistic notations. In English we typically double the following consonant if we want to shorten a vowel. Thus, the long-a in pater becomes a short-a in the word patter, but imagine if a common symbol were used rather than a letter, one that could be used throughout instead of a dozen different doubled letters—a certain economy of shapes is characteristic of relative notation and of the VMS.

The following example of Byzantine notation is from a manuscript in the British Library. Note how the symbols are curves and lines written in a linear fashion rather than flowing up and down on a musical staff.

I mentioned curves and lines because the VMS character set is unusual in having a strong emphasis on curves and lines, with many of the glyphs appearing to be composites of a few basic shapes.

Since relative systems were strongly tied to choral chants, and humans typically sing one note at a time (with Tibetan throat-singing being an exception) it wasn’t necessary to indicate simultaneous notes on a staff in the same way as one might for an instrument with several strings that are strummed at once.

This sample of Byzantine music illustrates how notes are expressed relative to one another with a concise set of basic symbols, rather than being laid out as ovals on a musical staff. Note that some of the symbols are drawn in red, like the ell-shape that resembles Greek gamma. This is called a gorgon and there are rules for whether it is placed above or below the associated symbol, just as the VMS has rules for whether a glyph appears at the beginning, middle, or end of a token, and additional rules for its associate-glyphs.

Now imagine if you were to transliterate this musical notation into an alphabet system. One might take a symbol like the gorgon and place it before or after its associated symbol, rather than above or below. This calls to mind the highly frequent “o” symbol in the VMS, which is often at the beginnings of V-words, and frequently precedes EVA-t or -k. Note also that this notation system is very rule-based and would exhibit many positional characteristics if rendered as text.

Byzantine music was documented in this 18th-century Serbian manuscript held in Greece (Schoyen MS 1897) and I include it because a variety of whorled diagrams were not uncommon in books of music.

There was a particular interest in relating “music of the spheres” to cosmological concepts in the Middle Ages and Renaissance, so some of the whorled and wheel-with-spokes images reflect these ideas, and the shapes became iconic designs found in many music manuscripts to describe these and other concepts. Wheels were also used to illustrate a variety of tonal systems.

In fact, it doesn’t surprise me that composer Edward Elgar chose symbol positions for his Dorabella cipher that appear to rotate through eight angles, the same number of tones as in a basic western scale (do, re, mi, fa, sol, la, ti, do).

Summary

There was a large body of relative notation in the early middle ages, but musical instruments improved (along with our ability to play them) and the staff system (which could more readily accommodate simultaneous multiple notes), gradually superseded it. The algorithmic quality of relative notation was almost forgotten.

I know that people have assigned notes to the VMS glyphs and played them as music (I’ve done this myself), but relative notation isn’t about assigning a tone or chord per glyph, it’s a prioritized system describing tone, duration, direction of the pitch, and nuance, and the modifiers are applied in a certain order (and sometimes change based on what is being combined). When you scan it visually, it is concise, repetitive, and positional, as is Voynichese. It’s the closest analogy I’ve seen to the structure of the VMS text, and I wasn’t even planning to mention it until I had more time to explore it, but extra time doesn’t seem to be coming my way.

————— = + = —————

The frequent repetition in Voynichese is somewhat reminiscent of songs or verse, but there’s something more to it—even songs and verse have more positional variety than VMS glyphs.

Relative notation systems range from simple to very sophisticated, but many of the more sophisticated ones can be expressed in about 10 to 20 symbols, depending on how they are placed. In other words, the musical “alphabet” can be written with a smaller character set than many human alphabets.

What if the VMS were the notes themselves, rather than lyrics, lists, or narrative text, or were a constructed language built on the same concepts as relative musical notation, where one-to-one correspondence doesn’t apply, where modifiers determine how a glyph should be read?

Perhaps one of the glyphs is like the petaste, a symbol that represents a one-step tonal ascent. Imagine a symbol that says, “Don’t read the previous glyph as t, read it as the letter that follows it in the alphabet.” Or imagine if gallows-k meant something different depending on whether it’s followed by EVA-y, or ch or ol or od (Janus Pairs).

Many of the ideas common to relative musical notation have direct analogs in the cipher world and since chants were popular in monasteries, as was the development of ciphers, monks monks may have transferred some of these ideas from one to the other as the old notation systems faded away.

 

J.K. Petersen

© Copyright 2017 J.K. Petersen, All Rights Reserved

Oceans of Starry Notions

Research is the systematic search for knowledge. Editorializing is presenting one’s opinions and interpretations, sometimes with examples specifically chosen to prove one’s point. When it comes to the Voynich Manuscript, it’s probably best to emphasize the former, since very little is actually known about the VMS.

Spirals and whorls were discussed recently on the voynich.ninja forum and, on October 15, 2017, D.N. O’Donovan posted a brief blog comprising a montage of seven images with the Latinesque title: Floribus campis Coeli. There is no commentary and I have only read a few of O’Donovan’s blogs, so I don’t know the background on these images, but one of the captions reads,

“As noted in the first of my posts mentioning this whorl motif in Beinecke MS 408, one finds early examples in Ephesus, Antioch and Rhodes but it reached the South-western Mediterranean no later than the 7thC AD.”

I haven’t made a systematic study of spirals or whorls, I’ve mostly concentrated on the Voynich Manuscript text and plants, but I have gathered a few images along the way.

Spiral reliefs in wave and garland patterns decorate the Temple of Tarxien on the island of Malta [image courtesy of Wikipedia].

It’s my understanding that spiral and whorled imagery date back at least to the Maltans, before 2,500 BCE, which is considerably earlier than the 7th century CE mentioned in O’Donovan’s caption, and I would consider Malta, which had close ties to the Iberian Peninsula, to be sufficiently connected to the SW Mediterranean to be relevant to this discussion.

Megalithic courtyards, as the Maltan Temple of Tarxien, are well-decorated in wave- and plant-like spirals, and the Romans who occupied Malta from the 3rd century BCE, continued the tradition in their mosaics.

Next to a picture of the “Mosaic Ephesus”, which is a spiral with a sawtooth design, O’Donovan adds,

“In illustrating this mosaic, I was showing the antiquity of spiral armed forms – here it represents ‘all the world under the sun’. In other cases it might represent the sun itself. In one image from the Vms, it represents the rhumbs as I’ve explained.”

Spiral garland patterns carved into spoglia. [Image courtesy of Rag Rose’s blog.]

The mosaic mentioned by O’Donovan is on the Curetes walkway in Ephesus, Turkey, and is accompanied by many other mosaics and carvings with circular and feather-like overlapping designs, as well as natural images of dolphins, ducks, doves, dogs, deer, lions, and floral garlands.

Ionic columns in the area also include spiral motifs, as do decorative edges. Since many of the spiral carvings are integrated with floral garlands, it appears that most of the spiral and whorled designs in this complex were inspired by flora and fauna rather than celestial objects.

For reference, here are spiral images from the Voynich Manuscript:

The figure on the left fills most of the page and spirals in a clockwise direction, with text filling the spokes. There is an Armenian astrological diagram that is similar in construction (circles, spokes, and text associated with the spokes) but it does not include the T-O map or the cloudband-like scallops or star-shapes in the central portion. [Edit: 10/26/17 I forgot to mention when I posted this that the Armenian sun-cross was a prevalent symbol, usually consisting of a spiral sun, or a sun-symbol surrounding a cross. You can see examples on Google search.]
The spiral on the right is much smaller, comprising only the center of the page, and radiates in four directions toward other imagery. If you look closely, you’ll see that it originally had nine lines to mark the edges of the spiral arms, which doesn’t bear any relation to the four radiating lines or the six-pointed star, and doesn’t work well if you are trying to paint each section in alternate colors, so the painter fudged the colors on the bottom, with a thin stroke of yellow to separate two blue sections that ended up next to each other.

The Way-Back History on Whorls

Ancient spirals and whorls are found throughout the world, especially in the Americas, Buddhist Asia, Malta, Greece, Turkey, Africa, Ireland, and Scandinavia.

One of the easier ways to make attractive patterns from a piece of wire is to wrap it in a spiral—no exemplars needed—but there are also spirals in the ancient and medieval world that appear to be talismans, or to embody a more specific religious significance. Some patterns are purely decorative, or based on nature (e.g., a curled snake) rather than on religious symbology. One has to study the culture to interpret them correctly.

Studies of ancient imagery are often based on guesswork about the superstitious and spiritual beliefs of cultures for which we have limited information, but some spirals have been found in megalithic sites that are oriented toward the solstices or equinoxes and thus are thought to represent the sun.

Brittle star fossil found in Mt. El Kissan, southern Morocco {Image courtesy of Fire & Ice].

The picture on the right might look like a petroglyph drawn by a sun-worshipping culture, but it’s actually a brittle-star fossil (Ordovicia) from Morocco.

In the Mediterranean, the patterns of nature were dear to the hearts of ancient people. Even today, the postage stamps of Malta show a rich appreciation of nature’s beauty.

If you look at star shapes and spiral motifs on ancient vases and bowls, you will see many designs inspired by starfish, sun stars (an animal that resembles the starfish), sea urchins, and anemones. Even the little lines and colors in the centers of starfish and sea urchins can be found in Greek decorative arts and Roman mosaics (more on this below).

The Mycenaeans took most of their inspiration from marine life, rather than from the world above them. That’s not to say they were indifferent to the sky… as sea-people, stars were very important to them for navigation, but iconographic analysis has to acknowledge their strong bond to the sea.

Double Entendre

Double meanings are possible in imagery that has multiple interpretations. The stars at the Temple of Karnak in Luxor, for example, are numerous and golden against a blue background, so one immediately thinks of stars, but if you look closely at the way they are drawn, and consider the fact that water is also frequently painted blue, then you have to acknowledge that they may be inspired by starfish, or perhaps be a simultaneous reference to “the stars above and the stars below” [click the pic to see it larger].

Cultural Exchange

Surprisingly similar quad-spirals have been found on ancient ornaments in both Greece and Sweden (right).

While Scandinavia and the Mediterranean seem far from one another, there was trade between the Norse and early inhabitants of the Iberian peninsula.

The Basques may have served as a communications conduit between the north and the Mediterranean. They were expert mariners and whalers, equal to the Vikings in their seafaring prowess, and crossed paths with the Vikings at stopping points along the coasts of Norway and Iceland often enough that they learned some Icelandic.

The spiral is also a megalithic motif in pre-Celtic Ireland, and the Vikings apparently coerced or kidnapped Hibernian women on their way to Iceland, a fact that is reflected in the DNA of the Icelandic people. Thus, the women of Ireland may have contributed decorative arts to Viking culture.

Spirals are also found in the Canary Islands, whose “discovery” and plunder occurred prior to the creation of the Voynich Manuscript.

Thus, the similarity between northern and southern spirals may not be coincidental.

The beautiful spiral on the right bears a strong resemblance to some of the medieval manuscript illustrations containing sun spirals. It is dated to c. 300 CE from Birkenes in southeastern Norway. Some think the design may have originated in Asia, but there are similar spirals (with protrusions on the edges of the main arms) from Sanda, in Gotland, Sweden (c. 400 to 600 CE) and the Gotland picture stones, in turn, resemble Mediterranean designs.

Thus, one sees a chain of communication between the Norse, the Hibernians, and the Mediterraneans, possibly via the Iberian Peninsula, and a pattern of spirals in megalithic and classical art that may be rooted in communication rather than coincidence.

Spirals in Manuscripts

Rayed faces and suns are common to manuscripts from many cultures (they are frequently found in Arabic and Latin manuscripts, as well as the VMS). Spirals are more difficult to find, however, and many of them are more religious than astronomical, but there are some  provocative spirals and whorls in the Rothschild Canticles (MS 404, c. 1300) held at the Beinecke Library, that are interesting to examine:

The image on the left, featuring a central spiral with long rays is surrounded by four figures, each with arms outstretched, emerging from cloud bands. The VMS includes a number of images with four figures, some of them with their lower bodies deep in textured patterns. The image on the right also features four figures in the corners, two apparently celestial, the other two terrestrial, and there are round spirals between the rays of the inner whorl.
The central image has a whorl with long starfish-like arms around a central circle with cloudband-shapes radiating in two directions (and rimming the top and bottom edges of the frame). At the base is a face peering out from a crescent moon.
A further image (not pictured) includes four figure in the corners, and three faces in the central wheel with faces ringed by turban rolls not unlike the rolls that frame the faces on the VMS star pages.

There are many other manuscripts with spiral and whorled imagery, these just happened to be at hand, so I include them as visually appealing examples.

Summary

As I mentioned, I have not made a systematic study of these shapes, in fact I’ve barely looked at the parts of the VMS that include them, so I offer the information above as a “quick grab” from my files for those with a specific interest in VMS whorls.

 

J.K. Petersen

© Copyright 2017 J.K. Petersen, All Rights Reserved