Form and Numbers: Culminating Information on Medieval Music

Entering my third week of research, I have been conducting structural analyses of 4 separate pieces written during the Ars nova in order to be able to view the layouts of isorhythm and retrograde motion in a detailed, yet still concise, way. The 4 pieces are listed below:

  • Garrit gallus / In nova fert / Neuma by Philippe de Vitry
  • Tuba sacre / In arboris / Virgo sum by Philippe de Vitry
  • Quant en moy / Amour et biaute / Amara valde by Guillaume de Machaut
  • Ma fin est mon commencement by Guillaume de Machaut

I have found analyzing these pieces to be both challenging and rewarding. It’s so interesting to see how the number of measures in the phrases form repeating patterns that sort of play off of each other to create a sound that is so seamless. The composers purposefully used and manipulated the numbers behind the pieces with such complexity that is so striking to me, considering they were only written in the 14thcentury. This research project has really opened my eyes to the depth of the musical innovations around the Ars nova.

I have found one problem with the pieces that I have chosen for analysis. Three of them (the first three listed) are a form called isorhythmic motet. In these pieces, this means that the tenor (lowest) voice of the three-part piece forms a repeating rhythmic pattern, called a “talea”, that is underneath two moving lines. The tenor is often based on a sacred chant. However, the fourth piece I analyzed, Ma fin est mon commencement, is a form called a rondeau. This is a form in which the lines make the pattern ABaAabAB. Machaut employed this structure in such a way that the “B” (or “b”) section is the same as the “A” (or “a”) section, except it is performed in retrograde motion. I find the idea of this aural palindrome fascinating. In fact, this was the piece that really inspired my idea for exploring the use of mathematical patterns in Medieval music, which I later refined into exploring isorhythm and retrograde motion. While I was considering not including Ma fin est mon commencement in my research once I realized the discrepancy in form, I now feel it would be a vital aspect of the project. The piece was really an inspiration for me and it provides an outstanding example of retrograde motion.

Now that I have basically completed my analyses of the 4 pieces, I feel like I am ready to begin writing my final paper. This will probably take some time, as I tend to generate a lot of further ideas while I am writing. I want the first part of the paper to be a summary of the Ars nova, with its society, religion, and musical innovations. This would also include descriptions and examples of isorhythm, retrograde motion, and changes to notation and rhythmic structure. I want to conclude this first section by discussing numerical symbolism, which I feel would be an interesting and relevant addition. In the second part of the paper, I will go through each of the 4 pieces in the order listed above and discuss their structure, text, symbolism, and connections to each other. I plan on adding to my analyses while I am writing by trying to connect the text more to the numerical patterns.

As my research project is more of an exploration of concepts than a discovery of new information, my paper will largely be a compilation of the information that I have learned over the course of my work. However, I will hopefully be able to generate new ideas on symbolism and meanings. At any rate, I hope that this paper and information might be useful to someone interested in further exploring the numerical-based structures of pieces in the Ars nova.


  1. smmullis says:

    Hi Mary. This is such interesting research, and I know your paper is going to be full of fascinating information. I look forward to seeing your presentation. I don’t know much about Medieval music – any knowledge I do have is of the Baroque era and forward. However, I suppose I always associated early European music with the Church, so I was surprised to read in your earlier blog post that the four pieces you are analysing are secular in nature. I think it is a great idea to include in your essay a discussion of the social and religious contexts of the Ars Nova, since this would help readers (like me) understand the context in which the musical pieces in question would be performed. I imagine also that the trends in music during this period would correspond to other artistic trends, depicting secular concepts rather than sacred ones. I am curious about the subject matter of the texts in the four pieces…do they reflect stories or legends (I know Greek mythology has long been a popular subject)? But that is outside the scope of your research, and in works of such rhythmic and melodic complexity and detail, text might be quite unimportant.
    You also mentioned in an earlier post the idea of numerical symbolism. This idea has come up during my own research into Native American dance, a subject in which music is inextricably involved. I am led to wonder whether there is symbolism in Native American songs as well as in the dancing. It is very likely.
    I hope I will get the chance to see your presentation so that I can better understand Ars Nova music. It seems like you have made lots of connections and comparisons during your research process which will make for an excellent final product.

  2. Hi Mary! Your research sounds absolutely intriguing. I studied the relationship between music and mathematics only briefly for a project in high school, and the relationship between the two seemingly polar opposite fields is astounding. Part of what fascinates me so much from your blog post is what you called an “aural palindrome.” After a quick Google search, I find that “Ma fin est mon commencement” means “My beginning is my end,” which can be said of a palindrome.
    What also drew me into your topic is the way in which you view the pieces of music. To me, it seems as if you are analyzing them as if you are analyzing a poem. As I am an English major, I noticed this immediately. Your analysis of the form of the rondeau is redolent of the analysis of the rhyme scheme of a poem. Your study of notation and rhythmic structure is like analyzing the line breaks and enjambment of lines in a poem to create a certain feeling in the audience.
    I greatly look forward to your final analysis, and I cannot wait to see how you synthesize the paper. Good luck on the rest of your research.

  3. mcshannon says:

    Hi Sally! Thank you for your comment. I found the sacred and secular aspects of the music and society to be quite interesting throughout my research. In fact, although the society was becoming increasingly secular (comparatively for the time), many of the pieces still had sacred contexts, especially through number symbolism! Some of the texts definitely did have mythological contexts, especially the piece Garrit gallus / In nova fert / Neuma. The pieces also had references to current events and Biblical stories. Your research sounds very interesting and I would love to know what you find in relation to numerical symbolism. Good luck with the rest of your research.

  4. mcshannon says:

    Hi Alexa! Thank you for your comment. Yes, the palindromes in Ma fin est mon commencement are incredibly interesting! Through analysis, I found there were palindromes in not only the sound, but also in the mathematical structures of the pieces, which seems so complex for the time period. I did do a large part of my analysis as an analysis of a poem. I actually found that many composers at the time were also poets, so the similarity in structure is very natural. Thanks again for your thoughts and good luck with your research, as well!