Week 9b- Arithmology, Music, and the Multitudes

Please add some pithy comments on the readings for Wednesday.  Please post them by Tuesday night.

Here are some questions to consider:  Would you call what Boethius is describing as music?  How does out-of-tune singing fit in with this system?  How might Boethian music have a relationship to the divine?  Do Martianus’ numerological observations make any sense?  Do they live on today?  How does the story of Pythagoras and the blacksmith fit with Boethius’ ideas about theory and observation?  Do you sense more Aristotle or Plato?  Do you remember learning the basics of music?  Did you learn those basics before or after numbers?  Why is it that the major scale (and the minor scale for that matter) is not an octave split up into equal parts?  Who among you like to relax to Schoenberg?  Feel free to play with the virtual monochord and piano (links on the syllabus page) and make some observations relevant to the readings.


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16 thoughts on “Week 9b- Arithmology, Music, and the Multitudes

  1. I want to start by saying how struck I was by the idea that through counting separate, distinct things they become sort of identical, at least in terms of their one-ness.
    I can’t quite get to grips with what that means more broadly, but it’s kind of a beautiful idea. We all share in that one-ness I guess.

    To continue on in the aesthetic appreciation vein, I also found the Boethius reading rather beautiful in parts – “Whoever penetrates into his own self perceives human music. For what unites the incorporeal nature of reason with the body if not a certain harmony, and, as it were, a careful tuning of low and high pitches as though producing one consonance?”

    I’ve never thought of the human self as being musical, but I think it’s a nice idea, and I suppose we are often told to ‘listen’ to our hearts or to what’s inside. Obviously there has long been some connection between our inner selves and an inner voice or inner music.
    The idea that when our body is not in tune with our reason we are sort of ‘off-key’ is an interesting one too. I suppose that when we are very upset we do cry or wail or moan, and when we are frustrated we might make annoyed noises, so there may be some truth to that. When our minds and bodies are in harmony we are unlikely to make unpleasant sounds.

    • I, too, love that uniting of body and spirit through musical harmony part in Boethius.
      It is interesting to think of all the ways we use these musical ideas as metaphors. So and so is “in tune with” something else. To jive with something. Beat of a different drummer… Boethius is sort of suggesting that this isn’t a metaphor. It’s really the way it is.

  2. I was struck in the Boethius reading by the power he gives music. He treats music not as something man-made, but as almost having an otherworldly power and control over those who listen to it. This power, of course, is dependent on the type of music played. Words like “capricious” and “promiscuous” are used to describe some of the more lowbrow musical selections, reminiscent to me more of today’s popular music than what I think they would have been listening to in that era. Along with power, Boethius writes about the inability to separate humans and music, and says that all humans who seek pleasure are linked to music. Does the type or temperament of the human then predict the type of music they are linked to? Later he discusses the inequality of consonances, and states that certain people are able to perceive music better than others. Does this have to do with physically hearing the music, or being able to interpret it? The way he describes the process of hearing seems to be pretty accurate and close to the modern description.

    • Yeah.. I love how he takes some swipes at low-brow music. He sounds like a snobby old fuddy duddy.

      “Does the type or temperament of the human then predict the type of music they are linked to?” Interesting issue. Clearly different temperaments are linked to different modes of music (Phyrgian, Lydian, etc.), making me wonder just how innate music is if it is so subject to climate and social character…

      His description of pulsations is incredibly suggestive. He doesn’t quite quantify frequency and comparisons of frequency, but he is nibbling around the edges of that one. Pretty astute.

  3. I agree about that Boethius quote. It really stuck out to me. It is a really cool way of looking at the “Mind/Body Problem”. I did find Boethius’s discussion of cosmic music pretty strange in a lot of ways. Martianus’s numerical observations were pretty cool. They gave numbers (which are intangible concepts) tangible connections with life, religion, science, etc… At times, I found some connections to be a little bit of a stretch, simply scraping to find patterns. When writing essays or reading, I usually listen to classical music (this reading included). So it felt funny to be reading about the effects of music while feeling its effects. I really like the connections between mathematic ratios and the fact that we like to hear harmonies of those ratios in musical notes.

    • Leibniz has a great quote: “Music is the pleasure the human mind experiences from counting without being aware that it is counting.” Leibniz VI.15, letter to Christian Goldback.

      The numerological (arithmological) stuff is quite interesting. Some of it is still with us… like our special status for 7. It seems like people have a difficult time distinguishing metaphor from reality, cause from correlation, pun from literal truth.

  4. What was most striking to me about the Boethius reading (seems like it piqued more interest than the Capella) is the structure of the book. His introduction reminded me of his Consolation of Philosophy, especially when he personified music and, as Amy wrote, gave music certain qualities that usually aren’t associated with music. It’s clear that music, like other things, goes through periods of development, but it struck me that he described the development of music in terms of character values (or vices).

    Initially, I searched for some connection to Boethius’ other piece that we read for this week on arithmetic, expecting him to parse out music in terms of unity and numbers. So I was surprised that he didn’t get to what is generally considered as arithmetic (ratios) until the end of our reading, but this way allowed for a clearer reasoning of why arithmetic can even be used to understand music to begin with. From the senses to hearing to the power of music and its influence on the mind to pitches to consonances–Boethius breaks music down bit by bit, noting things that normally wouldn’t be thought or talked about. Whereas he begins by saying generally that music, because it’s natural, is powerful and is an art to be mastered, by the end of the reading for today, he shows the components in pitch and consonance that make music appealing to the ear.

  5. I found the Boethius piece interesting to read, although I do not agree with all of it. I agree with what Boethius said about music being easy to understand and how different types of music can have different effects on people’s moods, depending on their characters. However, I do not agree with Boethius’ statement “No path to the mind is as open for instruction as the sense of hearing.” Really? This is a serious statement to make without ample evidence to back up the claim. I think that a good writer could make equally plausible arguments for any of the five senses. He hasn’t sold me.

    • Does the sense of smell affect you as strongly? Are you inspired to motion by a photograph like you are by a song? The possibilities are certainly there, but somehow music just seems so strong compared to other senses.. especially in terms of affecting moods.
      Boethius is perhaps being a tad hyperbolic. Music is his wheelhouse.
      Boethius might not have sold me on his ideas either.. .but I enjoy letting him take me on a ride, just for fun.

  6. Music is apparently associated with morality. I found that the statement about our ability to see that in music the beautiful harmony that exists, in turn, exists in ourselves. We are “put together” in the same way, harmoniously. He is not only referring to music, but to sound in general! For example, a call of triumph in battle. We are influenced by sound that we hear and make. I find myself disagreeing with Boethius when he says that a musician will not be able to find joy in melody without understanding the structure of the sound. Although it fascinates me, on a physical level, to learn about the way that sound waves work and do, in fact, have an impact on a molecular level, I enjoy, write, and sing music without any prior knowledge of music theory. I think this, though, supports his claim much more. I innately understand sound and music and harmony in a way that allows me to develop melodies without any knowledge of the theories behind why they are harmonious to my/others’ ears. I do like to consider that math governs everything in our existence, and I believe it is important (as he points out on page 13 about “multiples” and “superparticulars”).

    The “quadrivial disciplines” include counting and number theory. There is a hilarious moment where the idea of Number is distinguished as entirely abstract, something to be assigned when counting, not to be “confused with untrustworthy sensual characteristics like softness or even size” (29). Numbers only have quantity in relation to each other: Oneness. Everything comes from the One! And Unity is described completely in a Plotinus-like way, as being indivisible in the sense that half of Unity is just two complete Unities, and cannot actually be halved at all, for if it were it would not be Unity; it is a continuous flowing spring that is, itself, it’s only source.
    The number eight apparently has “eightness” along with being eight Unities. This made me think of Alice in Wonderland and the term “muchness” being used to describe the character traits of Alice. It seems to be something that embodies the essence of the number, such as eight, although eight is already assumed to be abstract. It would make sense, to me, if the eight counted cupcakes on a table had eightness, a trait that arrives upon counting them and having them in a space together.

    I had a hard time reading the Marriage of Philology and Mercury. Something about the story made it frustrating for describing arithmetic. I feel it is much easier to see examples for math than have it explained with words alone. Also, all the different qualities of the numbers became overwhelming.

    • -”he says that a musician will not be able to find joy in melody without understanding the structure of the sound.” I also wonder if one must always know in order to appreciate. But I feel like Boethius is trying to figure out why certain intervals are so pleasing and others are not. His mathematical theory makes sense, up to a point, and was influential for about 1500 years. I still cannot enjoy Schoenberg like I can Bach. And Stravinsky or Ives seem to use dissonance in order to set off consonance rather than to push into dissonance alone. I’m still trying to come to grips with this stuff.

      -”I believe it is important (as he points out on page 13 about “multiples” and “superparticulars”).” Why? I know what you mean. But why?

      -”Unity; it is a continuous flowing spring that is, itself, it’s only source.” I like how you found the poetry of Plotinus in that section. I’ll have to rework that and fit that in.

  7. When thinking back to my childhood trying to remember the first time I learned numbers and the first time i learned the fundamentals of music I know for a fact that I learned numbers first even though I do not really remember. Thinking about the Boethius reading when he discusses the unity of the human and music and their connection and this aspect of oneness and it being natural. That music can come from a human naturally and their inseparability. So going back to thinking about learning numbers/arithmetic and music I remember learning numbers being forced and memorized and did not understand the meaning although i understood the symbol. However when I think about learning music when i was a child it did not feel that way but it rather felt natural. I started thinking now of how pitches, tunes and as Boethius dicusses how to the human this sensation of certain sounds at the right pitch is pleasant etc is all formulaic in a sense. Pitch comes from math and numbers so really when you dissect music it is also numbers. Numbers maybe are the unity of sound and music which is unified with the human however I did not feel connected with numbers.
    I also liked the Boethius piece in general talking about the power of music and sound with the human and the concept of harmony. Music has for a long time and more and more today plays a big role in the healing process for humans both physically and mentally. To have Boethius break down music to this level, even down to the numbers we can understand the connection more because of the basic elements which it is composed of.

    • -”when I think about learning music when i was a child it did not feel that way but it rather felt natural” Agreed. I don’t remember learning about music. It just was. I find it interesting that music that I listened to as a child has stuck with me. My favorite musical pieces are from my formative years. I still find new stuff that I like, but it is never as deeply rooted in my soul/psyche/spriritus/sensorium/noggin.

      I used this before, but it is again relevant. Leibniz has a great quote: “Music is the pleasure the human mind experiences from counting without being aware that it is counting.” Leibniz VI.15, letter to Christian Goldback.

  8. One of the biggest problems for dualistic accounts of the mind-body problem (generally the ones that cite some sort of non-physical spirit or soul) is: okay, if I have this non-physical mind, how does it cause things in the physical world? For example: how does my non-physical mind cause my very physical body get up and go make coffee? But Boethius has an idea, that music and/or harmony “unites the incorporeal nature of reason with the body”.

    A musical or harmonic explanation of this relationship is one of the coolest ones that I’ve ever heard, and I think it has a lot of promise. Harmony is at once a physical, mathematical, and phenomenological thing. It rests in the relationships between different things, harmony being a GOOD relationship between different things. This line of thinking, I think, has the potential to give an account of how a non-physical mind and a physical body could be joined.

    However, harmony in music is a matter of a relationship between different notes. Different notes are different tokens of the same type, however. So while different notes are, you know, different, they do have similarities. How important is this similarity in type in possible harmony? Are the mind and the body different tokens of the same type?

    (Sorry this is late; I passed out after watching the election.)

  9. The mind/body solution using the abstract/intellectual force of music is pretty cool.
    I imagine that Boethius’ three types of music (human, cosmic, and instrumental) allow for different types of “tokens,” as you call them. The music becomes some sort of metaphysical structure upon which physical and metaphysical entities can hang. This is certainly how premoderns viewed it. Architecture and art theory is awash in this harmonic stuff. The Bible even has some cryptic references.
    And then modern theory utilizes harmonic analysis all the time. It’s definitely weird.

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