William M. Briggs

Statistician to the Stars!

Music, God’s Gift to Man–and to Robots? — Guest Post by Bob Kurland

Editor’s note: The original post can be seen at Kurland’s place.

A few days ago my wife pointed out a news item announcing a robot that (or who?) can compose a symphony, tailored to uplift the listener’s mood. Whoaa! A robot! Artificial Intelligence whatever, it takes soul (both of the vernacular and theological variety) to write music.

I have written elsewhere about music as God’s gift to man (see here and here), and I’ll try not to repeat myself here. I want to examine whether art, as we like to understand the term, can be forthcoming from artificial intelligence in the following general context: can computers (robots/androids) be made to be self-aware, to have consciousness, to go beyond what is programmed into them. Whether a robot can compose music is a piece of that puzzle. Most importantly, can that artificial intelligence derive emotional satisfaction from the creative process?

We should ask, then: is music God’s gift to man, and, if it is such a gift, can we say that God wishes to extend it to “beings” with artificial intelligence, intelligence created by man, not God?

As in much else involving the intersection of science and religious belief, science fiction (more properly, “speculative fiction”) occasionally yields more insight than either philosophy or theology. One story, “A Work of Art” by James Blish, (WARNING: SPOILER!) examines whether a transitional sort of artificial intelligence, “mind sculpting”, can produce the same sort of music as the live composer. Here’s the story.

A man wakes up, recalling his last moment of darkness. Informed that he is Richard Strauss, resurrected, he is asked to compose a work in his own style. He does so, basing it on a Greek myth. The work is performed to thunderous applause, which he realizes is not for the music, but for the mind sculptors who have changed him from one totally unversed in music to a composer. But, here’s the kicker: there’s enough of Richard Strauss in him to realize that the music he has composed is only a pastiche, a musical collage of Strauss’s known works. There is nothing original, nothing of the artist in it.

So, the “Work of Art” is not the music—it is the mind sculpture. God inspires man to create music, as the quote above from J.S. Bach would have it. The computer can only imitate what man has already created.

Music & Math

Thomas Fiore, Music and Mathematics:

Can one similarly find an “equation” to describe a piece of music? Or better yet, can one find an “equation” to predict the outcome of a piece of music? We can model sound by equations, so can we also model works of music with equations? Music is after all just many individual sounds, right? Should we invest time and money to find these equations so that all of humankind can enjoy predictable, easily described music? The answer to all of these questions is predictable and easily described: a series of emphatic ‘NO’s’! There is not an equation that will model all works of music and we should not spend time looking for it.

The relation between number and music was discovered in the 6th Century BC by Pythagoras (yes, he of the “Pythagorean Theorem”). He found that if the string lengths on a Greek lyre were in the ratio 2:1, they sounded harmonious—this interval between the notes sounded by the two strings is an octave; if the lengths were in the ratio 3/2, a different harmonious interval, “a perfect fifth” sounded; if the lengths were in the ratio 4/3, yet another harmonious interval, “a perfect fourth”, sounded.

Let’s skip 2500 years and proceed to contemporary times, summarizing the material given in the linked article by Thomas Fiore. As a player of an instrument keyed to E-flat (the alto clarinet) I am familiar with the mathematical operation of transposition, adding intervals to go from my key to concert (in this case, adding -3 modulo 12).

Inversion is the operation of going from a major key to a minor: if x is the note number on the chromatic scale (0:C. 1:C#. 2:D,…, 11:B—white keys and black keys on a piano), then inversion is the operation -x, or equivalently in modulo 12 arithmetic, 12-x. So, Tn(x) is the transposition operation on the note x to give x+n, and In(x) is the inversion operation on the note x to give -x+n (note: 0=12 in modulo 12 arithmetic). For example, upon the operation I0(x), the C major chord (0, 4, 7 or C, E, G) goes to the F minor chord (0, 8, 5 or C, F, G#); and T2(x)*I0(x) operating on the C major chord gives (2, 10, 7 or D, A, #,G), a G minor chord.

The 24 operations, Tn(x), In(x) are elements that satisfy the properties of a mathematical entity called a “group”: there is an identity, an inverse for each element, and closure—any combination of operations yield another operation of the group. The group designation for the Tn/In group is D24, the dihedral group of 24 elements. Now group theory is related to descriptions of symmetry, and in particular symmetry of geometrical objects. A geometrical object having the symmetry belonging to the D24 group is the icositetrahedron.

Fiore applies this mathematical analysis to several musical works: Bach’s Fugue #6 in D minor, Wagner’s Prelude to Tristan and Isolde, Hindemith’s Fugue, Beethoven’s Symphony #9 (2nd movement), the “Elvis Progression”, the Beatles “Oh Darling”. The analysis adds a great deal to one’s appreciation of these works (I can’t, in truth, say this about Elvis’s stuff or the Beatles’ song, since I’m not familiar with those); however, I ask the question (answered in part below), is this all there is to music?

If a mathematical analysis of a musical piece could tell us all there is to know (and feel) about the piece, it would seem reasonable that computers could then compose music—any sort of music. However, I claim that this complete analysis is not possible. Even in that most ordered and mathematical of music, the Bach Fugues, there are occasional deviations and lapses from the mathematical operations, as discussed by Fiore.

If one thinks about the works of Mozart, what might come to mind is music that like Bach’s, is orderly (see the Divertimento in D Major), However, in one of his most important works, the Great G Minor Symphony (#40), the fourth movement contains powerful dissonance and tonal progressions anticipating those centuries later.

I can cite works that are moving, not because they follow orderly intelligible lines, but precisely because they do not: the eerie soprano clarinet solo in the Witches’ Sabbath movement of Berlioz’s Symphonie Fantastique; Stravinsky’s Rite of Spring; Thelonius Monk’s “Round Midnight“, and many more in classical and jazz—in music.

Symmetry and order is beautiful, but the human mind wants more than that. Symmetry in physics is beautiful (see God, Symmetry and Beauty I: The Standard Model and the Higgs Boson), but nature ultimately is more than an ordered model fit to equations. Can a computer see the beauty in the disordered pattern of a meadow, or the night sky? I don’t think so.

I’ll wind up with a final anecdote. Many, many years ago on my first academic assignment the head of the department involved with the newly burgeoning discipline of computer science (it was a management / business administration group) gave a lecture on artificial intelligence. After the lecture, as legend has it (I wasn’t there), a humanities professor asked him, “Would you want your daughter to marry one (a computer, that is)?” His answer was, “Yes, if she loved him.” Another version has it that someone shouted from the audience, “Why not, his wife did.”

I defy anyone to produce a computer analysis of that humor.

Finally, I haven’t said anything about God and music, or God and mathematics. My point in this post is that music is a gift, not to be explained as an evolutionary spandrel, and if it is a gift, it can be presumed to come from God.


  1. Trigger Warnings

    February 4, 2017 at 7:43 am

    I guess we can assume Briggs is not a fan of John Cage…


  2. Music may have its moments but Cage used the rest of the day.

  3. It’s pretty hard to create a ‘mere pastiche’ of a 4-voice Bach Chorale, let alone a Strauss symphony. Athanasius Kircher (thanks, Bob Mounger) is one of a long line of ‘polymaths’ who drastically underestimated the difficulty.
    For fun: real composers were often instructed in the principles of voice-leading by Johann Joseph Fux’s 1725 “Gradus ad Parnassum” — I think some exercises Beethoven did for Haydn based on the ‘Gradus’ still survive. (Haydn, at the time at least, proved to be an indifferent and inattentive teacher, and Beethoven quit).
    “Voice-leading” is the more general term, which applies to virtually all Western music, including Bach Chorales; “counterpoint” would be a subset of voice-leading. Even further afield: a very, very good but less well-known Baroque Czech composer, Jan Dismas Zelenka (look for his Masses, particularly, as well as his ‘famous’ trio sonatas) studied voice-leading under Fux.

  4. Of course, I can see how a machine could assemble original compositions that would sound like a man-made composition. I suppose there could be quite some usefulness to it. Like a man, the machine would, of course, know a little something about music. Ask a five-year-old to tap away at the piano and you might get something cute, but you’re probably not going to get anything like what one would call music. Even that five-year-old, as dramatically complex a thing as he is, would require training, and listening and studying and so forth, to be able to play a nice piece. So, context here is pretty much everything. Are any of us ever making “original music?” Musicians have been arguing about that one forever! Believe me, for-ev-er.


  5. Well done, Bob.

    Back when I was a young man it was fashionable for shopping precincts to play programmed sequences of tones that were called “computer music”… entirely hateful to “musos” but hypnotic to the apathetic. Much like the cruel mind and soul destroying “modern” popular “music” that could be (and often is) churned out of computer programmes.

    Yes, indeed! Long ago I opined that diatonic music is a gift of Heaven delivered by Angels for the glory of Creation.

  6. Milton Hathaway

    February 5, 2017 at 4:47 pm

    As an engineer, I believe I can mangle this topic.

    A lot of ambitious computer programmers start with the goal of replacing a creative activity with a computer program. We can call this “artificial intelligence”. Eventually reality sets in, and the programmer moves on, or sometimes settles for a CAD (computer-assisted design) approach. The resulting “CAD tools” are all over the map, but I think a common thread in the more successful ones is that the programmer adapts to the human input/output (I/O) method rather than forcing the human to adapt to existing computer I/O methods.

    For example, a CAMC (Computer-Assisted Music Composition) system that uses an actual musical instrument as an input device (e.g., a piano keyboard) can be expected to be more successful than one that uses a computer keyboard. But what about those of us that have no formal musical training, or any skills in playing a musical instrument?

    I keep coming back to the fact that everyone appreciates music, even those of us with zero skills in creating our own. What can be done for us, to allow us to create our own music that fit’s our general preferences, or even our moment-by-moment preferences.

    It seems like with the proper I/O device and CAMD system, anyone should be able to create music that closely meets their listening preferences. It could be done with normal computer input devices, a keyboard and mouse. But a more successful input device might be an “air instrument”, or an conductor’s baton. Or brain waves?

    Not that this would be easy to do. The CAMC system creator would probably have to be a highly trained musician to start with, which could be a big stumbling block. I have noticed that the skilled musicians I know tend to be pretty snobbish about music, and tend to treat the musical tastes of the untrained as inferior to their own. I view formal musical training as a double-edged sword – it opens up a new world of analytical musical appreciation, but closes off another world of pure experiential listening. Perhaps an analogy might help convey what I getting at. I once sat near a multilingual speaker, and I would overhear her phone conversations. I didn’t understand any of the languages, but the Portuguese struck me as a particularly beautiful language. I remarked on this once, and she reacted with surprise – she was so familiar with the language as a communication tool that she didn’t see the beauty in it. She gave another language as an example of a beautiful language, and it was one she didn’t speak.

    I suspect that the attitude of trained musicians toward the untrained wanting to make their own music with the aid of a computer as “don’t try this at home, best leave it to the professionals”.

  7. Interesting comment, MH. I believe the Japanese have tried to do what you describe in your comment, i.e. enable someone (unversed in musical theory and/or talent) compose music to his own taste, using some sort of feedback or neural network training systems (this is just a guess, since I haven’t read the original article). Nevertheless, even though such a procedure be successful, I’ll hazard the opinion that it won’t be “good” music, which demands originality that isn’t granted to those without musical talent and, should I add, to computers or those who program them (unless they have that talent to begin with).

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