4 ms·

I admit I'm a Radiohead fan. But music theory isn't much rooted in math -- I mean, sure, there's a bit of math involved, there are composers (mostly within the

by jtheory 15y ago

I admit I'm a Radiohead fan. But music theory isn't much rooted in math -- I mean, sure, there's a bit of math involved, there are composers (mostly within the last 60 years) who've decided to build lots of math into their music (but much of it is aggressively unlistenable, OR they did lots of extra work dressing up the mathematical stuff in "kind on the ear & brain" regular old music to make it sound nice...), and if you dig into the acoustics of music, or DSP, there's math there. But music theory itself is mostly the somewhat-arbitrary documentation of what music is doing (not in mathematical terms), and sadly even the terms that involve numbers don't even do it consistently. The easter eggs are cool -- but I wouldn't listen to the music regardless if I didn't like the melodies, orchestration, "feel" and so on in most of it. (Radiohead is quite melodic, on the whole).

MartinCron 15y ago
I agree that the math connection is pretty... loose, although it always impresses me when a good musician (like my guitar instructor) can transpose on the fly. "Oh, I wonder what this would sound like in A Major instead of C Minor?" The same guitar instructor re-introduced me to Radiohead, and some of the most joy I've ever had as an aspiring musician was hearing some of those chords come together in unexpected and beautiful ways.
- gnaritas 15y ago
  Transposing on a guitar is trivial, it's not like piano where changing keys changes fingering. On a guitar, you can just move to a new position and play the same fingerings, bam new key.
  - MartinCron 15y ago
    That doesn't work if you're going to do a minor/major change, though, and it also doesn't work if any of your chords have open strings in them. Not all chords are "moveable" chords.
    - gnaritas 15y ago
      Not all chord phrasings are movable, but all chords are. Name any chord, there's a movable version of it.
  - jtheory 15y ago
    Guitar or piano, it's still just patterns that are generally well burned-in. Study any instrument seriously and you'll play scales enough that they're quite natural "forms" that you just lay on the keyboard/fretboard in your imagination. Playing a melody through a different scale pattern (as long as they have the same number of notes... whole tone etc. are off-limits here) is fairly easy. Something with chords, or multiple melodies, and especially if it doesn't stick to its starting key, takes a little more planning ahead (assuming you can't just move up/down the guitar neck, or add a capo... that's of course trivial), but is still mostly applying the same technique - laying the same notes into a slightly different (but very familiar) pattern. This is a really fun singing exercise, BTW, that many people can try (with minimal music training, though you'll need to know how to sing a minor scale first): take a really simple melody in a major key (most children's songs), and sing it in a minor key. Start with something like Row row row your boat or twinkle twinkle, then something like Happy Birthday -- which doesn't start on the first note of the scale -- is more challenging. :)
    - gnaritas 15y ago
      > Guitar or piano, it's still just patterns that are generally well burned-in. Sure, but it takes much less effort to play something in different keys on a guitar than on a piano because the fingers don't change just because the key did. It takes more practice on a piano to play a song you already know in another key, not really so for the guitar if you're using movable forms.
      - jtheory 15y ago
        Yup, I agreed with that already, I think, though it's a special case. If you're switching major/minor, for example, it's about equal... for some pieces slightly easier on piano because the scales are horizontally laid out more obviously, whereas some guitar fingerings won't easily convert by just shifting over a few notes of the scale -- you're limited by the way your fingers can bend.
        gnaritas 15y ago
        Agreed.
jwco 15y ago
I don't know what "music theory" is, and I agree that I wouldn't listen to Radiohead if I didn't like the melodies (there are other mathy/geeky bands out there I don't listen to, an extreme case being Information Society giving you instructions on how to configure a modem to translate their "song" into ASCII, no. 1 listed here: http://www.cracked.com/article_18896_10-mind-blowing-easter-eggs-hidden-in-famous-albums_p2.html http://www.cracked.com/article_18896_10-mind-blowing-easter-...). But some theories about music are very mathematical. We probably are just beginning to understand how to think about music in terms of math, because music is complex and (at least much of Western music) discrete. An article in Science in 2008 defines equivalence relations and uses n-dimensional symmetries to describe sequences of pitches in time. See here: http://www.sciencemag.org/content/320/5874/346 http://www.sciencemag.org/content/320/5874/346 and here: http://www.sciencemag.org/content/320/5874/328.full http://www.sciencemag.org/content/320/5874/328.full) I think there is some truth in a Leibniz quote: "The pleasure we obtain from music comes from counting, but counting unconsciously. Music is nothing but unconscious arithmetic." (http://www-history.mcs.st-and.ac.uk/Quotations/Leibniz.html http://www-history.mcs.st-and.ac.uk/Quotations/Leibniz.html) It's hard to say why I like Radiohead. At first I really didn't like them; I found Kid A (album) especially discomforting. I had to let go of a lot of pre- (mis?) conceptions about what makes music good before I could come to like it. I probably had to let go of a lot of pre- (mis?) conceptions about myself and my worldview at the same time to appreciate the lyrics. But now it's one of my favorite works of art.
zinkem 15y ago
I don't know if there is really any specific relationship between Radiohead and mathematics more than any other musician or composer, and I agree with you-- mathematics doesn't play into my feelings towards radiohead, they're a great band. But you point out "music theory isn't much rooted in math." I think the sentiment is true, music theory is generally taught and practiced without much thought to mathematics. However, the fundamental concepts music theory are based on are all analogous to mathematical statements. You can see what I'm talking about here. http://en.wikipedia.org/wiki/Music_and_mathematics#Frequency_and_harmony http://en.wikipedia.org/wiki/Music_and_mathematics#Frequency... You'll notice that a fundamental frequency is picked, and we give names to several related frequencies (octave, third, fifth etc). All of these labels are analogous to various multiplications of the fundamental frequency. We learn to recognize some of the simpler relationships, as they are easily identifiable (different chords are an example of this). Any one who can count can recognize a number on the number line and compare it to another number and tell if it's smaller or larger. Those who have begin to understand arithmetic can identify the difference between those numbers, and if they are multiples of each other. Advanced mathematicians can tell us about more complicated relationships. In music we have tones that can be ordered, and musicians learn through experience to make these same judgments about tones without even knowing it. Any amateur musician can hear a pair of tones side by side and recognize which is higher or lower in pitch. The more advanced ear can identify notes that are the same or they can tell you a harmonic relationship between them. This is a different way of experiencing mathematical relationships within an ordered set. At it's core, I think music theory is absolutely the study of finding which combinations of tones create the numerical relationships we find most appealing in sound.
- jtheory 15y ago
  This isn't much different from what I'm saying, I think -- you mention frequencies, which don't come up much in most study of music theory beyond more or less what you have in your comment. Beyond that, well, I suppose you could say it's "math", but that's a bit like saying price comparing at the grocery store (calculate the per-kilo price!) is math -- it won't have math geeks drooling. I can recognize intervals by ear, but it's just practice. You start out by "cheating" (twinkle twinkle starts with a leap of a perfect fifth, the NBC call sign with a major sixth, etc.), then you just learn it. I'll bet you could get the gist of it using the reference melodies pretty quickly. You can refer to the relations using basic math terminology, or just the music theory technology, but regardless it doesn't feel like anything beyond elementary math -- it goes much quicker into psychology territory.

by jtheory 15y ago

MartinCron 15y ago

I agree that the math connection is pretty... loose, although it always impresses me when a good musician (like my guitar instructor) can transpose on the fly. "Oh, I wonder what this would sound like in A Major instead of C Minor?" The same guitar instructor re-introduced me to Radiohead, and some of the most joy I've ever had as an aspiring musician was hearing some of those chords come together in unexpected and beautiful ways.

gnaritas 15y ago
Transposing on a guitar is trivial, it's not like piano where changing keys changes fingering. On a guitar, you can just move to a new position and play the same fingerings, bam new key.
- MartinCron 15y ago
  That doesn't work if you're going to do a minor/major change, though, and it also doesn't work if any of your chords have open strings in them. Not all chords are "moveable" chords.
  - gnaritas 15y ago
    Not all chord phrasings are movable, but all chords are. Name any chord, there's a movable version of it.
- jtheory 15y ago
  Guitar or piano, it's still just patterns that are generally well burned-in. Study any instrument seriously and you'll play scales enough that they're quite natural "forms" that you just lay on the keyboard/fretboard in your imagination. Playing a melody through a different scale pattern (as long as they have the same number of notes... whole tone etc. are off-limits here) is fairly easy. Something with chords, or multiple melodies, and especially if it doesn't stick to its starting key, takes a little more planning ahead (assuming you can't just move up/down the guitar neck, or add a capo... that's of course trivial), but is still mostly applying the same technique - laying the same notes into a slightly different (but very familiar) pattern. This is a really fun singing exercise, BTW, that many people can try (with minimal music training, though you'll need to know how to sing a minor scale first): take a really simple melody in a major key (most children's songs), and sing it in a minor key. Start with something like Row row row your boat or twinkle twinkle, then something like Happy Birthday -- which doesn't start on the first note of the scale -- is more challenging. :)
  - gnaritas 15y ago
    > Guitar or piano, it's still just patterns that are generally well burned-in. Sure, but it takes much less effort to play something in different keys on a guitar than on a piano because the fingers don't change just because the key did. It takes more practice on a piano to play a song you already know in another key, not really so for the guitar if you're using movable forms.
    - jtheory 15y ago
      Yup, I agreed with that already, I think, though it's a special case. If you're switching major/minor, for example, it's about equal... for some pieces slightly easier on piano because the scales are horizontally laid out more obviously, whereas some guitar fingerings won't easily convert by just shifting over a few notes of the scale -- you're limited by the way your fingers can bend.
      - gnaritas 15y ago
        Agreed.

jwco 15y ago

I don't know what "music theory" is, and I agree that I wouldn't listen to Radiohead if I didn't like the melodies (there are other mathy/geeky bands out there I don't listen to, an extreme case being Information Society giving you instructions on how to configure a modem to translate their "song" into ASCII, no. 1 listed here: http://www.cracked.com/article_18896_10-mind-blowing-easter-eggs-hidden-in-famous-albums_p2.html http://www.cracked.com/article_18896_10-mind-blowing-easter-...). But some theories about music are very mathematical. We probably are just beginning to understand how to think about music in terms of math, because music is complex and (at least much of Western music) discrete. An article in Science in 2008 defines equivalence relations and uses n-dimensional symmetries to describe sequences of pitches in time. See here: http://www.sciencemag.org/content/320/5874/346 http://www.sciencemag.org/content/320/5874/346 and here: http://www.sciencemag.org/content/320/5874/328.full http://www.sciencemag.org/content/320/5874/328.full) I think there is some truth in a Leibniz quote: "The pleasure we obtain from music comes from counting, but counting unconsciously. Music is nothing but unconscious arithmetic." (http://www-history.mcs.st-and.ac.uk/Quotations/Leibniz.html http://www-history.mcs.st-and.ac.uk/Quotations/Leibniz.html) It's hard to say why I like Radiohead. At first I really didn't like them; I found Kid A (album) especially discomforting. I had to let go of a lot of pre- (mis?) conceptions about what makes music good before I could come to like it. I probably had to let go of a lot of pre- (mis?) conceptions about myself and my worldview at the same time to appreciate the lyrics. But now it's one of my favorite works of art.

zinkem 15y ago

I don't know if there is really any specific relationship between Radiohead and mathematics more than any other musician or composer, and I agree with you-- mathematics doesn't play into my feelings towards radiohead, they're a great band. But you point out "music theory isn't much rooted in math." I think the sentiment is true, music theory is generally taught and practiced without much thought to mathematics. However, the fundamental concepts music theory are based on are all analogous to mathematical statements. You can see what I'm talking about here. http://en.wikipedia.org/wiki/Music_and_mathematics#Frequency_and_harmony http://en.wikipedia.org/wiki/Music_and_mathematics#Frequency... You'll notice that a fundamental frequency is picked, and we give names to several related frequencies (octave, third, fifth etc). All of these labels are analogous to various multiplications of the fundamental frequency. We learn to recognize some of the simpler relationships, as they are easily identifiable (different chords are an example of this). Any one who can count can recognize a number on the number line and compare it to another number and tell if it's smaller or larger. Those who have begin to understand arithmetic can identify the difference between those numbers, and if they are multiples of each other. Advanced mathematicians can tell us about more complicated relationships. In music we have tones that can be ordered, and musicians learn through experience to make these same judgments about tones without even knowing it. Any amateur musician can hear a pair of tones side by side and recognize which is higher or lower in pitch. The more advanced ear can identify notes that are the same or they can tell you a harmonic relationship between them. This is a different way of experiencing mathematical relationships within an ordered set. At it's core, I think music theory is absolutely the study of finding which combinations of tones create the numerical relationships we find most appealing in sound.

jtheory 15y ago
This isn't much different from what I'm saying, I think -- you mention frequencies, which don't come up much in most study of music theory beyond more or less what you have in your comment. Beyond that, well, I suppose you could say it's "math", but that's a bit like saying price comparing at the grocery store (calculate the per-kilo price!) is math -- it won't have math geeks drooling. I can recognize intervals by ear, but it's just practice. You start out by "cheating" (twinkle twinkle starts with a leap of a perfect fifth, the NBC call sign with a major sixth, etc.), then you just learn it. I'll bet you could get the gist of it using the reference melodies pretty quickly. You can refer to the relations using basic math terminology, or just the music theory technology, but regardless it doesn't feel like anything beyond elementary math -- it goes much quicker into psychology territory.