4 ms·

I was expecting a bit more category theory. But I was glad to see that he alludes to the duality of minor chords and major chords. A simple way to look at it i

I was expecting a bit more category theory. But I was glad to see that he alludes to the duality of minor chords and major chords. A simple way to look at it is like this: Pick two notes, i.e., an interval. Then pick a note in the middle of the two notes. The dual chord is the one where you swap the up and down chromatic distances. Then if you happened to pick a 5th interval, and you happened to pick the major 3rd as middle note, then the minor is dual to it. But you can go further. Pick the octave and choose the 5th now as your middle note. Then the 4th is dual to this. You can drop the chromatic condition and work in a key with a scale and things like that. Also, the 12 chromatic notes form a group with inverses as duals. Then the 5th is dual to the 4th, but now the 3rd will be dual to the 6th—equivalent to the interval construction where you take the octave above.

motohagiography 6y ago
I too was thinking there would be a category theory angle on this, but of course it makes sense to have diverse interests. The question of whether musical notation is Turing complete, and what it might mean if it were, would have been an interesting one for a category theorist to examine.
fenwick67 6y ago
This is why I like the guitar/bass over the piano, because these relationships show themselves when you play. On a piano, if you go from C to E# the hand shape is totally different than A to C, even though the intervals are the same, so this relationship isn't intuitive.
- dhosek 6y ago
  I'm guessing that you learned guitar before piano? My first instrument was piano and I don't really think about hand shape when I play chords on it. My internal visualization of music is primarily founded on a piano keyboard with musical staves as secondary. I will say that playing multiple musical instruments gives the same kind of multiple ways of looking at a thing that multiple programming languages does. One of the things that was a little strange for me when I first picked up the flute was the idea that lower notes were further away from me as opposed to being closer the way that I was used to thinking of them with bass (particularly double bass which was my first stringed instrument). Meanwhile, on brass instruments, different pitches don't really have any spatial location at all.
  - dhosek 6y ago
    (I'd also add that while I can play multiple instruments, I don't necessarily play most of them well).
  - fenwick67 6y ago
    I took piano lessons at age 9 for about a 6 months but it never really took and I didn't practice. I played trombone for 3 years junior high, but didn't really practice then, either. Then I took music theory and composition classes in college, which revealed to me that thinking in intervals and scale degrees made way more sense to me than staves and note names. At that point bass and guitar clicked and really complemented that way of thinking. I should also add I'm really only competent at one instrument which is bass guitar, probably because I played in a church praise band for a bit which made me actually have a reason to practice.
  - bobbiechen 6y ago
    My first instrument was also piano (classical). I never really thought of hand shape while playing chords either, but I understand the parent comment - since your hand position does change, it makes the absolute key much more important, and it makes it more difficult to see the relative jumps. I don't think I ever had a good feel for how chords relate to each other before I started playing the accordion recently. On the left hand of an accordion, every chord interval is identical - C major to D major is just two positions away, exactly the same as D major to E major. It's also arranged in the circle of fifths, so any chord progression can be arbitrarily transposed (until you run out of range on the ends) That really helps me feel how chords progress and for the first time I'm feel comfortable playing chords by ear in real-time.
    - parenthesis 6y ago
      > It's also arranged in the circle of fifths So that's why the accordian player I walk past on the promenade always sounds like he's playing Autumn Leaves: circle of fourths/fifths chord progressions are very natural to play on the instrument. (Of course, he's not playing Autumn Leaves; that's just the first tune I think of with that chord progression; but there are zillions. The Beatles' You Never Give Me Your Money, and I Will Survive are a couple of other famous popular music ones.)
jmiskovic 6y ago
I've read your post several times and I don't get how this duality is useful and how to apply it. The "duality" of major/minor seems very different that "duality" of 4th and 5th. One completely changes music harmony, while other is basically interchangeable. When is it useful to think in these terms?
- mikorym 6y ago
  Exactly because they have effects that sound different and are instances of the same general principle. Edit: The idea is not to stop there. You also have the minor 7th chord being dual to the major 7th chord (with the octave added implicitly). Those two chords are often used together in jazz music. In this case the interval you use to get the upper note is a 4th. And depending on which interval you are focusing on, and what kind of scale you use (if not chromatic) this simple concept can get much more interesting. I agree that playing for example C E G and then C Eb G sounds like a "change", but I don't think the theory gives you complementary chords in sequence. They connect ideas with each other. In that sense it makes sense for a major chord to be dual to a minor chord.

motohagiography 6y ago

I too was thinking there would be a category theory angle on this, but of course it makes sense to have diverse interests. The question of whether musical notation is Turing complete, and what it might mean if it were, would have been an interesting one for a category theorist to examine.

fenwick67 6y ago

This is why I like the guitar/bass over the piano, because these relationships show themselves when you play. On a piano, if you go from C to E# the hand shape is totally different than A to C, even though the intervals are the same, so this relationship isn't intuitive.

dhosek 6y ago
I'm guessing that you learned guitar before piano? My first instrument was piano and I don't really think about hand shape when I play chords on it. My internal visualization of music is primarily founded on a piano keyboard with musical staves as secondary. I will say that playing multiple musical instruments gives the same kind of multiple ways of looking at a thing that multiple programming languages does. One of the things that was a little strange for me when I first picked up the flute was the idea that lower notes were further away from me as opposed to being closer the way that I was used to thinking of them with bass (particularly double bass which was my first stringed instrument). Meanwhile, on brass instruments, different pitches don't really have any spatial location at all.
- dhosek 6y ago
  (I'd also add that while I can play multiple instruments, I don't necessarily play most of them well).
- fenwick67 6y ago
  I took piano lessons at age 9 for about a 6 months but it never really took and I didn't practice. I played trombone for 3 years junior high, but didn't really practice then, either. Then I took music theory and composition classes in college, which revealed to me that thinking in intervals and scale degrees made way more sense to me than staves and note names. At that point bass and guitar clicked and really complemented that way of thinking. I should also add I'm really only competent at one instrument which is bass guitar, probably because I played in a church praise band for a bit which made me actually have a reason to practice.
- bobbiechen 6y ago
  My first instrument was also piano (classical). I never really thought of hand shape while playing chords either, but I understand the parent comment - since your hand position does change, it makes the absolute key much more important, and it makes it more difficult to see the relative jumps. I don't think I ever had a good feel for how chords relate to each other before I started playing the accordion recently. On the left hand of an accordion, every chord interval is identical - C major to D major is just two positions away, exactly the same as D major to E major. It's also arranged in the circle of fifths, so any chord progression can be arbitrarily transposed (until you run out of range on the ends) That really helps me feel how chords progress and for the first time I'm feel comfortable playing chords by ear in real-time.
  - parenthesis 6y ago
    > It's also arranged in the circle of fifths So that's why the accordian player I walk past on the promenade always sounds like he's playing Autumn Leaves: circle of fourths/fifths chord progressions are very natural to play on the instrument. (Of course, he's not playing Autumn Leaves; that's just the first tune I think of with that chord progression; but there are zillions. The Beatles' You Never Give Me Your Money, and I Will Survive are a couple of other famous popular music ones.)

jmiskovic 6y ago

I've read your post several times and I don't get how this duality is useful and how to apply it. The "duality" of major/minor seems very different that "duality" of 4th and 5th. One completely changes music harmony, while other is basically interchangeable. When is it useful to think in these terms?

mikorym 6y ago
Exactly because they have effects that sound different and are instances of the same general principle. Edit: The idea is not to stop there. You also have the minor 7th chord being dual to the major 7th chord (with the octave added implicitly). Those two chords are often used together in jazz music. In this case the interval you use to get the upper note is a 4th. And depending on which interval you are focusing on, and what kind of scale you use (if not chromatic) this simple concept can get much more interesting. I agree that playing for example C E G and then C Eb G sounds like a "change", but I don't think the theory gives you complementary chords in sequence. They connect ideas with each other. In that sense it makes sense for a major chord to be dual to a minor chord.