8 ms·

Guitar Decomposed: 5. Mutating the Third

123 points by lelf 6y ago

dehrmann 6y ago
> The first such transformation is to lower the third by one step to obtain a minor triad. For some reason, we perceive minor chords as sad or melancholy, sometimes a bit whiny. I'd love to hear more on "some reason." In a way, it's so arbitrary, and maybe it's a cultural bias, but so sad. And the minor iv chord, so sad. https://www.youtube.com/watch?v=RQFtvAfHndE https://www.youtube.com/watch?v=RQFtvAfHndE, right when he sings "when September ends," but there's are so many other examples.
- nineteen999 6y ago
  > Minor chords? In pop and rock? They're used all over the place. It's more rare to not find one in a song. Minor chords with added sevenths, yeah, less common. Yeah, exactly my first thought, pick any Beatles, Pink Floyd or Radiohead album for the most mainstream, off-the-top-of-my head examples.
  - dehrmann 6y ago
    I deleted that part when I realized the author might have meant altered minor chords (like the minor iv in a major key), not just a generic I–V–vi–IV.
- nicetryguy 6y ago
  > I'd love to hear more on "some reason." Modern science has no idea! I've researched a fair bit. We don't know how the brain intreprets frequency combinations or why different ones sound good or bad together or evoke certain moods. Math can explain harmonics and the circle of fifths and how to assemble keys and modes, sure, but no one knows the Why or How of the internals between the ears. It is just cultural bias and repetition that we intrepret some note and chord combinations a certain way or is there something more fundamental going on with the hardware? Good question! Nobody knows. All we have is anecdotal evidence and the trial and error of the musicians and composers who make it. Music is still a mystery.
  - devin 6y ago
    I get a little annoyed at this notion of minor vs major. It's not binary. Subtle changes in tonality can shift back and forth between minor and major and diminished and augmented and so on. Most listeners will interpret a passage as "minor", but that doesn't mean it's so. Complex harmony can be reduced to minor or major but it robs it of all of its nuance.
    - nicetryguy 6y ago
      I mean if you move down 3 notes from any Major key you have your Minor key with the same exact notes, like C Major and A Minor. I usually compose with a Major or Minor key in mind, but it's kind of a reference and not a be all end all. I like sharp 4's which work great usually and don't fit in either key. A flat 7 sounds great in a major key too, usually. I agree with you mostly, and i am annoyed by people who are adamant about the rules of a key, but it helps me to have a key in mind to both play and compose, even if i break the rules of it. I find improvising on piano / guitar is nearly impossible if you don't know the key, even after many years of playing both.
      - parenthesis 6y ago
        If you think in terms of modes, then using a sharp 4 in major you can think of as lydian (the 4th mode of major) or lydian dominant (has a flat 7 too, the 4th mode of melodic minor). In minor, there's lydian minor (the 4th mode of harmonic major). Major but with a flat 7 is mixolydian (the fifth mode of major). It is everywhere in popular music. My favourite thing at the moment is major 7 sharp 5 chords (or an augmented triad with also a major 7th). These chords arise in harmonic and melodic minor (in both cases chord 3), and in harmonic major (chord 6). But they also sound great as substitutions for what is 'supposed' to be a major 7 chord.
    - Stratoscope 6y ago
      One of my favorite examples of this is Dreams by Fleetwood Mac, but that may be because I've been practicing it on harmonica. The song begins (with note names and relative major scale numbers): Now here you go again A C D E D C 6 1 2 3 2 1 (low) But that's not how Stevie Nicks sings it. She starts the word "go" very flat, not quite all the way down to the Eb, but maybe 70 cents down from the E? And then she slides up to the E from there. Listen to her sing it and you will know what I'm talking about. If you have an instrument where you can play either the straight notes or the notes with that slide, play it both ways and you will hear the difference. This song is fun and easy to play on harmonica, including the pitch bends, if you get or make the right harp. You need a High C Melody Maker, which you can order from Seydel or you can take a Lee Oskar F Major and retune it into a C Melody Maker: raise the blow 3 from C to D, and raise the draw 5 and draw 9 from Bb to B. How do you retune a harmonica? You file the reeds! Take off some weight near the free end of a reed and it will vibrate faster, giving it a higher pitch. More strangely, you can also lower the pitch a little by thinning the reed near the fixed end.
- recursive 6y ago
  > lower the third by one step to obtain a minor triad But it's lowered by a half step...
  - djaychela 6y ago
    Depends on your language use - hrs talking in terms of semitones throughout the article, so thats correct; you're thinking in terms of whole /half steps (so you would be correct if the article was written in those terms). I think talking in semitones helps clear up any misunderstanding over the explicit intervals present in a chord (and I've found that very useful when talking to guitar pupils who only know guitar and want to understand theory, particularly because the guitar neck is made of semitones), but if someone knows more scale theory (or plays piano), then talking in scale steps makes more sense.
    - anjc 6y ago
      > Depends on your language use 'Step' has a specific meaning in music and it doesn't mean 'semitone'. Why not just use semitone seeing as that precisely describes what's intended? Conflating meanings seems like it could be confusing. "The tritone of this note is 6 steps up" "Gotcha, so the tritone of C is B" "No no, by step I currently mean tones, not semitones" "Ah, so 3 scale tones, ok" "No just 3 tones, or 6 steps" "Ok, I'll count 6 steps, 1,2,3,4..."...just use the correct word.
      - main_gi 6y ago
        "Step" refers to an interval gap of "half step" or "whole step". In a way, I could see this as a "specific meaning", but since it refers to a group of intervals and not a single one, I would be quite open to a definition where '1 step' is always '1 half step', since both 'semitone' and 'half step' imply a less useful fundamental value of 2 half steps, even though music that involves only whole steps is quite dissonant and uncommon (the whole tone scale). Your entire hypothetical dialogue is confusing as well, since your hypothetical person isn't using correct words either. The situation where C + 6 of something = B is with scale degrees (C moved 6 scale degrees up is B). And then you say "I currently mean tones", when 6 "tones" has the exact same grouping problem you are criticizing (because 'whole tone' and 'semitone' have the exact same meaning as 'whole step' and 'half step', only now 'scale tone' is in the group too). This artificially lengthens the example. "The tritone of this note is 6 steps up" "Gotcha, so the tritone of C is B" "No, that's scale degrees, by 'step' I mean 'half step'." "Oh, so it's F# then." Done.
- canjobear 6y ago
  It’s a learned cultural association. People who have not been exposed to Western music don’t even distinguish consonance from dissonance. https://pubmed.ncbi.nlm.nih.gov/27409816/ https://pubmed.ncbi.nlm.nih.gov/27409816/
  - slaymaker1907 6y ago
    This is incorrect. Consonance or dissonance is based on physical properties of the sounds. As the paper mentions, pleasantness of the consonance vs dissonance varies from culture to culture. The paper specifically mentions in the abstract that the other cultures were able to distinguish consonance from dissonance.
    - zozbot234 6y ago
      The physical property is generally called "roughness" (mostly to disambiguate wrt. the structural sense of 'dissonance' in composition) and is really more of a psychoacoustic property, since it relates to a feature of hearing known as critical bandwidth.
  - enriquto 6y ago
    > People who have not been exposed to Western music don’t even distinguish consonance from dissonance. This is false. Any person with a functioning auditory system can hear the beating when you play two very close notes. It is also trivial to model mathematically, using elementary trigonometry. And the beating of periodic waves of very close frequency is precisely the dissonance (especially when the partials of the two notes are close, but do not coincide exactly). Whether this audible beating or dissonance is "good" or "bad", and what is its place in music, is an entirely cultural phenomenon. But the phenomenon itself is not a cultural construction, it is a physical thing. Western music uses dissonance as a tension before a final resolution, and this is of course an arbitrary choice for our musical language.
- viraptor 6y ago
  If you're into that, check out Adam Neely's channel. There's been a few videos on that and related topics: https://youtu.be/6c_LeIXrzAk https://youtu.be/6c_LeIXrzAk (Spoiler: lots of historical context about tuning systems, but also raising the issue of timbre of specific instruments)
- fredsanford 6y ago
  https://www.youtube.com/watch?v=oqrfPnGy1tM https://www.youtube.com/watch?v=oqrfPnGy1tM Leave My Girl Alone by Stevie Ray Vaughan is pretty much a master class for a guitar player that wants to mess around with 3rds and 7ths. At 3:19 is the best example of slightly messing with the 3rd and resolving to the 1 that I can remember hearing. The solos center around bent 3rds, 4ths, b5ths and 7ths.
- skeletor_999 6y ago
  I think that the language we use might be limiting our analysis of this topic. We often describe minor keys as sad, but I don't think that really describes the emotion. Dark is also used, but doesn't necessarily imply sadness. Dark has problems too, as it's more vague. Even though many people would describe certain songs as sounding sad, I don't think that it usually makes them feel sad. Can a song be sad if it doesn't make you feel sad? Heavy metal wouldn't be popular if it actually made you unhappy. Personally, it can improve my mood if I feel sad. Conversely, a really "bubblegummy" pop song would get on my nerves, but I would still describe it as sounding happy. I'm not even sure that we could come up with better labels using common words. The emotions caused by music are pretty unique (at least for me).
- spopejoy 6y ago
  One thing is minor is unquestionably more dissonant than major; a major chord (in just intonation) is one of the most powerful sounds in existence which is why Baroque music almost always ends on major -- ie not to "sound happy" but to end with a bang. This dissonance is related to why a composer like Bach has many, many compositions in minor (and massive ones like the B-minor mass), but not much later, you see composers using minor less and less as they moved towards more consonance (along with modulation of course). For instance, in all of Mozart's violin sonatas there's only one minor. And it's freaking awesome ... but he didn't want to write more than that. I think that while dissonance was interesting to Bach, it was less so through the rest of the common period, so that favors major. I would also add that Salsa as a genre uses minor keys for happy tunes all the time.
madhadron 6y ago
From the first post in the series: > We now use the so called equal temperament system... Unless I'm playing a piano, no, I don't. And since I have an electric piano, I have been known to set it to meantone, but I accept that I'm a freak. Even on a guitar you have a fair amount of variation in pitch based on pressure and position of the left hand fingers relative to the fret. Not as much as on old instruments with gut frets, but it's there.
- viraptor 6y ago
  But given the frets are placed to divide the length of the string in a specific place, you're aiming to play equal temperament, right? You're using that system on a typical guitar, even if the sounds don't match exactly. Of course it's not going to be perfect, but it's still closer to 12TET-with-noise than some specific mediaeval tuning.
  - Tade0 6y ago
    Yes and no. Those who play electric guitars with distortion prefer to approach Just Intonation(for a given key) as it doesn't have so much intermodulation. There is an attempt to tune guitars close to equal temperament trademarked as True Temperament: https://www.truetemperament.com/faq/ https://www.truetemperament.com/faq/ I for one am happy when my 12th and 24th frets are in tune. Solos sound off and weak if these two don't hold.
    - japanoise 6y ago
      To use computing slang to talk about music: this is just ricing. At best you'll sound out of tune with the rest of the band, at worst you'll run into wolf intervals and other issues with just intonation. This touches on the biggest reason we stick with 12-tone equal temparament in the West: social reasons. Having a standard means we can play together, in groups or at jams, without having to negotiate which tuning system we use (an argument most working musicians I've met see as utter wank and a waste of time).
      - 6y ago
mikorym 6y ago
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.
jvandonsel 6y ago
I love this series of posts. I've always wondered why guitars have irregular tuning and this explanation makes sense.

123 points by lelf 6y ago

> The first such transformation is to lower the third by one step to obtain a minor triad. For some reason, we perceive minor chords as sad or melancholy, sometimes a bit whiny. I'd love to hear more on "some reason." In a way, it's so arbitrary, and maybe it's a cultural bias, but so sad. And the minor iv chord, so sad. https://www.youtube.com/watch?v=RQFtvAfHndE https://www.youtube.com/watch?v=RQFtvAfHndE, right when he sings "when September ends," but there's are so many other examples.

nineteen999 6y ago
> Minor chords? In pop and rock? They're used all over the place. It's more rare to not find one in a song. Minor chords with added sevenths, yeah, less common. Yeah, exactly my first thought, pick any Beatles, Pink Floyd or Radiohead album for the most mainstream, off-the-top-of-my head examples.
- dehrmann 6y ago
  I deleted that part when I realized the author might have meant altered minor chords (like the minor iv in a major key), not just a generic I–V–vi–IV.
nicetryguy 6y ago
> I'd love to hear more on "some reason." Modern science has no idea! I've researched a fair bit. We don't know how the brain intreprets frequency combinations or why different ones sound good or bad together or evoke certain moods. Math can explain harmonics and the circle of fifths and how to assemble keys and modes, sure, but no one knows the Why or How of the internals between the ears. It is just cultural bias and repetition that we intrepret some note and chord combinations a certain way or is there something more fundamental going on with the hardware? Good question! Nobody knows. All we have is anecdotal evidence and the trial and error of the musicians and composers who make it. Music is still a mystery.
- devin 6y ago
  I get a little annoyed at this notion of minor vs major. It's not binary. Subtle changes in tonality can shift back and forth between minor and major and diminished and augmented and so on. Most listeners will interpret a passage as "minor", but that doesn't mean it's so. Complex harmony can be reduced to minor or major but it robs it of all of its nuance.
  - nicetryguy 6y ago
    I mean if you move down 3 notes from any Major key you have your Minor key with the same exact notes, like C Major and A Minor. I usually compose with a Major or Minor key in mind, but it's kind of a reference and not a be all end all. I like sharp 4's which work great usually and don't fit in either key. A flat 7 sounds great in a major key too, usually. I agree with you mostly, and i am annoyed by people who are adamant about the rules of a key, but it helps me to have a key in mind to both play and compose, even if i break the rules of it. I find improvising on piano / guitar is nearly impossible if you don't know the key, even after many years of playing both.
    - parenthesis 6y ago
      If you think in terms of modes, then using a sharp 4 in major you can think of as lydian (the 4th mode of major) or lydian dominant (has a flat 7 too, the 4th mode of melodic minor). In minor, there's lydian minor (the 4th mode of harmonic major). Major but with a flat 7 is mixolydian (the fifth mode of major). It is everywhere in popular music. My favourite thing at the moment is major 7 sharp 5 chords (or an augmented triad with also a major 7th). These chords arise in harmonic and melodic minor (in both cases chord 3), and in harmonic major (chord 6). But they also sound great as substitutions for what is 'supposed' to be a major 7 chord.
  - Stratoscope 6y ago
    One of my favorite examples of this is Dreams by Fleetwood Mac, but that may be because I've been practicing it on harmonica. The song begins (with note names and relative major scale numbers): Now here you go again A C D E D C 6 1 2 3 2 1 (low) But that's not how Stevie Nicks sings it. She starts the word "go" very flat, not quite all the way down to the Eb, but maybe 70 cents down from the E? And then she slides up to the E from there. Listen to her sing it and you will know what I'm talking about. If you have an instrument where you can play either the straight notes or the notes with that slide, play it both ways and you will hear the difference. This song is fun and easy to play on harmonica, including the pitch bends, if you get or make the right harp. You need a High C Melody Maker, which you can order from Seydel or you can take a Lee Oskar F Major and retune it into a C Melody Maker: raise the blow 3 from C to D, and raise the draw 5 and draw 9 from Bb to B. How do you retune a harmonica? You file the reeds! Take off some weight near the free end of a reed and it will vibrate faster, giving it a higher pitch. More strangely, you can also lower the pitch a little by thinning the reed near the fixed end.
recursive 6y ago
> lower the third by one step to obtain a minor triad But it's lowered by a half step...
- djaychela 6y ago
  Depends on your language use - hrs talking in terms of semitones throughout the article, so thats correct; you're thinking in terms of whole /half steps (so you would be correct if the article was written in those terms). I think talking in semitones helps clear up any misunderstanding over the explicit intervals present in a chord (and I've found that very useful when talking to guitar pupils who only know guitar and want to understand theory, particularly because the guitar neck is made of semitones), but if someone knows more scale theory (or plays piano), then talking in scale steps makes more sense.
  - anjc 6y ago
    > Depends on your language use 'Step' has a specific meaning in music and it doesn't mean 'semitone'. Why not just use semitone seeing as that precisely describes what's intended? Conflating meanings seems like it could be confusing. "The tritone of this note is 6 steps up" "Gotcha, so the tritone of C is B" "No no, by step I currently mean tones, not semitones" "Ah, so 3 scale tones, ok" "No just 3 tones, or 6 steps" "Ok, I'll count 6 steps, 1,2,3,4..."...just use the correct word.
    - main_gi 6y ago
      "Step" refers to an interval gap of "half step" or "whole step". In a way, I could see this as a "specific meaning", but since it refers to a group of intervals and not a single one, I would be quite open to a definition where '1 step' is always '1 half step', since both 'semitone' and 'half step' imply a less useful fundamental value of 2 half steps, even though music that involves only whole steps is quite dissonant and uncommon (the whole tone scale). Your entire hypothetical dialogue is confusing as well, since your hypothetical person isn't using correct words either. The situation where C + 6 of something = B is with scale degrees (C moved 6 scale degrees up is B). And then you say "I currently mean tones", when 6 "tones" has the exact same grouping problem you are criticizing (because 'whole tone' and 'semitone' have the exact same meaning as 'whole step' and 'half step', only now 'scale tone' is in the group too). This artificially lengthens the example. "The tritone of this note is 6 steps up" "Gotcha, so the tritone of C is B" "No, that's scale degrees, by 'step' I mean 'half step'." "Oh, so it's F# then." Done.
canjobear 6y ago
It’s a learned cultural association. People who have not been exposed to Western music don’t even distinguish consonance from dissonance. https://pubmed.ncbi.nlm.nih.gov/27409816/ https://pubmed.ncbi.nlm.nih.gov/27409816/
- slaymaker1907 6y ago
  This is incorrect. Consonance or dissonance is based on physical properties of the sounds. As the paper mentions, pleasantness of the consonance vs dissonance varies from culture to culture. The paper specifically mentions in the abstract that the other cultures were able to distinguish consonance from dissonance.
  - zozbot234 6y ago
    The physical property is generally called "roughness" (mostly to disambiguate wrt. the structural sense of 'dissonance' in composition) and is really more of a psychoacoustic property, since it relates to a feature of hearing known as critical bandwidth.
- enriquto 6y ago
  > People who have not been exposed to Western music don’t even distinguish consonance from dissonance. This is false. Any person with a functioning auditory system can hear the beating when you play two very close notes. It is also trivial to model mathematically, using elementary trigonometry. And the beating of periodic waves of very close frequency is precisely the dissonance (especially when the partials of the two notes are close, but do not coincide exactly). Whether this audible beating or dissonance is "good" or "bad", and what is its place in music, is an entirely cultural phenomenon. But the phenomenon itself is not a cultural construction, it is a physical thing. Western music uses dissonance as a tension before a final resolution, and this is of course an arbitrary choice for our musical language.
viraptor 6y ago
If you're into that, check out Adam Neely's channel. There's been a few videos on that and related topics: https://youtu.be/6c_LeIXrzAk https://youtu.be/6c_LeIXrzAk (Spoiler: lots of historical context about tuning systems, but also raising the issue of timbre of specific instruments)
fredsanford 6y ago
https://www.youtube.com/watch?v=oqrfPnGy1tM https://www.youtube.com/watch?v=oqrfPnGy1tM Leave My Girl Alone by Stevie Ray Vaughan is pretty much a master class for a guitar player that wants to mess around with 3rds and 7ths. At 3:19 is the best example of slightly messing with the 3rd and resolving to the 1 that I can remember hearing. The solos center around bent 3rds, 4ths, b5ths and 7ths.
skeletor_999 6y ago
I think that the language we use might be limiting our analysis of this topic. We often describe minor keys as sad, but I don't think that really describes the emotion. Dark is also used, but doesn't necessarily imply sadness. Dark has problems too, as it's more vague. Even though many people would describe certain songs as sounding sad, I don't think that it usually makes them feel sad. Can a song be sad if it doesn't make you feel sad? Heavy metal wouldn't be popular if it actually made you unhappy. Personally, it can improve my mood if I feel sad. Conversely, a really "bubblegummy" pop song would get on my nerves, but I would still describe it as sounding happy. I'm not even sure that we could come up with better labels using common words. The emotions caused by music are pretty unique (at least for me).
spopejoy 6y ago
One thing is minor is unquestionably more dissonant than major; a major chord (in just intonation) is one of the most powerful sounds in existence which is why Baroque music almost always ends on major -- ie not to "sound happy" but to end with a bang. This dissonance is related to why a composer like Bach has many, many compositions in minor (and massive ones like the B-minor mass), but not much later, you see composers using minor less and less as they moved towards more consonance (along with modulation of course). For instance, in all of Mozart's violin sonatas there's only one minor. And it's freaking awesome ... but he didn't want to write more than that. I think that while dissonance was interesting to Bach, it was less so through the rest of the common period, so that favors major. I would also add that Salsa as a genre uses minor keys for happy tunes all the time.

madhadron 6y ago

From the first post in the series: > We now use the so called equal temperament system... Unless I'm playing a piano, no, I don't. And since I have an electric piano, I have been known to set it to meantone, but I accept that I'm a freak. Even on a guitar you have a fair amount of variation in pitch based on pressure and position of the left hand fingers relative to the fret. Not as much as on old instruments with gut frets, but it's there.

viraptor 6y ago
But given the frets are placed to divide the length of the string in a specific place, you're aiming to play equal temperament, right? You're using that system on a typical guitar, even if the sounds don't match exactly. Of course it's not going to be perfect, but it's still closer to 12TET-with-noise than some specific mediaeval tuning.
- Tade0 6y ago
  Yes and no. Those who play electric guitars with distortion prefer to approach Just Intonation(for a given key) as it doesn't have so much intermodulation. There is an attempt to tune guitars close to equal temperament trademarked as True Temperament: https://www.truetemperament.com/faq/ https://www.truetemperament.com/faq/ I for one am happy when my 12th and 24th frets are in tune. Solos sound off and weak if these two don't hold.
  - japanoise 6y ago
    To use computing slang to talk about music: this is just ricing. At best you'll sound out of tune with the rest of the band, at worst you'll run into wolf intervals and other issues with just intonation. This touches on the biggest reason we stick with 12-tone equal temparament in the West: social reasons. Having a standard means we can play together, in groups or at jams, without having to negotiate which tuning system we use (an argument most working musicians I've met see as utter wank and a waste of time).
    - 6y ago

mikorym 6y ago

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.

jvandonsel 6y ago

I love this series of posts. I've always wondered why guitars have irregular tuning and this explanation makes sense.