
Guitar Decomposed: 5. Mutating the Third - lelf
https://bartoszmilewski.com/2020/05/27/guitar-decomposed-5-mutating-the-third/
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madhadron
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.

~~~
nicetryguy
I still think its fair to say we use the equal temperment system. It is a
widely accepted standard. You're right, fret pressure alone can absolutely
raise the pitch 5/10 cents, my Gibson SG has some deep frets and can do double
that.

I am surprised with all of the technology and VSTs we have now no one really
uses self adjusting Just intonation or challenges A 440. Musical /
mathematical / technical ability are a rare trinary intersection. It saddens
me that no one is really trying to push the envelope of acoustic instruments
or even new ways of producting digital sound. It's the same old Square and Saw
waves with the same instruments we have had for hundreds of years. Sadly i
think musicianship has all but died in Gen Z, quantization / pitch correction
/ take splicing / overuse of compression are rampant, and every popular artist
is basically as fake as Milli Vanilli. Protools has raised a generation of
lazy and uncreative musicians with awful rhythm. Get off my lawn! Ok i'm done.

~~~
TheOtherHobbes
Microtonal music really isn't hard to find. It's just not very popular,
because it's too niche for mainstream listeners.

And most popular VSTs - Serum, Pigments, Massive, Phaseplant - all use
wavetables and not 'the same old square and saw waves.'

Modern pop really isn't any more generic than 30s/40s jazz, 50s rock and roll
and bubblegum, and so on. That's why it's called popular music and not
experimental music.

~~~
thanatropism
There's a def "greatest hits" effect with jazz. I mean, how awesome is "Minnie
the Moocher", etc.

There's also a "trailblazer" effect which is kind of weird because it doesn't
happen in classical music. Namely that we listen a lot more to Miles Davis and
Coltrane than the random swing band of their age. Heck, Miles gets more props
than the sublime big band swing of Duke Ellington.

~~~
deirdresm
Honestly, out of all the things I've been paid for over the many years of my
career, the one that gives the the most pleasure, thinking back, is being paid
as an extra for The Blues Brothers.

Watching Cab Calloway do Minnie the Moocher in the 70s? Live? Paid for it?
Priceless.

Working for Apple was awesome, as were the other places I've worked, but for
sheer enjoyment per dollar, the Palladium in the 70s wins.

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dehrmann
> 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.

~~~
nicetryguy
> 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
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
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
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.

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mikorym
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.

~~~
jmiskovic
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
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.

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

