Guitar Decomposed: 5. Mutating the Third
bartoszmilewski.com
bartoszmilewski.com
> 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.
Of course it's not going to be perfect, but it's still closer to 12TET-with-noise than some specific mediaeval tuning.
There is an attempt to tune guitars close to equal temperament trademarked as True Temperament:
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.
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).
https://qph.fs.quoracdn.net/main-qimg-659a2269b3cf8608d61d56...
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.
https://www.ethanhein.com/wp/2019/jacob-colliers-four-magica...
That's just the beginning. He posts long breakdowns of his tracks on YouTube explaining everything he does in detail. He's not only a musical virtuoso, but he's incredibly adept at recording and Apple's Logic/tech in general, so he's able to blend those skills seamlessly.
With Jacob and others getting people interested in tunings and unusual harmony, there are now lots of people on YouTube creating music that exploits shifting tunings or alternate systems like 24TET, etc. So to the grandparent post, don't worry - there has never been a time when so many young people are playing with and exploiting tuning systems to create interesting music.
I don't know this to be true, I see people building weird musical instruments all the time. As for electronic sounds (it's not always digital) the modular community is absoultely teeming with expression. Here are some fun guys: https://youtu.be/AGN5N4vn5Bs
[0] http://www.garygarrett.me/?page_id=1922 [1] https://youtu.be/jA1C9VFqJKo
This is not possible with purely technological means. To "retune" and "adjust" even a single piece of music in a way that approaches just intervals you'd need an in-depth analysis of all meaningful dissonances, consonances, modulations, perhaps repetitions/imitations etc. etc. in the actual piece; and these are often not even evident from the actual notes because all music uses ornamentation at a variety of levels, hence lots of judgment calls are involved in the process. Where instruments are easy to retune in a flexible way (not really true of guitars, due to the use of physical frets) and the actual music allows for it, performers do use alternatives to equal temperament, such as a variety of "meantone" temperaments.
Yes, but almost nobody is dropping raw 808 kick samples onto their tracks. Even though it's a "traditional sound", usually artists do quite a bit of work to transform it. Kind of like what, you know, "real" composers do with "real" musical traditions.
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.
Even considering the stuff that Queen did for tracks like Bohemian Rhapsody where they used dozens of layered tracks isn't really the same thing. They used that layering to create a sound that wasn't possible, otherwise. But the tracks themselves were made from recording real people playing real instruments.
Modern pop, in comparison, is just about commoditization, slapping out a track at as little cost as possible. Everything gets lined up on a rigid beat grid, neutering any texture or feel in the song.
Rick Beato has a great video on what exactly is going on and why there actually is a significant difference with "post-ProTools" pop from previous years. https://youtu.be/L-8EbHkc8tc
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.
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.
Go listen to some of Dimebag Darrell’s solos. They sound ridiculously bad if played in whole semitones. Fair enough, he’s fairly bluesy. But other genres of metal give the distinction you give the left hand to the right too - variations in pick attack wildly change the sound.
I’m guessing it’s fair to suggest that similar things exist in all genres of music, and on all instruments.
And how about the whammy bar? Maybe guitarists aren't consciously using it to untemper their intervals, but to say "rock guitar" is locked to tempered tuning is incorrect.
Chaotic orbits for "waves", running audio through cmos gates to produce pitch changes, running ADSRs through a filter to produce more random envelopes,... and he seems to come up with new module ideas monthly if not more often.
My most favorite recent module of his is based on cellular automata.
Unfortunately some sound examples are missing but a few of them are still online.
BTW, Sethares' research https://en.wikipedia.org/wiki/William_Sethares goes way beyond tuning music to simple ratios. His whole book is about working with a model of sounds being "in tune" with one another that doesn't just boil down to that.
You should explore more electronic music. This is either an intentional attack or an ignorant statement.
Edit:
> musicianship has all but died in Gen Z
See South Park S15E07 "You're Getting Old"
Actually, the way a piano is tuned is pretty funky.
The rigidity of the strings means the higher 'harmonics' of a note get sharper and sharper. If you tune the fundamentals to exact equal temperament a piano sounds out of tune, because the upper partials of lower notes are pretty sharp versus the lower partials of higher notes.
Hence the frequences of the fundamentals are stretched out such as to get the inharmonic partials as in tune sounding as possible between different notes.
This is why you hire a piano tuner to tune your piano.
Idk... I think it's more about the hassle. People I've known let their piano get really out of tune (like we are talking a quarter tone off for some tones "just avoid those"), to the point where their own amateurish tuning would be a big improvement, before they call the tuner over.
The lowest notes, generally have one string that makes the note. The middle, have two strings (persumably to make it louder).
the high notes have 3 strings per note.
So sometimes playing one key is actually playing three tones.
Pictures from a violin/piano maintenance building school make it a little clearer: https://www.nbss.edu/full-time-programs/piano-technology/cur...
I have an electric, but, yeah, point taken. And half the time I have it set as a harpsichord anyway.
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, right when he sings "when September ends," but there's are so many other examples.
Yeah, exactly my first thought, pick any Beatles, Pink Floyd or Radiohead album for the most mainstream, off-the-top-of-my head examples.
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.
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.
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.
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)
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.
So yes, you ask a good question, but in fact there is some knowledge of the hardware which supports the empirical observations of musicians and composers.
and yes, music is still a mystery. There is a lot more going on than scale, pitch, and harmonics.
But it's lowered by a half step...
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.
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.
(Spoiler: lots of historical context about tuning systems, but also raising the issue of timbre of specific instruments)
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).
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.
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.
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.
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.
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.
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.
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.
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.)
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?
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.