The best part is there’s a third layer here where these beautiful symmetries between science, math and art also can come up again and again as they share mathematical descriptions to the point where one can influence the understanding of the other. So putting on my former reformed scientist hat, I totally get where Jörg was going with this 
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This thread got pretty deep!
I personally have a kind of engineering mind so when I want to “show off” I tend to be more mechanical and understand what I am doing and why it sounds the way it sounds.
So I am trying to think as quick as possible, where are new chord tones (1 3 5 7) relative to where I’m at in the current chord, and how to get there.
The easiest way I’ve found to do this is just to drill arpeggios in every key every day. I’ve started immediately jumping to anchor points I never had before, like “I’m moving to G, so there is… oh D is next to my finger” but this isn’t a long thought it’s just becoming really fast.
That thinking combined with “is it a good idea to stay in this position right now” kind of drives how I improvise / “wing it” over a song.
I always think the term “Nashville Numbers” is weird because the key and chord both have “numbers” associated with them, but usually you are well aware before hand of how the chords are planned, ie 1 4 1 4 1 1 1 1 1 4 1 4 4 4 4 4, and I try to keep “where in the chord I am” in my most active memory.
So I just try my best to really break every chord into notes and notes are all over the fretboard. F A C E there’s a ton of those and “shapes” associated with wherever they are.
F A C E into C E G Bb ? (1 → 5) It’s almost like a mini game. Half your chord is already being played so your change is either approaching G or Bb? It all depends on the music. Writing like this is much easier than doing it on the spot 
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I knew you were… your statement just seemed both so off-handed and deep at the same time… and it reminded me of Plato’s Theory of Forms (and the famous Allegory of the Cave).
For everyone so inclined, here is a good intro to those ideas:
Otherwise, they are also at the core of Neal Stephenson’s fantastic (but rather difficult) read “Anathem”:
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At home practicing I’d geeked it out sometimes with scales and modes but live on stage I’m all muscle memory and instinct, hit or miss I don’t think about what I’m going to just let it happens.
Bad things can happen when you anticipate your next move worse concentrating hard on whatever you are doing at the moment. The fastest way to skip out of the pocket is to ask yourself this simple question “Am I alternating my plugging fingers”. Try it and watch yourself fall apart and imagine asking yourself that while performing live 
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Lol! Yes I do this mistake sometimes… "Am I getting lazy and playing with 1 finger really fast? Should I just keep doing it? No… it must go back to playing correctly… wait what beat am I even on was that the chord change?!!
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Wow, that’s hilarious and sad at the same time.
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Not sad really (funny yes) that guy can play rings round me. His timing is fantastic.
He just never learned theory.
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It’s especially helpful if you play with a number of different vocalists who always want to change the key on you.
It’s also an easier way to memorize songs, IMO, and it makes the similar chord progression in different songs more obvious, especially when they’re in different keys.
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This. If you get into the frequencies of the notes, they’re not arbitrary at all. What we call the notes is arbitrary. We could’ve easily used different letters of the alphabet or something. But the notes themselves are specific and scientific, as are intervals and chords.
A video from Adam Neely really blew my mind. Sorry I don’t remember specifically which one it was. But he was diving into the frequencies of the notes in various intervals and showing how the intervals that are pleasing to the ear when played at the same time (chord) are intervals with even ratios between the frequencies.
Even more mind blowing was the talk he did on how if you speed up polyrhythms enough, they become chords. Which makes sense, as a rhythm is really a frequency, but still blew my mind because I’d never thought of it that way before.
I can give you that link:
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Comparing music to language is a great analogy! I’ll take it one step further. You could say music theory is the grammar of music.
You can speak and understand English just fine without knowing anything about grammar. But if you’re going to write a story, you’d better know your grammar!
I think music is very similar. I think even most people with no music training can hear a wrong note (especially in the bass line!), but they can’t tell you why it’s wrong or what a better note would be.
In the same way any reader can tell fairly quickly if a story isn’t good. But they don’t know why.
For casual music listeners and book readers, they don’t really need to know why. They just know what they like vs what they don’t like, what’s bad vs what’s good.
But a pro, writer or musician, needs to understand why something doesn’t work, so they can fix it, improve it, and make something people will enjoy and pay attention to.
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Yeah I only ever encountered it during voice lessons and voice classes. And The Sound of Music, of course.
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The Nashville system is nice for us non-engineers because it’s the same for any key. 
But yeah it can get pretty awkward saying like “I’m going from the 5 of the 1 to the 1 of the 5.” 
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I’ve seen this too when I performed a lot on trumpet. By the time the performance came, I had the music mostly memorized and didn’t need to think about what I was doing. It was all muscle memory by that point. And in fact if I did think too much about what I was doing during a performance, I’d screw up. So lots of thinking in practice, little to no thinking (other than counting rests) during performance.
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I just meant it’s sad because if he learned theory he’d be even better, and he’d be better able to more easily communicate with other musicians.
I’ve known lots of musicians who refused to learn theory, but I’ve never known one who learned it and regretted it. When I finally started learning it myself, I wished I’d learned it years ago.
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Proper spelling is another crucial aspect of good communication in any language.
That’s why chords written in a chart are in Roman numerals (uppercase for Major; lowercase for minor).
For example, a classic 12-bar blues chord structure would be written as I-IV-V, as opposed to 1-4-5.
In contrast, the chord tones of an arpeggio would be written as 1-3-5, specifying the first, third, and fifth scale degrees of a given key. In this example, the “3” would be either a major or minor interval third relative to the 1 (root).
Generally, if someone were to say to a bandmate, “This tune goes ‘one for a measure, four for a measure, then back to one for two measures’,” it translates to mean the I (root) chord, the IV chord, and back to the I (root) chord.
Bottom line: It pays to know how to use the Nashville system.
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I’ve fallen down a deep Wikipedia physics rabbit hole. It’s math all the way down.
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I’ve spent like $500 on math and EE/CS signal processing textbooks with an audio focus in the last six months - and I already had a background there
these little diversions can be costly
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Yup! Fortunately so far I’ve only gone to the university of Wikipedia for my nuclear engineering post-bac which is very affordable.
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Engaging Full Nerd Mode here:
One of the things I was thinking of is Spherical Harmonics. So far they have come up twice in my career - the second time when a math researcher was using them to describe 3D lighting models at one game company I worked at. I told him I was very familiar with them and he was pretty dubious as it was relatively new for graphics at the time; he was looking at the first few and was surprised I could describe what the next few looked like.
It’s because you study them extensively in Physical Chemistry. They will be very familiar shapes to Jörg.
In addition to 3D computer graphics lighting, they also happen to be the models used for the mathematical description of the shapes of the electron orbitals in molecular orbital / valence bond theory. And the biggest reason Chemistry students like me had to study math up to partial DiffEq. Which I flunked
Anyway fast forward to now and I am deep in Laplace’s math again, this time for audio programming. And struggling because of being a poor student when I studied it originally. Oh well.
The synergies and overlaps between science, math, engineering and art always blow my mind.
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