Earlier quoted context omitted.
> Another way to look at it is that the current notation system isn't the best overall, it's just the most tolerable trade-off between a bunch of mutually-incompatible requirements. Isn't most tolerable trade-off between multually-incompatible requirements another way of saying "best overall"? Totally agreed there are useful local overrides of standard notation. Tablature is one example, and there are others. I would…
> Isn't most tolerable trade-off between multually-incompatible requirements another way of saying "best overall"? I could have said that better. What I meant was that standard notation isn't better than every other system according to every metric we could use to compare such things. Gary Garrett has more lattice demos on Youtube. Here's one that's an animation of an example in Harmonic Experience by W. A. Mathieu (…
This is totally true; tablature is better for beginning guitar players to learn to play specific songs on the guitar.
The only reason tablature doesn't supplant standard notation is that the metric under which it's superior is much narrower -- it's only for guitars, and only better than standard notation for beginners.
I don't think standard notation is necessarily the best overall, by I do think it happens to be the best overall, the best we've got today. And I'm not convinced it will ever become a choice, as opposed to standard notation evolving like it has in the past to incorporate new ideas.
Thanks for the explanation of the lattic layouts; I hadn't noticed the triangle orientation part, I only got as far as seeing that horizontal lines formed the circle of fifths. I can't tell what the plus and minus symbols mean, do you know? Usually those are used for diminished and augmented chords and not single notes, so is Bb- another name for A that is useful under the lattice system?