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.
Replacing standard notation for all uses may be doomed to failure, but replacing standard notation for some particular use case (especially new use cases that weren't anticipated when standard notation settled into its current form) may be a very useful thing to do.
Computers also give us a few new options, such as displaying notation in a time-varying form, or using three dimensions, or notating the music in some universal language that isn't necessarily easy to read but that can be easily rendered in any desired notation.
Lattice notation for instance is something I really like, but I don't know how to represent it without some kind of animation.
Lattices generalize to higher dimensions, which means they might be amenable to virtual reality or even some sort of human-brain interface that allows you to experience 4 or 5 spacial dimensions at the same time.
> 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 wouldn't call those replacements for standard notation though. Both notations exist, both serve different purposes, neither is going away, there's no either-or question to be resolved.
The lattice videos are super interesting! Thanks for sharing that. I want to watch a few more and understand his layout choices -- I think I kinda get it, triads form triangles. These don't encode anything temporal though, so this is a visualization that helps understand harmony spatially, but is not a musical notation and can't encode a song, right?
> 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 (which uses lattices extensively to explain harmony and is the best reference I know of for explaining how to understand them): https://www.youtube.com/watch?v=I49bj-X7fH0
A 3-5 lattice is a grid where one axis is fifths (powers of 3 in just intonation) and another axis is major thirds (powers of 5). Garrett implies a third axis for septimal flatted seventh (i.e. barbershop 7th) intervals. Since the grid is leaning to the right, the diagonals that lean the left are minor thirds. Powers of 2 (octaves) are usually ignored. Triangles that are flat on the bottom are major triads. Triangles that are flat on top are minor triads.
There isn't an obvious way to encode a whole song onto a single lattice diagram in a way that could be printed on a page and still be readable. They seem to work pretty well as animations or as static illustrations to explain chord transitions, though.
> 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.
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?
It's a way to identify distinct pitches that are usually treated as the same in equal temperament.
For instance, in just intonation 2 (the major second of the scale) has a frequency that makes a ratio of 9/8 relative to the tonic, but sometimes you might want a slightly flatter major second with a ratio of 10/9. So, that note is label 2- to distinguish it from the regular major second.
Replacing standard notation for all uses may be doomed to failure, but replacing standard notation for some particular use case (especially new use cases that weren't anticipated when standard notation settled into its current form) may be a very useful thing to do.
Computers also give us a few new options, such as displaying notation in a time-varying form, or using three dimensions, or notating the music in some universal language that isn't necessarily easy to read but that can be easily rendered in any desired notation.
Lattice notation for instance is something I really like, but I don't know how to represent it without some kind of animation.
Here's an example I stumbled across on Youtube awhile back of the kind of thing I mean: https://www.youtube.com/watch?v=jA1C9VFqJKo
Lattices generalize to higher dimensions, which means they might be amenable to virtual reality or even some sort of human-brain interface that allows you to experience 4 or 5 spacial dimensions at the same time.