It sounds mathematical in some ways (there are certainly numbers in there); but when you look closer it's inconsistent and/or just plain weird.
When you start writing code working with scales, intervals, triads, seventh chords, etc., the oddities really become obvious. The base unit of movement is the half-step; but the full-step is almost a useless concept -- a major scale is a seemingly random pattern of half and whole steps, major and minor intervals included in it. Whole notes refer to note duration. A whole tone scale is about the intervals between pitches. Looping the pitches from G back to A, but most starting counting at the C (for the simplest major scale).
There are historical reasons for the oddities; but it wouldn't be too hard to come up with better... it's much like language that way, though. Think of all of the inconsistencies in English -- yes, we'd be better off in many ways if we could just fix all of the broken bits (e.g.: the past tense of "lead" is "led", but the past tense of "read" is written "read"... but pronounced "red"). But we can't -- because everyone's using the broken version, there is a huge corpus of knowledge written in the broken version, etc. etc..
I read about a thing called hummingbird notation - uses the same clefs, but changes noteheads, staffs and sharps/flats. Your opinion may differ, but here is a group of folks who spent a lot of time coming up with a "system" and it does not strike me as an improvement.
Have there been other attempts?
I have fewer problems with notation than with theory terminology & concepts, personally.
There are alternatives that get a lot of use -- esp. TAB and various types of chord charts; but they're not as general purpose as standard notation.
In addition to the amount of existing literature, there's also the matter of developing the skill to read it. I'm tethered to "standard" notation because I developed fluent sight-reading ability as a kid, and I continue to practice it. I daresay that learning a new notation system would be virtually prohibitive at my age.
Every town has a cadre of musicians with similar skills, which in turn creates an incentive for composers and arrangers to continue using standard notation. And some notations are considered to be useful for one thing but not another. For instance, tabulature is used for teaching the electric bass, and documenting transcribed bass lines, but nobody can sight-read tab well enough for it to be an alternative to standard notation for performance use.
I actually had such an experience not too long ago. I play mostly jazz, which has its own notational traditions. But a bandleader hired me, who had her repertoire written out using the Nashville Number System. Though her charts were simple, my brain had to work in overdrive for that entire gig.
It's pretty much what you'd expect, zero-based integers that represent semitone intervals. Sometimes they write chords in curly brackets, like {0,3,7} for the major triad.
Integer Notation also happens to be pretty much equivalent to the 0-127 based MIDI notes--in the sense that it's also zero-based integers representing semitones.
https://en.wikipedia.org/wiki/Integer_notation actually redirects you to "Pitch Class". Also very useful and mathematically sound, it's the same idea but with modulo-12 arithmetic.
There's also a concept known as inverted intervals, which are formed by moving downwards instead of upwards. The inverse of a major third is a minor sixth, because that's the interval you get (modulo octaves) by moving down a major third from your root note. The inversion n is given by 9-n. With zero-indexing, inversions would be given by simple modulo seven arithmetic.
How would that be better?
>The inversion n is given by 9-n. With zero-indexing, inversions would be given by simple modulo seven arithmetic.
Again, how module arithmetic is simpler than a simple deduction from 9?
It would be better because a fifteenth is a double octave, but eight times two is not fifteenth.
> Again, how module arithmetic is simpler than a simple deduction from 9?
Because you'd be able to base both concepts on octaves (well, renamed to sevenths) being seven steps on the scale.
How undiscoverable? I grew up in a fairly music-oriented family and played a lot of instruments as a kid, but didn't formally study music theory. It wasn't until I read parent that I realized "fifth", "third", etc. are 1-indexed ordinals, and not some inscrutable scheme involving fractions. Everything suddenly makes way more sense.
I feel fairly confident that sane terminology would greatly ease this problem.
I don't doubt that it could be improved, but I don't think it's all that bad, considering how many people do learn music theory.
Maybe not for you, but it certainly took me a moment to convince myself that that is true.
Anyway, yes, you've shown correctly that mod 7 arithmetic is useful, proving half the great-great-somethingth-parent's point. Now, the remaining interesting cases are the inversion case and the multiplication case, where 0 based is simpler (for me) than 1 based.
Also, the idea of using the word "octave" for "mod 7" is already pretty broken, and is what caused me my initial hesitation.
Coming from a family of musicians and artists, it's all pretty foreign to me. And I used to take lessons, and occasionally sit and work my way through a beginner guitar book. I've always heard music theory to be pretty obtuse and challenging. I'm sure if I put in some hours to understand the fundamentals it'd make a lot more sense, and read it at home with a little dedication it'd be a bit easier. It's truly interesting.
[0] - https://www.youtube.com/watch?v=pF8oIKLlBsI#t=132 [1] - http://www.imdb.com/title/tt0115819/?ref_=fn_al_tt_1
A Major 10th mod-7 is a Major 3rd regardless of zero or one-based indexing, the only difference is which notes in the current key you're actually talking about (in the key of C it would be E or D for one-based and zero-based indexing respectively)
I don't know that it's any easier to remember "the tonic is 0" than it is to remember "the tonic is 1"
If you are concerned about that, then wouldn't calling an octave "a seventh" (your proposed fix) be equally concerning? Eight (octave) is not seven.
The fact that this interval of seven notes is called an "octave", named after the number 8, is entirely because of our 1-based system that double-counts the note you start on.
If we had a 0-based system, it wouldn't be called an "octave". It would be named after the number 7. Let's call it a 7-interval, to avoid confusion with actual music terms.
In a 0-based system, you could say, for example, that two 2-intervals make a 4-interval because 2 * 2 = 4.
In the 1-based system we really have, you have to say "two thirds make a fifth", and the mathematical connection is not obvious.
What do you suggest? We could invent new words - great, instead of an octave we now have a zargablub. Not terribly helpful.
Or we could give concepts more explicit names - instead of octave, we now have interval-between-two-pitches-with-logarithm-base-two. But all the experts will soon abbreviate this to something else, and soon enough we'll have the same problem we started with.
Or we could try to find a modern word that explains the concept better than the legacy one, but that means that all material from before the change is going to become very hard to understand unless you know all synonyms for a given concept. And since language is always evolving, in 50 years people will complain that your once modern and easy to understand word is now obscure terminology.
Really, what do you suggest? Jargon is hard for the newcomers, but there's a reason it exists- it enables experts to communicate clearly and non ambiguously about specific concepts and ideas. It's infinitely better for things to be hard to get acquainted with in the first 6 months, and then you get to used it, than to have a field where no progress is made because no one can communicate.
It's kind of like software, actually - these days, it's all about ease of use and being able to pick up an application and use it in 5 seconds flat without having to read a manual. Which is fine if your software is Snapchat or Instagram, but terrible if you're building a synthesizer or video editor or statistics package. In some cases, it is worth having something that's hard to learn but is very powerful once you've gotten past the initial hurdle, because while you will only be a beginner for a short while, once you are past that you will be an expert for the rest of your life. (these ideas are developed in Jef Raskin's The Humane Interface)
So there is a certain usefulness to it, and I comfort myself by knowing that our words are mostly all arbitrary anyway.
Also, it's totally fair to raise an issue without having a solution or suggestion. And the lack of one doesn't make the issue less valid.
And "zargablub"? Straw-man territory...
Sure it's fair, but is it helpful? I guess in some way it is helpful to raise awareness of the issue but then what? We all stand around with our hands in our pockets, whistling away.
Organic is usually better than "master planned". Evolution et al...
I'll be your first, then. Agreed.
> ... I believe they developed their overall understanding almost independent of the terminology, ....
That certainly happened here. E.g., that (say) 2^(4/12) is pretty close to 5/4 is an interesting fact that requires no knowledge of music terminology to grasp. That we call a pair of notes whose frequencies are roughly in this ratio a "major third" is just trivia to memorize.
For musicians, this is actually precisely opposite. Performing and composing musicians absolutely never use the ratio of fundamental frequencies. They constantly use thirds and think of them as the third note in the major scale, which is the most common scale.
Personally, I find most music terminology to be fairly decent, but I grew up with it, so perhaps I'm the type of person you describe. There is some ambiguity in terminology, some of which is inherent in the dual usage of certain harmonies (is it an A minor 7th flat 5, or a C minor 6th?), and some of which is simply the historical result of competing notations (is it a diminished 7th or a minor 7th flat 5?). However, I think most of the terminology is at least somewhat self-hinting, and the weird random names are few enough to be memorized or looked up when needed (like all the Italian words to notate dynamics and tempo). It certainly doesn't seem particularly worse than the terminology used in, say, computer science or computer programming.
The other reality is that we tend to teach theory from a perspective that explains simple music and progresses to the more complex, and then chronologically. This may be helpful for practicing musicians, but it does little to explain how the fundamental tonal concepts for together (scale structure, harmonic progression/voice leading, timbre, and tuning).
I'm intrigued, got any more info or links on what sort of big steps have been made in the past decade?
Not really. At least in Europe, and at least for the last couple of centuries, musicians learned and developed their understanding of music through studying its formal theory and terminology.
The only exception was autodidacts, which through common in folk music traditions, was not common in urban environments in Europe for classical or contemporary popular music.