I don't agree that this is an improved notation at all.
It has its advantages, it highlights the physical distance between notes in a uniform way across key signatures. But it obscures harmonic function, which is much more important.
Array indexes starting at 0 is unintuitive for beginners, I would never recommend a programming student learn arrays starting at 1 just to make it easier.
Proper playing technique is often unintuitive for the beginning musician, but encouraging it for accessibility will be destructive to their progress.
Conceptualizing a new difficult concept in a way that makes sense to you is good, foregoing convention is bad.
There are some people, maybe not many, that have a difficult time trying something new unless they have something familiar to form a relationship, even if the relationship is inaccurate and requires iterative improvement.
We might say, that finding the Rosetta Stone hindered those who knew Greek trying to learn hieroglyphs.
I was deathly afraid to try woodworking until someone showed me how to construct familiar angles on the machines using basic trigonometry. After I had a tiny relationship formed, I was able to experiment on my own (and then adopt woodworking vocabulary, to become entrenched in that community).
I think using some arithmetic rules to entice someone who knows arithmetic, but otherwise is awkward around music theory, is an agreeable compromise to get them on the way.
> I think using some arithmetic rules to entice someone who knows arithmetic, but otherwise is awkward around music theory
The biggest win from that POV would actually be numbering the diatonic scale degrees starting at 0 for the tonic, and the diatonic intervals starting at 0 for the unison. Unfortunately, it heavily conflicts with all sorts of existing notations. But once you think of the third as a "2" interval, the fourth as a "3", the fifth as "4" etc. you can arbitrarily add intervals together and to scale-degrees, without having to constantly correct for the archaic 1-based counting.
So you would subscribe to the notion that BASIC is not a proper introductory language because it hides some of the theoretical CS complexities while exposing the lowest hanging fruit to beginners?
I wasn't introduced to programming through BASIC so I can't speak to your analogy, but I believe you've taken me to say "hiding complexity is wrong." I don't think any point that I've made can be interpreted this way. There's plenty of low hanging fruit for beginner music theorists. "V7 resolves to I" is low hanging fruit, and it has tons of underlying complexity that you don't need to understand as a beginner. It's understood by every educated musician. My point is that if you want to be understood by other musicians you should learn this:
There's actually established notation in music theory for this[0]. Because it IS a super convenient way to look at notes. Doing otherwise would be akin to using Roman numerals for calculus.
From personal experience, I worked with this notation a little bit. I spent a lot more time getting the hang of traditional notation. Not only is integer notation intuitive immediately, but number combinations like {0,4,7,12} become memorable very quickly and yes when I look at it (even if I saw it outside of musical context!), I would know it's a major chord.
That is, personally, I learned about the traditional notations (because you can't learn music theory and avoid those, or miss out on most of the material :) ). But that took me deliberate effort. On the other hand I wrote some python classes for converting between notes and chords and traditional notation and integer notation, seeing the patterns in those numbers required no effort at all, it's right there. The traditional notation has of course the same patterns, but they are obscured by layers of translation.
I think integer notation could be used a lot more, especially when teaching music theory. But traditional notation is also useful, partly because many people know it, partly because integer notation is less suitable for certain instruments.
This is very nice example of the contrast in the two nomenclaturess, so thanks for that.
The problem with "V7 -> I" is precisely that it hides all the internal structure and encourages rote learning. Rather than encouraging the musician/composer to think about what that resolution actually consists of in terms of shifting intervallic relationships within the chords, it encourages you to just learn the transition itself.
Which of course is also its strength!
You might think that after centuries of musical composition across many different cultures that we'd have fully explored all the 4096 scales that exist within 12TET or even all the 4096 scales that exist for any given 12 tone tuning system.
But this is far from the case - witness how revolutionary Messaien's modes were. The conventional language is great for conveying meaning/intent/practice if the goal is to remain solidly inside the parameters of western musical practice circa 1100 to the present day.
But it's fairly inadequate if your goal is explore the rest of the music possibilities presented by psycho-acoustics, or even just those derived from (say) musical cultures which use microtones.
I also note that there's not a single comment in this thread regarding rhymthic structure, again reflecting the western emphasis on a particular (simplistic) understanding rather than the highly developed music cultures built around rhythm across Africa and Asia.
> I also note that there's not a single comment in this thread regarding rhymthic structure, again reflecting the western emphasis on a particular (simplistic) understanding rather than the highly developed music cultures built around rhythm across Africa and Asia.
This is so true. I've been wanting to learn about rhythmic theory for about as long as I've been studying music theory (harmony). But while you can find youtube videos and webpages full of explaining musical harmony all over the place, information about rhythmic theory is far and few between.
Most I've been able to find is either very abstract, like Euclidean Rhythms, which are interesting and weird but only explore equidistant grids (no swing). The other information is usually about really specific cultural rhythms. Both are good and useful, but I feel like they combine into less than 20% of the total theory about rhythm that I believe should be there. There's really a lot to it and I'm still looking for some fundamental theories about repetition and expectation and tension/release. The latter is very important in rhythm, but as far as I'm aware, the music theory about harmonic tension and release (chord progressions etc) seems so much more complete than what I've been able to find about rhythm.
Nonetheless I do think that music theory jargon is too dense and could do with some reform in terminology and notation. A lot of obscure terms could possibly be replaced (longer) plainspeak terms that expresses their function and meaning. At the moment, though a good concrete example eludes me, perhaps be something in lines of 'scale' -> 'basis', 'tonic' -> primary, etc..
Without a good concrete example, this sounds like a terrible idea.
Scale -> basis makes no sense to me. The scale climbs up and down, like how you scale a ladder. The basis… does not do that.
Tonic, dominant, subdominant are used mostly in discussions about functional harmony. The biggest reason why it would be a total disaster to rename tonic -> primary is because we already use the terms primary and secondary here! For example, V is the “primary dominant” but nobody actually says the word “primary”. Primary chords are taken from the scale of the tonic, and secondary chords are taken from a different scale. So V/V is a “secondary dominant”.
Perhaps 'ordered basis' for 'scale'. Or perhaps 'discrete spectrum', just searching for a term that conveys its meaning intrinsically.
I had in mind a reform akin to how modern lisps have rename CAR and CDR to first and rest respectively. For example the Lydian Mode, could be referred to by a codeword that can be unwrapped to understand what exactly it is.
In general I am always in favour of trying to advance the expressiveness and meaningfulness of notations in all fields, and I think that is something that should be continuously evolved, trying to find better way to say things.
Scale is nice and short, it’s one syllable, and it goes up and down like how you scale a ladder. “Ordered basis” and “discrete spectrum” sound outright hostile to me. We want to make musical scales accessible to five-year-old kids here, not undergraduate math students. This is not the way terminology should evolve.
I can get behind car/cdr -> first/rest.
I could get behind renaming the modes, but I’m not sure how to rename them. I would be hesitant to name them after notes or using numbers, since that would be confusing. As it is, I can say “C dorian scale” and that’s a pretty concise and unambiguous name for a series of notes. Maybe I could say “C minor, natural sixth scale”. It’s a bit verbose and modes are fairly rare. It’s also a bit weird—would I then say “A dorian scale” as “A minor, sharp sixth scale”? Already I’m a bit confused by this terminology. Maybe “A minor, major sixth scale”? The “major minor” is a bit weird.
The trick with advancing expressiveness and meaningfulness is that 1) you are going to have to memorize new meanings even if the words are familiar and 2) if it’s not usable by experts, it won’t be adopted by experts and you’ll end up with at worst, multiple incompatible sets of terminology.
Face it—I’m going to have to do a fair bit of memorization to learn music theory. It is unavoidable with music theory as it is with other subjects. So I might as well pick nice, short words like “scale” which make some intuitive sense, rather than pick “ordered basis” which is a total mouthful. After all, I will only spend a short amount of time memorizing terms, and a much, MUCH longer time using them.
As I said in my other comment, I had to do a lot more memorization to learn to recognize typical patterns (like chords and scales) in traditional notation, while integer notation ... well, for starters I just about came up with it myself, before I learned it's (of course) an established way of notation in music theory. Second I just wrote some code to play around with the numbers, basically for myself to try and make sense of the traditional system, because it seemed (to me) easier to convert the bunch to numbers and see what chords come out. What happened is that, really through no effort on my own, I started recognizing the numerical patterns for what they mean in musical theory.
It's really that much more intuitive. Give somebody CEGC' and GBD'G' or give them {0,4,7,12} and {7,11,14,19}. And as a bonus, if you can read clock, you already know how to do modulo 12 arithmetic! 14:00 is 2pm, 19:00 is 7pm, therefore that last one can also be written as {7,11,2,7}.
I don't want to do away with traditional notation, it has its advantages. But I do think that integer notation can be used very effectively and should be used more, when teaching the fundamentals of music theory.
I’m familiar with this already. It’s unambiguous but it’s fairly verbose. Our notation already places the diatonic scales in a privileged position, so it makes sense that we have special names for modes of the diatonic scale.
The system is most useful for describing / exploring certain types of atonal music. I’m going to make an unfair generalization—most people are interested in tonal music. You can see that the references here are to Forte’s The Structure of Atonal Music and Rahn’s Basic Atonal Theory. So if that’s your jam, by all means, go and make atonal music. But I’m a fan of using modes of common scales, so I like having concise names like phrygian, mixolydian, and dorian.
So my own take on this is that it's not really about atonal music at all. The musical universe in which this is presented (certainly in the article I referenced) is already using 12TET, and where a specific scale (of the 4096 possible) has a known name in 1 or more cultures, it is cited (this includes the western "church mode" names that you mentioned).
It's still unclear how much "tonal music" is simply a shared set of cultural assumptions and practices, and how much arises from acoustic physics and acoustic perception. So ... rather than a priori priviledging a specific group of interval sets ("major", "minor" plus "a few modes"), why not start by exploring the full universe of all possible (12TET) interval sets (aka "scales"). By using an explicitly mathematical approach one can bring some analysis techniques to bear on the "full universe" that are not readily available when stuck in traditional western theory and notation. To me, this approach accomplishes two things. The first is that it offers a bridge to non-western musical traditions. The second is that it offers a common core from which to understand both "tonal" and "atonal" music, particularly their similarities and differences.
Finally, its a particular bug of mine when people connect "modes" and "scales" as you do in the your final sentence. What is important in (almost) all musical traditions are not the specific notes used to form the pitches that make a piece of music, but the intervals between the pitches, and their ordering. There's significant evidence that we are vastly more sensitive to relative pitch (intervals) than absolute pitch - play the same series of intervals starting from a different tonic/root and we experience it in almost the same way. Change the interval series (i.e. the scale), and we hear a much more noticeable difference. So, the major scale is just an interval series, and the "modes of the major scale" are also just interval series. There is no inherent relationship between them, other than one can construct them by rotation. The modes do not "belong" to the major or minor scales, nor vice versa (indeed, in fact the major and minor scale are just modes too ... just an interval series).
And now really finally: we actually don't have special names for most of the possible interval series that can constructed from the diatonic notes. We have a very limited number, and from my reading and understanding it is unclear if the ones we have names for are priviledged by physics and perception, or are mostly the result of historical precedent.
Array indexes starting at 0 is unintuitive for beginners, I would never recommend a programming student learn arrays starting at 1 just to make it easier.
Proper playing technique is often unintuitive for the beginning musician, but encouraging it for accessibility will be destructive to their progress.
Conceptualizing a new difficult concept in a way that makes sense to you is good, foregoing convention is bad.