Why aren't notes and intervals plain numbers?

Beginner question:

If we were to leave the historical context aside and redesign the system of musical notation: would we base this around the 12 steps we've divided octaves in?

What strikes me as very confusing and weird is that the notes and intervals (and even the layout of some instruments like the piano) is based around the major scale.

Am I correct in assuming this is just born from the historical context, where perhaps this 7 notes array is all there was, or is there any other reason?

Could we simply call the notes by numbers and their intervals maybe in flat ordinals (or the other way around)? What would we lose by doing that?

It would be awesome if answers can cite technical advantages of the current system vs flat numbers (I already assume a great deal of what we have nowadays is historical, but it's still a struggle for every beginner, I wonder if there are other reasons)

Edit: I'm interested in finding motivation to study theory, but I'm having trouble getting over the feeling that it's way more complex than it should be, so any argument helps

• Does it make a lot of sense to cite technical advantages when the field is primarily artistic? What’s the advantage in using numbers to distinguish notes? I have a degree in mathematics and even I don’t like numbers that much. Aug 14, 2018 at 23:43
• @ToddWilcox ha! valid point. I think the distances are inherently and intuitively mathematic: if you named the notes from 1 to 12, the distance between note 3-7 will be (7-3) or (3+12-7) in inversion I'm just a bit sad that this is so easy to figure out mentally but I'm probably months away from doing that mentally and quickly with the standard notation. So I want to convince myself it has a reason other than "it's the way it is" to motivate me to learn I'm an engineer btw, weirdly enough I do like numbers when they seem to make sense to use Aug 15, 2018 at 0:03
• numbers are used heavily in modern atonality (pitch set classes), rhythmic analysis ("The Geometry of Musical Rhythm", Toussaint), and the somewhat older art of the construction of canon ("Technique of Canon", Norden) Aug 15, 2018 at 14:59
• There are also significant mathematical relationships between the frequencies of notes when the 12 note octave is used (going up an octave doubles the frequency). Numbering the notes might be quite confusing given the instrument-specific roles of numbers. Music has a lot of sets of information, and in many cases has to use different numeral systems to express different cardinal values (Roman numerals are used for positions on guitar whereas Arabic numerals are used for fingerings). There is an argument to be made that using numbers might actually make music more confusing. Aug 16, 2018 at 0:44
• @Ambluj thanks for your input! I could argue though, that the frequencies increase logaritmically, so this would even generate a direct relationship between the note and it's frequency Think about this: what if we name them in base 12: "0123456789AB" We could name the octave directly in a compound number eg: 7A is the A note in the 7th octave. This notation would also be directly linked to the log of the frequency, would it not? Sorry for the random thought :) Aug 16, 2018 at 0:59

Western music makes harmonic sense in relation to diatonic scales. A simple-minded accompaniment to nuersery school kind tunes is singing a third or sixth above or below. That's conceptually simple but it doesn't map to a simple concept in chromatic intervals: you get a haphazard sequence alternating between minor and major thirds (3 or 4 semitones). Trying to play this kind of thing on an inherently chromatically organized instrument (like a chromatic button accordion) takes quite a bit of practice.

And if you want to analyze that kind of stuff (as well as the harmonic frame a melody moves in), there just is no way around relating it to the diatonic scale it is based on. There are a few instruments with uniform keyboard layouts: apart from the mentioned chromatic button accordion, there is the Jankó keyboard for pianos. Their principal advantage is that they make transposition easy and thinking in semitones. This advantage was not enough to let the Jankó keyboard survive/thrive compared to the disadvantage of not being related to any diatonic scale (which our notation is based on as well as our harmonies). The chromatic button accordion is basically the only thriving member of uniform keyboard layouts and that's mainly because it's so much more compact than a piano keyboard, making a better fit for the instrument class.

So in short: it has been tried. There were lots of treatises particularly around the musical theoretical advantages of the Jankó keyboard and predictions that everybody would be using it. This hasn't happened.

For better or worse, Western music (several developments outside of the classic frameworks aside) is rooted in diatonic scales and trying to ignore this is a hindrance rather than a help to understanding.

• Thanks for your insight! I'd like to note that from my POV most string instruments are also equally distributed in semitones Actually I think fewer ones have the diatonic scale so baked in like the piano If you have other examples I'd be really interested in knowing them Aug 15, 2018 at 12:55
• Thanks for your participation and contribution "user52307" ;-) Plus 1 (but who's counting numbers?). Aug 19, 2018 at 17:57

You are correct- the reason standard notation is not orthogonal (i.e. a step can be a half tone or a whole tone (or more or less, with accidentals) depending on where it is on the staff, clef, and key signature) is historical. In some sort of orthogonal notation it would certainly be easier to learn the intervals.

But that's not all there is to reading music. As Todd mentioned in the comments above, reading music has more to do with art than technical advantages. And the art of Western music is still, even today, mostly based around scales that have the same pattern of whole and half steps they did when notation was being developed. This pattern is built into the standard staff notation, so you can depict music from Bach to the Beatles in a way that's easy to read.

Sure, there is the drawback you mentioned: there's a fair amount to learn. And an orthogonal system would be simpler for twelve-tone music. But for the bulk of the music most people do, standard notation is pretty hard to beat for readability. And that's what notation is intended for: not for easy frequency analysis, but for musicians.

• So, when you say "readability", you mean that the current system is compact in notation? I can't disagree with that, getting a system where we give all notes the same importance to work with notation would definitely be a challenge, so here's a valid point in favor of it, thanks! Aug 15, 2018 at 12:57
• @Alvaro - If I understand correctly what you mean by "compact", I agree. Standard notation is biased towards heptatonic scales, of the pattern WWHWWWH, starting at any point, and these scales make up the bulk of Western music. Aug 15, 2018 at 15:20