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A dozenal notation for western music (netlify.com)
45 points by sambf 7 months ago | hide | past | web | favorite | 22 comments



The thing all of these new notations miss is the fact that western music is constructed stacking thirds on top of each other.

A major chord is a root, a 3rd on top of it, and another minor 3rd (or R+3+5 relative to its root). Add another 3rd (R+3+5+7) for a major 7th chord. Add another minor 3rd (R+3+5+7+9) for a major 7th(9) chord. Etc.

This is easy to see at a glance, both in pentagram (where thirds are line-to-line or space-to-space) and solfege/letter form (where a C chord is C-E-G, or Eb for minor, but always E). This is the reasoning behind enharmonic notes like G# and Ab (same frequency, different name), so E major is E-G#-B, and F minor is F-Ab-C. Chord inversions are then super easy to identify: G-C-E is C major in first inversion.

The notation looks great for mathematical operations, but it's not a replacement for solfege as a quick reading/writing notation. It misses a lot of implicit intent.


This is like saying functional programming languages miss the fact that application software is written with objects.

Alternate approaches to notation aren't meant to supplant traditional notation. It'll be centuries before today's notation goes anywhere. It's very well established and does indeed do a good job of representing traditional western music.

New notations just make other styles of music more legible, which makes it easier to compose them, and easier to perform them.

There's no competition involved, nor anything being doomed to failure.


Sorry, I submitted my comment too early by mistake (fat finger on mobile phone) and I heavily edited it before I noticed your reply (your last paragraph won't make sense).

You got a nice point there. I guess I conflated western music with triadic chords, when in this case it just means 12TET.


Yep, this is the brilliance of the staff and the associated notation system.

All chords and scales are spelled the same, just with different accidentals. For instance, all variants of triads starting on all variants of D are spelled D-F-A. The one with no accidentals happens to be D-minor. D-major is D-F#-A. D#-minor is D#-F#-A#. D#-major is D#-F##-A#. And so on. By holding this pattern, chords always look the same on the staff no matter what key you're in, which makes reading and writing tonal music easy, once you get the hang of it. The key signature captures everything that varies between keys. Although, on instruments that represent pitches differently in how you physically play them, the difference between keys is very noticeable.

The problem with dozenal notation is that intervals have to be identified by subtraction instead of their shape on the staff, which is a lot of mental effort. That said, the staff requires its own mental effort depending on what you're doing. For example, translating from staff notation to guitar fingering is a difficult exercise in real time, which motivates the need for tablature.

For some styles of music and some instruments, I can see dozenal being nice. But for the most part, it would be more useful to use standard pitch notation (e.g. C#5), because it makes intervalic/tonal relationships more obvious, at the cost of an occasional additional glyph per note.


The one other thing I'd add about standard pitch notation is that you do have to memorize what flavor of chord each of the seven triads without accidentals is in order to infer what modification an accidental will make. But this is just seven facts to memorize, instead of unusual addition and subtraction tables.


> G# and Ab (same frequency, different name)

This is only true for equal temperament.


Is this mostly renaming the notes or is there something more? That said it is a useful way to think about some musical concepts. It's the same as integer notation for pitch classes if I'm understanding correctly: https://en.wikipedia.org/wiki/Pitch_class#Integer_notation.


Yep, seems to be pitch class notation with T and E replaced with a and b. People interested in this kind of orthogonality should definitely check out Introduction to Post Tonal Theory by Joseph Straus. Even outside of the serial contexts people traditionally associate with that notation, there are interesting things that can be done with it.


I wonder whether the author is familiar with musical set theory? This is a very rich branch of modern music theory that makes use of some very similar ideas. https://en.m.wikipedia.org/wiki/Set_theory_(music)


That takes me back! I did a lot with set theory (music) back in college.

Somewhat related to that, I had a teacher that also worked out a harmonic theoretical framework based on overall degrees of dissonance and consonance which had some relatively interesting properties for analyzing both common practice and later music within the same framework. It had something akin to set theory's interval classes, but rather than representing a pure measurement of scalar intervals, it was measuring relative dissonance of intervals and groups of intervals. The dissonance values were on an arbitrary scale, but the system nonetheless provided an interesting and different perspective on musical constructs and harmonic progression.

At the time I knew the person that put this together, I think it was his thesis that he was writing... I'll have to see what ever became of it (of course, I haven't talked to the guy in over 30 years... but hey... )


Out of curiosity, who was the teacher? I used to study this stuff and may have come across their work.


I did a quick Google and found him at: https://www.weber.edu/performingarts/shannon_roberts.html

The working paper at the time was called "Global Relative Dissonance Theory" or something to that effect. I think I'll drop him a note and ask about it. My hunch is that it didn't see much interest outside of the school (University of Utah at that time), but I also more or less left any academic music pursuits around that same time so I just might not be in the know.


This highlights the tension between wanting to navigate the instrument, easily vs wanting to understand the music easily in terms of scales and tonal theory. Standard music notation is great for understanding the notes in the context of the scales and chords that you're using, while guitar tablature is excellent at telling a guitar player how to play the notes.

As a pianist, I'm certainly not looking for this, but a piano keyboard is designed exactly the same way that standard music notation is; the notes for a C major scale are the default, and then there are the other notes that you can access differently. I would suspect that vocalists would prefer standard notation also, since their ear naturally understands things in terms of the scales that they are used to.

From talking to advanced classical guitar players, I get the sense that standard musical notation is generally preferred over tablature. They know where the notes are already, so they don't need notation that tells them where the notes are. Their chief aim is to play the music in a way that understands the material and treats it well, so for them the standard music notation that provides easy musical understanding is an advantage.

I've programmed some things that worked with music, and it's annoying to have to convert between standard notation and integers that represent unique notes. This proposed notation system might make an ideal specialized notation for programming music applications.


In guitar playing, I am constantly thinking about the distance the notes in terms of frets (half steps) but it’s relative. Making the pitch a digit where 0 is C and 6 is always f# (or whatever) doesn’t quite work with how I think musically and I’m not sure it’s an improvement.

You’re dropping the notation relating to keys, why still base it around C? I’d prefer to make A zero, or E, for guitar players.

I do like having the octave embedded in the notation.

I’m not comfortable with using 0-9 and a-b as pitch. The last two (known for hundreds of years as G and g#) stand out awkwardly.

Maybe just ditch the whole thing and use Hz.


If you take the log of the frequencies in Hz [1], then the difference between notes is a fixed step. A fixed step means that you can index the notes with an integer. So this notation is close to representing things in Hz. It's fairly easy to interpret each note as a duodecimal integer and write an equation for the corresponding frequency in Hz. BTW, why 'dozenal' and not 'duodecimal'?

A more interesting question in my mind is if you're going to change things up, why keep 12 notes per octave? Why not 8 notes per ... octave :-) Or 16?

Also, since this is a log scale, could we write a new notation which indeed does have 8 notes per 'octave', but which uses a different definition of an 'octave', and could be used to write the same music we play today.

[1] http://pages.mtu.edu/~suits/notefreqs.html


It’s the use of 0-9, a-b that I find awkward and object to.

Why not have 16 notes per octave? Uh... wow, well, because it sounds bizarre and would make it difficult to play all existing western music in addition to confusing to every musician practiced in contemporary standard music. Why not 8? Hmm. Are you actually a musician or just speculating?


Not a musician at all. See my other comment which contains links explaining the utility of 12-note octaves.


Your opinion on this resembles a blind person who has never painted deciding that painters could use 5 primary colors instead of 3. Or, maybe we should make do with 2 because it works out cleanly.

12 note octaves are not ‘utility’, it’s how almost every single piece of music you’ve ever heard was constructed. Breaking the octave into smaller units creates sounds that are off putting and unfamiliar. Check out ‘microtonal’ music. There is also Indian music that uses divisions like 20 per octave.

It seems your analysis and suggestions are based purely on mathematical concepts of this notation. However, it’s not useful to consider this this notation divorced from its implementation.



In my opinion those do a terrible job of explaining why we have a 12 note system of music.


Very intersting. I wonder if that’s the kind of mathematical tricks that yaron herman’s teacher taught him. I’ve always wondered what those could have been.

https://en.m.wikipedia.org/wiki/Yaron_Herman

Edit : so it seems that method was somethin called the Schillinger system, based on numbers.. but i couldn’t find anything more detailled online.





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