
A dozenal notation for western music - sambf
https://dozenal-music.netlify.com/
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kaoD
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.

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swatcoder
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.

~~~
kaoD
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.

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jay-anderson
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](https://en.wikipedia.org/wiki/Pitch_class#Integer_notation).

~~~
tokenrove
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.

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lapsed_theorist
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)](https://en.m.wikipedia.org/wiki/Set_theory_\(music\))

~~~
sbuttgereit
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... )

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acjohnson55
Out of curiosity, who was the teacher? I used to study this stuff and may have
come across their work.

~~~
sbuttgereit
I did a quick Google and found him at:
[https://www.weber.edu/performingarts/shannon_roberts.html](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.

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odyssey7
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.

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code_duck
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.

~~~
chrispeel
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](http://pages.mtu.edu/~suits/notefreqs.html)

~~~
code_duck
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?

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

~~~
code_duck
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.

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bsaul
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](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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zipotm
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