A new Staff Notation based on Parity | Maths and Music | N J Wildberger
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- čas přidán 27. 07. 2024
- Many people over the years have lamented that our current musical notation, based as it is on the rather idiosyncratic design of the piano's white and black key system, is a hindrance to musical learning and understanding. I fully concur with this view. It is long past time to consider rationally what better alternatives there are.
In this video I bring a mathematical orientation to this question, and propose a vastly simplified system, in which the parity distinction between even and odd is reflected in the visual distinction between black and white notes, in which sharps and flats are entirely removed, where the treple and bass clefs are read exactly in the same way, and where transposition from one key to another is so much simpler. This will be a major help in understanding also the structures of chords in musical theory.
In keeping with this I also propose a modification of our notation for the length of notes
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It makes sense, Norman, but would best be implemented by teaching it "ab origine" (from the beginning). I view musical notation as another language I had to learn. First English, then music, and that with two "dialects", treble and bass clefs. I'd be hard pressed to try learning a new one now, much as trying to learn the Dvorak keyboard for typing as opposed to the "QWERTY" which I first learned over 50 years ago.
Keep up the good work; you stretch my brain into new territories, provoking lots of thought :)
Thanks for this! Nice to see another system without flats and sharps! There are obvious weaknesses with our standard music notation, but in changing it I still lean to a simpler adjustment with an unchanged five lines in the staff, only separated by a bigger white space with three higher and two lower line groups, standing for the black piano keys (see the Klavar and Trigram notations). Twisting it 90 degrees clockwise you get the piano keys, which leads to less learning needed to get started. Chords with the same intervals between notes are the same chords but in different keys.
Love it! Also, the 4-beat, 2-beat, and 1- beat notations can easily be adapted to 3/4 time signatures by just having a 4-beat note with 3 bars -- one side(e.g. left) is exactly as the left side of the 4-beat notation and the other side of the circle has only the top or bottom half of the right of the 4-beat vertical line (so it literally looks like 3 short strokes: 2 on the left making a continuous vertical segment centered at the circle and 1 on the right).
My wife uses a notation that doesn't use a staff at all. It uses digits for notes, with various decorations to modify them or indicate an octave. That's used by most if not all the sections in the band, with specific options based on the capabilities of that instrument.
Base 12 digits would have an advantage here, since the octave has 12 tones (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, where A and B can be switched to other symbols as well, since you sometimes need to mix numbers with letters; in that case, why not using ¤ (= 10) and # (=11) instead).
Elegant! I would love to see more chords represented in their two forms. Also makes me curious about how inversions of chords relate to other chords, and whether this notation could make those relationships more obvious.
Hi I will be talking about those things for sure.
Thanks!
What is it Dr. Wildberger can’t do. My goodness
Ahhhh 😌
The patterns suddenly emerge naturally
Very interesting, especially from the point of view of a guitarist. I would love to see an example of a melody written in this notation.
Many thanks. Might i suggest another steady light source in future videos. Many videos look dark. Ex: note the transition pre- and post-3:39
Thanks for the suggestion
It would be nice to have a piano with alternating white and black notes as well.
That is such an interesting idea! Thanks
Great ideas here!
For the 4-beat note would not a stemless note do the job, instead of the breve with its two vertical lines? The white whole note is already used for this. You would just be adding a black form.
Yes thanks Brendan. That’s a good point.
Great video Norman. On a different, but intimately related note. You are missing the point of floating-point numbers.
Base 10: 0.5 minute X 0.5 minute = 0.25 minute - 1/4 minute.
Base 10: 30 seconds x 30 seconds = 900 seconds - 1/4 hour.
Base 60: 30 seconds x 30 seconds = 15.00 minutes - 1/4 hour.
30 is the only sexagesimal digit 1-59 which in square has 100% carry over. 28^2= 13.04 29^2= 14.01 30^2= 15.00 31^2= 16.01 32^2= 17.04
This is an arithmetical miracle, which doesn’t happen in any other number base in place-value notation.
The Number theoretical explanation is found in the Prime Number List. The product of the first three prime numbers is thirty, and all but the first prime number are odd, and odd times thirty always leaves thirty in base sixty.
Therefore 30/60 is the constant of the infinite prime number list to answer your question mister Riemann.
Kind regards,
Michiel Karskens
I may be speaking prematurely - but it seems your proposal might be easier in a composition whose keys are modulating a lot - but with the tradeoff of not communicating the key at all in a composition that doesn't have as many accidentals.
Granted, string and brass instruments are more invariant to sharps and flats than a piano, but the key signature is still deeply rooted in western composition and therefore grounding the notation to a key does come with benefits.
That’s a good point, and we will be looking to find ways of addressing that issue. However, still within this new parity staff notation system
Can you play actual music - a Mozart sonata, say - from this notation? (Without knowing that piece before, I mean.)
Sure you could, after you’ve practised of course
Your system looks really great for scales, but is very confusing for chords. You get multiple different black/white patterns depending on whether the chord root is white or black.
Also, the major and minor chord patterns look too similar.
As an autodidact, guitar teacher, and fellow notation inventor, I have come to know that staff notation is poorly taught and poorly communicated.
It’s a logically asymmetrical _diatonic_ system that conveys a lot of information when the underlying music theory is understood. Specializing in a diatonic system means that it’s crufty and inelegant when it comes to chromatic and microtonal music - more crufty and inelegant than necessary for sure, but not so much that it can’t be tolerated when chromatic and microtonal music are not the norm.
In making a new system, it may be worth the effort to target the other end of the spectrum - microtonal music. I can imagine coloring in the top/bottom or right/left to get 24-tet or both to get 36-tet, instance.
I do like your use of the clock. It’s so underutilized. If you take every odd number on the clock and swap it with its opposite (1-7, 3-9, 5-11) you get the notes in harmonic order instead of chromatic order - traditionally known as the circle of fifths - which is *not* about key signatures. The harmonic clock is basically half of all western music.
Speaking of clocks, my very non-standard non-staff notation features them: github.com/counternote/cnote/blob/master/spec.md#clock
It’s just a spec for now because compilers are hard, but soon™ there will be a guide and a compiler and a webapp.
The musical notation system is pretty bad, but it's been standard and stable for centuries. Math notation could use both of those things.