Parity staff notation (PSN) for music | Mathematics and music | N J Wildberger
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- čas přidán 27. 07. 2024
- Parity staff notation is a simplified musical system which is not prejudiced towards the keyboard, which removes the need for sharps and flats, which treats the treple clef and bass clef in exactly the same way, and which has the possibility of dramatically enhance our understanding of music. Happily it can be put into practice just using standard music notation, or indeed actually just a lined notebook is sufficient. We will see that scales and chords become so much simpler to understand in this system.
This is part of the Maths and Music Playlist.
Video Contents:
00:00 Parity Staff Notation (PSN)
2:51 A 12 tone approach to black and white notes
7:39 Two Staves
17 :18 Two Uniform Scales
19:38 Major Scales
24:54 Example of Scales
27:24 Crossing Between Staves
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I started learning "classic" music staff notation 3 months ago, and indeed it drives me nuts. It feels too arbitrary and unsystematic (have to learn each note essentially 5 times), you have to keep too much state in your head (key and accidentals), you can't read off intervals from it easily and uniformly, etc. This makes so much more sense!
It turns out that none of staff notation is arbitrary despite the way it feels. Staff notation has a perspective, an assumption, an opinion - that everything be diatonic - which is to say any seven consecutive notes on the circle of fifths.
This collection of seven notes we named with the first seven letters of the alphabet. Every key has the notes ABCDEFG, though some of them have to be raised sharp and others lowered flat, but an Ab is still an A in this system. The letters act as ordinal numbers - Ab and A never occur within the same key - passing tones are not part of the key.
While the notes come from the circle of fifths, the staff conveniently places notes in thirds, which easily represents the fundamental harmony of the major chord - the 4th, 5th, and 6th harmonics. And this brings up the sticking point for most learners - a third is either a 3-step or a 4-step, But if you learn what I like to call the Star of Thirds CEGBDFA and the quality of the chord each makes as a root (major, minor, diminished), you no longer have to think about notes themselves, you just know that A in the key of G is minor but major in the key of E.
Remember those Magic Eye images? Staff notation is kind of like that. Once you see it, it’s hard to unsee, but it’s also really hard to see to begin with - it just looks like noise.
Please note that none of what I have said invalidates NJW’s exploration and proposal or your experience. I just think that we should steelman the other perspective. It also doesn’t help the learning process to feel like it’s all just useless rote memorization propped up by a cult of tradition, so I hope this helps.
Thanks @@integerdivision for your insights! Yes, of course all of that had reasons -- past musicians weren't all idiots who liked to torment students 🙂 It seems to me that much of it came from the time of just temperaments (is that the right English term?, i.e. when e.g. C# and Db were actually two different tones). These days (centuries even), most instruments we come across don't any more ("well tempered", i.e. the 2^(octave + tone/12) exponential frequency scale), and staff notation sort of didn't catch up with this.
But honestly, my biggest difficulty is that the placement of a note in different octaves on the staff is so completely irregular, that's where the "have to learn each note 5 times" comes from. This PSN solves that beautifully.
Anyway -- hysterical raisins, the world is full of non-optimal things which are hard to change. 110 V or brittle US power plugs, QWERTY keyboard layout, city traffic organization, etc..
I enjoy how the black/white notes represent the smooth scales of the diatonic (3/4) and melodic minor (5/2). I can see how it starts to become intuitive. This is going to be very useful for chords.
I look forward to chords, minor scales (I could work them out but you present things well so I'll wait!), and how you denote duration since now you show what is essentially whole notes and un-stemmed quarter notes. I have a reason to wait for the next ones, thanks, Norman!
I'm liking this with the exception of the black and white notes; filling in black notes seems overly time consuming when writing by hand. When writing traditional notation I use a horizontal dash for a notehead in a space, and a 45 degree dash for a notehead through a staff line. That could be adapted to your system: maybe use a horizontal dash for your white notes and 45 degree dash for black notes, or perhaps a -45 degree dash for white, 45 degrees for black, which works better for notes on a line.
So the octave above middle C is now on the B? That is hard to follow.
That's how a new system works. If you're going to challenge a new system's proposal you have to look from a newbies perspective, who doesnt even know what notes are yet. (not to disrespect you)
it already is the case with bass and treble that middle c is equally spaced between them
I do wonder how to notate rhythm if 'open/closed'-ness is being used to notate pitch rather than half/whole notes vs others
He addresses rhythm in a previous video
@@integerdivision which one? not seeing it from the titles
czcams.com/video/lYvni9k6le8/video.html&si=fWByaWHl9Molc88I
at 19:50
I think this will take you to the previous video in the Maths and music playlist: m.czcams.com/video/lYvni9k6le8/video.html&pp=iAQB
Thank you. This is interesting.
brilliant!
How do you denote which octave a stave is in? For example, violin vs cello? Or is the lowest C possible on an instrument tied to the 0/0 tone
Of course strictly speaking 0/0 refers to a specific frequency, I just meant the 0/0 location
If you know music theory then you know that people mostly play major keys which is the root 3rd and 5th note of the major scale which is only three notes that are consistently being played in most happy music
What is the purpose of having a stave at all? If the base12 numbering system represents pitches then set notation is sufficient.
There's more (useful) information content in a staff representative than a set representative and hence easier to read/play
Please see Antonio de Nicholas’ book « Avatara » for Hindi notation and musical structure, including semi-tones
Love your vibe!
Parity with what ? Parity bits in bytes? This is just numbers modulo 12. The tuning of instruments depends heavily on Pythagorean tuning, « natural » tuning and the facts that notes such as C# are not D flat except in Well-Tempering. But you know that from your own studies
Parity as in even/odd.
Good point about well tempering vs. other tunings. Parity Staff Notation (PSN) assumes Well-Tempering by default. It will be interesting to see how it works with instruments other than the piano, such as the guitar.
this is it man charts that dance tools are analogue but 3d printing their being sold out to be digital for a cheaper world
Am I having a stroke?
lol stroke it out highlight trolls!@@integerdivision
We don't do arithmetic with roman numerals and we shouldn't have to do music with the common notation. This system is long overdue.
I love you so much, but this is literally the same thing as standard staff notation and you've removed whole and half notes.
He removed the #'s and the b's (as we should've done a long time ago)
no he replaced them with notation which already has a use, half and full notes.@@nrrgrdn