Parity staff notation (PSN) for music | Mathematics and music

Parity staff notation (PSN) for music | Mathematics and music | N J Wildberger

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@MartinPitti 10 ай бұрын

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!

@integerdivision 10 ай бұрын

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.

@MartinPitti 10 ай бұрын

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..

@kendebusk2540 10 ай бұрын

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!

@deanrubine2955 10 ай бұрын

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.

@sub-harmonik 10 ай бұрын

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

@integerdivision 10 ай бұрын

He addresses rhythm in a previous video

@sub-harmonik 10 ай бұрын

@@integerdivision which one? not seeing it from the titles

@craig4320 10 ай бұрын

kzbin.info/www/bejne/oorZn5xvoJufm5o&si=fWByaWHl9Molc88I at 19:50

@integerdivision 10 ай бұрын

I think this will take you to the previous video in the Maths and music playlist: m.kzbin.info/www/bejne/oorZn5xvoJufm5o&pp=iAQB

@pjmoran42 10 ай бұрын

So the octave above middle C is now on the B? That is hard to follow.

@aryanahire2337 10 ай бұрын

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)

@integerdivision 10 ай бұрын

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.

@jacobcleveland1594 10 ай бұрын

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

@jacobcleveland1594 10 ай бұрын

Of course strictly speaking 0/0 refers to a specific frequency, I just meant the 0/0 location

@tjeva4963 10 ай бұрын

What is the purpose of having a stave at all? If the base12 numbering system represents pitches then set notation is sufficient.

@jacobcleveland1594 10 ай бұрын

There's more (useful) information content in a staff representative than a set representative and hence easier to read/play

@dougr.2398 10 ай бұрын

Please see Antonio de Nicholas’ book « Avatara » for Hindi notation and musical structure, including semi-tones

@theoremus 10 ай бұрын

Thank you. This is interesting.

@itsinis 10 ай бұрын

brilliant!

@dougr.2398 10 ай бұрын

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

@craig4320 10 ай бұрын

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.