Standard Staff Notation Issues | Maths and Music | N J Wildberger
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- čas přidán 27. 07. 2024
- There are two major issues in representing music on a written page: how to systematically specify the pitch of a given note, and how to systematically specify the duration of a given note. We introduce some of the standard features of our system by looking at a famous Mazurka Op 7 No. 2 of F. Chopin.
In the Western world, our solution to the first of these issues is firmly rooted in the particular architecture of the piano, in which the white notes are seen as first class citizens, and the black notes as second class citizens. I want to stress the arbitrariness of this current system, as well as its intrinsic lop-sidedness. Unfortunately all musicians, whether or not they play keyboards, are forced to use this particular idiosyncratic system, and of course centuries of use and overfamiliarity renders it largely immune to critical examination.
The second issue of note duration is certainly somewhat more systematic, but still has some rather ad hoc elements, notably the use of the distinction between black noteheads and white noteheads to separate quarter notes from half notes (and whole notes).
However we will see that in fact interesting alternatives to both issues have been raised, and in our next video we will add our own contribution: a balanced "parity" system for music notation.
This is part of the Maths and Music Playlist: please check out the other videos in the series at • Maths and Music
You can check out my TikTok (music) channel: www.tiktok.com/@njwildberger The latest offering is my take on Frederic Chopin's Waltz Op 70 No 2 in A Major. Can amateur musicians offer up something of value? It's an interesting question which I hope to take up more in coming videos.
A big THANK YOU to all my Patreon supporters, and also to Members of this channel's sister CZcams channel: Wild Egg Maths.
Video Contents:
00:00 Introduction to staff notation
1:10 Mazurka F. Chopin
2:18 Current musical notation conventions
8:14 Main Issues: How to represent notes
13:20 Examples
14:04 How to represent length/extent of notes
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Been following you for years on and off...damn cool to see you play the piano so well as well being a great Mathematician and educator. Love your videos. 😊
Thank you for the concise introduction: Up until now prior to your description, I'd not had an adequate synopsis presented as pertains to representing music in the conventional manner for this society.
What would an AI do? is an open question, although it entails an answer to "What can an AI do?" which assumes an operational definition with respect to utility in the mechanical sense such that the answer is given by a machine or person (Persons not being machines or aspects of the AI meaning a distinction is necessary) where the output has categorically determined what isn't AI or what Artificial Intelligence is not.
In that there is an adjectival modifier with "Intelligence" (Intellectio: To decide or choose between), there must then be a reason to specify (Either as a modular sub-routine of a super-ordinate patterning such as is familiar to the mathematically inclined) why all "Intelligence" (Whether it be a being or type of being such as the noun form would indicate or an attribute of an entity is not ascertained at first pass) isn't artificial [Or more crucially whether artificial as a specifier is appropriate in any event, assuming it is either (1) then redundant or (2) unnecessary given the obvious implication that such an object is an artifice].
It is incredible how much information is embedded in musical notation. And with lots of training and conditioning, a human can decode that information and translate it to movements of the body to recreate the intended sounds in real time. It's really amazing and I am always in awe of someone that can look at Chopin's music and make it come out right.
But, this musical notation does not integrate well with our digital world. Many contemporary composers are working in midi-based systems where each note is a set of information defining the tone, duration and velocity. Tones are represented as integers on a scale of 0-127 - with 60 being middle C. And instead of a staff, visually we can see a track as a grid with time on the x axis and tone on the y.
With this approach, musical compositions can be defined entirely with numbers and orchestrated with algorithms.
Video Contents
00:00 Introduction
1:10 Mazurka F. Chopin
2:18 Features
8:14 Main Issues
13:20 Examples
14:4 Standard Conventions
I am a singer and I think conventional music notation works great for it. You don't have to worry about black keys when you are singing because it's easy to adjust yourself to any key. The main thing that could help me with singing is a clear marker everywhere of where the root note is, maybe this could be an arrow pointing to the line that has the first note of the scale.
Hi. One obvious thing you could do, that doesn't change too much of the already established notation system, is to make a small room between the third and fourth line, so that the five lines come to represent the "black keys" of the piano. This would erase the need for notation to make the notes represent higher or lower notes, since all 12 are represented.
You could of course continue the five lines upwards (and, for the base notes, downwards) if you need, as are done in the standard system, by adding one or more lines, and including the rooms where they belong to imitate the system of white (in between lines) and black keys (= the lines) on a standard piano keyboard.
But is the effort worth it? I've played score and guitar tab and banjo tab. The learning curve is noting compared to differential geometry.
I've used piano roll notation in composing music (Acid Pro 7). It makes sense. But can you read it?
Just for the sake of congruence: Would you take seriously the sayings of musicians about how to systematize maths writing?
Sure, I would, if what they said mad sense