Tibetan musical notation | Hacker News Reader

Tibetan musical notation

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I play the guqin (古琴), a Chinese zither-like instrument which I believe is the oldest instrument in the world for which musical notation exists. Like the Tibetan notation, it doesn't indicate rhythm or duration of notes, just succession. Until a hundred years ago or so, people were just assuming they knew what the melody sounded like, and to this day you will hear different interpretations of the same piece that simply make different assumptions about the duration of notes.

Wouldn't that be equivalent to guitar tabs?

Tabs are actually written in beats and bars. Technically you are correct that the duration of each note is not entirely prescribed however as it's set into a strict rhythm notes in guitar tab don't exceed their max duration in context.

This image illustrates it well

https://i.stack.imgur.com/2hRnd.png

I'm not sure those rythm annotations below the notes are part of the "standard" tab notation.

But then, I'm not sure there's such a thing as a "standard" tab notation.

That style of notation is more of the "paid for" notation we're all familiar with. Something you'd find in a tab book along the front row of shelving at record stores (remember those!). For those of us who were in the internet tabs heyday: this was a delicacy - among simply things like having correct notation.

The whole point of tab is it's shorthand mentality (As I'm sure you're aware of). It can mean whatever you want it to mean. I grew up learning guitar on a tab system created by my teacher, which I've never really seen duplicated before, but was based off of chord diagrams (even for non-chords).

Yeah the books were great! I also discovered that Italians used solfa after seeing an Italian blink 182 tab book at a holiday camp!

So it had the chord names written like Do-M La-m...

The rhythm annotations aren't part of standard tab (I didn't intend to suggest that as a standard tab). My point of sharing that image was to show what the position of the numbers in the tabs implies.

It's true there's a very diverse range of tabs, but as far as a canonical version goes, they have bar lines and numbers are positioned in time.

Not related to Tibetan musical notation, but the notation of Gregorian chant is also an interesting system and quite accessible (and probably interesting) to musically inclined modern students, self-taught or otherwise (the scale is movable).

See:

https://www.sanctamissa.org/en/music/gregorian-chant/choir/l...

http://media.musicasacra.com/books/chironomy.pdf

https://www.youtube.com/watch?v=sRQ11bYvfVQ

Another style I enjoy is Byzantine chant, though I only recently realized it has its own notation:

https://cappellaromana.org/divine-liturgy-music/

Indeed, Byzantine chant is glorious! It admits of many styles.

For example, the Antiochian and Russian (in translation to English, at least in parts):

https://www.youtube.com/watch?v=3VNdXMFleBM

https://www.youtube.com/watch?v=NcxAodBOvOU

This is a most remarkable rendition of Russian Great Vespers:

https://www.youtube.com/watch?v=Vya2xSYSz1c

I am moved every time I listen to it, a masterpiece! I believe the setting is by Sergei Rachmaninoff.

Russian liturgical music is not Byzantine chant. Yes, traditions like Znamenny can ultimately be traced back to Byzantine music, but along the way they evolved into something different. Later, Western polyphonic singing that had nothing to do with the Byzantine tradition was imported, and that informed the work of many prominent 19th-century and early 20th century Russian composers of sacred works.

That is why in the Orthodox Christian world, people perceive such a distinct difference between the liturgical singing of e.g. Greece, Albania, or Romania, and the singing of e.g. Ukraine or Russia.

Fair enough, but there is an audible relationship — it's not apples to oranges, as discernible even in the recordings linked in my previous comment.

Similarly, in the West the one-voice Gregorian chants are not separated by a great gulf from the polyphonic pieces that gained prominence in the 1500s.

One can listen to a Gregorian choir sing the Regina caeli laetare and then listen to a rendition of Palestrina's Sicut cervus without the feeling of crossing into a wholly alien musical universe:

https://www.youtube.com/watch?v=yzMa0qzwagA

https://www.youtube.com/watch?v=0yd5EE0hAB8

An example of Byzantine notation of the 15th antiphon of Holy Thursday (with English instead of Greek!)

http://www.agesinitiatives.com/dcs/m/dedes/en/tr/d069/hw/b/a...

I’ve always wondered, is there a better way to annotate music? Essentially, we are transcribing temporal patterns into spatial 2D patterns. Discrete notes were created to allow for hand written notation, but if we assume notation doesn’t need to be handwriting-compatible, I wonder if we can do a better job of capturing details? Perhaps some kind of spectral/FFT scroll?

In the late 20th-century, as tape parts and live electronics became more common in avant-garde classical music, various novel conventions arose to represent the electronic part on the score. This was not so people could duplicate the electronic parts themselves – they had often been painstakingly created in centers like IRCAM over months, and so they were provided to performers on a tape or as a collection of software. But the representation of the electronic part on the score helped the human performers playing their traditionally-noted parts keep in time with the electronics.

Yes and no. You need to be able to sight read it, so it has to be similar to the current system, but without the baggage.

I've wondered the same thing. Guitar tablature is a more intuitive notation for me to understand than piano, by far, so I wonder if there is an alternative for piano that feels as simple.

There are some[0], but not quite as radical as I would expect, they still seem to use the same basic look and feel.

[0] http://musicnotation.org/systems/

Guitar tablature is not a notation for music though, it's a notation for how-to-play-something-on-the-guitar. And yes, that's a very relevant distinction here - when it comes to music, there's nothing more intuitive than the well-established notations that we already have (with a few very limited caveats, of course). And I'm not just talking about Western notation, either - the number-based notation that's in widespread use in East Asia is also highly intuitive and perhaps more so.

And that distinction really only exists for instruments like the guitar that can play the same note on multiple strings. Piano music on staves is already very similar to a piano roll, at least on the y axis. You still have to learn the notation for different durations (the x axis), but there's not much mystery over how to physically play the notation on a piano, other than some potential for tricky fingerings. There is also fairly standard staff notation for fingerings, both for piano music and classical guitar music (in my experience, it's much more important for the latter).

>And I'm not just talking about Western notation, either - the number-based notation that's in widespread use in East Asia is also highly intuitive and perhaps more so.

Do you have any more information about this? Fpr example, scores of Chinese music using the Indian/Arabic number system? I know that number notation is used as a mataphor for gamelan music—by westerers, which has caught on natively (although which might be frowned upon) for archival purposes, at least.

The number metaphor for tones clashes with the number metapor for the counting of beats, which is ubiquitous in Western music. But perhaps there are different metaphores in East-Asian music.

There is Klavarskribo [1], more or less the keyboard-equivalent of Tabulature for stringed instruments.

[1] https://en.wikipedia.org/wiki/Klavarskribo

I like this! It's sort of like the piano rolls you see in DAW sequencers.

I've made a toy page for it - https://naivesound.com/klavar/ Click on the columns to put a note, add more height if needed, edit the title, then print it to PDF. I often use it to write down simple melodies when playing the piano. Also, there are two blank PDF templates - https://github.com/naivesound/naivesound.github.io/tree/mast...

Relevant: https://news.ycombinator.com/item?id=17993223

Our product Soundslice is more or less trying to do this: https://www.soundslice.com/

The philosophy is that music notation will never be able to capture the subtlety of a performance — so syncing the notation with real recordings/videos is a much richer learning experience than notation alone.

Soundslice is pretty awesome!

Useful but if it's intended for learning (to play not to play), a systematic way of describing the harmony would be a good step forward

The map is not the territory. Furthermore, the language of the map limits how the territory can be described. So "better way to annotate music" depends, at least in part, on the kind of music you're annotating.

This really came home to me when I was studying frame drumming of the central Asian plains. In Western notation terms, this music has very complex and difficult "time signatures", but that's because it's not metric in the same way as European music. If you think of it in its own terms, it's actually pretty easy to understand. Just break the rhythm down into sub-beats of 2, 3, or 4 pulses. So for example, a 13 beat long line might be 23233. Try counting that out loud - one two one two three one two one two three one two three - and you'll immediately hear it. But it's hell to notate in Western notation. And it gets worse when pieces turn into meta-sequences that have "bars" of varying length.

I've long been involved with the free improvisation scene, and improvisation always happens within some sort of set of rules. How do you notate something that's made up on the spot, within a framework? Take blues guitar leads as an example. They tend to stick within pretty limited pentatonic scales, against the underlying triplet shuffle feel of American music, but they're not "notated", really.

This leads to other, alternative notation systems that more aptly describe the style of music at hand, like the Nashville Number System.

Reminds me of a Charles Mingus anecdote I came across today:

> The reed player Yusef Lateef recalled his own experience learning Mingus music: “On one composition I had a solo and, as opposed to having chord symbols for me to improvise against, he had drawn a picture of a coffin. And that was the substance upon which I was to improvise.”

https://fdleone.com/2016/01/29/charles-mingus-the-jazz-works...

Additive meter is actually a well-known concept even in Western music. It's clearly needed even to make sense of, e.g. "5/4" or "7/4" meter, which yes, are sometimes found in the repertoire - because these are already ambiguous in practice: does the 5 in "5/4" mean "3+2" or "2+3"? You need to know that in order to understand the music and figure out how it goes - to make it "meaningful" as someone else said.

Additive meter just shows where the concept of "time signature" breaks down The pulse of the music is not apparent from the notation. So it doesn't even fully explain Western music, much less non-Western music. (That said, while 7/4 exists in the repertoire, it's exceedingly rare - European music tends to be very simple rhythmically, compared to Indian, Arabic, or most African music.)

"The map is not the territory."

I'm stealing this phrase. Increasingly in music production, the map is the arrangement of rectangles on the screen, but it's a poor substitute for understanding the ebb and flow of the music.

In getting past notation by internalizing our knowledge of the music, we build a mental map of how we feel about the territory.

Feel free; I stole it myself! It's from the Polish scholar Alfred Korzybski, who made many interesting observations about how language itself limits our understanding of the world.

>I’ve always wondered, is there a better way to annotate music?

Not really. Western staff notation is heavily optimised for intelligibility by an expert user. It's not very intuitive, it barely works at all for non-western pitch systems, but a trained musician can read, understand and reproduce complex scores in real time. For the primary users of western musical notation, that is an essential, non-negotiable feature that negates every disadvantage.

Western notation leans heavily on both visual pattern recognition and an understanding of music theory. It can be read in chunks, like written natural language. When you're reading this comment, you're not parsing individual letters, you're recognising whole words and phrases. It's the same for music notation - a skilled user sees chords, progressions and scale fragments rather than individual notes. They are parsing the dots and lines as meaningful musical information, not purely abstract pitch and duration data.

It's not a particularly precise or machine-readable system, but it's not supposed to be. Where we need machine-readability, we have MIDI and OSC - they're totally unreadable by humans, but they convey a vastly greater range of data at vastly greater precision than any traditional notation system.

Notation encodes as much detail as is musically relevant and no more. For example, we typically only use eight levels of loudness, from ppp to fff. It's not really useful for the composer or the performer to encode very precise loudness information, because human musicians can't reproduce that level of precision.

We could have that same intelligibility for less-expert users if we didn't have all the legacy gunk. Of course, the expert users have a vested interest in having a more-exclusive club. Nearly all of them would reject anything new.

A simple improvement is to give each of the 12 common pitches within the octave a distinct position on the staff. This eliminates accidentals from typical music, leaving them only needed for quarter-tone compositions. Sight-transposition becomes trivial, possibly within reach of beginners.

> A simple improvement is to give each of the 12 common pitches within the octave a distinct position on the staff.

This doesn't work - the staff becomes too large, or the registral range it covers becomes way too small. The current staff has evolved to be readable without expressly counting the lines or spaces, via visual subitizing. If you add more lines, you lose this property and sight-reading becomes infeasible. Plus, diatonic pitch is actually meaningful in a musical sense, and it's useful to have a notation that references it. That's why we use for instance C, D, E, F, G and not <0>, <2>, <4>, <5>, <7>.

(This also describes the very real problems w/ Klavarskribo, BTW.)

Key signatures and accidentals have a practical benefit in indicating the tonal centre. All pitches are not equal, at least not at any given moment. Sharps and flats look like a kludgy hack, but they provide clear visual hints of highly relevant musical information.

There are alternatives to just having a huge number of lines. Western music notation already has one: the grand staff has a gap in the middle. Simply put a gap with a single ledger line between each octave and you get a system that looks an awful lot like the current system. It's like spreading two octaves over a grand staff, but with a more modest gap in the middle.

So you can still have sight-reading. You also get fully arbitrary sight-transposition, which today is only possible for the very most elite musicians.

But you want each key to look different because physical instruments are all tied to a key. If every transposition looks the same then you've just turned a visual transposition problem into a physical transposition problem.

Physical instruments aren't really tied to a key.

Transposing instruments only even exist because sight-transposing is so difficult. There is nothing fundamental about an instrument that makes it transposing. We only use that kludge because of the difficulty sight-transposing.

Suppose you do have a transposing instrument though. It's in Bb, and you'd like to play music written for an instrument in F. Very few musicians can do that without hesitation.

The same applies when there is a desire to shift the entire piece of music up or down. Perhaps you are using a hecklephone instead of a lupophone, so you shift everything up. Perhaps you just lost a trumpet player with an unusually high range, and thus need to shift everything down. It would be great to be able to expect all players of ordinary skill to be able to do this without hesitation.

BTW, I'm aware that one needs to avoid troublesome notes and things like impossible trombone glissandos. This doesn't change the general truth of the above.

> Western music notation already has one: the grand staff has a gap in the middle. Simply put a gap with a single ledger line between each octave and you get a system that looks an awful lot like the current system.

Except that's not how a multi-staff partition works. Each staff has a clef that determines it's offset; they can be the same or wildly different. They also usually signify different "voices" or instruments, further encoding musical nuance beyond pitch and tone.

You say it doesn't work but it's been used in a variety of ways such as singing video games (eg. SingStar) and music trackers [1], and it works just fine.

[1] https://en.wikipedia.org/wiki/Music_tracker

Working in a game where mistakes don't really matter and working for professional music production where mistakes and restarts cost $$$$$$$ are nowhere close to being the same thing.

Sure. And orchestras can hire teams of page turners so that people can play more than 3 measures at a time without stopping. And conductors can . . . I don't even know what a staff that large would look like for a full orchestral score. I guess you can just give the conductor a screen and have it scroll continuously. And then the orchestras can hire an ops team to support the scrolling screens.

Starts to sound a lot like the same kind of thinking that gave us service oriented architecture and a new javascript framework every week. Just hire shitloads of more people to make sure it all works when it needs to. Because it's easier for beginners! In fact, with this new notation system that simplifies everything so much, you could probably fire all the older more expensive musicians in the orchestra and hire a bunch of juniors for a lot less money!

They use screens and color cues for performances where a live orchestra plays back the soundtrack of a film in sync with the projection. Professional musicians are a lot more open to alternative representations and technology integration then you might be aware.

The screens are for the conductor, not the musicians. They're following the conductor's direction and don't need to know what cues they're playing to, nor can they take their eyes off their score.

There simply isn't the money in the budget to bugger about with clever ideas in a sync session. Merely having a session with an orchestra is already a luxury for many productions, because most composers can knock out a reasonably convincing orchestral soundtrack in VSL at a fraction of the cost.

An orchestra is an extraordinarily efficient musical machine if they're doing what they were trained to do. If you want innovation, don't hire an orchestra - experiments get very expensive very quickly when you're paying ~$50 a minute for the privilege.

https://www.youtube.com/watch?v=HaWGWQJVVBI

No, the height increase is only by a factor of 12/7, which is about an extra 71%. Compensating for this, there is a width reduction caused by the loss of accidentals. There is also no need to waste space on unused octaves, so there might not be any height increase at all for some pieces of music.

Trivial transposition is a highly desirable property.

>Of course, the expert users have a vested interest in having a more-exclusive club.

I am an almost entirely self-taught jazz musician. I learned to read notation begrudgingly, assuming it to be an archaic hurdle put in place by snobbish classical musicians. My view of classical musicians has not changed, but my view of notation has.

A lot of people think that programming languages are a similar archaic hurdle and set out to build a visual programming environment that will be easy for beginners to use. Somewhere along that journey, they invariably realise that a) syntax is one of the easiest parts of programming, b) there is no good visual metaphor for recursion and c) the Deutsch limit is a cruel master. You can do simple scripting with a box and arrow diagram, you can teach kids to blink an LED, but you can't write a compiler.

The advantages of stave notation (and the disadvantages of alternative systems) are non-obvious, but they are very real. Critiques of notation usually sound like "command lines are stupid, everything should be a GUI" - they're not wrong per se, they just miss the point.

> ...there is no good visual metaphor for recursion...

Now, now. You're on a site that's literally named after one!

I'm taking classical piano lessons currently, and I have much the same reaction. I don't love all the strict rules imposed by western music, but I do love the notation and theory, because it generalized in interesting ways across tunings and notation.

Just like I learned C (for example) before imagining my own languages, or how I've learned many libraries before writing my own, I also appreciate the structure of classical notation for what it is.

>c) the Deutsch limit is a cruel master.

I generally despise visual programming but MaxMSP does this pretty well. You can nest components in an almost object-oriented fashion. Prior textual programming experience doesn't massively help learning the language though, it's a whole different paradigm and it's def not easy for beginners.

Do you know if the nestability thing applies to puredata (open source Max/MSP)?

I haven't touched puredata yet but C&G's Organelle is looking really amazing right now.

Yes, you can create subpatches (http://write.flossmanuals.net/pure-data/subpatches/) and abstractions (http://write.flossmanuals.net/pure-data/abstractions/).

I'm happy with standard notation when playing the piano or something that can only play one note at a time (e.g. trumpet), but I still can't get my brain to read it fast enough when playing the guitar.

I know tab notation exists to help with this, but it loses much of the detail encoded in standard notation - note lengths being the most obvious example. There have been attempts to create a hybrid notation and there are books with tab printed below the stave(s), but neither work well.

If anyone's found any alternative notations that work well for guitar, I'd love to see them.

I've played from books that had tabs with note stems, beams and flags attached to the numbers with the same meaning as in standard notation (this can't distinguish between a filled and unfilled note-head, but in guitar music one rarely needs to notate anything longer than a crotchet/quarter-note so it's not really an issue). I never really learned standard notation, but I do know some of the basics and found it useful.

But this would make it much harder to sight-sing typical melodies, eg one whose notes are all diatonic to G major.

Reason: a melody whose notes are all diatonic to G is almost indistinguishable from one whose notes are all diatonic to C in your system while in the current one they are quite distinct. Furthermore, your system would make it very easy to count chromatic distance between notes, but harder to count the diatonic distance (or the scale degree a note lies on).

It's interesting how staunchly people will defend "standard Western musical notation" but I agree with you - from a design point of view it looks like notation originally designed to match a piano keyboard which has then had many years of extra features inelegantly bolted on to it. It works well enough for the keys of C or Am but gets progressively more ridiculous the further you depart from those keys. And transposition is a mess.

Some people seem to think that standard musical notation is "right" and you can't possibly have any alternative notation and yet this is clearly false. There are at least two or three alternative forms of musical notation in wide use today. Most guitarists use tablature notation because it's better suited to that instrument - standard musical notation is less useful on guitar since it doesn't clearly capture the different ways that a single chord can be played. So it makes sense to have a special notation for that instrument.

Secondly chord charts are used by musicians everywhere because they're very concise at conveying the chord structure of music and often that's all the information you need. Standard notation is just way too much information in that case.

The third, less commonly seen form of musical notation is just like the one you've described. It's seen in video games like SingStar[1] and in modern music composition software such as Ableton Live[2] and others. It's used so often in music composition software because as you've noted it's very intuitive and far less cumbersome than standard musical notation. Transpositions become trivial and everything just makes more sense.

[1] https://www.gamesmen.com.au/media/catalog/product/cache/1/im...

[2] http://whereisdarran.com/wp-content/uploads/2014/02/Screen-S...

> It works well enough for the keys of C or Am but gets progressively more ridiculous the further you depart from those keys.

If you're in something other than C or Am, you're supposed to use key signatures to point that out and clean up the notation. C/Am is just the default.

"Standard musical notation is ambiguous when used on guitar", actually it isn't if you mark strings and fingerings as needed. This is widespread practice, each instrument has its own "tweaks" on the basic system. Standard notation in particular is quite hard to work with on guitar, and one can see why so many people just rely on tablature - but ambiguous it's not.

Chord charts may be "concise" but they don't actually convey harmonic structure very well, not least because of the multitude of informal conventions and the ambiguity that these create; figured bass notation (while admittedly not very well known) does a far better job of it overall. For example, "walking" bass lines become immediately apparent in thoroughbass.

My point was that these notations exist for a purpose and are popular. They do and they are.

Why would tablature be so popular on guitar if standard musical was overwhelmingly better? Tablature is intuitive, expressive and concise when used with guitars. Just as standard musical notation has its strengths so does tablature. Ok, tablature's poor at expressing rhythm but standard musical notation's terrible for transposition. So they're all just different tools with different strengths.

The one thing that "standard notation is overwhelmingly better" at is notating music, and making it understandable as such. Some people care about this enough that they'll put in the effort to use standard notation even on guitar; some just want to focus on how each specific piece should be played on the instrument, for which tab is quite optimal. It's even quite common to have a format where both are notated, on separate staves.

(For that matter, standard musical notation is not even that terrible for transposition once you understand how key signatures work, via the cycle of fifths. It's a bit tedious, but it absolutely can be done; one can even learn to transpose directly on sight. And good tablature notation will of course include accurate info about rhythm, there are quite easy ways of doing this.)

I’d argue that tablature is terrible for transposition as well in most cases, sure you can just +/- N semitones from each fingering in the ideal case but that breaks down as soon as you have voicings or melodies with open strings and need to transpose down e.g. a half step. Capo at 11 gives a very different character.

>actually it isn't if you mark strings and fingerings as needed

You mean, if you add tablature above each chord (or, effectively, transcribe that information via numbers, etc)? :)

When the parent said standard notation, he meant the one without this augmentation, for which it wasn't quite optimized.

>Standard notation in particular is quite hard to work with on guitar

That's the point - that it's not the use case the notation primarily was designed for. Guess we all agree here, don't we?

Accidentals and key signatures are a feature, not a bug. There's a reason we don't just write everything in C major.

Western notation is kind of amazing. It encodes timing by horizontal space, pitch distance by vertical space, harmonic distance by accidentals complexity, and has a sort of symmetry around A 220 in clefs, and the octave which is the most basic interval happens to be the height of one staff.

I can see why it's not easy to give up.

Where it suffers is in notating timbre, so you get things like the orchestral score which isn't really all musical information but also leaks implementation details.

I've always been fascinated by the possibility of a chromatic western notation though, which would require way less learning but would therefore not centre around the C major scale.

Imagine it as a piano with all alternating black and white notes, no gaps.

Now there are 6 white and 6 black notes per octave.

You would only have to learn two positions to have learned all scales and all chords (like sliding moving a bar chord on a guitar).

I don't know that it would be better. It might be soulless but it also reduces the redundancy of learning harmony and theory and suddenly jumping up a key is as simple as physically moving up a key.

Look into chromatic keyboards like the Jankó keyboard or the Isomorphic keyboard.

You'd also need different keyboards and notation if you start considering music not built around the octave.

Thanks for that I hadn't seen the Jankó keyboard, although the purely physical fix doesn't deal with my bigger frustration that the accidentals and quirks of scale centric notation requires a huge investment in theory learning to learn Western music in more than one key... Having taught theory from scratch a couple of times as well as learned it, it's been a lifelong frustration that the same thing written a different way can be massively more complex even though the semi-tonal pattern is identical. I'd go as far as to say that the language and notation around scales actually obfuscates the patterns and then when you really understand the circle of 5ths you realise it's just a veneer and your mind can just translate it.

Really interesting reference. Will definitely read more into Jankó.

Interesting almost every pro musician I know uses the chord numbers to convey this information orally more than they use the note names. And when I did degree in jazz it was always focused on the numbers.

Musicians clearly understand the patterns, but it's beginners that I'm concerned with. After decades of study / practice most systems are workable.

> Where it suffers is in notating timbre

There are a great many annotations to individual notes: lines, accents, staccato dots, slurs and brackets, dynamic markings etc. etc. that indicate timbre, and you've always got the fallback of just writing out what you want, and it's even acceptable to not even use Italian these days!

I played around a bit with stroke-based notation a few years back: http://archagon.net/blog/2016/02/05/rethinking-musical-notat... In theory, you could annotate arbitrary pitch-based music with this approach, even if it uses different tunings or scales.

If I have more time, I'd like to develop it into a more robust product one of these days—especially with things like MIDI Polyphonic Expression gaining traction.

Here's one attempt.

https://www.hummingbirdnotation.com

Thanks for posting. I'm the creator of this notation. If anyone has any questions, I'm happy to give my thoughts!

You can perfectly represent music using a 1D representation, or 2D, it doesn't really matter because Musical notation is a cognitive problem, not a technical one (the latter was solved by Shannon).

It's not so much how do you encode pitches and timing information (this is trivial today), but how to convey the meaning of the encoding and how effectively a musician can recreate the piece from the representation.

Weaver pointed this in his forward to Shannon's magnum opus [1], on the topic of the three levels problems in communication. The first level, the "technical problems" are those of encoding information into symbols for transmission (in the abstract sense), whereas the "semantic" problems cover how one conveys intent or meaning behind the information (and that it is impossible for meaning to be clarified by the sender, in general), and finally the "effectiveness" problems which cover how the receiver conducts action based on the information communicated.

Musical notation is purely a semantic and effectiveness problem, and over the past few thousand years we have found that there is no optimal solution, and that listening to the original music and having direction or instruction are as important as the symbols on the page. The notation itself is a simplex transmission from the author (or transcriber) to the performer, instruction/direction helps make it somewhat duplex to improve (but not solve) the semantic problem, while listening is the end-all, be-all solution provided you have source material recorded and training to interpret it.

The forward to Shannon's theory of communication is really essential reading for all software/electrical engineers imo:

[1] The Mathematical Theory of Communication, Weaver & Shannon http://www.magmamater.cl/MatheComm.pdf

I really, REALLY like these 3 "levels". They map to programming language perfectly (as we'd expect), syntax is encoding, semantics is the logic we think we're going to get (hypothesis, remember it's computer "science"), and the effectiveness is what actually happens. We love computers because they almost always do what we want them to do, but people like to forget that nothing is perfect.

All communication, regardless of with whom or what, is lossy.

A piece of classical music is not a static data structure that can be compressed and sent over a channel.

Classical musicians don't recreate pieces, they actively create them. The fact that scores allow different interpretations is a feature, not a bug.

There is no definitive interpretation, and there is no "semantic problem" to "solve." And there is a lot more involved than playing the right notes at the right times in the right order.

Not even a performance by the composer is definitive.

Yes, there's lots of different approaches (I've been fiddling with these ideas for 20 years). Among the most interesting is conversion of note data to polar coordinates, using pitch class as the angular component and octave as as the amplitude. You can also represent musical pitches on hexagonal layouts, as graph structures, perturbations of strange attractors in n-d phase space...

>You can also represent musical pitches on hexagonal layouts, as graph structures, perturbations of strange attractors in n-d phase space...

Interesting conecpts. Are there any examples you could post?

I wrote a blog post trying to explain some of the subtleties of Western musical notation - http://www.moderndescartes.com/essays/musical_notation/

I think better systems exist, but it's hard to design one without understanding the span of functionality that the current system is capable of handling. And once you've spent the 15 years it takes to fluently read Western musical notation, it's hard to think any other way...

Worth clarifying the curators of this text are Emma Lewis and Devin Zuckerman from the Buddhist Digital Resource Center, and not Google, as the article misleadingly suggests.

This is very reminiscent of early European neumes: https://en.m.wikipedia.org/wiki/Neume

Here's a good example: https://catapultingintoclassical.files.wordpress.com/2015/11...

Some other fun examples of points in the music notation space are the various notation systems used by traditional Japanese musical instruments... For instance, the shakuhachi (a type of bamboo flute) has a system where various combinations of fingerings/blowing technique are each assigned distinct characters (the same pitch, but achieved with different fingerings, and therefore having different tone colors, will have different characters). Rhythm and ornamentation are then indicated with various annotations on these characters. You could maybe make the analogy that Japanese music notation relates to Western classical notation in a similar way to how Chinese characters compare to alphabetical systems...

Other instruments have similar (but generally mutually unintelligible!) systems, with different characters assigned to particular notes/techniques peculiar to those instruments.

Off topic: Chanting in an ancient language (which you probably don't even understand) isn't what buddha taught and music does cause suffering (according to the teachings)

The earliest teachings were apparently passed down orally for several hundred years before being written down. I think it's a bit presumptuous to claim specifics of what the Buddha taught, other than the broad strokes: Four Noble Truths, Eightfold Path, jhana-based meditation, etc.

But the teachings also say to take personal experience and science over any book teachings or otherwise from other people, and chanting (if you listen to the video in the article, it's chanting they are talking about, not really music) has been shown in studies to relieve stress and have benefits: https://www.lionsroar.com/buddhist-researchers-find-that-rel...

Personally, I meditate with Chan Buddhists who aren't nearly as chant crazy as the Pure Land Buddhists, but even they have a chant about the five skandhas before we start quiet meditation.

Well, there are different variants of Buddhism. Tibetan Buddhism is pretty different from, say, Zen.

Yes there are, but as an aside, Zen chants Sanskrit too. It's a common practice.

According to which teachings?

Siddhartha Gautama

"music does cause suffering (according to the teachings)"

A mind attached to music causes suffering.

"The problem is not enjoyment; the problem is attachment." ~Tilopa

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