Roland Gurt, a musician and regular reader here, recently asked whether I could explain some of the computer science terminology that keeps appearing in these posts – terms like functional programming, immutability, and transducers – in layman's terms, and preferably from a musical point of view.

I was genuinely glad to be asked.

At this stage of Ooloi, nothing has yet been drawn on the screen. What has been happening is work on problems that sit underneath notation, problems that have been considered 'mostly solvable' at best since the 1980s. The deterministic accidental system I recently wrote about is one such problem. It looks abstract because it has to be. It deals with musical meaning before anything becomes visible.

This post is an attempt to explain why these terms keep appearing, and what they actually refer to, without turning this into a programming tutorial. It's written for musicians who are curious, not for programmers who already know the vocabulary.

​One reason Ooloi can attempt this at all is that it's a new system.

Most notation programs in use today have roots in techniques from the 1980s and 1990s. Internally, they tend to look surprisingly similar. They represent music in roughly the same way and rely on the same architectural assumptions: object-oriented design, mutable state, and large codebases written in C or C++.

Once a system has grown for decades on top of those assumptions, it becomes extraordinarily difficult to rethink its foundations without breaking everything at once. We saw Finale collapse in 2024 for precisely this reason.

There have been only two real departures from that lineage. One was Igor Engraver in the 1990s. The other was Dorico from 2016. Dorico has much in common with Igor Engraver in terms of musical data representation, and it made important advances. But even Dorico still rests on the technological assumptions of that era: object-oriented design, mutable state, and C++ at its core.

Ooloi puts all its money on a different assumption, namely that those older techniques fundamentally are architecturally inadequate for the problem of music notation as we now understand it. That inadequacy has consequences for users: accidentals behaving oddly, freezes and delays, limited scalability, no real collaboration, and poor use of modern multi-core machines.

​To address these problems, Ooloi uses an entirely different set of techniques.

​It also needs to be said very clearly that music notation, from a computer science perspective, is an extremely hard problem.

It's not 'a word processor for music'. That analogy has done lasting harm.

Music notation sits in the same general complexity class as compiler construction, symbolic mathematics systems, or advanced typesetting engines. It combines several difficult aspects at once: hierarchical structure, temporal meaning, long-range context, simultaneous layers, and a visual representation that's not a straightforward reflection of the underlying data.

A compiler reads a stream of symbols, builds meaning from context, enforces consistency rules, and produces deterministic output. Music notation does all of that, and then adds engraving conventions, historical practice, performer expectations, and visual clarity on top.

If you approach this domain with tools designed for relatively static documents or interactive graphics, you end up fighting the problem instead of modelling it. The result is systems that work impressively most of the time, but fail in edge cases, which in music aren't rare.

​Before any technical terminology enters the picture, there's a simple musical requirement.

If you engrave the same piece twice, you should get the same result twice.

Not roughly the same. Not 'close enough'. The same.

Most notation software quietly gives up on this requirement. Instead, they rely on rules of thumb: 'this usually works', 'this is how engravers tend to want it', 'clean this up manually if it looks odd'. Musicians have learned to live with that because, for a long time, there was no alternative.

From a musical point of view, this is deeply unsatisfactory. It means the system doesn't really know what it's doing. When things get complicated, it starts guessing. And once guessing enters the picture, everything downstream becomes fragile.

Determinism simply means that given the same musical input, the system makes the same musical decisions every time.

​Imagine packing a suitcase before a trip. You put clothes, toothpaste, shoes inside. Once the suitcase is closed and checked in, you make decisions based on what you packed. You don't buy extra clothes at the airport because you trust they're already there.

Now imagine that, while the suitcase is in transit, someone silently changes its contents. In a trivial case this is merely annoying. In a serious system – air-traffic control, medical records, nuclear command – it's catastrophic: people might die.

To reason about anything, you must be able to trust the past.

In computer science, immutability means this: once a thing has been created, it never changes. If you need a slightly different version, you don't alter the original. You create a new one. The old one remains exactly as it was.

This sounds wasteful until you realise that modern systems can do this efficiently by sharing structure internally. This is where a bit of Harry Potter magic comes in. If someone changes one shirt, they get a new suitcase with just that one shirt changed, while you still have your original suitcase, untouched and with the original shirt still inside.

In music notation this matters because the domain is full of remembered context. Accidentals depend on what happened earlier. Key signatures establish expectations. Voices interact. If earlier musical facts can silently change while later decisions depend on them, determinism collapses.

​Most people already understand from school what a function is.

If x is 100, the result is always 101. Not sometimes. Always.

That property is determinism.

Now imagine that x is not a number but a suitcase. If the function's result depends on what is inside the suitcase, you must be absolutely certain that the contents haven't changed since last time. And for this, the suitcase needs to be one of our magical suitcases. Otherwise, calling the same function twice with what looks like 'the same input' might silently produce different results. The consequences range from a missing accidental to obliterating Tokyo.

Functional programming is simply the discipline of insisting on this property at scale. Functions don't reach out and change things behind your back. They don't depend on hidden mutable state. They take inputs and return results without any such surprises.

In Ooloi this matters because musical decisions must be reproducible. If accidental decisions or tie behaviour depend on invisible state changes, the system cannot be fully trusted, even if it usually looks right.

A central idea in Ooloi is to treat the score as something that flows.

Music is read from left to right. Context accumulates. Decisions depend on what has already passed. Accidentals are remembered and later forgotten. Grace notes steal time from what they follow. Tuplets locally distort time.

This is not a static tree that you occasionally inspect. It's musical meaning - semantics - unfolding over time.

Once you accept that, you need a way to traverse this stream efficiently without constantly rebuilding lists or retracing paths.

​And this brings us to transducers.

​Imagine a high-security prison complex with multiple buildings, floors, and endless cells. Every day, a warden must traverse the entire structure to take stock of what's inside. And he must do it in the same order each day, just as the notes in a piece must be played in the same order each time.

Most of the warden's effort goes into navigation: remembering routes, tracking where he's been, writing lists just to keep his place. He does this over and over again, every day.

A transducer is like giving the warden Ariadne's thread. But again, there's magic involved: the thread weaves from cell to cell of its own accord. The route through the maze is fixed and reliable. Navigation stops being the problem. 

Better still, the warden doesn't even have to walk, thanks to more magic: the thread acts like a firehose and sends back all the information to the origin. The warden can sit in his office while the traversal happens and receive a continuous stream of information about what's found along the way. He can devote his entire attention to the meaning of the data, not how to walk the prison complex.

The crucial point is that traversal and processing are separated. The route is handled once. The real work happens as data flows past, without intermediate lists or repeated navigation.

In Ooloi, transducers allow musical meaning to be processed in exactly this way. The system doesn't build a large structure and then analyse it afterwards. It reacts to musical facts as they appear, deterministically and efficiently.

This is what a transducer is. Then there's even more wizardry involved in that several transducers can be stacked on each other to perform even more abstract operations. The path has been abstracted away, the distractions are gone, and the flow of  meaningful musical data is all that matters.

​These terms aren't ideology, and they're not badges of virtue. They're simply the most precise language I've found for describing how musical meaning behaves when you try to handle it rigorously.

The music comes first. The vocabulary follows.

​I'm re-reading Gardner Read's Music Notation from 1974. I bought my copy in 1977, which makes me 16 at the time – old enough to take it seriously, young enough to believe comprehensive understanding was achievable through diligent study. Later, this book would influence Igor Engraver's formatting decisions, though not always in ways I'd care to defend today.

What strikes me now is what Read doesn't cover. There's nothing about ledger line thicknesses, actual distances in spaces between noteheads and accidentals, sit-straddle-hang rules, slur curvatures, or tie formatting. None of the engraver-level detail that Elaine Gould's Behind Bars (2011) and Ted Ross's The Art of Music Engraving & Processing (1970, but I didn't discover it until much later) document so comprehensively. Read gives you musical orthography – what symbols mean and when to use them – but not typographical execution.

​When Magnus Johansson published examples of Igor's output on NOTATIO recently, I experienced that particular species of discomfort that comes from seeing your 25-year-old work through 2025 eyes. The ledger line thicknesses were wrong. The beam slants were inconsistent. We clearly knew nothing about sit-straddle-hang.

So what made Igor well-received? Not typographical perfection, that's certain.

First, integrated parts. Only Composer's Mosaic had them at the time, and Igor had them long before Finale or Sibelius. This alone solved a workflow problem that cost professional copyists days of manual labour.

Second, the user experience didn't fight the music. After spending years with Finale on The Maids – full score, parts, piano reduction – I ended up hating Finale. I've called it 'as user-friendly as a cactus' more than once. Creating something that didn't actively work against the creative process was evidently a sufficient innovation.

Third, note entry was fast and powerful. The modal Flow Mode interface that would later vanish completely from notation software for 23 years gave professional users substantial note entry and editing speed improvements. When you're saving many hours per score, you'll forgive a few ledger lines being slightly too thin – and there was a setting for that anyway.

Fourth, we had stellar MIDI playback and a semantic model that made things consistent rather than a collection of rules-of-thumb. That alone provided predictability. And everything could be adjusted – the absence of automatic sit-straddle-hang rules just meant more manual interventions.

The landscape in 1996 made these trade-offs reasonable. The streamlined experience outweighed what we today immediately see was missing.

​2025 is not 1996.

The leading programs have improved considerably since 1996. They're genuinely competent at beam placement and formatting – not flawless, but competent enough that egregious errors are rare.

A new program entering this landscape must get the foundations correct from day one. Beam placement, slurs, ties, accidental positioning – these must be flawless, not 'good enough to ship'. The field has progressed, and users' baseline expectations have risen accordingly.

This is as it should be. But there's something deeper that hasn't been solved.

Here's what I've stated repeatedly: Ooloi is not about 'disruption' or market share. The entire motivation is to escape what commercialism leads to and create something modern, scalable, and architecturally correct from the ground up. Why? Because music notation is an extremely messy and difficult field of computation, and it requires correctness to address its long-standing problems of scalability and accuracy.

This starts with internal representation.

The old programs – and many modern ones still in broad use – were all based on a paradigm inherited from MIDI. MIDI was the standard for pitch representation at the time, and all notation software needed MIDI output for playback anyway. This meant pitches were MIDI numbers (0-127) with attachments indicating whether they were sharp or flat. Figuring out musical context – for instance, to determine what accidentals to draw – had to be derived from something with no connection to musical structure whatsoever. It had to be inferred from context each time.
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That's at the root of the problems programs still have with accidentals. The internal representation is designed around the presentation – the visual aspect – not around the meaning, the semantics, of the music.

And of course, MIDI has no concept of microtonality, which is why notation programs struggle with microtonal entry, presentation, and playback.

Furthermore, for duration, these early programs based their rhythmic representation on a raster of 480 subdivisions – ticks – of a quarter note (TPQN: Ticks Per Quarter Note). A quarter note is 480 ticks long in some arbitrary tempo, an eighth is 240, and so forth. This is the equivalent of pixels in a JPEG, which means there's a limit to what the raster can represent.

The number 480 isn't evenly divisible by very many factors. This leads to all the problems we're still seeing in music notation programs. Various kinds of duct tape – rules of thumb, arbitrary rounding, tolerance spans – have to be used. When tuplets are nested, the approximation errors compound. We're still seeing the effects of this unfortunate MIDI heritage in 2025.

A MIDI-derived representation centred on presentation – the visual aspect – will always have difficulty interpreting what the music means. That interpretive layer is essential for presenting it correctly and consistently.

For that, you need a semantic model, which turns this on its head. The representation is 'musically correct' and detached from its presentation. Once this is in place, you can make informed decisions instead of relying on rounding and rules-of-thumb. It also makes things like playback trivial, which in MIDI-based systems is paradoxically complex.
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​Igor Engraver was, I believe, one of the first programs – possibly the very first – to use a fully semantic internal model. It was also the first to model the real world by using Musicians playing Instruments, which allowed new and powerful abstractions.

It's interesting that Dorico also has this arrangement, though they call their Musicians 'Players' – but it's the same thing. I have no idea whether Daniel Spreadbury was inspired by Igor here, but it's not unlikely. On the other hand, introducing Musicians/Players into the representational hierarchy is a logical choice once you commit to semantic modelling.

I'm not certain Dorico has a fully semantic model, though it's closer than any other program I know of. LilyPond doesn't, despite its sophisticated batch nature. One telling diagnostic: look at how they handle remembered accidentals for grace notes, and how they treat them rhythmically. Another: how durations are represented. If they're floating-point numbers, they're approximations. For true accuracy in all situations, you need rational numbers – infinite precision, always correct. Anything else eventually leads to problems.

If a program has problems with edge cases or behaves inconsistently when dragging things cross-staff, check how it represents pitch and duration. If floating-point is involved, or rasters of ticks (480 or otherwise), the representation isn't semantic. The program might still handle 95% of hairy accidental placements competently. But when it starts having problems with tied notes across key changes or grace notes at measure starts, you know rules-of-thumb are involved – which means results can never be fully deterministic.

Ooloi is fully semantic with the explicit intention of making results fully deterministic.

This might not matter if you're satisfied with what capable commercial programs achieve today. That's legitimate – they handle about 95% of cases well. But if you depend on the remaining 5%, or if you spend your days as an engraver adjusting those 5% repeatedly, then you understand what I mean by deterministic results saving considerable time.

Now, on to Gould and Ross – books that weren't available when Igor was created. We'd inevitably have implemented their specifications had we had time. But as you know, I was ousted from my own company by venture capital pop zombies before we could. They thought guitar tablature was more important than correct engraver-level beaming.

This time, there will be no guitar tablature at the expense of correct beaming and orthography. All things in their proper order. Lead sheets are kid's stuff, comparatively speaking, and will be added later as plugins.

​Bärenreiter, Durand, Peters, Schott, Universal Edition. Publishers whose engravers spent ten years learning how to disappear behind their craft.

The copper-plate aesthetic: bold, confident, generous. Staff lines weighty enough to guide the eye, noteheads round enough to feel sung, stems drawn with conviction.

Modern digital engraving forgot this. It grew thin, bloodless — optimised for screens instead of for musicians.

The lineage is clear, and the standard unchanging: those 1920s scores, those shortened ledger lines, that unspoken discipline that still knows how to sing.

We all worship at that shrine.