# Development log

# November 19th, 2025

## Rhythm

Developing a theory of rhythm for unheard.

There is a natural tension between relative and
absolute positioning of time objects in time.

Let me try to define relative positioning.

Absolute positioning is positioning a time object at an absolute
location on a timeline. For example, an absolutely positioned
time object might span [1 4]. Part of the definition might include
the constraint that the position of absolutely-positioned
time objects is known at compile time.

A relatively positioned time object is positioned relative to some
other entity (a container or another time object, for example).
A time object is relatively positioned if the related entity's
position is not known at compile time.

Maybe a more interesting differentiation is time objects that
are known to exist at compile time vs time objects that are not.

Relative positioning makes the following challenging:
 - 

Relative positioning makes seeking challenging, since you have
to play through the timeline to get to an event. It is also
not obviously clear how temporal indexing would work with

Absolute positioning is substantially less flexible. How do
loops work 

I think this is probably one of the hardest pieces for me to get right. I'll be doing a lot of writing to help me better understand the problem space. Here are some of my high-level goals:

 - A composer should be able to decompose their composition into phrases, just like a programmer can decompose a program into functions. (Hint: phrases are functions!) A composer should be able to work on a phrase in isolation, at times iterating upon it without regard for the entire composition. At other times, it should be easy for the composer to hear a phrase in concert with other phrases.
 - It should be intuitive for a composer to write a piece that changes between time signatures.
 - It should be intuitive for a composer to express polyrhythms.
 - The playback engine should provide affordances for starting loops or phrases at the next downbeat. This interacts with the polyrhythm constraint in various ways. Regardless, I want to minimize surprise.
 - Seeking (that is, jumping to a point in a composition) should be instantaneous. This has far-reaching consequences: in particular, it precludes certain kinds of iterative composition, where state t2 = f(state t1).
 - Looping should be easy and flexible. Note, though, that the ban on iterative composition imposed by the previous bullet point seems to imply that looping can't exist at all! Fortunately, I have some theories for how to resolve this conflict. They need to be worked through, though.
 - It should be possible to slow down the tempo of a song to (nearly) arbitrarily small values. Same for speeding up. This would allow for some kind of rhythmic fractals, where tempo slows down forever (while new subdivisions of tempo appear continuously). I've been looking into how "infinite zoom" fractal renderers represent zoom steps numerically, and hope to lift some of that into the playback engine.
 - Related to the above, I want to provide some kind of mechanism for expressing recursive rhythms – that is, a rhythm that plays concurrently at tempo t, 2t, 1/2t, 4 t, 1/4t, etc. (A composer would specify the number of iterations they want to play above and below t.) This mechanism would account for tempo zooming automatically.

As the theory of rhythm develops, I'll find that some of the above goals are fundamentally incompatible, so I'll have to make choices. That will be part of the fun.

## Key questions

 - The monotonic clock is ticking. That's cool. But what is the
 relationship between monotonic clock time and a note's actual input?
 That is, how does a clock (wall or pulse) query a note's presence?
 Especially when they are composed?
   
## Things I'm pretty sure about

 - Base unit should be a beat, and durations should be expressed
   as fractional beats (e.g. 1/4, 2/1).
 - Take a look at my "static" topology diagram, and consider that
   flows can bind to positions. Given that, maybe it is possible
   to have dynamic topologies. Put differently: As long as every
   dynamic topology input flow is continuously defined, then going
   "back in time" can mean "reversing the current state". This
   _DOES NOT_ mean reversing time, or even guarenteeing that what
   you play backward is the same as what you play forward.

What might happen when you hit play under this model?
You pass a flow into a player
The player sets time to init-time
The pulse clock starts pulsing

## Random notes

What is the "smallest time unit" that we want to represent?
We have to specify the number of "smallest time units" in a pulse.

I _think_ this is tightly tied to recursive zooming in. We can
specify durations as [128th notes, zoom level]
We increment zoom level when zooming in

We can set a "max frequency" for control information (say 100hz).
Then, our time-recursive function can short-circut any recursive objects
whose children have a minimum frequency that falls below the max frequency.
This will require that time objects emit min-frequency metadata,
which can be derived by finding the longest child.

This is a wild theory - test this tomorrow.

Actually, a better solution would be to just put the composer in control.
The composer should specify that they want n doublings or halvings of
a given phrase played concurrently.


## Solving for:

## Time signature changes
How does this interact with looping?

## Concurrent phrases with differing time signatures

It should be possible for concurrent time signatures to emit
their:
 - Offset
 - Numerator
 
They can be then merged together to create a data structure
containing lazy seqs of "beats" at each combination
Actually, just provide a function that takes offsets and numerators
and the "combination" that you're looking for, and returns
a lazy seq of beating indices

## Tick frequency

Monotonic clock frequency is tied to doubling or halving of tempo,
along with "discrete nyquist"

### Looping

What would it mean for each "phrase" to have its own derived timeline? 
(Maybe not literally a phrase, maybe some container designed for this).
and what would it mean if these phrases could have timeline offsets
that repeat?

### Jump back

Similar to a repeat in music theory. A timeline GOTO.

### Static repeat

Not actually a loop. This is calling a phrase again and again,
adding the phrase's length to the offset at each repetition.

## Phrase isolation
It should be easy to play a phrase by itself. In fact, it should be possible to
loop a phrase so yo can just hear it while you're working on it

Should create repl.play and repl.repeat:

(play phrase)
(play phrase 130)

(repeat phrase)
(repeat phrase 130)

(stop)

### Start a phrase at the next downbeat


### Start a phrase at the next polyrhythmic co-downbeat


### Abstract phrases away as functions


### Make seeking both easy to reason about and performant


### Sensible reverse playback (rolling a tempo from pos to neg)


### Express fractional notes sensibly

# November 20th, 2025

## Summary of yesterday's "theory of rhythm" noodling:

Must support:
 - Playing a phrase in isolation
 - Looping
 - Seeking
 - Time signatures and time signature changes
 - Coming in at the next downbeat
 
 Don't box out:
 - Polyrhythms
 - Unlimited slowing and speeding

 Looping means a few things:
 - Jumping back, identical to a repeat in music notation. Timeline goto.
 - Static repeat. That is, play phrase x n times. Note that this is is
   repeating, not looping. 

Insights:
 - Don't support iterative composition, where f(t2) = f(f(t1)).
   Iterative composition makes seek time linear with composition
   length. 
 - The monotonic clock frequency is closely related to the maximum
   number of events per second that we want to emit. 
 - Theoretically, infinite zoom could automatically derive the number
   of doublings and halvings to play by looking at the monotonic
   clock frequency and the longest event in a phrase. Doublings
   that would result in no event changes due to all events falling
   below the monotonic clock sampling rate could stop upward
   recursion. This seems complicated to implement in practice,
   but would technically work. (Think nyquist.)
 - Concurrent time signatures could emit their start offset and
   numerator. We could provide a function that takes offsets and
   numerators and returns a lazy seq of polyrhythmic downbeat
   positions.

Open questions:
Should base unit should be a beat, with durations based
as fractional units of a beat (e.g. 1/4, 4/1)? Or should base unit
account for time signature denominator? My hunch is that the internal
representation should be fractional beat, with helper functions that
convert current time signature to fractional beats.

## More brainstorming

Let me try to describe how the various decisions suggested above
could compose. I'll start at the end, and work backward.

You have a musical phrase representing your composition
or a part of it, and you want to play that phrase. The phrase
is a `timeline` object. The playback engine will query the
timeline object.

First,
you connect it to the playback engine:

```
(on-deck phrase input-map-f output-map-f)
```

`input-map-f` is a function that accepts the playback engine's available input
subsystems (initially just `{:midi midi-message-flow}`, but potentially
containing things like dmx and osc,) and returns a flow of a map wiring up the
input arguments of the composition.

Now, play the song:

```
(play 120)
```

`play` starts the clock, querying the timeline object as needed.

```
(pause)
```

`pause` pauses the piece.

```
(resume)
```

`resume` resumes the piece.

```
(play)
```

`play` with no arguments starts the piece from the beginning.

```
(loop)
```

`loop` with no args automatically resets the playback
position to the beginning at the end of the piece.

```
(loop start end)
```

This form of `loop` loops a segment of the composition.

(Aside: A pulse clock emits integers at the pulse rate. The
emitted integer represents the current _zoom level_.)

Open question: The playback engine queries the timeline at clock
positions. How does this relate to zoom levels? Is zoom level
part of the query?

### Random thoughts

Right now, phrases are eagerly composed together. This means that
if you redefine part of a piece, you have to redefine all of its
dependents, too. This might make interactive development annoying.

# November 21st, 2025

## Key insights

There is no need for a minimum rhythmic division! Just use fractions of a beat,
all the way down to the time-object / interval tree. It seems obvious in
hindsight.

## New ideas

Phrases can be named (at invocation time, not definition time). This will allow you to quickly jump to a phrase.

Then, in the UI, we can the tell you where you are and where you can jump to.

Note that since phrases can be nested, phrase names are concatenated into a
vector of [outer inner], arbitrarily many deep.

Looping can be enabled / disabled for a named phrase.

When the playhrad rolls into an enabled loop, it will play until the end of the
phrase, at which point it will jump the timeline back to the start of the looped
phrase. This works with nested phrases / loops. If nested loops are enabled, the
innermost loop takes precedence.

## TODO:
Document the bug that could occur if two tim object flows invocations shared an identity
Write down idea about the difference between a tree and a dag
Write down the static topology decision / summarize theory of time.

## November 22nd, 2025

To think about:

 - What about wanting to change note durations live? Coupling notes directly to time objects
   seems like it might be too strict
 - What if phrases / groups were also time objects? I feel like I'm fundamentally questioning everything :/
 - Maybe create "static-note" which is a time object, and "dynamic note" which is not?

Maybe this panic is not a big deal. I think I should go ahead and continue with "note as fixed duration". After all, a note doesn't _have to_ play during the entire duration. It's more like it _can_. Swing, variability, etc. can all still be accomplished via other means.

## November 25th, 2025

Okay, time to write down some confusion.

What do all the time objects eventually get merged into?

Something with the following qualities:
 - It is a data structure representing various output effect providers, e.g. MIDI
 - Each output effect provider has its own... mergin semantics?
 - Time objects are created and destroyed?
 
 Is it possible / does it make sense to differentiate over the
 stream of all events emitted from a phrase? One dimension to differentiate
 over would be the flow associated with a particular time object. I already
 know how to do this - I could modify the reconcile-merge function to accomplish this.
 
I think there is probably another dimension that I'm not thinking of. In my
original group operator, I emitted a value for content in the "enabled" state,
and I emitted the empty set in the "does not exist" state. My original `poly`
performed a set union of all active notes. This then would have been differerntiable;
I could have used the differentiate function from my new missionary.util.

What is less clear to me is how to achieve the same behavior with time objects.
I think that I could modify note to return e.g. the empty set in my note
function. But how would I then group them? Would I want to couple the
grouping context with note?

OH! Maybe we want to group-by e.g. :note? That is, each time object-producing
function would be able to direct its contents to a differentiable grouping operator
for that particular type?

Remember that this was the original definition of poly and group:

(defn poly
  [& notes]
  (m/signal (m/cp (apply union (m/?< (apply m/latest vector notes))))))

;; TODO: Group could actually wrap note, rather than using explicitly
;; WIll introduce a lot of GC churn, though
(defn group
  [clock start end content]
  (m/cp (let [content (m/signal content)]
          (if (m/?< (m/latest #(<= start % end) clock))
            (m/?< content)
            (m/amb #{})))))

Oh, here's an idea. What if we merged the union semantics from poly with the
lifecycle semantics of reconcile-merge? That is, rather than emitting from
each time object's flow, we instead unioned the latest elements from each time object?
Can I do that?

Why did poly originally work?

Each note emitted either the empty set or a set containing its value.
Multiple notes' groups were merged emit-wise:

#{1} #{} #{} -> #{1}
#{1} #{2} #{} -> #{1 2}
#{} #{2} #{3} -> #{2 3}

That is, _each note's state_ was sampled on each emit. This is due to the
behavior of m/latest. latest is fundamentally not a differentiable operator.

The behavior of reconcile-merge is more like:

#{1} -> #{1}
#{} -> #{} ;; Failure! We forgot about the presence of #{1}

Could we turn that into:

{} -> #{}
{1 true} -> #{1}
{2 true} -> #{1 2}
{1 false} -> #{2}
{3 true} -> #{3}

Yes! We could! And in fact this is what the differentiate function does.

Now, how do we get {1 true} and {1 false}? That is, where do we define
that 1 has been created and then destroyed?

One of the things that m/latest relies on to work is the notion of "being
able to sample everything at once." That is, "sampling all notes at once.""

The set-events function is allowing us to group lifecycle events by time-object
flow.

We could use time-object lifecycle information to emit {id true} at the start
of a time object's lifecycle and {id false} at the end, but this would require
that we have a notion of identity for each time object. The question is, do
we always? Imagine (note ... (m/ap (m/?< clock))), e.g. the value of a note
is dynamic. Then, what is its identity?

Ah! So this is one of the core differences between emit-wise grouping using
m/latest, and differentiated lifecycles. The former allows for _anonymous_
object identities, while in the latter, objects really do need IDs.

But do the IDs need to be visible? I think maybe not. (might be wrong, though.)
It might be possible to create identities for them within the body of reconcile-
merge. (Generate one, then create :up, then include on emit, and then :down).

I like this idea.

## November 28th, 2025

Very happy with wednesday's progress. Time to nail down a few more things.

1. How should I match phrases up to input sources?
2. How should I account for there eventually being multiple input media
   types, like OSC, DMX, etc., all with their own semantics?
3. How should input sources flow through phrase composition?

Currently, `note` and `phrase` are called differently in a way that doesn't
make much sense to me. I need to play with that syntax a bit, too.

There's another interesting question that is really sticky. Imagine for
a moment that I eventually want to take musical-like inputs from multiple
sources, e.g. midi and OSC. I want to perform a similar mapping on the
output side. Imagine I want to map from MIDI in to OSC out. This suggests
that using MIDI as my internal representation for harmonic information
probably isn't the best idea, even if it is the easiest. Another example
is non-standard tunings, or music where one wants frequency-level control.
Okay, so what would the internal representation of harmonic information
be? I want something fairly flexible but not crazy. Probably just
[frequency amplitude] to begin with.

Anyway. I need to start thinking about these things, which are all related.

Let's do some experimenting.

Here is a current example:

```clojure
(defn triad
  [>c >tonic]
  (phrase
    ;; This is a major cord,
    ;; held 32 32nd notes.
    ;; The tonic can vary.
    (note >c 0 0 32 >tonic)
    (note >c 0 0 32 (m/latest #(+ % 4) >tonic))
    (note >c 0 0 32 (m/latest #(+ % 7) >tonic))))

(defn drums
  [>clock]
  (phrase (note >clock 1 1 1 (m/ap kick))
          (note >clock 1 9 1 (m/ap kick))
          (note >clock 1 17 1 (m/ap kick))
          (note >clock 1 25 1 (m/ap kick))
          (note >clock 1 1 1 (m/ap hat))
          (note >clock 1 5 1 (m/ap hat))
          (note >clock 1 9 1 (m/ap hat))
          (note >clock 1 13 1 (m/ap hat))
          (note >clock 1 17 1 (m/ap hat))
          (note >clock 1 21 1 (m/ap hat))
          (note >clock 1 25 1 (m/ap hat))
          (note >clock 1 29 1 (m/ap hat))
          (note >clock 1 5 1 (m/ap snare))
          (note >clock 1 13 1 (m/ap snare))
          (note >clock 1 21 1 (m/ap snare))
          (note >clock 1 29 1 (m/ap snare))))

(defn song'
  [>clock >tonic]
  (phrase ((triad >clock >tonic) 0)
          ((triad >clock (m/latest #(+ % 12) >tonic)) 0)
          ((drums >clock) 0)))
```

Things that stand out:
1. It is interesting that `phrase` doesn't take a flow.
2. I don't like that `note` takes a midi :ch argument. Too
   coupled with a particular output medium. (But I also don't want
   to get _too far_ from the specific output medium and risk creating
   surprising behavior.)
3. These examples aren't actually great because we don't actually do
   much that is interesting with argument passing.
4. The invocation of triad and drums in song is gross.
5. It is unclear how happens-before relationships would be structured.
6. We pass clock in explicitly, but it isn't actually clear why.
7. Should we encourage phrases to use argument names that are coupled
   to input types, or to give them names that are meaningful to the
   music itself?
8. How do I want to specify outputs?

Here is a first pass at rewriting:

```clojure
(defn triad
  [>tonic]
  (phrase
    ;; This is a major cord,
    ;; held 32 32nd notes.
    ;; The tonic can vary.
    (note 0 0 32 >tonic)
    (note 0 0 32 (m/latest #(+ % 4) >tonic))
    (note 0 0 32 (m/latest #(+ % 7) >tonic))))

(defn drums
  []
  (phrase (note 1 1 1 (m/ap kick))
          (note 1 9 1 (m/ap kick))
          (note 1 17 1 (m/ap kick))
          (note 1 25 1 (m/ap kick))
          (note 1 1 1 (m/ap hat))
          (note 1 5 1 (m/ap hat))
          (note 1 9 1 (m/ap hat))
          (note 1 13 1 (m/ap hat))
          (note 1 17 1 (m/ap hat))
          (note 1 21 1 (m/ap hat))
          (note 1 25 1 (m/ap hat))
          (note 1 29 1 (m/ap hat))
          (note 1 5 1 (m/ap snare))
          (note 1 13 1 (m/ap snare))
          (note 1 21 1 (m/ap snare))
          (note 1 29 1 (m/ap snare))))

(defn song'
  [>tonic]
  (phrase ((triad >tonic) 0)
          ((triad (m/latest #(+ % 12) >tonic)) 0)
          ((drums) 0)))
```

Looks cleaner without clock. This doesn't mean that
clock can't be passed explicitly, just that it isn't necessary
by default.

What about specifying outputs? Already there is an interesting
decision to make. On drums, would one want to treat each drum as
its own output, or treat them as simply different parts of the same
instrument?

What is an output? Is it an instrument? I think the only honest answer
is that this question can't be answered in general. Sometimes it will
make sense to think of a cow bell as an instrument, and sometimes as a
component of a percussion kit.

The point of an output, I think, is to somehow group output information
together. I think it is fair to say that everything on the same output
will share some semantics. From a programming perspective, the state
of an output should be uniform: a single data structure, and a single
merge operation.

The data structure and merge operation shouldn't be re-written for each
instrument. There will only be a few of these. Keyed instruments like
pianos will be able to share a single data structure and merge operation,
even if a harpsichord won't make use of velocity information.

When writing a phrase, one specify the data structure and merge
operation. This actually isn't a property of the phrase, though, it
is a property of the particular part of the phrase that is being
described. Remember that a phrase may have many instruments in it,
and therefore many data structures and merge ops.

This makes me wonder: beyond phrase and time object, is there another
concept that I should introduce? Something like "instrument"? 

```clojure
(defn triad
  [>tonic]
  (phrase
    (instrument keyboard
      (note 0 32 >tonic)
      (note 0 32 (m/latest #(+ % 4) >tonic))
      (note 0 32 (m/latest #(+ % 7) >tonic)))))

(defn drums
  []
  (phrase
    (instrument percussion
      (note 1 (m/ap kick))
      (note 9 1 (m/ap kick))
      (note 17 1 (m/ap kick))
      (note 25 1 (m/ap kick))
      (note 1 1 (m/ap hat))
      (note 5 1 (m/ap hat))
      (note 9 1 (m/ap hat))
      (note 13 1 (m/ap hat))
      (note 17 1 (m/ap hat))
      (note 21 1 (m/ap hat))
      (note 25 1 (m/ap hat))
      (note 29 1 (m/ap hat))
      (note 5 1 (m/ap snare))
      (note 13 1 (m/ap snare))
      (note 21 1 (m/ap snare))
      (note 29 1 (m/ap snare)))))
```

Oh, interesting. `triad` isn't just a keyboard concept!

Instrument feels like a pretty specific name. I don't think I love that.

But it is bringing up an interesting thought. Phrases compose together,
but it seems like things like `notes` _do_ have some kind of wrapper
context that separates them for a phrase. We can actually see this distinction
repeated in the programming context, with the presence of `lift`.

Maybe `lift` and `instrument` are the same thing?

How would the generic concept of a triad be expressed outside
of the instrument context? Here's what I mean. I want to support the
creation of the music theory concept of a triad and import it into any
instrument such that it can be used in any phrase.

Oh, maybe the problem is that the triad helper function should actually just
be something that returns three flows, one for each note in the interval.
Or even a flow-returning function that takes a root and a degree?
e.g.

```clojure
(defn piano
  [>root]
  (let [triad (theory/triad :major >root)])
  (phrase
    (instrument keyboard :keyboard ;; keyboard is the name of a data structure / merge op;
      (note 1 32 (triad 1))        ;; :keyboard is declaring an abstract output destination
      (note 1 32 (triad 3))
      (note 1 32 (triad 5)))))

(defn drums
  []
  (phrase
    (instrument percussion :drums
      (note 1 (m/ap kick))
      (note 9 1 (m/ap kick))
      (note 17 1 (m/ap kick))
      (note 25 1 (m/ap kick))
      (note 1 1 (m/ap hat))
      (note 5 1 (m/ap hat))
      (note 9 1 (m/ap hat))
      (note 13 1 (m/ap hat))
      (note 17 1 (m/ap hat))
      (note 21 1 (m/ap hat))
      (note 25 1 (m/ap hat))
      (note 29 1 (m/ap hat))
      (note 5 1 (m/ap snare))
      (note 13 1 (m/ap snare))
      (note 21 1 (m/ap snare))
      (note 29 1 (m/ap snare)))))

(defn song'
  [>root]
  (phrase ((piano >root) 0)
          ((piano (m/latest #(+ % 12) >root)) 0)
          ((drums) 0)))
```

Question: How would I handle the fact that triad might represent notes
as notes, while an output method might represent in frequencies? I think
I would want some kind of `note` protocol that can convert between different
representations.

I think it does make sense that, unlike phrases, outputs / instruments
can't be nested.

Can a phrase have multiple instruments / outputs? I think the
answer should probably be "yes". That would mean abstractions could
return instruments rather than phrases. This would be nice because
it would remove a layer of unnecessary naming in the naming tree. Example:

```clojure
(defn piano
  [>root]
  (let [triad (theory/triad :major >root)])
  (instrument keyboard :keyboard ;; keyboard is the name of a data structure / merge op;
    (note 1 32 (triad 1))        ;; :keyboard is declaring an abstract output destination
    (note 1 32 (triad 3))
    (note 1 32 (triad 5))))

(defn drums
  []
  (instrument percussion :drums
    (note 1 (m/ap kick))
    (note 9 1 (m/ap kick))
    (note 17 1 (m/ap kick))
    (note 25 1 (m/ap kick))
    (note 1 1 (m/ap hat))
    (note 5 1 (m/ap hat))
    (note 9 1 (m/ap hat))
    (note 13 1 (m/ap hat))
    (note 17 1 (m/ap hat))
    (note 21 1 (m/ap hat))
    (note 25 1 (m/ap hat))
    (note 29 1 (m/ap hat))
    (note 5 1 (m/ap snare))
    (note 13 1 (m/ap snare))
    (note 21 1 (m/ap snare))
    (note 29 1 (m/ap snare))))

(defn song'
  [>root]
  (phrase :first-verse
    ((piano >root) 0)
    ((piano (m/latest #(+ % 12) >root)) 0)
    ((drums) 0)))
```

Okay, important to note here:
1. I think the name associated with the call to `instrument` is actually
   setting the name on the implicit `phrase` that the call to instrument is
   returning.
2. A goal that I am trying to achieve here is implicit, unambiguous naming. Here,
   I've accomplished that for drums ([:first-verse :drums]) but not for piano.
   Let's try again?

```clojure
(defn piano
  [>root]
  (let [triad (theory/triad :major >root)])
  (instrument keyboard
    (note 1 32 (triad 1))
    (note 1 32 (triad 3))
    (note 1 32 (triad 5))))

(defn drums
  []
  (instrument percussion
    (note 1 (m/ap kick))
    (note 9 1 (m/ap kick))
    (note 17 1 (m/ap kick))
    (note 25 1 (m/ap kick))
    (note 1 1 (m/ap hat))
    (note 5 1 (m/ap hat))
    (note 9 1 (m/ap hat))
    (note 13 1 (m/ap hat))
    (note 17 1 (m/ap hat))
    (note 21 1 (m/ap hat))
    (note 25 1 (m/ap hat))
    (note 29 1 (m/ap hat))
    (note 5 1 (m/ap snare))
    (note 13 1 (m/ap snare))
    (note 21 1 (m/ap snare))
    (note 29 1 (m/ap snare))))

(defn song'
  [>root]
  (phrase
    ((piano >root) :piano-1 0)
    ((piano (m/latest #(+ % 12) >root)) :piano-2 0)
    ((drums) :drums 0)))
```

Here, `phrase` is returning an invokable object that receives a name. If I were
to repeat song twice, we would get:

```clojure

(defn song
  [>root]
  (phrase
    ((song' >root) :first-verse 0)
    ((song' >root) :second-verse 32)))
```

Now we have the following unambiguous output addresses:

{:first-verse [:piano-1 :piano-2 :drums]
 :second-verse [:piano-1 :piano-2 :drums]}


Here's an aesthetic goal - make phrase invocation look more like:

```clojure
(defn song'
  [>root]
  (phrase
    (piano >root :piano-1 0)
    (piano (m/latest #(+ % 12) >root) :piano-2 0)
    (drums :drums 0)))

(defn song
  [>root]
  (phrase
    (song' >root :first-verse 0)
    (song' >root :second-verse 32)))
```

I'm still not sure that I understand what a `note` is. What are other
objects like it? You could make something like a `pulse`, representing a
sine wave controlling an LFO. I guess from a programming perspective,
a note is an instance of some kind of object that becomes a signal
associated with output state and an ouput 'context' that explains how
similar objects get merged together. That output context receives a
name, and the name is guaranteed to be unique through multiple
nestings.

Here's a question. Should phrases be responsible for renaming their
children? This could help control name explosions, where a long composition
could have many many names to map before playback.

Yeah, that seems worth exploring. You could have some kind of rename map:

(phrase
  {[:first-verse :piano-1] :piano-1
   [:second-verse :piano-1] :piano-1
   [:first-verse :piano-2] :piano-2
   [:second-verse :piano-2] :piano-2
   [:first-verse :drums] :drums
   [:second-verse :drums] :drums})

This would mean that you could do

```clojure
(play {:piano-1 midi-out-1 :piano-2 midi-out-2 :piano-3 midi-out-3} song)
```

Big question: Why is there this difference between the way
I represent inputs (arguments) and outputs?

Questions from today that remain open:

1. What does this look like with a more complex example?
2. What do happens-before relationships look like? (Marco?)
3. Why do inputs look familiar (arguments) while outputs look strange (keywords)?
4. Do we need this instrument / output concept? What is it, exactly? What does it do?
5. How would a swung clock fit into all of this? Here again, time seems a little
   different. Swung clocks need to interact with timeline selection.
   Time objects should probably specify their clock. At playback time,
   you define one or more clocks.
6. I don't curently have a good answer to crossfades.
7. Need to brainstorm more on loops / goto / portals and their relationship
   with phrases.

Insights:

The point of an output, I think, is to somehow group output information
together. I think it is fair to say that everything on the same output
will share some semantics. From a programming perspective, the state
of an output should be uniform: a single data structure, and a single
merge operation.

The data structure and merge operation shouldn't be re-written for each
instrument. There will only be a few of these. Keyed instruments like
pianos will be able to share a single data structure and merge operation,
even if a harpsichord won't make use of velocity information.

From a programming perspective,
a note is an instance of some kind of object that becomes a signal
associated with output state and an ouput 'context' that explains how
similar objects get merged together. That output context receives a
name, and the name is guaranteed to be unique through multiple
nestings.

Music theory concepts like triad can be expsosed as flow-returning functions.

Outputs / instruments can't be nested, unlike phrases.

A phrase can contain multiple instruments / outputs.

Create a note protocol that generalizes over concrete note representation.

Phrases can simplify the names of their children by providing a rename map.

Concepts to test:

1. Confirm that working on a phrase in isolation and working on a whole piece are
   similarly simple

Other random thoughts:

It seems worth giving time objects explicit 
Every leaf must be a time object
At this point, time objects should contain other metadata, like their path from
enclosing phrases
Time objects and phrases should have a similar... calling convention? with regards to
offset (almost certainly) and duration (maybe)
Time objects will eventually need a serializable identity for display purposes
Both time objects and phrases should be reified for display/interactivity
purposes

## November 29th, 2025

As an exercise, I'd like to create a function that compiles strudel
mini notation down to my IR.

https://strudel.cc/learn/mini-notation/
https://strudel.cc/learn/mondo-notation/
https://strudel.cc/learn/factories/
https://strudel.cc/learn/time-modifiers/

And why this?

https://strudel.cc/learn/stepwise/

Also do a dissection of strudel's alignment system:

https://strudel.cc/technical-manual/alignment/

And this section on voicing:

https://strudel.cc/understand/voicings/

---

What would it mean to reify temporal specifiers, so that they become objects
which can be shortened / lengthened through a series of operations? Keeping in
mind that these little windows encapsulate arbitrary values. They would compose
into a callable which can somehow be invoked with the time object itself, e.g.
the note(s)


## December 1st, 2025

TODO upcoming:

 - Inspired by strudel, define a language of musical modifiers
 - Read notes of Nov. 28