Model Clock time signature change behavior after Ableton's

[josiah-wolf-oberholtzer]

When changing time signature, it applies retroactively against the last time signature change marker - effectively the time origin or wherever a time signature change marker was created.

Time signature change markers always create a new downbeat, even if that means truncating the measure preceding them (e.g. 3/8 of the way into a 4/4 bar).

[josiah-wolf-oberholtzer]

Implementation thoughts:

• Add last_downbeat_offset and last_downbeat_measure_number to clock state
• Add a set_downbeat bool to ChangeCommand
• Add a set_downbeat bool to Clock.change(), Clock.cue_change() and Clock.schedule_change()
• If setting the downbeat, update last_downbeat_offset, and increment last_downbeat_measure_number if necessary
• Update Moment.measure_offset calculations to make use of last_downbeat_...

[josiah-wolf-oberholtzer]

Starting the clock would look like:

    async def start(
        self,
        initial_time: Optional[float] = None,
        initial_offset: float = 0.0,
        initial_downbeat_offset: float = 0.0,
        initial_downbeat_measure_number: int = 1,
        time_signature: Optional[Tuple[int, int]] = None,
    ):
        ...

We're going to have to rework the existing ClockState's previous_measure and previous_time_signature_change_offset members, and all of the math referring to them.

All measure math / measure offset math needs to be relative to the last recorded downbeat.

[josiah-wolf-oberholtzer]

Might be able to drop the initial_ prefix.

Consider:

    async def start(
        self,
        time: Optional[float] = None,
        offset: float = 0.0,
        downbeat_offset: float = 0.0,
        downbeat_measure_number: int = 1,
        time_signature: Optional[Tuple[int, int]] = None,
    ):
        ...

I'm honestly not sure what the utility of the time argument is here... was it to synchronize with other clocks? Possibly for NRT applications actually...

Anyways, this also opens up the possibility of a seek(...) API:

    async def start(
        self,
        offset: float = 0.0,
        downbeat_offset: Optional[float] = None,
        downbeat_measure_number: Optional[int] = None,
        time_signature: Optional[Tuple[int, int]] = None,
    ):
        ...

... where time_signature, downbeat_offset, downbeat_measure_number are optionally recalculated from the current state.