from numbers import Real

type _RealNumber = int | float | Real
type _TimeSignature = tuple[int, int]

def tick2second(tick: _RealNumber, ticks_per_beat: _RealNumber, tempo: _RealNumber) -> float:
    """Convert absolute time in ticks to seconds.

    Returns absolute time in seconds for a chosen MIDI file time resolution
    (ticks/pulses per quarter note, also called PPQN) and tempo (microseconds
    per quarter note).
    """

def second2tick(second: _RealNumber, ticks_per_beat: _RealNumber, tempo: _RealNumber) -> int:
    """Convert absolute time in seconds to ticks.

    Returns absolute time in ticks for a chosen MIDI file time resolution
    (ticks/pulses per quarter note, also called PPQN) and tempo (microseconds
    per quarter note). Normal rounding applies.
    """

def bpm2tempo(bpm: _RealNumber, time_signature: _TimeSignature = (4, 4)) -> int:
    """Convert BPM (beats per minute) to MIDI file tempo (microseconds per
    quarter note).

    Depending on the chosen time signature a bar contains a different number of
    beats. These beats are multiples/fractions of a quarter note, thus the
    returned BPM depend on the time signature. Normal rounding applies.
    """

def tempo2bpm(tempo: _RealNumber, time_signature: _TimeSignature = (4, 4)) -> float:
    """Convert MIDI file tempo (microseconds per quarter note) to BPM (beats
    per minute).

    Depending on the chosen time signature a bar contains a different number of
    beats. The beats are multiples/fractions of a quarter note, thus the
    returned tempo depends on the time signature denominator.
    """