Beat

In RPE, beat is the time unit for all events. It is represented as an int[3] and displayed in RPE as [0]:[1]/[2].

The calculation for a single BPM is as follows:

double beat = RPEBeat[1] / RPEBeat[2] + RPEBeat[0];
double seconds = 60 / BPM * beat;

For multiple BPM calculation, refer to the Python example below.

Python Example

• Assume self.BPMList is a list[BPMEvent].
• Definition of BPMEvent:

@dataclass
class BPMEvent:
    startTime: Beat
    bpm: float

• In sec2beat, t represents seconds, and bpmfactor corresponds to the bpmfactor field in the judgment line.
• In beat2sec, t represents beats, and bpmfactor corresponds to the bpmfactor field in the judgment line.
• It holds that beat2sec(sec2beat(x)) == x and sec2beat(beat2sec(x)) == x both evaluate to True.

The functions are defined as follows:

def sec2beat(self, t: float, bpmfactor: float):
    beat = 0.0
    for i, e in enumerate(self.BPMList):
        bpmv = e.bpm / bpmfactor
        if i != len(self.BPMList) - 1:
            et_beat = self.BPMList[i + 1].startTime.value - e.startTime.value
            et_sec = et_beat * (60 / bpmv)
            
            if t >= et_sec:
                beat += et_beat
                t -= et_sec
            else:
                beat += t / (60 / bpmv)
                break
        else:
            beat += t / (60 / bpmv)
    return beat

def beat2sec(self, t: float, bpmfactor: float):
    sec = 0.0
    for i, e in enumerate(self.BPMList):
        bpmv = e.bpm / bpmfactor
        if i != len(self.BPMList) - 1:
            et_beat = self.BPMList[i + 1].startTime.value - e.startTime.value
            
            if t >= et_beat:
                sec += et_beat * (60 / bpmv)
                t -= et_beat
            else:
                sec += t * (60 / bpmv)
                break
        else:
            sec += t * (60 / bpmv)
    return sec