PHP

12 bytes:
<?php echo date('B'); ?>
48 bytes:
<?php echo sprintf("%03d",((time()+3600)%86400)/86.4|0); ?>

C, 56 bytes

main(){printf("%03d",(int)((time(0)+3600)%86400/86.4));}
Explanation:
  • %03d - tells printf to zero-pad up to 3 digits.
  • time(NULL)+3600 - gets amount of seconds (UTC) elapsed since epoch and adds an hour to it (UTC+1).
  • %86400 - divides epoch by the amount of seconds in a 24hr day and gets the remainder (representing seconds elapsed, so far, "today").
  • /86.4 - divide remaining seconds by 86.4 to get the ".beat" count since midnight (UTC+1).
Compile (MSVC):
C:> cl swatch.c
Compile (GCC):
$ gcc swatch.c
Java 143 bytes
import java.time.*;
interface A {
  static void main(String[] a) {
    System.out.format("%03.0f", LocalTime.now(ZoneId.of("UT+1")).toSecondOfDay() / 86.4);
  }
}
Javascript

    d=new Date();t=;console.log(Math.floor((360*d.getHours()+60*d.getMinutes()+d.getSeconds())/86.4));