from __future__ import annotations

from fractions import Fraction
from typing import NamedTuple

STANDARD_TUNING = ((6, 40), (5, 45), (4, 50), (3, 55), (2, 59), (1, 64))
MIN_FRET = 0
MAX_FRET = 20
MAX_FRET_SPAN = 4
WRITTEN_GUITAR_OCTAVE_OFFSET = 12

class TabPosition(NamedTuple):
  string_number: int
  fret: int
  midi: int

def within_fret_span(positions) -> bool:
  fretted = [position.fret for position in positions if position.fret > 0]
  return not fretted or max(fretted) - min(fretted) <= MAX_FRET_SPAN

def positions_for_pitch(midi: Fraction) -> tuple[TabPosition, ...]:
  if midi.denominator != 1:
    return ()
  return tuple(TabPosition(string, int(midi - open_midi), int(midi)) for string, open_midi in STANDARD_TUNING if MIN_FRET <= midi - open_midi <= MAX_FRET)