Doodles: Tuning Systems

%pip install tabulate

import math
import itertools
from IPython.display import display, HTML, display_html, display_markdown, 
    Markdown
from tabulate import tabulate

type Hz = float
type Note = int

A_440_Note = 69
A_440_Hz = 440.0

def note_class(n: Note) -> tuple[int, int]:
    octaves, steps = divmod(n, 12)
    return octaves - 1, steps

def note_name(n: Note) -> str:
    # MIDI note 24 is C1
    note_names = ['C', 'C♯/D♭', 'D', 'D♯/E♭', 'E', 'F', 'F♯/G♭', 'G', 'G♯/A♭',
        'A', 'A♯/B♭', 'B'] octaves, steps = note_class(n)
    return f"{note_names[steps]}{octaves}"    

assert note_name(24) == 'C1'

from typing import Callable

def equal_tempered(n: int) -> Callable[[Note], Hz]:
    return lambda x: A_440_Hz * pow(2.0, (float(x - A_440_Note) / float(n)))

def tempered12tet(n: Note) -> Hz:
    return equal_tempered(12)(n)

table = tabulate(
    [(str(n), note_name(n), f"{tempered12tet(n): 0.04f}") for n in range(60, 82)],
    tablefmt='html',
    headers=('MIDI Note', 'Note Name', 'Hz'))

display(HTML(table))

Semitones_In_P5 = 7 # There are seven semitones in a perfect fifth
Center_Note = 60    # C4
Fifths_Window = 6   # We want the table to show 6 fifths above and below Center_Note

# implementation

Start_Note = Center_Note - Fifths_Window * Semitones_In_P5
End_Note   = Center_Note + (Fifths_Window + 1) * Semitones_In_P5

note_range = range(Start_Note, End_Note)
fifths_batches = itertools.batched(note_range, Semitones_In_P5)

Headings = ('Note Class', 'Fifth', 'Octave', 'Unison', 'm2', 'M2', 'm3', 'M3', 'P4', 'a4')

rows = []

for i, fifth_batch in enumerate(fifths_batches):
    row = []
    unison = fifth_batch[0]
    octave, step = note_class(unison)
    row.append(str(step))
    row.append(str(i-Fifths_Window))
    row.append(str(octave))
    row.extend([note_name(n) for n in fifth_batch])
    rows.append(row)

table = tabulate(rows, 
                 tablefmt='html',
                 headers=Headings)
display(HTML(table))