joxn/gb_piano.py

## gb_piano.py
import math, itertools

def keyno(f):
    return 12 * math.log2(f/440) + 49

def gbfreq(n):
    return 131072/(2048-n)

def keyfreq(k):
    return math.pow(2, (k - 49)/12) * 440

def temper_cents(freq, actual):
    return 1200 * math.log2(freq/actual)

scale = itertools.cycle('C C♯ D D♯ E F F♯ G G♯ A A♯ B'.split())
oct = '₂ ₃ ₄ ₅ ₆ ₇ ₈'.split()
keys = {}
def update_keys(n):
    freq = gbfreq(n)
    key = round(keyno(freq))
    actual = keyfreq(key)
    if not (1 <= key <= 88):
        return
    temper = temper_cents(freq, actual)
    cn, cf, ca, ct = keys.setdefault(key, (n, freq, actual, temper))
    if abs(temper) < abs(ct):
        keys[key] = (n, freq, actual, temper)

for n in range(2048):
    update_keys(n)

head = '\nnote gb_n  key#   Hz actual  err'

cur_o = None
for (k, (n, freq, actual, temper)), note in zip(keys.items(), scale):
    o = oct[(k-16)//12]
    if o != cur_o:
        print(head)
        cur_o = o
    print(f'{note+o:4s} {n:4d}   {k:3d} {round(freq):4d}   {round(actual):4d} {round(temper): >+3d}¢')
	import math, itertools

	def keyno(f):
	return 12 * math.log2(f/440) + 49

	def gbfreq(n):
	return 131072/(2048-n)

	def keyfreq(k):
	return math.pow(2, (k - 49)/12) * 440

	def temper_cents(freq, actual):
	return 1200 * math.log2(freq/actual)

	scale = itertools.cycle('C C♯ D D♯ E F F♯ G G♯ A A♯ B'.split())
	oct = '₂ ₃ ₄ ₅ ₆ ₇ ₈'.split()
	keys = {}
	def update_keys(n):
	freq = gbfreq(n)
	key = round(keyno(freq))
	actual = keyfreq(key)
	if not (1 <= key <= 88):
	return
	temper = temper_cents(freq, actual)
	cn, cf, ca, ct = keys.setdefault(key, (n, freq, actual, temper))
	if abs(temper) < abs(ct):
	keys[key] = (n, freq, actual, temper)

	for n in range(2048):
	update_keys(n)

	head = '\nnote gb_n key# Hz actual err'

	cur_o = None
	for (k, (n, freq, actual, temper)), note in zip(keys.items(), scale):
	o = oct[(k-16)//12]
	if o != cur_o:
	print(head)
	cur_o = o
	print(f'{note+o:4s} {n:4d} {k:3d} {round(freq):4d} {round(actual):4d} {round(temper): >+3d}¢')