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September 7, 2018 14:35
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Convert GB note numbers to piano notes
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| 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}¢') |
Author
joxn
commented
Sep 7, 2018
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