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2 changed files with 198 additions and 1 deletions
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.dummy
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.dummy
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.
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198
strings.py
Executable file
198
strings.py
Executable file
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#!/usr/bin/python
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mm_to_in = 0.03937
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scale_length = 648*mm_to_in
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string_sets = {
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'regular light': (
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# (desired note, tension, and type)
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('E4' , 16, 'PL'),
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('B3' , 16, 'PL'),
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('G3' , 16, 'PL'),
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('D3' , 16, 'NW'),
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('A2' , 16, 'NW'),
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('E2' , 16, 'NW'),
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),
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'light jazz': (
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('E4' , 24, 'PL'),
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('B3' , 24, 'PL'),
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('G3' , 24, 'NW'),
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('D3' , 24, 'NW'),
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('A2' , 24, 'NW'),
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('E2' , 24, 'NW'),
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),
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'regular light (DADGAD)': (
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('D4' , 16, 'PL'),
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('A3' , 16, 'PL'),
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('G3' , 16, 'PL'),
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('D3' , 16, 'NW'),
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('A2' , 16, 'NW'),
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('D2' , 16, 'NW'),
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),
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'open G (6-string)': (
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('D4' , 16, 'PL'),
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('B3' , 16, 'PL'),
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('G3' , 16, 'PL'),
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('D3' , 16, 'NW'),
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('B2' , 16, 'NW'),
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('D2' , 16, 'NW'),
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),
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'open G (7-string)': (
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('D4' , 16, 'PL'),
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('B3' , 16, 'PL'),
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('G3' , 16, 'PL'),
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('D3' , 16, 'NW'),
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('B2' , 16, 'NW'),
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('G2' , 16, 'NW'),
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('D2' , 16, 'NW'),
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),
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}
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# D'Addario stock via http://www.daddario.com/upload/tension_chart_13934.pdf
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stock = (
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# (product name, unit weight)
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# plain steel
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('PL007' , .00001085),
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('PL008' , .00001418),
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('PL0085', .00001601),
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('PL009' , .00001794),
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('PL0095', .00001999),
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('PL010' , .00002215),
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('PL0105', .00002442),
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('PL011' , .00002680),
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('PL0115', .00002930),
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('PL012' , .00003190),
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('PL013' , .00003744),
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('PL0135', .00004037),
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('PL014' , .00004342),
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('PL015' , .00004984),
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('PL016' , .00005671),
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('PL017' , .00006402),
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('PL018' , .00007177),
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('PL019' , .00007997),
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('PL020' , .00008861),
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('PL022' , .00010722),
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('PL024' , .00012760),
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('PL027' , .00014975),
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# nickelplated steel round wound (XL)
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('NW017' , .00005524),
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('NW018' , .00006215),
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('NW019' , .00006947),
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('NW020' , .00007495),
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('NW021' , .00008293),
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('NW022' , .00009184),
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('NW024' , .00010857),
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# they have a NW025 used in EXL110BT but it's not listed
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('NW026' , .00012671),
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('NW028' , .00014666),
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('NW030' , .00017236),
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('NW032' , .00019347),
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('NW034' , .00021590),
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('NW036' , .00023964),
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('NW038' , .00026471),
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('NW039' , .00027932),
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('NW042' , .00032279),
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('NW044' , .00035182),
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('NW046' , .00038216),
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('NW048' , .00041382),
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('NW049' , .00043014),
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('NW052' , .00048109),
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('NW054' , .00053838),
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('NW056' , .00057598),
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('NW059' , .00064191),
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('NW060' , .00066542),
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('NW062' , .00070697),
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('NW064' , .00074984),
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('NW066' , .00079889),
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('NW068' , .00084614),
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('NW070' , .00089304),
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('NW072' , .00094124),
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('NW074' , .00098869),
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('NW080' , .00115011),
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)
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A = 440
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notes = {
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'C' : 0,
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'D' : 2,
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'E' : 4,
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'F' : 5,
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'G' : 7,
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'A' : 9,
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'B' : 11,
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}
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rel = (2**(1/12.))
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def note2freq(name):
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sharp = name[1] == '#'
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flat = name[1] == 'b'
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if sharp or flat:
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note = name[0:1]
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octave = int(name[2])
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else:
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note = name[0]
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octave = int(name[1])
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num = notes[note]
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if sharp:
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num += 1
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if flat:
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num -= 1
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fullnum = num + 12*(octave - 5)
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return A*rel**(fullnum + 3)
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def test(name, expected):
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print('{:3} gave {: 9.2f} Hz\nexpected {: 9.2f} Hz'.format(name, note2freq(name), expected))
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if False:
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test('C2' , 65.41)
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test('Ab4', 415.30)
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test('A4' , 440.00)
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test('B4' , 493.88)
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test('B#4', 523.25)
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test('Cb5', 493.88)
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test('C5' , 523.25)
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print()
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test('E4' , 329.63)
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test('B3' , 246.94)
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test('G3' , 196.00)
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test('D3' , 146.83)
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test('A2' , 110.00)
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test('E2' , 82.41)
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uw_const = 386.4
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def uw2tension(uw, freq):
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return (uw*(2*scale_length*freq)**2)/uw_const
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def tension2uw(t, freq):
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return (t*uw_const)/(2*scale_length*freq)**2
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outfmt = '{:<6} at {:> 5.2f} lbs ({:>+4.2f})'
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finalfmt = 'total: {:>7.2f} lbs ({:>+5.2f})'
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def print_ideal_stock(strings):
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total_tension = 0
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total_desired_tension = 0
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for note, tension, kind in strings:
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freq = note2freq(note)
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uw = tension2uw(tension, freq)
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closest = ('n/a', 0)
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for name, stock_uw in stock:
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if kind and name[:len(kind)] != kind:
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continue
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if abs(stock_uw - uw) < abs(closest[1] - uw):
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closest = (name, stock_uw)
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closest_tension = uw2tension(closest[1], freq)
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diff = closest_tension - tension
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print(outfmt.format(closest[0], closest_tension, diff))
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total_tension += closest_tension
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total_desired_tension += tension
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error = total_tension - total_desired_tension
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print(finalfmt.format(total_tension, error))
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print('for a scale length of {:>5.2f} inches'.format(scale_length))
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for name, strings in string_sets.items():
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print()
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print('"{}"'.format(name))
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print_ideal_stock(strings)
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