gists/strings.py

#!/usr/bin/python

mm_to_in = 0.03937
scale_length = 648*mm_to_in

string_sets = {
    'regular light': (
        # (desired note, tension, and type)
        ('E4' , 16, 'PL'),
        ('B3' , 16, 'PL'),
        ('G3' , 16, 'PL'),
        ('D3' , 16, 'NW'),
        ('A2' , 16, 'NW'),
        ('E2' , 16, 'NW'),
    ),
    'jazz light': (
        ('E4' , 24, 'PL'),
        ('B3' , 24, 'PL'),
        ('G3' , 24, 'NW'),
        ('D3' , 24, 'NW'),
        ('A2' , 24, 'NW'),
        ('E2' , 24, 'NW'),
    ),
    'regular light (DADGAD)': (
        ('D4' , 16, 'PL'),
        ('A3' , 16, 'PL'),
        ('G3' , 16, 'PL'),
        ('D3' , 16, 'NW'),
        ('A2' , 16, 'NW'),
        ('D2' , 16, 'NW'),
    ),
    'regular light (open G, 6)': (
        ('D4' , 16, 'PL'),
        ('B3' , 16, 'PL'),
        ('G3' , 16, 'PL'),
        ('D3' , 16, 'NW'),
        ('B2' , 16, 'NW'),
        ('D2' , 16, 'NW'),
    ),
    'regular light (open G, 7)': (
        ('D4' , 16, 'PL'),
        ('B3' , 16, 'PL'),
        ('G3' , 16, 'PL'),
        ('D3' , 16, 'NW'),
        ('B2' , 16, 'NW'),
        ('G2' , 16, 'NW'),
        ('D2' , 16, 'NW'),
    ),
}

# D'Addario stock via http://www.daddario.com/upload/tension_chart_13934.pdf
stock = (
# (product name, unit weight)
# plain steel
    ('PL007' , .00001085),
    ('PL008' , .00001418),
    ('PL0085', .00001601),
    ('PL009' , .00001794),
    ('PL0095', .00001999),
    ('PL010' , .00002215),
    ('PL0105', .00002442),
    ('PL011' , .00002680),
    ('PL0115', .00002930),
    ('PL012' , .00003190),
    ('PL013' , .00003744),
    ('PL0135', .00004037),
    ('PL014' , .00004342),
    ('PL015' , .00004984),
    ('PL016' , .00005671),
    ('PL017' , .00006402),
    ('PL018' , .00007177),
    ('PL019' , .00007997),
    ('PL020' , .00008861),
    ('PL022' , .00010722),
    ('PL024' , .00012760),
    ('PL027' , .00014975),

# nickelplated steel round wound (XL)
    ('NW017' , .00005524),
    ('NW018' , .00006215),
    ('NW019' , .00006947),
    ('NW020' , .00007495),
    ('NW021' , .00008293),
    ('NW022' , .00009184),
    ('NW024' , .00010857),
    ('NW025*', .00011875), # from the EXL110BT, an approximation
    ('NW026' , .00012671),
    ('NW028' , .00014666),
    ('NW030' , .00017236),
    ('NW032' , .00019347),
    ('NW034' , .00021590),
    ('NW036' , .00023964),
    ('NW038' , .00026471),
    ('NW039' , .00027932),
    ('NW042' , .00032279),
    ('NW044' , .00035182),
    ('NW046' , .00038216),
    ('NW048' , .00041382),
    ('NW049' , .00043014),
    ('NW052' , .00048109),
    ('NW054' , .00053838),
    ('NW056' , .00057598),
    ('NW059' , .00064191),
    ('NW060' , .00066542),
    ('NW062' , .00070697),
    ('NW064' , .00074984),
    ('NW066' , .00079889),
    ('NW068' , .00084614),
    ('NW070' , .00089304),
    ('NW072' , .00094124),
    ('NW074' , .00098869),
    ('NW080' , .00115011),
)

A = 440
notes = {
    'C' :  0,
    'D' :  2,
    'E' :  4,
    'F' :  5,
    'G' :  7,
    'A' :  9,
    'B' :  11,
}
rel = (2**(1/12.))
def note2freq(name):
    sharp = name[1] == '#'
    flat  = name[1] == 'b'
    if sharp or flat:
        note = name[0:1]
        octave = int(name[2])
    else:
        note = name[0]
        octave = int(name[1])
    num = notes[note]
    if sharp:
        num += 1
    if flat:
        num -= 1
    fullnum = num + 12*(octave - 5)
    return A*rel**(fullnum + 3)

def test(name, expected):
    print('{:3} gave {: 9.2f} Hz\nexpected {: 9.2f} Hz'.format(name, note2freq(name), expected))
if False:
    test('C2' ,  65.41)
    test('Ab4', 415.30)
    test('A4' , 440.00)
    test('B4' , 493.88)
    test('B#4', 523.25)
    test('Cb5', 493.88)
    test('C5' , 523.25)
    print()
    test('E4' , 329.63)
    test('B3' , 246.94)
    test('G3' , 196.00)
    test('D3' , 146.83)
    test('A2' , 110.00)
    test('E2' ,  82.41)
    import sys
    sys.exit(0)

uw_const = 386.4
def uw2tension(uw, freq):
    return (uw*(2*scale_length*freq)**2)/uw_const

def tension2uw(t, freq):
    return (t*uw_const)/(2*scale_length*freq)**2

if False:
    scale_length = 25.4825
    D3 = note2freq('D3')
    print('NW024  {:10.8f} == 0.00010857'.format(tension2uw(15.73, D3)))
    print('NW025* {:10.8f} == ?         '.format(tension2uw(17.21, D3)))
    print('NW026  {:10.8f} == 0.00012671'.format(tension2uw(18.38, D3)))
    import sys
    sys.exit(0)

outfmt = '{:<6} at {:> 5.2f} lbs ({:>+4.2f})'
finalfmt = 'total:   {:>7.2f} lbs ({:>+5.2f})'
def print_ideal_stock(strings):
    total_tension = 0
    total_desired_tension = 0
    for note, tension, kind in strings:
        freq = note2freq(note)
        uw = tension2uw(tension, freq)

        closest = ('n/a', 0)
        for name, stock_uw in stock:
            if kind and name[:len(kind)] != kind:
                continue
            if abs(stock_uw - uw) < abs(closest[1] - uw):
                closest = (name, stock_uw)

        closest_tension = uw2tension(closest[1], freq)
        diff = closest_tension - tension
        print(outfmt.format(closest[0], closest_tension, diff))

        total_tension += closest_tension
        total_desired_tension += tension

    error = total_tension - total_desired_tension
    print(finalfmt.format(total_tension, error))

print('for a scale length of {:>5.2f} inches'.format(scale_length))
for name, strings in string_sets.items():
    print()
    print('"{}"'.format(name))
    print_ideal_stock(strings)