guitar tension ideal string finder

data.py

# (product name, unit weight)

# D'Addario stock via http://www.daddario.com/upload/tension_chart_13934.pdf
# Circle K String stock http://circlekstrings.com/CKSIMAGES/UnitWeightChart130105.pdf

# string names don't necessarily match up with their actual product names

daddario_plain_steel = (
    ('DAPL007' , .00001085),
    ('DAPL008' , .00001418),
    ('DAPL0085', .00001601),
    ('DAPL009' , .00001794),
    ('DAPL0095', .00001999),
    ('DAPL010' , .00002215),
    ('DAPL0105', .00002442),
    ('DAPL011' , .00002680),
    ('DAPL0115', .00002930),
    ('DAPL012' , .00003190),
    ('DAPL013' , .00003744),
    ('DAPL0135', .00004037),
    ('DAPL014' , .00004342),
    ('DAPL015' , .00004984),
    ('DAPL016' , .00005671),
    ('DAPL017' , .00006402),
    ('DAPL018' , .00007177),
    ('DAPL019' , .00007997),
    ('DAPL020' , .00008861),
    ('DAPL022' , .00010722),
    ('DAPL024' , .00012760),
    ('DAPL027' , .00014975),
)

daddario_nickle_wound = ( # XL
    ('DANW017' , .00005524),
    ('DANW018' , .00006215),
    ('DANW019' , .00006947),
    ('DANW020' , .00007495),
    ('DANW021' , .00008293),
    ('DANW022' , .00009184),
    ('DANW024' , .00010857),
    ('DANW025*', .00011875), # from the EXL110BT, an approximation
    ('DANW026' , .00012671),
    ('DANW028' , .00014666),
    ('DANW030' , .00017236),
    ('DANW032' , .00019347),
    ('DANW034' , .00021590),
    ('DANW036' , .00023964),
    ('DANW037*', .00024872), # from the EXL115BT, an approximation
    ('DANW038' , .00026471),
    ('DANW039' , .00027932),
    ('DANW040*', .00029570), # from the EXL120BT, an approximation
    ('DANW042' , .00032279),
    ('DANW044' , .00035182),
    ('DANW046' , .00038216),
    ('DANW048' , .00041382),
    ('DANW049' , .00043014),
    ('DANW050*', .00044720), # from the EXL115BT, an approximation
    ('DANW052' , .00048109),
    ('DANW054' , .00053838),
    ('DANW056' , .00057598),
    ('DANW059' , .00064191),
    ('DANW060' , .00066542),
    ('DANW062' , .00070697),
    ('DANW064' , .00074984),
    ('DANW066' , .00079889),
    ('DANW068' , .00084614),
    ('DANW070' , .00089304),
    ('DANW072' , .00094124),
    ('DANW074' , .00098869),
    ('DANW080' , .00115011),
)

kalium_plain = (
    ('CKPL008 ',.0000142401458191),
    ('CKPL0085',.00001607510288),
    ('CKPL009', .0000180219146483),
    ('CKPL0095',.00002008032129),
    ('CKPL010', .0000222518914107),
    ('CKPL0105',.00002453144932),
    ('CKPL011', .0000269251480883),
    ('CKPL0115',.00002942561205),
    ('CKPL012', .0000320389593746),
    ('CKPL0125',.00003476567932),
    ('CKPL013', .0000376052948255),
    ('CKPL0135',.00004055150041),
    ('CKPL014', .000043607),
    ('CKPL015', .000050050),
    ('CKPL016', .000056961),
    ('CKPL017', .000064300),
    ('CKPL018', .000072088),
    ('CKPL019', .000080360),
    ('CKPL020', .000089031),
    ('CKPL021', .000098155),
    ('CKPL022', .000107666),
    ('CKPL023', .000117702),
)

kalium_hybrid_wound = (
    ('CKHW021', .000093873),
    ('CKHW022', .000103500),
    ('CKHW023', .000113985),
    ('CKHW024', .000124963),
    ('CKHW025', .000136054),
    ('CKHW026', .000144691),
    ('CKHW027', .000153146),
    ('CKHW028', .000161203),
    ('CKHW029', .000178551),
    ('CKHW031', .000198902),
    ('CKHW033', .000223217),
    ('CKHW035', .000249034),
    ('CKHW037', .000276237),
    ('CKHW039', .000304788),
    ('CKHW041', .000334965),
    ('CKHW043', .000366357),
    ('CKHW045', .000404956),
    ('CKHW047', .000447408),
    ('CKHW049', .000475438),
    ('CKHW051', .000512645),
    ('CKHW053', .000551898),
    ('CKHW055', .000584407),
    ('CKHW057', .000625704),
    ('CKHW059', .000679149),
    ('CKHW061', .000720293),
    ('CKHW063', .000765973),
    ('CKHW065', .000821116),
    ('CKHW067', .000870707),
    ('CKHW070', .000939851),
    ('CKHW073', .001021518),
    ('CKHW076', .001110192),
    ('CKHW079', .001188974),
    ('CKHW082', .001293598),
    ('CKHW086', .001416131),
    ('CKHW090', .001544107),
    ('CKHW094', .001677765),
    ('CKHW098', .001831487),
    ('CKHW102', .001986524),
    ('CKHW106', .002127413),
    ('CKHW112', .002367064),
    ('CKHW118', .002616406),
    ('CKHW124', .002880915),
    ('CKHW130', .003154996),
    ('CKHW136', .003441822),
    ('CKHW142', .003741715),
    ('CKHW150', .004051506),
    ('CKHW158', .004375389),
    ('CKHW166', .005078724),
    ('CKHW174', .005469937),
    ('CKHW182', .006071822),
    ('CKHW190', .006605072),
    ('CKHW200', .007311717),
    ('CKHW210', .008037439),
    ('CKHW222', .009091287),
    ('CKHW232', .009888443),
    ('CKHW244', .010907182),
    ('CKHW254', .011787319),
)

notes.py

#!/usr/bin/python

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)

if __name__ == '__main__':
    test_fmt = '{:3} gave {: 9.2f} Hz\nexpected {: 9.2f} Hz'
    def test(name, expected):
        print(test_fmt.format(name, note2freq(name), expected))

    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)

run.py

#!/usr/bin/python

from strings import print_ideal_stock

in_mm = 25.4
default_scale_length = 648/in_mm

sets = """
regular light
E4  16  PD
B3  16  PD
G3  16  PD
D3  16  WD
A2  16  WD
E2  16  WD

jazz medium
E4  24  PD
B3  24  PD
G3  24  WD
D3  24  WD
A2  24  WD
E2  24  WD

regular light (DADGAD)
D4  16  PD
A3  16  PD
G3  16  PD
D3  16  WD
A2  16  WD
D2  16  WD

fanned-fret bass
G2  35  WC  34.00
D2  35  WC  34.75
A1  35  WC  35.50
E1  35  WC  36.25
B0  35  WC  37.00

regular light (Open G 7-string)
D4  16  PD
B3  16  PD
G3  16  PD
D3  16  WD
B2  16  WD
G2  16  WD
D2  16  WD
"""

string_sets = {}
sets = sets+'\n\n'
title = None
for line in sets.splitlines():
    if not line:
        title = None
        continue
    if not title:
        title = line
        string_sets[title] = []
    else:
        fields = line.split()
        note, tension = fields[0:2]
        tension = int(tension)

        req = ''
        if len(fields) > 2:
            req = fields[2]

        length = None
        if len(fields) > 3:
            length = float(fields[3])

        string = (note, tension, req, length)
        string_sets[title].append(string)

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

run2.py

#!/usr/bin/python

from strings import print_tensions

in_mm = 25.4
default_scale_length = 648/in_mm

sets = """
E standard (super light balanced)
E4  DAPL009
B3  DAPL012
G3  DAPL015
D3  DANW022
A2  DANW030
E2  DANW040

E standard (medium balanced)
E4  DAPL011
B3  DAPL015
G3  DAPL019
D3  DANW028
A2  DANW037
E2  DANW050

C standard (medium balanced)
C4  DAPL011
G3  DAPL015
D#3 DAPL019
A#2 DANW028
F2  DANW037
C2  DANW050

C standard (jazz medium)
C4  DAPL013
G3  DAPL017
D#3 DANW026
A#2 DANW036
F2  DANW046
C2  DANW056

C standard (CKS-G6-14-59mb)
C4  CKPL014
G3  CKPL019
D#3 CKHW025
A#2 CKHW033
F2  CKHW045
C2  CKHW059

B standard (CKS-G6-14-59mb)
B3  CKPL014
F#3 CKPL019
D3  CKHW025
A2  CKHW033
E2  CKHW045
B1  CKHW059

D standard drop C (medium balanced)
D4  DAPL011
A3  DAPL015
F3  DAPL019
C3  DANW028
G2  DANW037
C2  DANW050
"""

string_sets = {}
sets = sets+'\n\n'
title = None
for line in sets.splitlines():
    if not line:
        title = None
        continue
    if not title:
        title = line
        string_sets[title] = []
    else:
        note, string = line.split()
        string_sets[title].append((note, string))

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

strings.py

#!/usr/bin/python

from data import *
from notes import note2freq

stock = []
stock += daddario_plain_steel
stock += daddario_nickle_wound
stock += kalium_plain
stock += kalium_hybrid_wound

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

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

outfmt = '\
{:<8} at {:>6.2f} lb ({:>+4.2f})'
finalfmt = '\
average:   {:>7.2f} lb ({:>+5.2f})\n\
total:     {:>7.2f} lb ({:>+5.2f})'
tension_outfmt = '\
{:<3} {:<8} at {:>6.2f} lb'
tension_finalfmt = '\
average:       {:>7.2f} lb\n\
total:         {:>7.2f} lb'

def print_ideal_stock(strings, scale_length=25.512):
    SL = scale_length
    total_tension = 0
    total_desired_tension = 0
    for note, tension, req, length in strings:
        freq = note2freq(note)
        if length:
            SL = length
        else:
            SL = scale_length
        uw = tension2uw(tension, freq, SL)

        kind  = len(req) > 0 and req[0]
        brand = len(req) > 1 and req[1]

        closest = ('n/a', 0)
        for name, stock_uw in stock:
            if kind and kind == 'P' and name[2] != 'P':
                continue
            if kind and kind == 'W' and name[3] != 'W':
                continue
            if brand and brand[0] != name[0]:
                continue
            if abs(stock_uw - uw) < abs(closest[1] - uw):
                closest = (name, stock_uw)

        closest_tension = uw2tension(closest[1], freq, SL)
        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
    average_tension = total_tension/len(strings)
    average_error = error/len(strings)
    print(finalfmt.format(average_tension, average_error, total_tension, error))

def print_tensions(strings, scale_length=25.512):
    SL = scale_length
    total_tension = 0
    for note, name in strings:
        freq = note2freq(note)
        uw = 0
        for stock_name, stock_uw in stock:
            if name == stock_name or name + '*' == stock_name:
                uw = stock_uw
                break
        if uw:
            tension = uw2tension(uw, freq, SL)
        else:
            tension = 0
        print(tension_outfmt.format(note, name, tension))
        total_tension += tension

    print(tension_finalfmt.format(total_tension/len(strings), total_tension))

if __name__ == '__main__':
    # DAd's data is all screwy so we use change scale lengths for a best-fit
    SL = 25.4825
    D3 = note2freq('D3')
    A2 = note2freq('A2')
    E2 = note2freq('E2')

    test_fmt = '{:8} {:10.8f} == {:10}'
    def test(name, unit, tension, note):
        print(test_fmt.format(name, tension2uw(tension, note, SL), unit))

    test('NW024' , '0.00010857', 15.73, D3)
    test('NW025*', '?'         , 17.21, D3)
    test('NW026' , '0.00012671', 18.38, D3)
    print()

    test('NW036' , '0.00023964', 19.04, A2)
    test('NW037*', '?         ', 20.23, A2)
    test('NW038' , '0.00026471', 20.96, A2)
    print()

    SL = 25.18
    test('NW039' , '0.00027932', 12.46, E2)
    test('NW040*', '?         ', 13.18, E2)
    test('NW042' , '0.00032279', 14.37, E2)
    print()

    SL = 25.02
    test('NW049' , '0.00043014', 18.97, E2)
    test('NW050*', '?         ', 19.68, E2)
    test('NW052' , '0.00048109', 21.15, E2)