This repository contains a basic analysis of data from string tension guides published by two major US string manufacturers. This analysis informs the development of the tealc Python package.
What follows is a slightly condensed display version of the code contained in
analysis.py and analysis.ipynb. analysis.py is the principal analysis script,
written in a format compatible with Jupyter notebook-friendly editors likw VSCode or
PyCharm Professional Edition (i.e. with pseudo-cells prepended by # %%).
analysis.ipynb is a traditional Jupyter notebook produced from analysis.py.
The version below contain static image scatterplots under the Visualization heading.
These plots are available as interactive plotly
plots in analysis.py and analysis.ipynb.
from pathlib import Path
import json
import numpy as np
import pandas as pd
import plotly.express as px
import statsmodels.formula.api as smf
ROOT = Path.cwd()
d = pd.read_csv(ROOT/'data.csv')For gauge/material items with unit weight data from both GHS and D'Addario, take the simple mean unit weight of both brands. Also include gauge/material items produced by only one brand. Format these data as JSON, keyed by material, to use as a unit weight lookup table when possible.
uw_means = d.groupby(['gauge', 'material'], as_index=False).mean()means_only = uw_means.loc[uw_means['brand2'] == 0.5,
['material', 'gauge', 'unit_weight']]
means_only = means_only.rename(columns={'unit_weight': 'uw_mean'})diffmeans = d.merge(means_only)
diffmeans['abs_diff'] = (diffmeans['unit_weight']
- diffmeans['uw_mean'])
diffmeans['prop_diff'] = (np.log(diffmeans['unit_weight'])
- np.log(diffmeans['uw_mean']))pp5 = len(diffmeans.loc[np.abs(diffmeans['prop_diff']) > 0.05]) // 2
pp10 = len(diffmeans.loc[np.abs(diffmeans['prop_diff']) > 0.1]) // 2
n_gauges = len(d['gauge'].unique())
print("Gauges with > 5 percent difference from GHS/D'Addario mean: {}/{}"
.format(pp5, n_gauges))
print("Gauges with > 10 percent difference from GHS/D'Addario mean: {}/{}"
.format(pp10, n_gauges))Gauges with > 5 percent difference from GHS/D'Addario mean: 21/88
Gauges with > 10 percent difference from GHS/D'Addario mean: 4/88
output = uw_means.loc[:, ['material', 'gauge', 'unit_weight']]
materials = list(output['material'].unique())
if Path(ROOT/'unit_weights.json').exists():
Path(ROOT/'unit_weights.json').unlink()
with open(ROOT/'unit_weights.json', 'a') as f:
f.write('{')
for m in materials:
key = (output.loc[output['material'] == m, ['gauge', 'unit_weight']]
.rename(columns={'unit_weight': m})
.set_index('gauge')
.to_json(indent=2))
if m != materials[-1]:
f.write(key[1:-2] + ',\n')
else:
f.write(key[1:-1])
f.write('}')mat_map = {
'ps': 'Plain Steel',
'nps': 'Nickel-Plated Steel Roundwound',
'ss': 'Stainless Steel Roundwound',
'pn': 'Pure Nickel Roundwound',
'fw': 'Stainless Steel Flatwound',
'pb': 'Phosphor Bronze Roundwound',
'8020': '80/20 Bronze Roundwound',
'8515': '85/15 Bronze Roundwound',
'bnps': 'Nickel-Plated Steel Roundwound',
'bss': 'Stainless Steel Roundwound',
'bfw': 'Stainless Steel Flatwound'
}
d['gauge_sq'] = np.power(d['gauge'], 2)
d['brand'] = d['brand2'].map({0: 'G', 1: 'D'})
d['mat_long'] = d['material'].map(mat_map)p_ps = px.scatter(d[d['material'] == 'ps'], x='gauge_sq', y='unit_weight',
trendline='ols', title='Plain Steel Strings',
hover_data={'gauge': True, 'gauge_sq': False, 'brand': True},
width=600, height=400)
p_ps.show()
elec_mat = ['nps', 'ss', 'pn', 'fw', ]
elec_filter = [mat in elec_mat for mat in d['material']]
p_elec = px.scatter(d.loc[elec_filter], x='gauge_sq', y='unit_weight',
trendline='ols', title='Electric Wound Strings',
hover_data={'gauge': True, 'gauge_sq': False, 'brand': True},
width=600, height=400,
color='material', color_discrete_map={'nps': '#008080',
'ss': '#800080',
'pn': '#40E0D0',
'fw': '#EE82EE'})
p_elec.show()
acou_mat = ['pb', '8020', '8515', ]
acou_filter = [mat in acou_mat for mat in d['material']]
p_acou = px.scatter(d.loc[acou_filter], x='gauge_sq', y='unit_weight',
trendline='ols', title='Acoustic Wound Strings',
hover_data={'gauge': True, 'gauge_sq': False, 'brand': True},
width=600, height=400,
color='material', color_discrete_map={'pb': '#8B4513',
'8020': '#FFD700',
'8515': '#D2691E'})
p_acou.show()
bass_mat = ['bnps', 'bss', 'bfw', ]
bass_filter = [mat in bass_mat for mat in d['material']]
p_bass = px.scatter(d.loc[bass_filter], x='gauge_sq', y='unit_weight',
trendline='ols', title='Bass Strings',
hover_data={'gauge': True, 'gauge_sq': False, 'brand': True},
width=600, height=400,
color='material', color_discrete_map={'bnps': '#008080',
'bss': '#800080',
'bfw': '#EE82EE'})
p_bass.show()
Build unit weight models of the form: 
Build OLS models for each string material separately for ease of use and interpretation. Write constants and coefficients for each material to JSON for use when unit weights are not available from the lookup table created in the Mean unit weights section.
def short_table(fitted_model, title=None):
"""Abbreviated single-variable OLS results table"""
coef = round(fitted_model.params['gauge_sq'], ndigits=4)
se = round(fitted_model.bse['gauge_sq'], ndigits=4)
t = round(fitted_model.tvalues['gauge_sq'], ndigits=2)
p = round(fitted_model.pvalues['gauge_sq'], ndigits=4)
r2 = round(fitted_model.rsquared, ndigits=4)
cw = 10
if title is not None:
title = f' {title} '.center(5 * cw, '=')
else:
title = '=' * (5 * cw)
chead = ''.join([ch.rjust(cw) for ch in ['Coef.', 'SE', 't', 'Pr>|t|', 'R^2']])
cval = ''.join([str(v).rjust(cw) for v in [coef, se, t, p, r2]])
table = '{}\n{}\n{}'.format(title, chead, cval)
return tablemat_list = d['material'].unique()
tension_models = dict()
for mat in mat_list:
mod = smf.ols('unit_weight ~ gauge_sq', data=d[d['material'] == mat]).fit()
print(short_table(mod, title=mat_map[mat]), '\n')
tension_models[mat] = {'const': mod.params.loc['Intercept'],
'coef': mod.params.loc['gauge_sq']}================== Plain Steel ===================
Coef. SE t Pr>|t| R^2
0.2269 0.0027 84.05 0.0 0.9939
========= Nickel-Plated Steel Roundwound =========
Coef. SE t Pr>|t| R^2
0.1926 0.0034 55.93 0.0 0.98
=========== Phosphor Bronze Roundwound ===========
Coef. SE t Pr>|t| R^2
0.1987 0.0013 158.85 0.0 0.9981
============ 80/20 Bronze Roundwound =============
Coef. SE t Pr>|t| R^2
0.193 0.0011 170.88 0.0 0.9986
============ 85/15 Bronze Roundwound =============
Coef. SE t Pr>|t| R^2
0.1985 0.0016 126.26 0.0 0.9979
=========== Stainless Steel Roundwound ===========
Coef. SE t Pr>|t| R^2
0.1876 0.0033 57.16 0.0 0.99
============= Pure Nickel Roundwound =============
Coef. SE t Pr>|t| R^2
0.2155 0.0032 67.8 0.0 0.9961
=========== Stainless Steel Flatwound ============
Coef. SE t Pr>|t| R^2
0.1831 0.0034 53.21 0.0 0.9895
========= Nickel-Plated Steel Roundwound =========
Coef. SE t Pr>|t| R^2
0.1805 0.0019 94.15 0.0 0.9943
=========== Stainless Steel Roundwound ===========
Coef. SE t Pr>|t| R^2
0.1691 0.0033 51.6 0.0 0.9867
=========== Stainless Steel Flatwound ============
Coef. SE t Pr>|t| R^2
0.1845 0.0019 98.31 0.0 0.9972
with open(ROOT/'tension_models.json', 'w') as f:
json.dump(tension_models, f, indent=2)