From bb5eabbd5689cc737597a1e4093ed6e597415eba Mon Sep 17 00:00:00 2001
From: Connor Olding <cloningdonor@gmail.com>
Date: Mon, 29 Sep 2014 21:15:51 -0700
Subject: [PATCH] .

---
 .dummy     |   1 -
 strings.py | 198 +++++++++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 198 insertions(+), 1 deletion(-)
 delete mode 100644 .dummy
 create mode 100755 strings.py

diff --git a/.dummy b/.dummy
deleted file mode 100644
index 945c9b4..0000000
--- a/.dummy
+++ /dev/null
@@ -1 +0,0 @@
-.
\ No newline at end of file
diff --git a/strings.py b/strings.py
new file mode 100755
index 0000000..35d1492
--- /dev/null
+++ b/strings.py
@@ -0,0 +1,198 @@
+#!/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'),
+    ),
+    'light jazz': (
+        ('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'),
+    ),
+    'open G (6-string)': (
+        ('D4' , 16, 'PL'),
+        ('B3' , 16, 'PL'),
+        ('G3' , 16, 'PL'),
+        ('D3' , 16, 'NW'),
+        ('B2' , 16, 'NW'),
+        ('D2' , 16, 'NW'),
+    ),
+    'open G (7-string)': (
+        ('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),
+    # they have a NW025 used in EXL110BT but it's not listed
+    ('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)
+
+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
+
+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)