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4 changed files with 152 additions and 133 deletions
0
data.py
Normal file → Executable file
0
data.py
Normal file → Executable file
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notes.py
Executable file
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notes.py
Executable file
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@ -0,0 +1,52 @@
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#!/usr/bin/python
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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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if __name__ == '__main__':
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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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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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import sys
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sys.exit(0)
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58
run.py
Executable file
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run.py
Executable file
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@ -0,0 +1,58 @@
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#!/usr/bin/python
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from strings import print_ideal_stock
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in_mm = 25.4
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scale_length = 648/in_mm
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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, 'P'),
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('B3' , 16, 'P'),
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('G3' , 16, 'P'),
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('D3' , 16, 'W'),
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('A2' , 16, 'W'),
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('E2' , 16, 'W'),
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),
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'jazz light': (
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('E4' , 24, 'P'),
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('B3' , 24, 'P'),
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('G3' , 24, 'W'),
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('D3' , 24, 'W'),
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('A2' , 24, 'W'),
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('E2' , 24, 'W'),
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),
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'regular light (DADGAD)': (
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('D4' , 16, 'P'),
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('A3' , 16, 'P'),
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('G3' , 16, 'P'),
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('D3' , 16, 'W'),
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('A2' , 16, 'W'),
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('D2' , 16, 'W'),
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),
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'regular light (open G, 6)': (
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('D4' , 16, 'P'),
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('B3' , 16, 'P'),
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('G3' , 16, 'P'),
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('D3' , 16, 'W'),
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('B2' , 16, 'W'),
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('D2' , 16, 'W'),
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),
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'regular light (open G, 7)': (
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('D4' , 16, 'P'),
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('B3' , 16, 'P'),
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('G3' , 16, 'P'),
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('D3' , 16, 'W'),
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('B2' , 16, 'W'),
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('G2' , 16, 'W'),
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('D2' , 16, 'W'),
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),
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}
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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, scale_length)
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175
strings.py
175
strings.py
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@ -1,6 +1,7 @@
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#!/usr/bin/python
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from data import *
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from notes import note2freq
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stock = []
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stock += daddario_plain_steel
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@ -8,143 +9,22 @@ stock += daddario_nickle_wound
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#stock += circle_k_plain
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#stock += circle_k_hybrid_wound
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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, 'P'),
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('B3' , 16, 'P'),
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('G3' , 16, 'P'),
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('D3' , 16, 'W'),
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('A2' , 16, 'W'),
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('E2' , 16, 'W'),
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),
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'jazz light': (
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('E4' , 24, 'P'),
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('B3' , 24, 'P'),
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('G3' , 24, 'W'),
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('D3' , 24, 'W'),
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('A2' , 24, 'W'),
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('E2' , 24, 'W'),
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),
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'regular light (DADGAD)': (
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('D4' , 16, 'P'),
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('A3' , 16, 'P'),
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('G3' , 16, 'P'),
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('D3' , 16, 'W'),
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('A2' , 16, 'W'),
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('D2' , 16, 'W'),
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),
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'regular light (open G, 6)': (
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('D4' , 16, 'P'),
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('B3' , 16, 'P'),
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('G3' , 16, 'P'),
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('D3' , 16, 'W'),
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('B2' , 16, 'W'),
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('D2' , 16, 'W'),
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),
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'regular light (open G, 7)': (
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('D4' , 16, 'P'),
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('B3' , 16, 'P'),
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('G3' , 16, 'P'),
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('D3' , 16, 'W'),
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('B2' , 16, 'W'),
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('G2' , 16, 'W'),
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('D2' , 16, 'W'),
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),
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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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import sys
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sys.exit(0)
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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 uw2tension(uw, freq, SL):
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return (uw*(2*SL*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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if False:
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# DAd's data is all screwy so we use change scale lengths for a best-fit
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scale_length = 25.4825
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D3 = note2freq('D3')
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A2 = note2freq('A2')
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E2 = note2freq('E2')
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print('NW024 {:10.8f} == 0.00010857'.format(tension2uw(15.73, D3)))
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print('NW025* {:10.8f} == ? '.format(tension2uw(17.21, D3)))
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print('NW026 {:10.8f} == 0.00012671'.format(tension2uw(18.38, D3)))
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print()
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print('NW036 {:10.8f} == 0.00023964'.format(tension2uw(19.04, A2)))
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print('NW037* {:10.8f} == ? '.format(tension2uw(20.23, A2)))
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print('NW038 {:10.8f} == 0.00026471'.format(tension2uw(20.96, A2)))
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print()
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scale_length = 25.18
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print('NW039 {:10.8f} == 0.00027932'.format(tension2uw(12.46, E2)))
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print('NW040* {:10.8f} == ? '.format(tension2uw(13.18, E2)))
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print('NW042 {:10.8f} == 0.00032279'.format(tension2uw(14.37, E2)))
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print()
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scale_length = 25.02
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print('NW049 {:10.8f} == 0.00043014'.format(tension2uw(18.97, E2)))
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print('NW050* {:10.8f} == ? '.format(tension2uw(19.68, E2)))
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print('NW052 {:10.8f} == 0.00048109'.format(tension2uw(21.15, E2)))
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import sys
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sys.exit(0)
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def tension2uw(t, freq, SL):
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return (t*uw_const)/(2*SL*freq)**2
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outfmt = '{:<8} 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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def print_ideal_stock(strings, scale_length=25.512):
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SL = scale_length
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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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uw = tension2uw(tension, freq, SL)
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closest = ('n/a', 0)
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for name, stock_uw in stock:
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@ -155,7 +35,7 @@ def print_ideal_stock(strings):
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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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closest_tension = uw2tension(closest[1], freq, SL)
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diff = closest_tension - tension
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print(outfmt.format(closest[0], closest_tension, diff))
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@ -165,8 +45,37 @@ def print_ideal_stock(strings):
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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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if __name__ == '__main__':
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# DAd's data is all screwy so we use change scale lengths for a best-fit
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SL = 25.4825
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D3 = note2freq('D3')
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A2 = note2freq('A2')
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E2 = note2freq('E2')
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test_fmt = '{:8} {:10.8f} == {:10}'
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def test(name, unit, tension, note):
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print(test_fmt.format(name, tension2uw(tension, note, SL), unit))
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test('NW024' , '0.00010857', 15.73, D3)
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test('NW025*', '?' , 17.21, D3)
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test('NW026' , '0.00012671', 18.38, D3)
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print()
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print('"{}"'.format(name))
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print_ideal_stock(strings)
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test('NW036' , '0.00023964', 19.04, A2)
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test('NW037*', '? ', 20.23, A2)
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test('NW038' , '0.00026471', 20.96, A2)
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print()
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SL = 25.18
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test('NW039' , '0.00027932', 12.46, E2)
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test('NW040*', '? ', 13.18, E2)
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test('NW042' , '0.00032279', 14.37, E2)
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print()
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SL = 25.02
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test('NW049' , '0.00043014', 18.97, E2)
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test('NW050*', '? ', 19.68, E2)
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test('NW052' , '0.00048109', 21.15, E2)
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import sys
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sys.exit(0)
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