tunetbl.py

#!/usr/bin/env python
#
#  Compute piano tuning table
#  Author:  Yotam Medini  [email protected] -- Created: 2006/January/15
#

import sys

# Important interval ratios
half_tone_ratio = 2. ** (1./12.)
octave_plus_quint = 2. * half_tone_ratio ** 7

# Important frequencies
La  = 440. # Internationally agreed
Si  = La * half_tone_ratio ** 2.
Do1 = La * half_tone_ratio ** 3. # 'Do' above central octave


# Indices within octave that we need
DoIndex =  0
FaIndex =  5
LaIndex =  9
SiIndex = 11


# Fit a note frequency by octave-jumping into the central octave
def fit_note_central(freq):
    global Si;  # already computed outside
    global Do1; # already computed outside

    # To mark the upper-limit of the central octave,
    # we compute imaginary note in the middle between Si and Do1
    central_upper_bound = (Si + Do1)/2.

    # Move up - or make sure, the frequency is above the central octave
    while freq < central_upper_bound:
        freq = 2. * freq  # jump one octave above

    # Move down, the frequency until it is inside the central octave
    while freq > central_upper_bound:
        freq = freq / 2.

    return freq


equalNames = [
    "C",
         "C#=Db",
    "D",
         "D#=Eb",
    "E",
    "F",
         "F#=Gb",
    "G",
         "G#=Ab",
    "A",
         "A#=Bb",
    "B"
    ]


upHarmonicNames = [ # with Diez
    "Do",
         "Do-#",
    "Re",
         "Re-#",
    "Mi",
    "Fa",
         "Fa-#",
    "Sol",
         "Sol-#",
    "La",
         "La-#",
    "Si"
    ]


downHarmonicNames = [ # bemol
    "Do",
         "Re-b",
    "Re",
         "Mi-b",
    "Mi",
    "Fa",
         "Sol-b",
    "Sol",
         "La-b",
    "La",
         "Si-b",
    "Si"
    ]


# Frequencies-lists with dummy initial values
equalFrequencies        = 12 * [111.2]
upHarmonicFrequencies   = 12 * [222.3]
downHarmonicFrequencies = 12 * [333.4]


# In all tuning systems - we have:
equalFrequencies[LaIndex]        = La
upHarmonicFrequencies[LaIndex]   = La
downHarmonicFrequencies[LaIndex] = La


##########################################
# Compute the equal-interval frequencies #
##########################################
# Going up
fi = LaIndex + 1
while fi < 12:
    equalFrequencies[fi] = equalFrequencies[fi - 1] * half_tone_ratio
    fi += 1
# Going down
fi = LaIndex - 1
while fi >= 0:
    equalFrequencies[fi] = equalFrequencies[fi + 1] / half_tone_ratio
    fi += -1


############################################
# Compute the Up&Down Harmonic frequencies #
############################################
# 
# For this, we do quint (qvinta) jumps up & down.
# La -> Mi -> Si ...   or  La -> Re -> Sol ...
#


#######################################
# Compute the Up-Harmonic frequencies #
#######################################
#
# Going down until Fa (included)
fi = LaIndex
currFrequency = upHarmonicFrequencies[fi] # == La
while fi != FaIndex:
    fi = (fi + (12 - 7)) % 12  # 7 half-tones down
    currFrequency = fit_note_central(currFrequency / 3.)
    upHarmonicFrequencies[fi] = currFrequency
#
# Going Up until Fa (excluded)
fi = LaIndex
currFrequency = upHarmonicFrequencies[fi] # == La
fi = (fi + 7) % 12  # 7 half-tones up
while fi != FaIndex:
    currFrequency = fit_note_central(3. * currFrequency)
    upHarmonicFrequencies[fi] = currFrequency
    fi = (fi + 7) % 12  # 7 half-tones up


#########################################
# Compute the Down-Harmonic frequencies #
#########################################
#
# Going Up until Si (included)
fi = LaIndex
currFrequency = upHarmonicFrequencies[fi] # == La
while fi != SiIndex:
    fi = (fi + 7) % 12  # 7 half-tones up
    currFrequency = fit_note_central(3. * currFrequency)
    downHarmonicFrequencies[fi] = currFrequency
#
# Going down until Si (excluded)
fi = LaIndex
currFrequency = downHarmonicFrequencies[fi] # == La
fi = (fi + (12 - 7)) % 12  # 7 half-tones down
while fi != SiIndex:
    currFrequency = fit_note_central(currFrequency / 3.)
    downHarmonicFrequencies[fi] = currFrequency
    fi = (fi + (12 - 7)) % 12  # 7 half-tones down


# Print the combined table
sys.stdout.write("""
 --------------------------------------------------------
|  Equal-Interval     Up-Harmonic        Down-Harmonic   |
 --------------------------------------------------------
""")
for fi in range(0, 12):
    sys.stdout.write(
        "|  %-5s   %6.2f  |  %-5s   %6.2f  |  %-5s   %6.2f  |\n" %
        (equalNames[fi], equalFrequencies[fi],
         upHarmonicNames[fi], upHarmonicFrequencies[fi],
         downHarmonicNames[fi], downHarmonicFrequencies[fi]))
sys.stdout.write(" --------------------------------------------------------\n")
sys.exit(0)