.. include:: /project-links.txt
.. include:: /abbreviation.txt

.. getthecode:: twelve-tone-equal-temperament.py
    :language: python

===============================
 Twelve-Tone Equal Temperament
===============================
This section illustrates the twelve-tone equal temperament (12-TET).

.. code-block:: python

    import numpy
    import matplotlib.pyplot as plt
    
    from Musica.Math.MusicTheory import *
    from Musica.Theory.Temperament import *
    
    fifth_approximations = ET12Tuning.fifth_approximations(number_of_steps_max=20)
    print('Perfect fifth 3/2\n         1.5    {:.1f} cent'.format(
        float(Cent.from_frequency_ratio(FrequencyRatio.fifth))))
    for pitch in fifth_approximations:
        print('2**{:2}/{:2} {:.4f} {:.1f} cent'.format(
            pitch.number_of_steps,
            pitch.step_number,
            float(pitch),
            float(pitch.cent),
        ))


.. literalinclude:: twelve-tone-equal-temperament.stdout
    :lines: 1-5


.. code-block:: python

    number_of_octaves = 10
    octave_frequencies = [[ET12.frequency(octave_number, interval_number) for interval_number in range(1, 13)] for octave_number in range(1, number_of_octaves +1)]
    all_frequencies = []
    for octave_number in range(1, number_of_octaves +1):
        frequencies = octave_frequencies[octave_number -1]
        all_frequencies += frequencies
        print("Octave {:2} {}".format(octave_number, ['{:.2f}'.format(x) for x in frequencies]))


.. literalinclude:: twelve-tone-equal-temperament.stdout
    :lines: 8-17


.. code-block:: python

    figure = plt.figure(1, (20, 10))
    
    axe = plt.subplot(111)
    axe.set_title('Twelve-tone Equal Temperament')
    axe.set_xlabel('notes')
    axe.set_ylabel('Hz')
    axe.grid()
    for octave_number in range(number_of_octaves):
        x = octave_number * 12 + 1
        axe.axvline(x, color='blue')
        axe.text(x, 10, 'Octave {}'.format(octave_number +1), color='black')
    axe.semilogy(range(1, len(all_frequencies) +1), all_frequencies, 'o-')
    axe.axhline(y=440, color='red')
    axe.text(2, 460, 'A 440 Hz', color='black')
    axe.axhline(y=50, color='red')
    axe.axhline(y=60, color='red')
    axe.text(20, 65, 'Electric Network Frequency 50/60Hz', color='black')
    axe.axhline(y=20e3, color='red')
    axe.text(2, 22e3, 'Human Ear Limit 20 kHz', color='black')
    
    plt.show()
    


.. image:: 12tet.png
  :align: center