3.Variablity & Perfectionism in Music

1/20/2024

Allow me to start by laying down a logical truth that has grounds in both statistics and art: The more non-constant (variable) components we have in a system, the higher the entropy, the higher the probability for flaws & imperfections". I would like to make it clear that the previous statement is not to be interpreted in a vaccum, as "flaws" and "imperfections" do not exist statiscally and are ways for us to interpret data, in this context, art.

The above can be shortly summarized by the term "entropy". As the variables (musical instruments, musical keys, tempo, dynamics, tonality, timbre, texture, melody, harmony, form, rhythm, etc..) increase, the less chance of being "perfect" there is. I have went over the orchestra class I atteneded (at the time of writing this on paper before publishing it here, 1/2/2022) and I have surveyed my classmates, all of whom were musically skilled enough to philosophize on what sounds "good" and what doesn't sound "good" in musical theory, how to improve musical passages, and play well on other string instruments. I showed them multiple musical passage samples I wrote: The 1st was a whole note on the open-D string, the 2nd was 4-qarter notes on open-D string, the 3rd was 2-half notes on open-D string and E on the othe D-string; the other samples were of varying diversity of dynamics, note lenghts, and flats and sharps.

I had asked them "which sample was the most "perfect"", and after reading an argument, stating that "perfect" meant "needing the least amount of improvements", the overwhelming concensus went to the 1st sample, the simple whole note on open-D string. When asked about the most the most beautiful, the majority answered that the sample featuring descnending quarter notes was the most complex without sacrificing a beauty of a comforting pattern that is easy to process.

Synthesizing Music with MATLAB

1. User Input: The user specifies the duration of the generated music.
2. Note Generation: The program generates the note D with a specific frequency.
3. Waveform Creation: The program creates a sine waveform for the note.
4. Playback and Saving: The program plays the generated note and saves it as a WAV file.

function generateAndPlayNotesSequentially()
% Define the musical note 'D' and its corresponding frequency
note = 'D';
frequency = 293.66;  % Frequency for note D4

% Fixed volume
volume = 10;

% Note and rest durations
note_duration = 4;  % 4 seconds
rest_duration = 1;  % 1 second

% Number of notes
num_notes = 3;

% Sampling frequency (44.1 kHz)
fs = 44100;

% Generate the waveform for the note 'D'
t_note = linspace(0, note_duration, round(note_duration * fs));
waveform_note = volume * sin(2 * pi * frequency * t_note);

% Generate the waveform for the rest (silence)
t_rest = linspace(0, rest_duration, round(rest_duration * fs));
waveform_rest = zeros(1, length(t_rest));

    % Combine notes and rests
    combined_waveform = [];
    for i = 1:num_notes
        combined_waveform = [combined_waveform, waveform_note, waveform_rest];
    end

    % Normalize the combined waveform
    combined_waveform = combined_waveform / max(abs(combined_waveform));

    % Save the combined waveform as a WAV file
    filename = 'generated_music.wav';
    audiowrite(filename, combined_waveform, fs);
    fprintf('The generated music has been saved as %s\n', filename);

    % Play the combined waveform
    soundsc(combined_waveform, fs);

    % Display the generated notes information
    fprintf('Generated Note: %s\n', note);
    fprintf('Note Duration: %.2f sec\n', note_duration);
    fprintf('Rest Duration: %.2f sec\n', rest_duration);
    fprintf('Volume: %d\n', volume);
    fprintf('Number of Notes: %d\n', num_notes);

    fprintf('\n');
end

Adding Notes & Their corresponding Frequencies

function generateRandomNotes()
% Define the musical notes and their corresponding frequencies
notes = {'C', 'C#', 'D', 'D#', 'E', 'F', 'F#', 'G', 'G#', 'A', 'A#', 'B', 'Rest'};
frequencies = [261.63, 277.18, 293.66, 311.13, 329.63, 349.23, 369.99, 392.00, 415.30, 440.00, 466.16, 493.88, 0]; % 0 Hz for rest
    
% Ask user for the number of notes
num_notes = input('Enter the number of notes to generate: ');

% Initialize arrays for the frequencies and note names
chosen_frequencies = zeros(1, num_notes);
chosen_notes = cell(1, num_notes);

% Randomly choose notes and their frequencies
for i = 1:num_notes
    note_index = randi(length(notes));
    chosen_frequencies(i) = frequencies(note_index);
    chosen_notes{i} = notes{note_index};
end
    
% Set constant duration and volume
duration = 1; % 1 second
volume = 10; % 10 decibels
amplitude = 10^(volume / 20); % Convert dB to linear amplitude
    
% Sampling frequency
fs = 44100;

% Generate and combine waveforms for each note
combined_waveform = [];
for i = 1:num_notes
    t = linspace(0, duration, duration * fs);
    if chosen_frequencies(i) == 0
        waveform = zeros(1, length(t)); % Rest note
    else
        waveform = amplitude * sin(2 * pi * chosen_frequencies(i) * t);
    end
    combined_waveform = [combined_waveform, waveform];
end

% Normalize the combined waveform
combined_waveform = combined_waveform / max(abs(combined_waveform));

% Save the combined waveform as a WAV file
filename = 'generated_notes.wav';
audiowrite(filename, combined_waveform, fs);
fprintf('The generated music has been saved as %s\n', filename);
    
% Automatically play the saved WAV file
[y, fs] = audioread(filename);
sound(y, fs);
end
                

Variable Volume Values

function generateRandomNotes()
% Define the musical notes and their corresponding frequencies
notes = {'C', 'C#', 'D', 'D#', 'E', 'F', 'F#', 'G', 'G#', 'A', 'A#', 'B', 'Rest'};
frequencies = [261.63, 277.18, 293.66, 311.13, 329.63, 349.23, 369.99, 392.00, 415.30, 440.00, 466.16, 493.88, 0]; % 0 Hz for rest
                    
% Ask user for the number of notes
num_notes = input('Enter the number of notes to generate: ');
                
% Initialize arrays for the frequencies, note names, and volumes
chosen_frequencies = zeros(1, num_notes);
chosen_notes = cell(1, num_notes);
volumes = 10.^((3 + rand(1, num_notes) * 47) / 20); % Random volumes between 3 dB and 50 dB
                
% Randomly choose notes and their frequencies
for i = 1:num_notes
    note_index = randi(length(notes));
    chosen_frequencies(i) = frequencies(note_index);
    chosen_notes{i} = notes{note_index};
end
                    
% Set constant duration
duration = 1; % 1 second
                    
% Sampling frequency
fs = 44100;
                
% Generate and combine waveforms for each note
combined_waveform = [];
for i = 1:num_notes
    t = linspace(0, duration, duration * fs);
    if chosen_frequencies(i) == 0
        waveform = zeros(1, length(t)); % Rest note
    else
        waveform = volumes(i) * sin(2 * pi * chosen_frequencies(i) * t);
end
combined_waveform = [combined_waveform, waveform];
                        
% Print note details
fprintf('Note: %s, Frequency: %.2f Hz, Duration: %.1f sec, Volume: %.2f dB\n', ...
chosen_notes{i}, chosen_frequencies(i), duration, 20*log10(volumes(i)));
end
                
% Normalize the combined waveform
combined_waveform = combined_waveform / max(abs(combined_waveform));
                
% Save the combined waveform as a WAV file
filename = 'generated_notes.wav';
audiowrite(filename, combined_waveform, fs);
fprintf('The generated music has been saved as %s\n', filename);
                    
% Automatically play the saved WAV file
[y, fs] = audioread(filename);
sound(y, fs);
end