Crude thing

rootPitch.m

function p = rootPitch(key, note)
    notes = {'c', 'cs', 'd', 'ef', 'e', 'f', 'fs','g','gs','a','bf', 'b'};
    I = find(strcmp(notes, note));
    I = I-1;
    shift = 12*key;
    idx = shift + I;
    a = 2^(1/12);
    f0 = 16.35;
    p = f0*a^idx;
end

synth.m

clear variables;
Fs = 44100; % Sampling Frequency
Ts = 1/Fs; % Sample Time
T = 2; % Length of output
Px = 0.9999; % Fade Out Modulus
Ap = 0.4; % Amplitude Modulus
PitchRoot = rootPitch(4, 'a'); % Root Pitch
Pn = ceil(Fs/(2*PitchRoot)); % Number of partials to use
% This can be calculated.
% The human ear can only hear ~22050 Hz. We find how many partials we need
% to achieve such that we don't exceed that by much. Thus, since Fs is
% double the human hearing, and you'd run into issues with sampling if 
% you exceed Fs/2, we divide it by two then divide it further by
% the root pitch. Think such that Pn * PitchRoot = Fs/2. Solve for Pn. 

t=0:Ts:T;
y = zeros(Pn, Fs*2+1);

%Generate partials
for i = 1:Pn
    partialF = PitchRoot*i;
    amp = Ap^i;
    temp = amp*sin(2*pi*partialF*t);
    y(i,:) = temp;
end

% Composite them
partials = zeros(size(temp));
for i = 1:Pn
    temp = y(i,:);
    partials = partials + temp;
end

%Apply a fade out.
for i = 1:numel(partials)
    partials(i) = partials(i)*Px^i;
end