MDA Note: 2.2 Pitch

• Everything in music has the basis of Tone.
• The quality of tone is pitch, where as the intensity of tone is loudness.
• Two types of tone: pure tone vs. harmonic complex tones (actual music tone). identification:
  $$x(t) = sum_{n=1}^{N} A_n sin(2\pi f_n t+\phi_n)$$
  where $f_n = (n+1)f_0$, when $n>1, f_n$ is called overtone series.
• p21:

The strength of the individual partial and their phase shifts have (almost) no influence on the pitch percept. On the other hand, the strengths of the partials are crucial for timbre perception as described below.

A phenomenon widely discussed in psychoacoustics is the pitch of the residue. The pitch of the fundamental is heard even if the fundamental frequency component is eliminated from a harmonic complex tone.

• p25:

a semitone step comprises 100 cents; an octave corresponds to 1200 cents

• p27:

The MIDI standard assigns numbers to all notes from the bottom up starting with the even inaudible note A-1 with 8.176 Hz as midi-number 0. The notes are chromatically numbered all the way through so that the tone c' or C4 respectively with 262.626 Hz has the midi-number 60, the concert pitch of 440 Hz has the midinumber 69.

• p38: concept of beats
• Test of pure tone and harmonic_complex tone:

t = 0:0.001:2;
n = 7;
f = 440;
pure_tone = cos(2*pi*f*t);
harmonic_complex_tone = zeros([1,length(t)]);
for i = 1:length(n)
    harmonic_complex_tone += cos(2*pi*f*i*t);
end
sound(pure_tone);
sound(harmonic_complex_tone);

To make the tone more natural:

for i = 1:length(n)
    harmonic_complex_tone += cos(2*pi*f*i*t)/i;
end