The animation in Fig. 1 is designed to allow you to compare the first twelve partials of a harmonic series for C2 (a just tuning) with the same 12 pitches approximated in twelve-tone equal temperament (12TET). In the animation, each just partial is immediately followed by its approximation in 12TET. Just partials appear in in a red boxes. 12TET approximations appear in (gray boxes). The deviation of each 12TET approximation from a just tuning is indicated in cents (+/-). Pitch pairs are allowed to overlap so that beating may be heard. A chart summarizing the frequency calculations used to create Fig. 1 appears in Fig. 2.

Fig. 1. A comparison of the first twelve partials of a harmonic series for C2 vs. their approximation in 12TET.

Fig. 2. Frequency values and differentials for comparison.

Partial Number	1	2	3	4	5	6	7	8	9	10	11	12
US Standard Pitch Name	C2	C3	G3	C4	E4	G4	(Bb4)	C5	D5	E5	(F#5)	G5
Freq. in 12TET (Hz.) Based on A4 = 440 Hz.	65.41	130.81	196.00	261.63	329.63	392.00	466.16	523.25	587.33	659.26	739.99	783.99
Differential in cents	0	0	+2	0	-14	+2	-31	0	+4	-14	-49	-2
Freq. in a Just Tuning (Hz.) Based on C2 = 65.41 Hz.	65.41	130.82	196.23	261.64	327.05	392.46	457.87	523.28	588.69	654.1	719.51	784.92
C4 = middle-C All frequency calculations have been rounded to the nearest 1/100 Hz. The differential in cent indicates the discrepancy between to two systems.

This animation in Example 1 has a MIDI sound track. In order for it to sound correctly, QuickTime's pitch bend range must be set to its default of +/- 2 semitones. If you are interested in learning how to create simple musical QuickTime with MIDI animations like these click here.