EURASIP Journal on Audio, Speech, and Music Processing

Table 1 Frequency relationships between the overtones of a reference note n and its upper octave

From: Piano multipitch estimation using sparse coding embedded deep learning

Harmonic					Interval	Semitone	Variance cents
1	2	4	8	16	Prime (octave)	0	0
				17	Minor second	+ 1	+ 5
			9	18	Major second	+ 2	+ 4
				19	Minor third	+ 3	− 2
		5	10	20	Major third	+ 4	− 14
				21	Fourth	+ 5	− 29
			11	22	Tritone	+ 6	− 49
				23			+ 28
	3	6	12	24	Fifth	+ 7	+ 2
				25	Minor sixth	+ 8	− 27
			23	26			+ 41
				27	Major sixth	+ 9	+ 6
		7	14	28	Minor seventh	+ 10	− 31
				29			+ 30
			15	30	Major seventh	+ 11	− 12
				31			+ 45

Numbers under “Harmonic” indicate the overtone indices of n. Column indices of “Harmonic” indicate the octave numbers starting from 0. Variance cents in the last column are rounded up into integers

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