User:Obankston/Music

Below is a comparison between the first 63 harmonics and the intervals of 12-tone equal temperament (12tET), transposed into the span of one octave. Tinted fields highlight differences greater than 5 cents (1/20th of a semitone), which is the human ear's "just noticeable difference" for notes played one after the other (smaller differences are noticeable with notes played simultaneously).

Harmonic						12tET Interval	Note	Variance cents
					63	prime (octave)	C	−27
1	2	4	8	16	32			0
					33	minor second	C♯, D♭	−47
				17	34			+5
					35	major second	D	−45
			9	18	36			+4
					37	minor third	D♯, E♭	−49
				19	38			−2
					39			+42
		5	10	20	40	major third	E	−14
					41			+29
				21	42	fourth	F	−29
					43			+12
			11	22	44	tritone	F♯, G♭	−49
					45			−10
				23	46			+28
					47	fifth	G	−34
	3	6	12	24	48			+2
					49			+38
				25	50	minor sixth	G♯, A♭	−27
					51			+7
			13	26	52			+41
					53	major sixth	A	−26
				27	54			+6
					55			+38
		7	14	28	56	minor seventh	A♯, B♭	−31
					57			−1
				29	58			+30
					59	major seventh	B	−41
			15	30	60			−12
					61			+17
				31	62			+45

Computed by:

cents error, positive = frac(frac[log₂(harmonic)]*12)*100

cents error, negative = (cents error, positive) - 100, if (cents error, positive) > 50