Young temperament

The letter was read at the Society's meeting of 16 January 1800, and included in its Philosophical Transactions for that year.

In his first temperament, Young (1800) chose to make the major third C-E wider than just by ⁠1/4⁠ of a syntonic comma (about 5 cents, Playⓘ), and the major third F♯-A♯ (≈ B♭) wider than just by a full syntonic comma (about 22 cents, Playⓘ).

The following table gives the pitch differences in cents between the notes of a chromatic scale tuned with Young's first temperament and those of one tuned with equal temperament, when the note A of each scale is assigned the same pitch.

[5] In the second temperament, Young (1802) made each of the fifths F♯-C♯, C♯-G♯, G♯-E♭, E♭-B♭, B♭-F, and F-C perfectly just, while the fifths C-G, G-D, D-A, A-E, E-B, and B-F♯ are each ⁠1/6⁠ of a Pythagorean (ditonic) comma narrower than just.

[6] The exact and approximate numerical sizes of these latter fifths, in cents, are given by: f4 = 2600 − 1200 log2( 3 ) ≈ 698.04 If f3 and s3 are the same as in the previous section, and s4 Def══ f4 − 600 , the sizes of the major thirds in the temperament are as given in the second row of the following table:[7] The following table gives the pitch differences in cents between the notes of a chromatic scale tuned with Young's second temperament and those of one tuned with equal temperament, when the note A of each scale is given the same pitch.