Thomas Young's definition of the musical temperament that has become known as "Young #1", and its approximation that has become known as "Young #2"

From "Outlines of Experiments and Inquiries Respecting Sound and Light", originally published in Philosophical Transactions, vol 90, London, 1800. This page reproduces the text of Young's republication in A Course of Lectures on Natural Philosophy and the Mechanical Arts, London, 1807.

The unqualified term "comma" refers to the syntonic comma, as the values in the table make clear.

It appears to me, that every purpose may be answered, by making the third C : E too sharp by a quarter of a comma, which will not offend the nicest ear; E : G#, and Ab : C, equal; F# : A# too sharp by a comma; and the major thirds of all the intermediate keys more or less perfect, as they approach more or less to C in the order of modulation. The fifths are perfect enough in every system. The results of this method are shown in Table XII. In practice, nearly the same effect may be very simply produced, by tuning from C, to F, Bb, Eb, G#, C#, F#, six perfect fourths; and C, G, D, A, E, B, F#, six equally imperfect fifths. If the unavoidable imperfections of the fourths be such as to incline them to sharpness, the temperament will approach more nearly to equality, which is preferable to an inaccuracy on the other side.

Table XII.
A
B
C
 
C       50000
B       53224
Bb      56131
A       59676
G#      63148
G       66822
E#[sic] 71041
F       74921
E       79752
Eb      84197
D       89304
C#      94723
C      100000

1 C          +.0013487
2 G, F        .0019006
3 D, Bb       .0024525
4 A, Eb       .0034641
5 E, Ab       .0044756
6 B, C#       .0049353
7 F#, a comma .0053950

1 A, E   -.0023603
2 D, B    .0029122
3 G, F    .0034641
4 C, C#   .0044756
5 F, G#   .0049353
6 Bb, Eb  .0053950
D
 
1 Eb, G#, C#, F#  -.0000000
2 F, Bb, E, B      .0004597
3 C, G, D, A       .0010116

A shows the division of a monochord corresponding to each note, in the system proposed; B the logarithm of the temperament of each of the major thirds; C, of the minor thirds; D of the fifths; C and D being both negative.