ISOTONIC SYSTEM OF TEMPERAMENT, or the equal temperament of the musical scale, consists of 12 equal semitones, of the value 1 ÷ ¹²√2 = 51 &Sigma + f + 4 5/12 m. This system derives its chief consequence from the great number of writers, and the respectability of several of those who have appeared as its advocates ; among those who have fallen under our notice, we remember the names of D'Alembert, Broadwood, Cevallo, Chladni, Couperin, Crotch, Davis, Des Cartes, Emerson, Euler, Kirnberger, Kollmann, Marpurg, Merrick, Mersennus, Rameau, Riccio, Scrogs, Sorge, Sulzer, Vogler, &c. It is plain from the account given by most of the writers alluded to, that they had neither submitted this system to the test of experiment, or thoroughly calculated it and considered the harmonic effects of its grossly tempered chords, the thirds and sixths especially ; while many of them were utterly unacquainted with the true nature and limits of the musical scale, as appears from their statements, and as to what could or could not be done, owing to the immutable relations which any one of the tempered chords has with several others, and of the whole combined, in a regular douzeave.

In page 273 of our ninth volume, we have inserted a Table of the full particulars of a system, very carefully and minutely calculated, which Mr. Farey discovered in 1807, and first announced in the Philosophical Magazine, vol. xxvii. p. 65, not for the purpose of recommending or advocating the isotonic system of which we are now treating, as being adapted to use ; but for the purpose of shewing a practicable mode of exhibiting a new system, so indefinitely near to the true isotonic, that all its merits and defects might thereby be shewn, and the controversy so long subsisting regarding this system, ended by an appeal to actual and indisputable experiment.

In pursuing the same object, Mr. Farey has very recently recommended, in the periodical work above quoted, vol. xlix. p.447, the undertaiking of an experimental euharmonic organ, on a scale sufficiently extended to admit of exhibiting two or more octaves, of the great scale of intervals, 612 in the octave, which is given under our article INTERVAL, so contrived, that the merits of the isotonic, in common with a great number of other systems which have been proposed, may be put to the test of sufficient trial in musical performance ; by the use of those 12 Listonian notes, which approach nearest to the true isotonic notes respectively, or those of any other system, which may be submitted to this trial.

The Table of the true isotonic system, which we are now about to present to our readers, is exactly similar in its arrangement, and was calculated for the purpose of comparison with that of Mr. Farey's system, approximating to it, which has already been referred to in our ninth volume, p. 273, except that the 3d column there, which exclusively pertains to Mr. Farey's first system, now contains those 12 notes of his enlarged Listonian scale, which he has recently recommended to be tried in performance, as substitutes for the strict isotonic notes, which all the following columns o fthe Table now given, are occupied with. Before we arrive at the printing of TEMPERAMENT, in our work, we may hope to be able to announce that the experiments above alluded to have been made, and their results, and to give all the further particulars, in a tabular form, regarding the system of 12 notes, which are now contained in our third column below.

Isotonic Table

In pages 273 and 274 of our volume, which has been quoted, the sums of hte beats in each of teh six latter columns of the above Table will be found, compared with similar sums of the beats of Mr. Farey's equal temperament ; and several other comparisons and averages, by which the very near co-incidence of these two systems are shewn : the total number of beats in the two Tables, differ only .0063 of a beat, our of more than 847 beats!

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