HAWKES' TEMPERAMENTS of the musical scale. In the years 1798, and 1805, Mr William Hawkes published two pamphlets for recommending the adoption of an irre gular douzeave scale, wherein 9 of the Vth, viz. upon C, G, D, A, E, B, F ; and upon F and b•B should each be flattened 5th of a major comma, or be of the value 355.79842721+7f+31m ; two of the Vths, viz. on and perfect, or each =358E+71+31m ; and consequently, the resulting or wolf Vth, on G, =365 8141552E + 7 f + 30m. Many particulars concerning the notes and tempera of which system, may be seen in the Philosophical Magazine, vol. xxvi. p. 173 ; xxviii. p. 304 ; xxx. p. 5 ; xxxvi. p. 47 ; and vol. xxxvii. p. 129, in which last page the beats of each of its 68 tempered concords are calculated, by Mr John Barraud, brother to the chronometer maker.
In 1807, Mr Hawkes contrived, and in 1808 took out a patent for his methods of extending the scale of organs and piano-fortes to 17 notes in the octave, (sec the Phil. Mag. vol. xxxvii. p. 325) ; and in 1810, he published a third mu sical pamphlet, in which his object (as afterwards explain ed to Mr Farey, see Phil. Mag. vol. xxxvii. p. 321.) was to recommend, for the tuning of this his patent instrument, a regular dixstptave system, in which 16 of the fifths, viz. on C, G, D, A, E, B ; t$F, and ; and on F, bE, bA, 1,D, and should be each flat tened the 1-318th part of the octave, (or 1th of Mercator's comma), or each of the value 356.06851414-7431m, and the resulting or wolf fifth A to F, is of course =367.246346 i+.7430m. The beats of each of the 102 concords in this system, have been calculated by the Rev. C. J. Smyth of Norwich, and published in the Phil. Mag. vol. xxxvii. p. 323, to which table we shall refer instead of copying it ; because from Mr Liston's Essay on Perfect Intonation, p. 23. and 142. it appears, that Mr Hawkes has since (by let ter to Mr Liston we have been informed) changed his for mer opinion, and now recommends the Vths for'his patent instruments to be flattened cof a major comma, in which terms Mr Liston has given its temperaments in p. 22. It
may be proper, however, to add, that, in this new system, each of the 16 fifths above mentioned, will be =356.165356 +7f+ 31m, and the wolf fifth on A =366.1810841+7f+ 30m.
Mr Hawkes' patent piano-fortes are furnished with 24 strings in each octave, although 17 only are of different sounds, that is, all the long keys have two unison strings, from one to the other of which the hammers shift, at the same time that they do so from the 5 short-key notes tuned fats, to the five otherS tuned sharps, or vice versa ; it seems, however, to us, that 7 of these strings might probably be dispensed with, by allowing rather more space on each side the long-key strings A, B, C, D, E, F, and G, and making their hammers rather wider, so that after the shifting side wise of the key-board necessary to cause the short-key ham mers to move from A, r C, and to 17B, D, b•E, 17G, and 1,A respectively, or vice versa, the hammers of the long-keys may still continue to strike the same strings.
The objections which were so forcibly urged in Dr Kemp's Musical Magazine against the defect of these in struments, in not being able to give fat and sharp notes at the same time, or quickly succeeding each other, as com posers not unfrequently direct, seem to operate fatally against their introduction to general use. We have lately beard, that the organ which Mr Hawkes caused to he put up, a few years ago, in Christ Church, Blackfriars Road, in Surrey, has been either removed or altered to a common organ. We are aware, however, that this may have arisen from injudicious attempts at tuning this organ, according to one or other of the systems that we have mentioned in this article, instead of applying the MEAN TONE System, which alone, or one exceedingly near to it, (in the perfce• tion of its major third), seems applicable to this noble in strument. (q)