| Mr. URBAN, | Westminster, Oct. 1, 1813. |
Observing that the Rev. Henry Liston's "Essay on perfect Intonation," and his Euharmonic Organ, have come under the notice of your Musical Reviewer, in the Magazine for August last, p. 155, I am induced, as one of those who have several times listened with peculiar delight to the fine and novel effects of the perfect harmony produced on his Organs, at Messrs. Flight and Robson's Rooms, and witnessed the facility with which Mr. Samuel Wesley, and other performers, after a slight practice, were able to manage the pedals by which the same is produced, to trouble you with some remarks on the Musical Scale , with the hope of making the nature of the same somewhat more plain and evident than Mr. Liston has made it in his work above quotes, on account of his having adopted a Notation for expressing the Intervals, less convenient than one which I have discovered, and used for several years passt, and shall without further prreface proceed to apply to his Scale.
Within each Octave, as Cc, Mr. Liston has 59 intervals ; and on examining these it will be found that 11 of such intervals, between adjacent sounds, are very small and equal, each being in his notation 2T - t - 2H. Instead of this compound expression, which few practical Musicians will, I fear, take the trouble to understand fully, I substitute unity, or 1 of my Artificial Commas, of which 612 make the Octave or VIII, 358 the fifth or V, 197 the Major Third or III, and 254 the Minor Fourth (VIII - V) or 4th : as I have shewn in the "Philosophical Magazine."
By help of these four Numbers, others answering to all Mr. Liston's Notes, may easily be obtained, by going through his Tuning process, using + for addition,- for subtraction, and = for equal : viz.
From C = 0, take 358 = G, 358 + 358 - 612 = 104 = D ; 197 = E, 197 + 358 = 555 = B, 555 + 358 - 612 = 301 = F#, 301 + 358 - 612 = 47 = C# ; 197 + 254 = 451 = A ; 197 + 197 = 394 = G#, 394 + 358 - 612 + 140 + D#, 140 + 358 = 498 = A#, 498 + 358 - 612 = 244 = E# ; 394 + 197 = 591 = B#, 491 + 358 - 612 = 337 = F##, and 337 + 358 - 612 = 83 = C##.
Again, 612 - 358 = 254 = F, 254 + 612 - 358 =508 = Bb ; 612 - 197 = 415 = Ab, 415 - 254 = 161 = Eb; 415 - 358 = 57 = Db, 57 + 612 - 358 = 311 = Gb, 311 + 612 - 358 = 563 = Cb, and 415 - 197 = 218 = Fb, 218 + 612 - 358 = 472 = Bbb, which completes the 24 Notes of Mr. Liston's primary Scale, p.44.
Then, in order to produce the acute Notes, or Series comma higher than the above, we may begin at D, viz. 104 + 358 = 462 = A/, 462 + 358 - 612 = 208 = E/, and 208 - 197 = 11 = C/.
From which Note, exactly the same process being repeated, as above , the same series of notes will result, each 11 greatere than above, viz. G/ = 359, D/ = 115, E/ = 208, B/ = 566, F/# = 312, C/# = 58, A/ = 462, G/# = 405, D/# = 151, A/# = 509, E/# = 255, B/# = 602, F/## = 348, C/## = 94 ; F/ = 265, B/b = 519, A/b = 426, E/b = 172, B/b = 68, G/b = 322, C/b = 578, F/b = 229, and B/bb = 483, the 24 acute notes.
And in order to obtain the grave notes, or series comma lower than the first series, begin at A, viz. 451 - 358 = 93 = D\, 93 + 612 - 358 = 347 = G\, 347 + 612 - 358 = 601 = C\, 347 + 197 = 544 = B\ ; 93 + 197 = 290 = F\#, 290 + 197 = 487 = A#, 451 + 197 - 612 = 36 = C\#, 36 + 197 = 233 = E\# ; 601 - 197 = 404 = A\b ; 347 - 197 = 150 E\b ; and 565 - 358 = 207 = F\b, the 11 grave Notes.
These several Notes arranged, with their Numeral Values from C affixed, as in Mr. Liston's third Column at page 12, will stand thus, viz. o = 1st or key, 11 = 1/, 36 = #1\, 47 = #1 or I, 57 - 2d, 58, 68, 83 = ##1, 93 = II\, 94, 104 = II, 115, 140 = #II, 150 = 2\, 151, 161 = 3d, 172, 197 = III, 207, 208, 218 = b4, 229, 233, 244 = #III, 254 = 4th, 255, 265, 290, 301 = IV, 311 = 5th, 312, 332, 336 #V, 404, 405, 415 = 6th, 426, 451 = VI, 462 = VI/, 472 = b7, 483, 487, 498 = #VI, 508 = 7th, 509, 519 = 7/, 544, 555 = VII, 565 = 8th, 566, 576 = 8/, 591 = #VII, 601, 602 = #VII/, and 612 = VIII.
Which series of artificial commas, representing the 59 Notes of Mr. Liston's Scale, will be found equally exact (for all practical purposes), and vastly more convenient than either the "elements" or the "numeral measures" in his two last columns, for examining and proving every operation relating to Intervals and Chords, throughout his work : for which purpose I would recommend those who are about to enter on the study of the "Essay on perfect Intonation," to draw out on a card or paper the notes and numbers, and numerals, given above, in three columns, beginning with the highest, viz. c, 612, VIII, and descending to the lowest, viz. C, o, 1 ; and to supply opposite to them, a series for the octave above this, by adding 612 to the several numbers, and using small Letters thus, c/ 623, c\# 648, c# 659, db 669, c/# 670, d/b 680 &c. And it might be convenient to mark in pencil on the margin of Mr. Liston's work (which is sufficiently wide) the value of each chord in these artificial commas of mine ; thus in page 52 opposite line 19, wherein the chords [V/III] and [6/3] occur, write [358/197] and [415/161], line 20, opposite [VI/4] write [451/254] &c. ; and it might be further useful, after and between each number, to write the differences thus, [358/197] 161, [451/161] 254, and [451/254] 197 ; by which it would at once appear, that the intervals between the upper Notes of these Chords are 3d, 4th, and III, respectively, as Mr. Liston states. By the help of such a table, the Notes truly answer to any chord, however compound, or the chord resulting from any given combinations of Notes, may very readily be found, &c. &c.
Your Reviewer, in his introductory remarks, speaks of Temperament : it may not therefore amiss to mention, that the imperfect Fifth C# A\b (and 14 others) in Mr. Liston's Scale, viz. 404 - 47 = 357 is the proper Equal Temperament Fifth, which 12 times repeated above C, will make B# coincide with e ; for 357 X 12 - 612 X 6 = 612.
No judge of good Musick ever yet complained of the uniformly perfect harmony, or of the similarity of the keys in Concerts, where voices, violins, and perfect instruments only were admitted, and the bungling expedients of temperaments were wholly excluded ; nor will any such have the least cause to complain of the exclusion of wolves and temperaments, or the want of variety of expression, in performances on the Euharmonic Organ. That taste must surely be greatly vitiated, which can relish the novel variety of wolves and beating concords in preference to pure harmony, such as all our refined Concerts aim at, in excluding Keyed Instruments except from the Choruses.
Your reviewer does not fully explain himself, as to his doubts of the practicability of Mr. Liston's scale on a large Organ, viz. whether he refers to Messrs. Flight and Robson, on the bulk and expence of such an Instrument, or on the harmonic effects of the compound stops : on the latter head, I know several Musicians, who have rather hastily formed an opinion unfavourable to the effect of compoound stops. The experiment remains yet however to be tried ; but from the trials which can be made on the present Instruments, by putting down several of the notes of chords on the compound stops, although imperfect, because of the reinforcements, or doubling of the notes, most harmonic to each other, in such chords on compound stops, whereby the discordant intervals therein are overpowered and lost, cannot be thus imitated, - I am fully of opinion, that effects not less striking and delightful would result from compound stops, than from the simple ones that have been so successfully tried.
But, supposing that large Organs are never attempted on Mr. Liston's plan, I cannot see the justice of your Reviewer's inference, that the moderate-sized ones already constructed, must remain mere useless curiosities. - Are no Chamber or private Concert Organs wanted on nearly the same scale, as to bult and expence, as these Instruments now on exhibition? Are there no Music-schools, or places for study among us, where the practising of correct singing, and the study of harmony in all its curious combinations, by Composers for perfect Instruments, might be aided and safely guided by these improved Instruments?
No competent judge of the subject, or well-wisher to the improvement of this most delightful Science, will, I think, on consideration, venture to answer these questions in the negative, or refere to Tempered Instruments,even so improved as Loeschman's Organs and Piano Fortes, (with 24 sounds in each octave), as fully adequate and fit for the purposes above referred to.
Hoping that Mr. Liston's Essay will soon be more generally studied, and his Instruments referred to, for practically illustrating the precepts therein laid down, and unfolding the scientific views therein, I remain,
| Yours, & c. | JOHN FAREY, Sen. |