ENHARMONIC. 



47 



marked witli sharp and flat signatures shall be re- 

 presented by small characters. 



(No. 1.) (No. 2.) 



C major has b and e A minor has b and e 



D major has ct ft B minor has ci ft 



E major has At ft C minor has d< gt 



F major has c j a .1 D minor has e* a 



G major has f * b E minor has f * b 



A inHjor has gt rt F minor has gi c* 



6 major has aid* G minor has ai d 



(No. 3.) (No. 4) 



C mjnr lias f and c A minor has f and c 



B major has e/ b/ G minor has e/ b/' 



A major hus d/ a/ F minor has d/ a/ 



G major has c/g/ minor has c/ g/ 



F major has b/ f D minor has b/f 



E mjor has a/ e/ C minor has a/ e/ 



D major has g/ d/ B minor has g/ d/ 



But sharp and flat signatures at the cleff do not 

 merely mark the places of semitones, they also point 

 out the places, distances, and relations of full tones 

 to each other, to their respective semitones and re- 

 spective keys. For if the natural keys and their 

 semitones are by artificial keys and semitones trans- 

 posed, their relative full tones must be transposed 

 also. Hence, in constructing tables of the transposi- 

 tion of keys, the artificial signatures of every preced- 

 ing key are retained by every immediately subse- 

 quent key, until all the necessary signatures are ex- 

 hibited. Thus, in the ordinary modes of transposi- 

 tion, D major, with c s, retains the signatures of G 

 major ; hence D major has c * f s. A major with g 

 *, retains all the signatures of D major, hence, we 

 have A major, with c s f s g *, &c. The sharp 

 and flat signatures, therefore, according to the ordi- 

 nary methods of transposition, increase by one in 

 each successive key ; but by the scheme of artificial 

 keys and semitones, just now exhibited in columns, 

 the artificial signatures in each successive key will 

 increase by the ratio of two, which measure of in- 

 crease will give all the semitonic and full-toned sig- 

 natures necessary for each key. Accordingly, when 

 we would give all the signatures necessary for each 

 artificial key, we have only to attach the signatures 

 of each foregoing key to the signatures of the next 

 following key, without calculating for the places and 

 distances of relative keys and semitones, as is done 

 by the ordinary rules for transposing regular keys, 

 and more particularly for transposing the anoma- 

 lous irregular keys, which so frequently occur in 

 Scotch and Irish music, and in the compositions of the 

 great masters of the continent. For as full tones are 

 made of half-tones, to the attaching of -the semitonic 

 signatures of every preceding key to the semitonic 

 signatures of every following key, until we obtain all 

 the legitimate signatures, gives us the just expression 

 of the full and half tones, in relation to their proper 

 keys. For instance, if we look back to column No. 

 4, and attach the signatures of G minor to the sig- 

 natures of the next following key, F minor, then we 

 obtain all signatures of F minor, '. e. d/a/e/b/. 

 Again, attach the signatures of F minor key to the 

 signatures of E minor key, then you obtain the signa- 

 tures of E minor key, namely, Ec/g/ d/a/e/b/, 

 or in columns, you have the sharp and flat signatures 

 of A minor key : thus 



A b and e 



Bet ft 



C ds gs retain c f I 



D e * a * retain At gt et It 



Ef * b retain not. 



F gt cs retain f * 



G a t d t retain gt ct ft 



A f aadc 



Ge/b/ 



F d/ a/ retain e/ b/ 



EC/ gf retain d/ a/ e/ b/ 



D b/f retain not. to avoid chro. 



C a/ e/ retain b/ [mittics 



~ " d/ retain a/ e/T> 



B gf if retain a/ e/ bf 



Let us see whether this method applies for transpos- 

 ing all natural keys, regular and irregular. For the 

 purpose of brevity, the transposition of the entire 

 scale shall be given in one view. In order to en- 

 able the reader to judge of the accuracy of our trans- 

 position, let it be recollected that as in the above in- 

 stances of transposition, the couple of sharps and 



flats indicating the places of semitone are on the 

 left hand side most nigh their columns of keys : 



Raise 

 ::'<! place 

 3d place 

 4th place 

 Mli place 

 6th place 

 7th place 

 Lower 

 2d place 

 3d place 

 4th place 

 5th place 

 6th p lace 

 7th place 



ABC 

 BCD 

 C D E 

 D E F 

 E F G 

 F G A 

 GA B 

 ABC 

 GAB 

 F <- A 

 E F G 

 DBF 

 C D E 

 BCD 



D E F G with 

 E F G A 

 F G A B 

 G A B C 

 A B C D 

 B C D E 

 C D E F 

 D E F G with 

 C D E F 

 B C D E 

 A B C D 

 G A B C 

 F G A B 

 E F G A 



b e to six places along 

 ct ft [the stave 



d g * retain c if t 

 es a s retain d g* ci ft 

 fib retain not. to avoid 

 d tct retain fi [chrom. 

 a* d* retain gj ct ft 

 f and c to six places along 

 e/b/ [the stave 



d/a/retain e/ bf 

 c/g/retaind/a/e/b/ 

 b/f /retain not to avoid 

 B/e/retain b/ [chrom. 

 g/d/retaina/e/b/ 



We now proceed to consider accidental signatures 

 the peculiar use of which is known to every smatterer 

 in music. An accidental signature is a sharp, or a 

 flat, or a natural not placed at the cleff, but occur- 

 ring occasionally in the progress of an air. When put 

 before any particular note, it influences that note 

 only, as often as the note itself occurs on the same 

 line or space within the bar which contains it. On 

 the contrary, sharp or flat signatures placed at the 

 cleff, at the beginning of an air, on certain lines or 

 spaces of the stave, influence all the notes or letters 

 (together with their octaves), on these lines or spaces 

 throughout the entire air, notwithstanding the occa- 

 sional temporary counteraction of accidental signa- 

 tures. Generally speaking, a sharp raises, and a flat 

 depresses a note one half tone, whereas a natural 

 counteracts either a sharp or a flat, by bringing a 

 note to its primitive diatonic sound. According to 

 our formula, all accidental sharps ascend, and all 

 accidental flats descend in alphabetical and in arith- 

 metical series ; but it is by laws which distinguish 

 them peculiarly from signatures at the cleff. Unlike 

 signatures at the cleff, they vary in their symbolic form 

 in each successive series of transposed keys, without 

 augmenting in quantity ; for sharps, flats, and 

 naturals, in every stage of transposition, are continu- 

 ally, by substitution, taking each other's places ; the 

 signs of modulation are constantly changing, while 

 their value is invariable, and the signatures of every 

 preceding transposed key are in no case what- 

 ever attached in mass to the signatures of any next 

 immediately subsequent key. Now, in order that we 

 may know how to exhibit accidental signatures with- 

 out the toil of calculating their places and distances 

 from their relative keys, and without pondering with 

 hesitation whether we shall employ a sharp or a flat, 

 or a natural signature, in representing a change of 

 modulation, we remark, 1st. That when any natural 

 flat, as c, or f is once flattened or any natural sharp, 

 as b or e, is once sharpened by accidental signatures, 

 then this change brings us to another note, which is 

 sung as in the natural scale, and is consequently 

 marked by a natural ; for no natural flat c or f is 

 twice flattened, and no natural sharp b or e is twice 

 sharpened in the way of being once marked at the 

 cleff, and once marked accidentally by the same char- 

 acteristic symbol. For instance: c/ f /, brings us 

 to b n e n, and b * e s brings us to c n f . Yet it 

 is no less true that a natural flat c or f may be, and 

 often is, twice sharpened, once at the cleff, and once 

 accidentally at one and the same time, conversely a 

 natural sharp b or e may be twice flattened, once at 

 the cleff, and once accidentally. 2d. When any note 

 which is once sharpened or flattened at the cleff is 

 again sharpened or flattened accidentally, then this 

 change is indicated by a double sharp, thus ss, or 

 thus x ; or a double flat thus, //; which duplica- 

 tion of signature is equivalent to a natural accidental, 

 and is marked thus . For instance: b ff is equi- 

 valent to a , and c ss, is equivalent to d n. These 

 two circumstances account for the origin of acciden* 

 tal naturals in the following tables of transposition. 



