

T 



^<rC-**~+Z*% 



ENHARMONIC. 



645 



is of a small iron wheel, which is attached to an appara- 

 tus like a miner's lathe, and kept in motion by the foot. 

 The tools are tightened by a screw, and the stone to be 

 engraved is applied by the hand to the tool as it revolves, 

 and is shitted and conducted as required. The tools are 

 generally of iron, and sometimes of brass ; their forms 

 are various, generally resembling chisels and gouges: 

 some have small round heads like buttons, others flat, 

 Sec. ; and when the stone has been engraved, it is polish- 

 ed on wheels of hair brushes and Iripoli. 



See Strutt's Dictionary of Engraven ; Bryan's Dic- 

 tionary of Painters, Engravers, &c; Landseer on En- 

 graving; Heineken Idee Generate d'une Collection com- 

 fitette d'Estamfies ; Vasari Vile tie' Pittori ,- Oriandi, 

 Abecedario Piltorio ; Christ. Dicthnnaire des Monogram - 

 mes ; Papillon fdstoire de la Oravureen Bois ; Felibien 

 Princi/ies de V Architecture et des aulrcs Arts qui en de- 

 pendent. (i>. g.) 



ENHARMONIC Change, in music, is the occa- 

 sional substitution, during performance, of one interval 

 for another, differing therefrom, in a slight degree, in 

 order to avoid that departure from the original pitch, 

 which is called Divergency of Tune, (see tliat article.) 

 The Rev. Henry Liston, in his valuable work, entitled 

 An Essay on /infect Intonation, p. 72, after giving an 

 extract from Huygen's Cosmotheorios, remarks, that the 

 pitch, in singing, or on his organ, Sec. cannot be pre- 

 served by slightly tempering every interval, but must be 

 effected by substituting other notes, in particular situ- 

 ations; and, at page 120, he shews also, how, when the 

 musician, by a series of dominants, has wandered away 

 horn his principal key, may recover his lost ground, 

 while he seems to the hearer to be persevering in the 

 same course, by only substituting a particular note, either 

 higher or lower, by a schisma, by a major, or by a minor 

 comma, than the one that is written, in the ordinary no- 

 tation of music, and in which enharmonic changes are 

 all marked in his improved mode of writing musk for 

 the performer, on perfect instruments. 



Enharmonic Degree of Aristoxcnns, or Diesis qua- 

 ,/rantalis, is an interval, equal Jth of a major tone, or 

 IT; = 25.92713532 + f+2:r,, or 262+ }f+2im. Some 

 authors have called this the quarter tone major, and Mr 

 Hoyle denominates it the cnharmonical diesis. 



Enharmonic Degree of Euclid, is an interval thrce- 

 ihirlicths of the minor fourth, or 7 > T X4lh, =25526742 

 -f-f-f 2m, and its common log. is = 9875061,2634. 



Enharmonic Diesis, (greater £,) or diesis greater of 

 the mean-tone system, (see Vol. VII. Part II.) is an in- 

 terval whose rut;, is -iff, or ~, = 21 S + 3 m in Fa- 



vey's notation, =.9897000,4336 in common logs. = 

 .0102999.5664 in recip. logs., =0343153 in Euler's logs., 

 = 1 9091591 in major comma logs., =21.0157248 in 



schisma logs. In tuneable intervals it is VIII 3 III, 



=2VIII— 3 6ths, =41 — 2 111 + 3, by either of which 

 methods of ascending and descending, or vice versa, in 

 the tuning process, on an enharmonic organ of Liston's, 

 this interval may be tuned above or below any given 

 .note; already it will be found tuned thereon, above 

 #D, E, #G and #B, respectively. 



In the symbols explained in Plate XXX. Vol II the 

 following equations will be found to express the exact 

 relation of this interval to all the other intervals ther^'i 



6=R + *+ct 



= T + F+52 

 = ct+m + 9S 



=s- S =s-^ 



-It? -<-# 



=L— / =2S— t 



= 1-^ =T-2S 



=J— c = t — 2 tf 



£= 2c —2 £ = 2( J —32 



= 3c — £ =2\TII_3-6th 



= VIII— 3III 



£=2ld+63f— 19m £ = /+ c — *- 



= t+BI — d _L-|_ C £ 



= € +ct— 2 =S +c— c 



= c +ct-2S =tf + /__ S 



= *■ + c— /c =S+ C _p 



= ^ +2— ^c =T + ^—t 



= £+D — /c =T+€—T 



=s+2t; 



=212+2in 



= * + f-R = t +/-T 



=113+ m—e =r+y_ T 



=» J'- +R— € =4th+3d— 2III 



f,=2T— 2r— 52 £ = t — S _<J* 



-£""*—* =T~2 0f -_c 

 = ^ — r — 22 = T -f Q 



— e— s =T— a — } 



= S— /— S =2T— 2t— 2 



= P—-f—Z =3T— 3t— ,* 



= P— /— J-c a 



In that almost endless diversity of nomenclature, in 

 which theoretical writers on music have indulged, this 

 interval, besides the above, has received the denomina- 

 tion of a/iotome by some writers ; a/iotome major by Sa- 

 lomon, Uoethius, Sec. ; bacchius bv Rameau ; comma by 

 Chladni; (see Comma, Vol. VI. p. 639,) comma greater 

 by some writers; diesis by Euler, Liston, Sec; diesia 

 minor by Holder; diesc major by Rameau; diminished 

 second by Liston ; harmonia by Manning ; quarter note 

 by Boyce, Holder, Sec; quarter tone by several; tierce 

 wolf by Earl Stanhope, Sec. It is the error (b) of the 

 trumpet, and French horn minor sixth. 



Enharmonic Diesis (lesser) of the mean-tone- sys- 

 tem, (sec Vol. VII. Part II.) occurs adjacent to the half 

 notes of that system of temperament, is an interval equal 

 17.j2+f+l{m, =17.89376412 + 21)), whose common 

 log. is .99 12224,3171. 



Enharmonic Diesis of Aristoxcnus, is one quarter 

 of the major tone, fl", or his Enharmonic Degree 

 which see. 



Enharmonic Diesis of Euclid, one-tenth of the mi- 

 nor fourth, or -f'g x 4th, or his Enharmonic Degree 

 which sec. 



Enharmonic Ditone of Aristoxcnus, is an interval 



less than a minor fourth by half a nnjor tone, =4th JT 



= 2022 + 41+ 17 Jm, =202.0039. 122 + 4f + i7 m . : [s 

 common log. 9006375.2462. 



Enharmonic Ditone <> r Eucld, is an interval 24. 

 30ths of the rmjv - luurth, or -g < 4th, =203.2047 I 2 +' 

 4f+ 17.-.., whose common logarijhm is .9000490 1071 

 £<-*ahmonio Genus of theGruft music. SeeGENER A ' 

 Enharmonic Interval of Ci/od and Gregory, is'thV 

 Major Comma •«, which see. V 



Enharmonic quarter of a Tone ot Rameau, is the 

 Emharmonic Diesis -iff, which see. 



L 



