D i M 



744 



D I M 



Diminished 



Intervals. 



Cillwyhia DILLWYNIA, or Rotjiia, a genus of plants of 

 the class Diadelphia, and order Decandria. See Bo- 

 tany, p. 286. , 



DIMERIA, a genus of plants of the class Triandria, 

 and order Digjmia. See Brown's Prodromes Plant. 

 Nov. Holl. et Ins. Van Dicmen, p. 204 ; and Botany, 

 p. 116. 



DIMINISHED Intervals, in Music, according to 

 our nomenclature of this science, are any such intervals 

 as are less than their true quantity, by the semi-tone 

 minor or S, (=362-|~f-j-3m,) and in like manner we 

 call all intervals which are greater than their true quan- 

 tity by S, superfluous intervals, whether the same are 

 major or minor consonances, in either case. See the 

 list of sixty notes on Mr Liston's organ, in the Phil. 

 Mag. vol. xxxvii. p. 276". In speaking of regularly 

 tempered scales, Dr It. Smith in his Harmonics, second 

 edition, p. 165, says, " The interval of a minor conso- 

 nance augmented by a minor limma, (I, see our articles 

 Diesis and Limma of Tempered Scales,) makes the in- 

 terval of a superfluous consonance ; and the interval of 

 a minor consonance diminished by a minor limma, 

 makes the interval of a diminished consonance." 



If we examine Mr Liston's untempered or perfect 

 diatonic scale of the octave Cc, in p. 12, of his Essay 

 on perfect Intonation, we shall find, that the sharps and 

 thejlats are in every case but one, applied to major in- 

 tervals, (above C,) as I, II, III, &c. ; and this excep- 

 tion occurs with F, the minor fourth or fourth of this key: 

 this respects the giving of names to the notes or sounds. 

 Mr Liston's restriction of $'s to major intervals, and [/s 

 to minor intervals, and so applying his terms redundant, 

 (instead of superfluous,) and diminished, when treating 

 of intervals generally in pages 115 and 137, however 

 sufficient and well adapted the same may be to the pur- 

 poses of the practical musician, seem wanting in that 

 precision and method, which the subject is now capa- 

 ble of receiving in an elementary work. 



If the term superfluous, (or redundant,) had been li- 

 mited by Mr Liston to the quantity S, and also the term 

 dimished to the same quantity, as has been mentioned 

 above; and the marks $ and h, when thus used to describe 

 intervals, without reference to their place on the staff, or 

 as'marking particular notes, had also been restricted to S; 

 and when such intervals required to be named or mark- 

 ed, as occur upon C, E, and A, and below Eh and Ah, 

 vulgarly called their sharps and flats, (see Phil. Mag. 

 vol. xxxix. p. 275, ) but which are, in reality, each equal 

 to the semi-tone medius §, (472-f-/ , -f-4»j,) or S-f-c 

 instead of S, the same had been called acute-superfluous, 

 and marked %', and grave- diminished, and marked h N , 

 a very considerable improvement would have been made 

 in this truly valuable Essay, by avoiding all ambiguity. 

 In tempered scales these distinctions do not apply, and 

 $=/, and b=/, in all cases, as Dr Smith remarks above : 

 but for perfect instruments, and even for voices, C$', 

 E$', and A.$' and Ehh\, and A^h v had better be marked 

 at the beginning of the staff*, and wherever $ and h occur 

 to these notes respectively ; and then $ and h would, 

 in every case, denote the interval S, or minor semi- 

 tone. But at any rate, when treating of intervals and 

 chords, without reference to the particular notes which 

 form them, these distinctions ought not in future to be 

 omitted, and $J and \> sometimes be used to signify S, 

 and sometimes §, as Mr Liston has unfortunately done, 

 instead of writing %.% $'111, and #'VI; and fr"3, and 

 h v 6 ; or he should have abstained altogether from the use 

 of the marks >& and h, when not used with reference to 

 those at the cliff, (as observed by him at page 49,) and 



have used some other marks, attached to the numerals Diminished 

 of the intervals, correctly defining the distinction be- Intervals, 

 tween S and §, in the cases above referred to. *~ """ v"""" 



The analogy with the terms major and minor, to 

 which Mr Liston refers in p. 137, in excuse for the am- 

 biguity above complained of, cannot avail; for although 

 practical musicians often say, " a flat third," and in 

 works on thorough bass, &c. write \>3 and \j6, when 

 they mean the minor third and minor sixth, and " sharp 

 third" and " sharp sixth," when they mean the major 

 third and major sixth, &c. ; yet what theoretic writer, 

 or indeed any other, writes [jIII for 3rd (=1612 + 3 f 

 + 14m), or $3rd for III (=1972 + 4f-f-17 m), or 

 t>VI for 6th (=4152 + 8f + 36m), or %6 for VI 

 (=45l2 + 9f+39m), &c. : and yet we m&y tolerate 

 and safely use E'y and Ah to designate the notes an- 

 swering to the 3rd and the 6th of the key C, &c. as 

 mere names for these notes, and without reference to 

 their exact distance from any others in the scale, although 

 we consider these notes, the 3rd and 6th and others, as 

 equally determined by nature, and their place in the 

 scale fixed with the same mathematical accuracy as the 

 III. and VI. from which certain writers, during the in- 

 fancy of the science, as to correct theory, happened to 

 derive the former, and to name them accordingly: but 

 in speaking of the intervals between notes, terms and 

 marks that are definite and unvarying in their mean* 

 ing, ought alone to be tolerated or used by theoretic 

 writers of the present day, when mathematical accu- 

 racy can and ought to be given to every expression re- 

 lating to musical intervals, as we are taking so much 

 pains to shew in this department of our work. 



Mr Maxwell, in his " Essay upon Tune," p. 51, &c. 

 contends for and uses the words and marks sharp and 

 flat and ^ and \>, in one invariable sense as to magni- 

 tude, but he unfortunately fixed on § ( = 472+f+4m) 

 for the same, instead of c? (=362+f+3m), although 

 the former occurs in practice only half as frequently as 

 the latter. See Phil. Mag. vol. xxxix. p. 375. 



We shall mention below, the intervals in alphabetical 

 order, major and minor, to which we have seen the 

 term diminished prefixed, using the numerals and sym- 

 bols of our XXXth Plate, Vol. II. but omitting the 

 cols, f and m, in order to shorten the detail ; and only 

 mention the 2 s, which then are the artificial commas 

 of Farey, viz. 



Diminished Eighth, major, VIII — d = 5762; minor 

 8— rf=529S. 



Diminished Fifth, major, V — §=3112, and V J 



= 3222; minor, 5 — cf=3222. 



Diminished Fourth, major, IV — c?=2652; minor 

 4— §=2072, 4— d=2182. 



Diminished Fourth of Bemitzrieder, has a ratio £ Us. 

 — 1962 + 4f+ 17m, and its log. =.9035800,9412;'the 

 true minor fourth exceeds this interval by the apotome 

 or it is 4 — P. See Fourth Minor. 



Diminished Second, major, II — §=572, and II ef 



=632; minor, 2 — §=102, and 2— rf=2l2. 



Diminished Seventh, major, VII — d=5192; minor 

 7— §=4612, and 7—^=4722. 



Diminished Seventh of Calcott and Marsh, and 

 greater diminished seventh of Chambers ; it is equal to 

 three minor thirds, has a ratio 4xf, =4832 + 9f+ 42m, 

 and its log. =.7624562,6185 : the true minor seventh 

 exceeds this interval by the semitone subminimis, or it 

 is 7 — /, or 7' — rf. But it seems probable, from com- 

 paring pages 164 and 202 of Dr Calcott's Musical Gram- 

 mar, 1 st edition, that in the latter page the Doctor has 

 omitted the word " extreme," or " double," before 



