1864.] 



Mr. A. J. Ellis on Musical Chords. 



397 



The introduction of any one of these tones in conjunction with 1, 3, 5 and 

 their octaves will therefore form a discord, the harshness of which may be 

 frequently much diminished by the omission of 1 and its octaves for the 

 constituents 7, 15, 17, by the omission of 5 for the constituent 9, and by 

 the omission of 24 for the constituents 25, 27, 45. 



Using the notation of my former paper, where g = 63 : 64, and putting 

 in addition vij = 84:85, xj = 33:32, xiij = 39:40, 1^ = 255:256, and 

 xvij = 135 : 136, the tones 1 to 18 may be represented by the following 

 notes in terms of : — 



1, 



2, 



3, 4, 



5, 



6, 7, 8, 



9, 10, 



c^ 





G, c, 



e, 



ff, Zhb or vij a% c\ 



d?, e\ 



11, 



12, 



13, 



14, 



15, 16, 



17, 



xj/^ 





xiij a^, 





or vij a% b\ c^ 



Xzd''^ or xvij c% 



18, 



20, 



24, 



25, 



27, 45, 







e\ 





tff% 



f% 





This notation will show what are the musical names of the constituents 

 of musical chords, and how they may be approximately produced on an 

 organ, harmonium, or pianoforte. 



By the type of a musical chord is meant the numbers which express the 

 relative pitches of its constituents, after such octaves below them have been 

 taken as to leave only uneven numbers, which are then called the elements 

 of the type. By the form of the chord is meant the numbers before such 

 reduction. Thus the type 1, 3, 5 embraces, among others, the forms 

 1, 3, 5 ; 1, 2, 3, 5 ; 2, 3, 5 ; 4, 3, 5 ; 3, 8, 10 ; 6, 10, 16 ; 2, 5, 6, 8, 

 and so on ; hence the types of musical chords consist of groups of the 

 elements 1, 3, 5, 7, 9, 15, 17, 25, 27, 45. The type of a concord is 1, 3, 5, 

 and of a discord 1, 3, 5, P, or 1, 3, 5, P, P', where P, P' are any of the 

 numbers 7, 9, 15, 17, 25, 27, 45. Discords may be divided into strong 

 and weak, according as those disjunct tones with which the pulsative tones 

 principally beat are retained or omitted. These discords again may be dis- 

 tinguished into those which have one or two pulsative constituents. The 

 chords may also be grouped according to the number of elements in their 

 type, dyads containing two, triads three, tetrads four, and pentads five. 

 The number of elements in the type by no means limits the numbers of 

 constituents, as any octaves above any of the elements may be added. 



Hence it is possible to classify all the suitable chords of music according 

 to their type, as in Table VI., where the notes corresponding to each type 

 are added in the typical form only. A simple systematic nomenclature is 

 proposed in an adjoining column, and the names by which the true chords 

 or their substitutes are known to musicians are added for reference. Occa- 

 sionally two forms of substitution are given, as they are of theoretical im- 

 portance, although confounded on some tempered instruments. A mode of 

 symbolizing the chords is subjoined, in which several types are classed 

 under one family. A capital letter shows the root of major chords, either 



