HISTORY OF MUSICAL SCALES 423 



marked by frets get closer uiul closer together as the pitch rises. All 

 musicians know that this number of notes, twelve, is found confus- 

 ingly great for ordinary playing, and know the principles by which the 

 player selects certain notes for any tune. But this nudtiplicity of 

 notes has an important bearing on all studies on nonharnionic nmsic 

 made by harmonic musicians. For every sound within the compass 

 of the instrument comes very near to some one of the twelve n«tes and 

 may readily be represented thereby, owing to the difficulty the hearer 

 has in estimating deviations from the ftuniliar series und in noting them 

 down. The results of this approximation are to mask all deviations 

 from the twelve-tone piano scale, whether intentionally or accidentally 

 made, and to make it appear to musicians, first, that nearly all the music 

 of the world is performed substantially in our scale; and second, that 

 any other theoretical scales, such as those found auKjng Orientals, or 

 described by our European ancestors, are merely niathematical jug- 

 glery and of as little significance as proposals for a change that occa- 

 sionallv appear in modern musical or scientific journals. 



It is the purpose of this paper first to describe several types and 

 forms of instruments wideh^ used, each embodying a principle of scale 

 building distinctly unlike ours, though sometimes giving a result that 

 seems surprisingly familiar. Nearly all these instruments, it will be 

 noted, belong to what was called above the second or barbarous stage, 

 though a few of them come from countries where musicians have 

 reached the third and fourth stages. A second purpose is to present 

 a new and generic principle of primitive scale-building applicable to 

 the various types of instruments discussed. 



But before going further it must be recognized that the word 

 "scale" has many meanings. Perhaps the lowest and loosest is — the 

 series of sounds used in any nuisical performance, arranged in order of 

 pitch. The one that will most closely fit the present needs is — the series 

 of sounds produced upon a particular mstrument: Avhile th(» most 

 exact definition, but one applicable only where musical principles are 

 well developed is this: 



A i<cale is an indepenxiently reprocbiclhle s&rles (>t'.'«>iinds arranged 

 in order of pitchy reeognized a>< <i sf/indord and p'tted for mn-ucal 

 purposeii. 



While the last two definitions imply an instrument in which tne 

 scales are emV)odied, the limitation is in appearance only, for there is 

 no evidence that any musicians do have a standard series of tones, 

 unless they have one or more instruments embodying it, and have 

 learned the series directlv or indirectlv from such an instrument. 



