LECTURES TO SCIENCE TEACHERS. 



APPENDIX II. 



THE NATURAL FINGERBOARD WITH PERFECT INTONATION. 



THE digitals consist of three separate sets, of which those 

 belonging to four related keys, representing the notes 2, 5, 1, 

 4, are white; those belonging to three related keys, and 

 representing 7, 3, 6, are coloured the small round digitals 

 represent 7 minor, or the major seventh of the minor scale. 

 These are the same in all keys. 



This fingerboard can be made to consist of any number of 

 keys. 



The scales run in the usual order in direct line, horizontally, 

 from left to right along the fingerboard. 



The keys are at right angles to the scales, and run vertically 

 across the keyboard, from N Ciz in the front to C'$ at the 

 back, C being the central key. 



The scale to be played is always found in direct line, 

 horizontally between the key-notes marked on the fingerboard, 

 but the digitals may be touched at any point. 



The order of succession is always the same, and conse- 

 quently the progression of fingering the scale is identical 

 in every key. 



The 1st, 2nd, 4th, and 5th tones of the scale are played 

 by the white digitals ; the 3rd, 6th, and 7th, by the coloured. 



The sharpened 6tl\ and 7th of the modern minor scale are 

 played by the round digitals. The round digital, two removes 

 to the left as in the key of B flat, is related to that in the 

 key of C as 8 : 9, and supplies the sharpened sixth in the 

 relative minor of C ; so in all keys similarly related. 



Playing the scale in each key the following relations 

 appear 



