VIII. SPECIAL COLLECTIONS. 199 



2. The same Apparatus, consisting of 32 lingual tones, the 32 part tones of 



-2 

 the fundamental tone C =32 vibrations. 



On the overtone apparatus there result quite plainly the corresponding 

 difference-tones of all phases that may be chosen at pleasure ; also, up to a 

 certain point, the corresponding resultant tones. By means of this overtone 

 apparatus not only the waves and the quality of the sound can be demon- 

 strated, but likewise the different degrees of harmony of the various musical 

 proportions (rhythm), and of poly-accords in different keys and transpositions. 

 The latter, in particular, in combination with the tone limit apparatus for low 

 tones, mentioned hereafter. 



3. Tonometer, consisting of 65 lingual tones; every subsequent tone higher 



by 4 vibrations (waves) than the previous one, from c = 256 to c = 512 

 vibrations in a second ; with reed pipes. 



4. Tonometer, consisting of 33 tones ; each succeeding tone being 4 vibra- 

 tions higher than the preceding one, from c = 128 to c = 256 vibrations in 

 the second. 



(Note. By the number of vibrations given, double vibrations (waves) ar 

 always to be understood.) 



5. Tone-limit Apparatus, for low (pitch) tones ; consisting of 57 lingual 

 tones, with reed pipes, from c = 128 vibrations downwards to 8 vibrations in a 

 second, namely, from c= 128 to C- 1 = 64, every subsequent tone in the de- 

 scending scale lower by 4 vibrations than the next preceding tones from 

 C- 1 = 64 to C~ 2 = 32, each two vibrations lower, and, lastly, from C- 2 = 32 

 vibrations downwards, each one vibration lower as far as 8 vibrations. 



6. Tone-limit Apparatus, for high (pitch) tones ; consisting of 31 small 

 tuning-forks, the diatonic Durton scale c; d; e; f; g; a; h; c; 



24 : 27 : 30 : 32 : 36 . 40 : 45 : 48. 



through 4| octaves, namely, from c 5v = 2048 vibrations (double) to e viii = 40,960 

 double vibrations, with two bows. 



In order to be able to observe, and to perceive better and more distinctly 

 with the tone-limit apparatus for high tones (tuning-fork apparatus of 31 

 tuning forks), the ascending scale up to the highest pitch, it will be advisable 

 to intonate with two bows the scales in octaves, one after the other, and thus 

 to sound every tone with its octave simultaneously or one directly after 

 the other. 



7. Two large Gedact Pipes (stopped mouth pipes), whose pitch can be 

 lowered an octave, with small wind chest and wind trunk, for illustrating the 

 interference, waves, resultant tones, &c. 



a. Two smaller Gedact Pipes, with small wind chest and wind trunk, for the 



same purpose. 



b. Very powerful-sounding Lingual (reed) Pipe, accompanied by a large 



number of overtones, with bell-mouth : C~ r2 = 32 vibrations in a 

 second. 



c. Twenty-nine Resonators to the same, from the 4th to the 32nd overtone. 



(The resonators are conical, and made of zinc.) 



d. Reed pipe, with bell-mouth, C~ 1 = 64 vibrations. 



e. Four open and four stopped Labral Pipes, with small wind chest and 



valves, producing the C major accord : c : e : g \ c. 



8:10:12:16 



f. Accord Heed Pipe, producing the C major accord c : e : y : c : e : g : c 

 (The two apparatus e and/ are for demonstrating the quality of sound.) 



