228 S. A. Hageman — A Just Intonation Piano. 



This construction is essentially different from all previous 

 just intonation instruments in that it acknowledges no tone 

 cycles, and consequently no compromise in intonation however 

 small. 



Each semitone of the tempered chromatic scale is in turn 

 made the tonic or keynote of a separate just intonation scale 

 of twelve tones to the octave, whose intervals correspond to 

 those of the duodene given above. 



This affords a complete and correct chromatic scale of just 

 intervals besides a complete diatonic scale on the third below 

 the tonic, whose seven tones bear the same relation to each 

 other as those of the key itself. These same twelve tones com- 

 prise also four complete minor scales, founded respectively on 

 the tonic, fourth, fifth and sixth, and having both the ascending 

 and descending forms. Perfect triads, either major or minor, 

 or both, are found upon all but one of the same twelve semi- 

 tones, all without any change of intonation or use of pedals. 

 But by using the pedals all these scales and chords may be 

 duplicated on any one of the twelve tempered semitones as a 

 tonic or key. Four dominant sept-chords, with resolutions on 

 tonic triads a fifth below, should also be included in this esti- 

 mate for each key. In addition to the twelve just keys as 

 above, tempered intonation is always instantly available in 

 response to pressure of a pedal. 



These results summed up give one hundred and fifty-six 

 tones to the octave, or eleven hundred and forty-four in the 

 compass of seven and one-third octaves, against eight-eight in 

 the ordinary piano. 



The changes of tonality are practically instantaneous and can 

 succeed each other in any order with great rapidity, if it were 

 necessary, but the resources of a single key are so great that 

 even in the most intricate music the pedal changes will be 

 quite few. Many harmonies and progressions that would 

 seem to involve foreign tones, do not require the use of the 

 pedal at all but are found perfect and true, within the limits of 

 the principal key in use at the time. 



The way appears perfectly clear for the application of the 

 same general principles to pipe and reed organs without increas- 

 ing the number of pipes or reeds. 



The result of familiarity with just intervals during the work 

 of construction and since the satisfactory completion of the 

 instruments now in use at my home in Cincinnati, fully con- 

 firms all that Helmholtz and others have said as to the inex- 

 pressible sweetness and beauty of pure harmonics. 



Their clearness renders all music more intelligible as well as 

 agreeable, the musical sense is rapidly rendered more acute, 

 and tone perception and tone production matters of much 



