When Plate XIII. is divided up the middle of the column, as in Plate XIV., so as that one side may be slipped up a fifth, representing a new key one-fifth higher, its subdominant made to face the old tonic, the two new notes are then pictorially shown, the second being altered one comma and the seventh four commas. The key at this new and higher pitch is by Nature's unfailing care kept precisely in the same form as the first; and wherever the major scale is pitched, higher or lower, the form remains unaltered, all the intervals arranging themselves in the same order. The ear, and the voice obedient to it, carry Nature's measuring-rule in them, and the writing must use such marks as may truly represent this; hence the use of sharps, flats, and naturals; these, however, be it observed, are only marks in the writing; all is natural at any pitch in the scale itself. All this is equally true of the minor mode at various pitches. These two plates are only another and more pictorial way of showing what the stave and the signature are usually made to express. [Scientific Basis and Build of Music, page 114]
See Also
5.2 - Vortex Motions in Resonators
air column resonance
Cavity Resonator
double column
Figure 6.17 - Areas and Volumes - Relations and Proportions
Helmholtz Resonator
organ pipe
Ramsay - PLATE XIII - The Vertebral Column of the Musical Scale
Resonance
Resonator
Table 12.02 - Length Area and Volume Math
Volumetric Resonator