This plate is a representation of the area of a scale; the major scale, when viewed with the large hemisphere, lowest; the minor when viewed the reverse way. It is here pictorially shown that major and minor does not mean larger and smaller, for both modes occupy the same area, and have in their structure the same intervals, though standing in a different order. It is this difference in structural arrangement of the intervals which characterizes the one as masculine and the other as feminine, which are much preferable to the major and minor as distinctive names for the two modes. Each scale, in both its modes, has three Fifths - subdominant, tonic, and dominant. The middle fifth is the tonic, and its lowest note the key-note of the scale, or of any composition written in this scale. The 53 commas of the Octave are variously allotted in its seven notes - 3 of them have 9 commas, 2 have 8, and 2 have 5. The area of the scale, however, has much more than the octave; it is two octaves, all save the minor third D-F, and has 93 commas. This is the area alike of masculine and feminine modes. The two modes are here shown as directly related, as we might figuratively say, in their marriage relation. The law of Duality, which always emerges when the two modes are seen in their relationship, is here illustrated, and the dual notes are indicated by oblique lines across the pairs. [Scientific Basis and Build of Music, page 106]

The larger hemisphere of the Fifths is uppermost when taking the minor view of the plate, and suggests the idea of the minor being weighed downward, as it really is mathematically in the genesis of the scale, which is seen in the D of the minor being a comma lower than the D of the major. Taking the major view of the plate, the smaller hemisphere is uppermost, and suggest the idea of rising upward, as it really does in the [Scientific Basis and Build of Music, page 106]

mathematical genesis, as seen in its D being a comma higher than that of the minor. This gravity and buoyancy of the modes is a striking feature of them. In the Thirds it is different from the Fifths; the larger hemisphere of each third seems gravitating toward the center of the tonic chord. The area of the scale has then the aspect of a planet with its north and south poles, and pervaded by a tendency towards the center; the center itself being neutral as to motion. [Scientific Basis and Build of Music, page 107]

The Octave being divided into 53 commas, the intervals are measured, as usual, by these, the large second having 9-commas, the medium second having 8, and the small second 5. These measures are then made each the radius by which to draw hemispheres showing the various and comparative areas of the seconds. The comparative areas of the thirds are shown by the hemispheres of the seconds which compose them facing each other in pairs. The comma-measures of the various thirds thus determined are then made the radii by which to draw the two hemispheres of the fifths. The areas of the three fifths are identical, as also the attitudes of their unequal hemispheres. The attitude of the six thirds, on the other hand, in their two kinds, being reversed in the upper and under halves of the scale, their attitude gives them the appearance of being attracted towards the center of the tonic; while the attitude of the three fifths is all upward in the major, and all downward in the minor; their attraction being towards the common center of the twelve scales which Nature has placed between the second of the major and the fourth of the minor, as seen in the two D's of the dual genetic scale, - the two modes being thus seen, as it were, revolving [Scientific Basis and Build of Music, page 113]

See Also

Created by Dale Pond. Last Modification: Wednesday December 30, 2020 04:53:42 MST by Dale Pond.