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inversion

noun: a change that makes something the opposite of what it was before, or turns it upside down
noun: a term formerly used to mean taking on the gender role of the opposite sex
noun: (counterpoint) a variation of a melody or part in which ll ascending intervals are replaced by descending intervals and vice versa

The transposition of the lower and upper notes of an interval. In an inverted chord, the lowest tone is not its root; an inverted melody is one in which its intervals are inverted.

An interval is inverted by raising or lowering either of the notes using displacement of the octave (or octaves) so that both retain their names (pitch class). For example, the inversion of an interval consisting of a C with an E above it is an E with a C above it - to work this out, the C may be moved up, the E may be lowered, or both may be moved.

Under inversion, perfect intervals remain perfect, major intervals become minor and the reverse, augmented intervals become diminished and the reverse. (Double diminished intervals become double augmented intervals, and the reverse.) Traditional interval names add together to make nine: seconds become sevenths and the reverse, thirds become sixes and the reverse, and fourths become fifths and the reverse. Thus a perfect fourth becomes a perfect fifth, an augmented fourth becomes a diminished fifth, and a simple interval (that is, one that is narrower than an octave) and its inversion, when added together, equal an octave. See also complement (music). Wikipedia, Inversion


Ramsay
contrast. In the fifth, the ratio being 2:3, the excess of 3 above 2 is 1; this 1 bears a simple relation to both the notes which awaken it. The grave harmonic in this case gives the octave below the lower of the two sounds; 1 is an octave below 2. This is the simplest relation "a third sound" can have to the two which awaken it, and that is why the fifth has the smallest possible degree of contrast. The octave, the fifth, and the fourth may be reckoned as simple ratios; the major and minor thirds and their inversions as moderately complex; the second, which has the ratio of 9:10, and the major fourth F to B and its inversion, are very complex. [Scientific Basis and Build of Music, page 61]

SYSTEM OF THE THREE PRIMITIVE CHROMATIC CHORDS.


The middle portion with the zigzag and perpendicular lines are the chromatic chords, as it were arpeggio'd. They are shown 5-fold, and have their major form from the right side, and their minor form from the left. In the column on the right they are seen in resolution, in their primary and fullest manner, with the 12 minors. The reason why there are 13 scales, though called the 12, is that F# is one scale and G♭ another on the major side; and D# and E♭ separated the same way on the minor side. Twelve, however, is the natural number for the mathematical scales as well as the tempered ones. But as the mathematical scales roll on in cycles, F# is mathematically the first of a new cycle, and all the notes of the scale of F# are a comma and the apotome minor higher than G♭. And so also it is on the minor side, D# is a comma and the apotome higher than E♭. These two thirteenth keys are therefore simply a repetition of the two first; a fourteenth would be a repetition of the second; and so on all through till a second cycle of twelve would be completed; and the thirteenth to it would be just the first of a third cycle a comma and the apotome minor higher than the second, and so on ad infinitum. In the tempered scales F# and G♭ on the major side are made one; and D# and E♭ on the minor side the same; and the circle of the twelve is closed. This is the explanation of the thirteen in any of the plates being called twelve. The perpendicular lines join identical notes with diverse names. The zigzag lines thread the rising Fifths which constitute the chromatic chords under diverse names, and these chords are then seen in stave-notation, or the major and minor sides opposites. The system of the Secondary and Tertiary manner of resolution might be shown in the same way, thus exhibiting 72 resolutions into Tonic chords. But the Chromatic chord can also be used to resolve to the Subdominant and Dominant chords of each of these 24 keys, which will exhibit 48 more chromatic resolutions; and resolving into the 48 chords in the primary, secondary, and tertiary manners, will make 144 resolutions, which with 72 above make 216 resolutions. These have been worked out by our author in the Common Notation, in a variety of positions and inversions, and may be published, perhaps, in a second edition of this work, or in a practical work by themselves. [Scientific Basis and Build of Music, page 115]


This is an illustration of the chromatic chord resolving by two semitonic progressions and one note in common into four key-notes, which are shown in different positions and inversions; for example F A C F, A C F A, C F A C. Like a universal joint, the chromatic chord turns to each in a suitable form for resolution. [Scientific Basis and Build of Music, page 116]


Inverting notes of a chord
Intervals and Inversions explained
How to Play Major Chord Inversions on the Guitar
Negative Harmony Explained

Created by Dale Pond. Last Modification: Friday December 22, 2023 02:31:13 MST by Dale Pond.