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subdominant chord

Ramsay
In the laws of quantities and motions the three primary ratios, 1:2, 1:3, 1:5, with the three different units, F1, C3, and G9, the roots of the chords of the subdominant, tonic, and dominant, produce the three chords of the musical system major, the one not interfering with the other; and by an inverse process are produced, from B720, E240, and A80, its generating notes, the three chords of the musical system minor; the one chord not interfering with the other. In a similar way the chromatic chords can be produced from three different units, without the one interfering with the other; and, like the subdominant, tonic, and dominant chords of the diatonic scale, they are fifths apart. So we may call them the subdominant, tonic, and dominant chromatic chords. Each of the three chromatic chords has also kinship with the major and minor modes, from the way in which the diatonic minor triad is constituted a chromatic chord by its supplement coming in the one side from the minor, and on the other side from the major system. [Scientific Basis and Build of Music, page 53]

It is the function of the chromatic chord, in the course of its systematic development, to bring two notes, the one above and the other below, in semitonic progression to each of the three notes of the tonic chord; and likewise, without interfering with the imperial character of the tonic chord, it brings two notes in semitonic progression to each note of the other two chords; so that, although at first the subdominant and dominant chords are only like satellites to the tonic chord, they, with their chromatic chords, are now raised to the dignity of planets as it were, having the chromatic chords as their satellites. [Scientific Basis and Build of Music, page 57]

A second cause of difference in degree of contrast between two notes and other two notes in which the ratios are the same lies in this - whether the two notes belong to one chord or to different chords. Two notes in the subdominant chord have a different contrast from two in the dominant chord which have the same ratio. [Scientific Basis and Build of Music, page 61]

common, to mingle with more chord-society. So those added thirds which constitute compound chords are like accomplishments acquired for this end, and they make such chords exceedingly interesting. The dominant assumes the root of the subdominant, and so becomes the dominant seventh that it may be affiliated with the subdominant chords. Inversely, the subdominant assumes the top of the dominant chord that it may be affiliated with the dominant. The major tonic may exceptionally be compounded with the top of the minor subdominant when it comes between that chord and its own dominant; and the minor tonic may in the same way assume the root of the major dominant when it comes between that chord and its subdominant. The minor subdominant D F A, and the major dominant G B D, are too great strangers to affiliate without some chord to introduce them; they seem to have one note in common, indeed, but we know that even these two D's are a comma apart, although one piano-key plays them both, and the F G and the A B are as foreign to each other as two seconds can be, each pair being 9 commas apart, and G A are 8 commas apart. In this case, as a matter of musical courtesy, the tonic chord comes in between; and when it is the minor subdominant that is to be introduced, the major tonic assumes the top of that chord, and then turns to its own major dominant and suavely gives the two to enter into fellowship; for the tonic received the minor subdominant through its semitonic E F, and carries it to the major dominant through its semitonic B C, along with C in common on the one side and G in common on the other. When it is the major dominant that is to be introduced to the minor subdominant the minor tonic fulfills the function, only the details are all reversed; it assumes the root of dominant, and by this note in common, and its A in common with its own subdominant, along with the semitonic second B C on the one hand and the semitonic E F on the other, all is made smooth and continuous. The whole of this mediatorial intervention on the part of the tonic is under the wondrous law of assimilation, which is the law of laws all through creation; but when the tonic chord has fulfilled this graceful action, it immediately drops the assumed note, and closes the cadence in its own simple form.1 [Scientific Basis and Build of Music, page 71]

The varied effect of position in chords. When a chord stands as C E G C, having its root also at the top, it has its softest, dullest, most united effect; it is undramatic, with little contrast. When it stands as E G C E, having its third at the top and bottom, it has a more ticklish, interesting, far-away effect. In reveries composers often finish thus, as if it had vanished - an unsettled effect. When it stands as G C E G, with its top at top and bottom, it has its most dominant character - loud, swelling. In the position C E G C it stands mixingly with the subdominant C E f G a C, and in this its first position its unseen filling in is chiefly from the region of gravity; hence its soft, grave, dull, heavy effect; and it passes very easily to the subdominant chord. When it stands as G C E G it stands mixingly with the dominant G b C d E G, and has its third position and most brilliant effect and uprising, for its unseen filling in is then chiefly from the region of levity; and it passes easily to the dominant chord. When in its second position, its middle position E G C E, its unseen filling in is mixingly both subdominant and dominant, E f G a b C d E; it has then its most interesting and puzzling effect; on the one hand its softest, dullest, and one-est, on the other hand its most brilliant effect, as if it would at once both sink and soar. [Scientific Basis and Build of Music, page 72]

circumstances. And if we may add D to the subdominant chord of d F A C, so we may also, in other circumstances, add the subdominant chord as harmony to D, thus - D f a c, and no discord occur. There is only the interval of a second between F and G in this dominant 9th, and only an interval of a second between C and D in this subdominant 6th; a second standing alone is a discordant interval, as a poison by itself may kill; but as a poison by the processes of nature in chemistry compounded with something else may be an excellent medicine, so may a second when mixed and compounded with something else in music become an excellent harmony. Music is a great apothecary, skillful in compounds. [Scientific Basis and Build of Music, page 81]

"The notes as they naturally arise from unity have different degrees of development, and according to the degree of development of each note is its specific levity or gravity. The three notes which form the subdominant chord have different degrees of gravity; the three which form the dominant chord have different degrees of levity. The remaining note is the center of the tonic chord -

Subdominant - F, A, C E G, B, D - dominant

[Scientific Basis and Build of Music, page 95]

"All the bodies in the Solar System, in a general way, are attracted to the sun according to the Law of Masses; but all the satellites are attracted to their planets according to the Law of Distance. The subdominant and dominant chords in the Musical System, in a general way, are attracted to the tonic center; but each note in the octave scale is attracted to its nearest note by the Law of Proximity. [Scientific Basis and Build of Music, page 96]

ANOTHER LETTER TO A PUPIL.


The System of Musical Sounds might be sketched as follows : - Three different notes having the simplest relations to each other, when combined, form a chord; and three of these chords, the one built up above the other, form the system.

Three times three are nine; this would give nine notes; but as the top of the first chord serves for the root of the second one, and the top of the second for the root of the third, in this way these three chords of three notes each are formed from seven different notes.

The middle one of these three chords is called the tonic; the chord above is called the dominant; and the chord below is called the subdominant. The order in which these three chords contribute to form the octave scale is as follows : - The first note of the scale is the root, of the tonic; the second is the top of the dominant; the third is the middle of the tonic; the fourth is the root of the subdominant; the fifth is the top of the tonic; the sixth is the middle of the subdominant; the seventh is the middle of the dominant; and the eighth, like the first, is the root of the tonic.

In the first six chords of the scale the tonic is the first of each two. The tonic chord alternating with the other two produces an order of twos, as - tonic dominant, tonic subdominant, tonic subdominant. The first three notes of the octave scale are derived from the root, the top, and the middle of the tonic dominant and tonic; the second three are derived from the root, top, and middle of the subdominant, tonic, and subdominant. The roots, tops, and middles of the chords occurring as they do produce an order of threes, as - root, top, middle; root, top, middle. The first, third, fifth, and eighth of the scale are from the tonic chord; the second and seventh from the dominant; and the fourth and sixth from the subdominant. In the first two chords of the scale the tonic precedes the dominant; in the second two, the subdominant; and in the third two the tonic again precedes the subdominant; and as the top of the subdominant chord is the root of the tonic, and the top of the tonic the root of the dominant, this links three chords together by their roots and tops. The second chord has the top of the first, the third has the root of the second, the fourth has the root of the third, the fifth has the top of the fourth, and the sixth has the root of the fifth; and in this way these successive chords are woven together. The only place of the octave scale where there are two middles of chords beside each other is at the sixth and seventh. The seventh note of the octave scale is the middle of the dominant, and the sixth is the middle of the subdominant. These two chords, though both united to the tonic, which stands between them, are not united to each other by having a note in common, inasmuch as they stand at the extremities of the system; and since they must be enabled to succeed each other in musical progression, Nature has a beautiful way of giving them a note in common by which to do so - adding the root of the subdominant to the top of the dominant, or the top of the dominant to the root of the subdominant, and this gives natural origin to compound chords. The tonic chord, being the centre one of the three chords, is connected with the other two, and may follow the dominant and dominant; and either of these chords may also follow the tonic; but when the dominant follows the subdominant, as they have no note in common, the root of the subdominant is added to the dominant chord, and this forms the dominant seventh; and when the subdominant follows the dominant, the top of the dominant is added to the subdominant, and this forms the subdominant sixth. The sixth and seventh of the octave scale is the only place these two compound chords are positively required; but from their modifying and resolvable character they are very generally used. When the dominant is compounded by having the root of the subdominant, its specific effect is considerably lower; and when the subdominant is compounded by having the top of the dominant, its specific effect is considerably higher. In the octave scale the notes of the subdominant and dominant chords are placed round the notes of the tonic chord in such a way was to give the greatest amount of contrast between their notes and the tonic notes. In the tonic chord the note which has the greatest amount of specific gravity is its root; and in the octave scale it has below it the middle and above it the top of the dominant, the two notes which have the greatest amount of specific levity; and in the octave scale it has above it the middle and below it the root of the subdominant - the two notes which the greatest amount of specific gravity. The third note of the scale, the middle of the tonic chord, is the center of the system, and is the note which has the least tendency either upwards or downwards, and it has above it the root of the subdominant, the note which has the greatest amount of specific gravity, and it has below it the top of the dominant, the note which has the greatest amount of specific levity. Thus the root of the subdominant is placed above, and the top of the dominant below, the center of the system; the specific gravity of the one above and the specific levity of the one below cause them to move in the direction of the center. [Scientific Basis and Build of Music, page 98]


Here on the keyboard we see, nearest to the front, the great 3-times-3 chord of the full genesis of the scale from F1 to F64. When this chord is struck by the notched lath represented in front of the keyboard, the whole harmony of the key is heard at once. Behind this great chord are placed, to the left the subdominant, tonic, and dominant chords of the minor. D F A, A E C, E G B; and to the right the subdominant, tonic, and dominant chords of the major, F A C, C E G, G B D. When the notched lath is shifted from F to D, the minor third below F, and the 3-times-3 minor is struck down in the same way as the major, the whole harmony is heard; and the complete contrast of effect between major and minor harmony can be fully pronounced to the ear by this means. Behind these six diatonic chords, major and minor, on the part of the keyboard nearest to the black keys, are the three chromatic chords in their four-foldness, in both major and minor form. The center one shows the diatonic germ of the chromatic chord, with its supplement of G# on the one hand completing its minor form, and its supplement of A♭ on the other hand completing its major form. A great deal of teaching may be illustrated by this plate.

ERRATUM. - B♭, first chromatic chord, misplaced.
[Scientific Basis and Build of Music, page 104]

DIATONIC RESOLUTIONS, SIMPLE AND COMPOUND.


In the major system, when the tonic chord follows the subdominant one, there is one semitonic progression to the middle of the tonic, and one note in common with the root, so these two chords are linked together in different ways. When the tonic chord follows the dominant one, there is one semitonic progression to the root of the tonic, and one note in common with its top, so these two chords also are linked together in two different ways. When the tonic chord follows the compound dominant, i.e., the dominant seventh, there are two semitonic progressions, one to the middle and one to the root, and one note in common with its top, so these two are linked together in the same two ways; but the semitonic progression being double gives this resolution great urgency. And now we come to the two chords, the subdominant and dominant, which have no note in common, and must, when they succeed each other, be helped to come together. Nature teaches us how this is to be done by a process of borrowing and lending which will establish between them a similar relationship to that which keeps the continuity of the other chords in succession. We have seen that the top of the subdominant and the root of the tonic are a note in common to these chords, and so the top of the tonic and the root of the dominant also are a note possessed in common by these two chords. In like manner in this disjunct part, when the dominant follows the subdominant, the root of the subdominant is lent to the top of the dominant, and thus they come to have a note in common. The top of the [Scientific Basis and Build of Music, page 111]

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]

See Also


07 - Chart Showing the Conditions Governing Harmonious Chords
09 - Chart Defining the different Chord Associations
12 - Chart of Differentiation of Setting Chords on Vibratory Bar
antagonistic chord
Chord
chord aggregation
chord center
chord mass
chord media
Chord of B
chord of equation
chord of harmony
Chord of Life Windchime
Chord of Mass
chord of resonation
chord of sympathy
chord of the mass
chord resolution to center
chord-setting
coincident chord
coincident chord of sympathy
coincident sympathetic chord
compound chord
Concordant Chord Settings
Concordant Chords of Sympathy
dominant chord
etheric chord
Factor-chord
Figure 1.1 - Chord Signatures of Brain Convolutions
Figure 18.03 - Keely Chart Showing Acoustic Resonance of the Brain Chord
Figure 8.7 - Varying Degrees of Chordal Harmony and Discord
Full Harmonic Chord
harmonic attractive chord
life chord
Lost Chord
Mass Chord
MASS CHORDS
mass-chord
monochord
MUSICAL CHORDS
nine string chord
Subdominant
sympathetic chord
Sympathetic Chord Molecular
Sympathetic Chord Positive
terrestrial chord-masses
tetrachord
The Chord-Settings of Life
THEORY OF THE INDUCTION OF SYMPATHETIC CHORDS TO EXCITE ROTATION BY VIBROPHONIC TRAJECTION TO AND FROM CENTERS OF NEUTRALITY ON REVOLVING GLOBE
three chords
three chords of three notes
tonic chord
tonic subdominant
transmissive chord
13.38 - Theory of the Induction of Sympathetic Chords to Excite Rotation by Vibraphonic Trajection to and from Centers of Neutrality on Revolving Globe
14.13 - Full Harmonic Chord
19.02 - Theory of the Induction of Sympathetic Chords to Excite Rotation
8.21 - Signature same as Chord

Created by Dale Pond. Last Modification: Friday January 1, 2021 05:12:27 MST by Dale Pond.