US 3752031 A
Description (OCR text may contain errors)
0 United States Patent 11 1 1111 3,752,931 Mohos Aug. 14, 1973 TWELVE-TONE-ROW MODULATOR  Inventor: swan Mohos 300 w 109th St Primary Examiner-Richard B. Wilkinson New York NY 10025 Assistant Examiner-Lawrence R. Franklin Attorne ---Ed (I F.  Filed: Aug. 5, 1971 y war Levy 21 A I. No.: 169 79 I 1 PP 57 ABSTRACT 52 us. c1. 84/471, 84/473 A modmaw  Int. Cl. G09b 15/02 Sequences of meal notes mdudes a base plate  Field of 5 ch 84/470474" 477480 482 havm g letter names of musical notes arranged on its face in 12 vertical columns and at least 24 horizontal rows, and a square template divided into 12 vertical  References Cited columns andhl2d h OI'IZiIItaI drow of squares. The te n- UNITED STATES PATENTS SSW; 11222cl"oi iZeci i1iZ-ifilfiw i 1,467,032 9/1923 Florence 84/474 en d l d 1 1.588.470 6/1926 Schumann 84/473 0:21:21 :si tlfnir i: 356:; 3: l I t m 2,824,479 2/l958 De Rosa 84/473 X 0 a e p05 lo'ns 3.481.241 l2/l969 Gaillard 84/474 i grs g figi' or FOREIGN PATENTS OR APPLICATIONS I 262,888 11/1965 Australia 84/471 6 Claims 11 Drawing Flames l2 Tone- Row Modululor Chori-Ex C C C C C C C C C C C C B B B B B B B B B B B B 45 a a a a s a a a a 8" s e L d" 1/ ,2 A l l1 'l (EJ Q49 18 @1 9 a 32 Z I00 A A A A A A A A A A A A seeseseeeess- F F *F F FF*F F F FF*FE FFFFFFF-FFFFF EEEEEEEEEEEE E E E z e E E a s 5* s e 000000000000 0 c#c# Men 01* ca c9041 c C C cccccccccccc TWELVE-TONE-ROW MODULATOR The present invention relates to a novel device for use in the composition of music, particularly compositions formed entirely from a selected twelve-tone-row of frequencies and its various manipulations.
In the composing of music, the composer mentally establishes a selected succession and superimposition of different audible frequencies, and then transcribes these on paper in the form of notes. Generally, composers have conscious or instinctive rules for the construction of their musical compositions.
In modern music, only 12 specific frequencies and their exact multiples are used, these frequencies being called pitches or notes. The twelve notes are designated A, A sharp (or the equivalent B flat), B, C, C sharp (or the equivalent D flat), D, D sharp (or the equivalent E flat), E, F, F sharp (or the equivalent G flat), G, and G sharp (or A flat). The frequency ofG sharp is less than the first multiple of thefrequency of A.
One of the modern schools of composing has established as its basic rule the utilization of an arbitrary succession of the aforementioned 12 notes, each note appearing only once. The composer selectively chooses the succession of the 12 notes, and thereafter this order of notes is fixed and constitutes a unit called a twelvetone-rowf' The full composition is then formed of a varied succession of the twelve-tone rows, the rows being varied by established manipulations thereof.
The accepted manipulations of a twleve-tone row are transposing, inverting (to produce a product called an inversion"), and reversing (to produce a product called a retrograde). These manipulations can also be combined as follows: reversing and inverting (to produce a retrograde inversion"), transposing the inversion, transposing the retrograde, and transposing the retrograde inversion.
Up to the present time, these twelve-tone-row manipulations have been executed in a primitive manner, the composer mentally calculating the note changes for the manipulation, and transcribing them on a sheet of music. This processrequires the major portion of the composers time to be occupied with non-creative mechanical work rather than the creative work of composing itself. In forming the composition, the composer must mentally calculate and then transcribe a certain manipulation, for example a transposition. If it is then discovered that such manipulation is not in the proper order, the composer must erase and repeat the procedure until the proper manipulation is attained. Such efforts constitute a succession of distractions to the composer and tend to interfere withthe quality of the composition.
It is an object of the present invention to provide a twleve-tone-row modulator which enables a composer to perform all of the manipulations and combinations thereof manually and with extreme rapidity.
Another object of the invention is the provision of a twelve-tone-row modulator of the character described which permits the composer to obtain an instant visual reading of any desired manipulation of a selected twelve-tone-row, thereby freeing the composer from non-creative work and enabling him to devote his entire attention to the creative work of composing.
In accordance with the invention there is provided a twelve-tone-row modulator comprising a base plate and a template adapted to be placed in overlying poistion on said base plate Twelve vertical columns of musical notes in the chromatic order of musical scales are arranged on the face of the base plate, with identical notes of the vertical columns arranged in horizontal rows. The template is divided into squares arranged in 12 vertical columns and I2 horizontal rows corresponding to the columns and rows of notes on the base plate. 12 holes are punched in selected squares of the template to provide windows representing a selected twelvetone-row sequence of notes, and the punched template is then placed on the base plate in such various positions that the notes on the base plate are revealed through the windows in selected sequences representing the twelve-tone-row and inversions, trans positions, retrogrades, and retrograde inversions of the row.
Additional objects and advantages of the invention .will become apparent during the course of the following specification when taken in connection with the accompanying drawings, in which:
FIG. 1 is a plan view of the template and base plate constituting the modulator of the present invention;
FIG. 2 is a plan view of the template showing a series of holes punched therein to provide windows-arranged in the sequence of a selected twelve-tone-row;
FIG. 3 is a plan view of the base plate with the punched template of FIG. 2 applied thereto to reveal the selected twleve-tone-row;
FIG. 4 is a schematic view showing the manner in which the template of FIG. 2 is inverted to produce a retrograde inversion;
FIG. 4A is a plan view showing the base plate with the inverted template applied thereto to reveal a retrograde inversion of the selected twelve-tone-row;
FIG. 5 is a schematic view showing the manner in which the template of FIG. 2 is rotated to produce an inversion;
FIG. 5A is a plan view showing the base plate with the rotated template applied thereto in position to reveal an inversion of the selected twelve-tone-row;
FIG. 6 is a schematic view showing the manner in which the template in its position of FIG. 5A is inverted to produce a retrograde;
FIG. 6A is a plan view showing the base plate with the template in the inverted position of FIG. 6, applied thereto in position to reveal a retrograde of the selected twelve-tone-row;
FIG. 7 is a schematic view, on a smaller scale, showing the manner in which the template is moved upon the base plate to produce transpositions of the selected twelve-tone-row or any of its manipulated forms; and
FIG. 8 is a plan view of a modified form of template made in accordance with the present invention.
Referring in detail to the drawings, it will be seen that the twelvetone-row modulator of the invention comprises a square template 1t) and an elongated, rectangular base plate 12. Also provided with the modulator and constituting part of the assembly is a single-hole paper punch (not shown) of conventional type, which is employed to punch holes in selected areas of the template 10, in a manner to be presently described.
The template 10 is made of a flexible, durable material such as plastic, cardboard, or plastic-coated paper or cardboard. The front surface of the template I0 is provided with a series of eleven vertical lines 14 and a series of the same number of horizontal lines 16, the lines in each series being equally spaced to define even square boxes 18 on the surface of the template. As shown in FIG. 1, the square boxes 18 are arranged in '12 horizontal rows and 12 vertical columns. The rear surface of plate may be similarly divided into squares.
The rectangular base plate 12 is made of a rigid material which is preferably more durable than the template 10, such material being rigid plastic, metal, reinforced cardboard or the like. The plate 12 has a width the same as or slightly larger than the width of template 10, and a length somewhat longer than twice the length of one edge of the template 10.
For convenience, the front surface of the rectangular plate 12 may be marked with horizontal and vertical lines which divide the front surface into squares of the same size as the squares 18 of template 10. As shown in FIG. 1, twelve vertical columns of squares 20 are provided, and at least 24 horizontal rows of squares. In the illustrated embodiment, there is shown horizontal rows of squares 20.
I In each of the squares 20 is printed indicia 21 constituting the letter name of musical pitches or notes, each horizontal row of indicia 21 constituting a line in which the same note is repeated 12 times. As shown in FIG. 1, in each vertical column, the notes are arranged in ascending chromatic order, and extend upwardly at least two octaves. The lowermost row of squares 20 contains the note C and each succeeding row above contains the next note in the scale for 12 successive horizontal rows constituting one octave, after which the octave is repeated, and an additional row of the note C is included in the uppermost horizontal row of notes. It will thus be seen that in the intermediate portion of the rectangular plate 10 is the full ascending scale constituting the notes A, B flat, B, C, C sharp, D, E flat, E,
F, F sharp, G and A flat. This complete scale is bordered at top and bottom by sufficient portions of the scale to permit manipulation of the square template 10, in a manner to be presently described.
In practive, the twelve-tone-row modulator of the in vention is supplied to a composer or musical student or teacher in the form of a kit including a single preprinted rectangular plate 12 and a number of individual templates 10, each divided into squares as previously described. Each of the templates 10 provided inthe kit may be made of a different color for 'the purpose of readily identifying the particular twelve-tone-row which is to be punched on each template. Also supplied with the kitis the aforementioned paper punch which is of such size as to punch a hole conforming generally in size to the area of a square 18 of the template 10.
In utilzing the modulator, the composer first establishes the particular twelve-tone-row which will form the basis for his composition, and punches the row sequence on the template 10 in horizontal order from left to right. For example, it will be assumed that the twelve-tone-row devised by the composer consists of the notes B flat, D, C sharp, C, B, E flat, A, E, F, F sharp, G and A flat. The user may now place the template 10 alongside or upon the rectangular plate 12 with the lowermost horizontal row of squares 18 registering with the row of squares 20 of plate 12 containing the first note of the row, namely the note B flat. He then punches a hole 22 in the lowermost square 18 of the first, or left-hand vertical column of template 10 which hole corresponds to the note B flat. He then moves to the next vertical column, and punches a hole 24 in the square 20 four above the lowest horizontal row, which square registers with the row of notes D on the rectangular plate 12. In the same manner the successive vertical columns from left to right are punched with holes 26, 28,30, 32, 34, 36, 38, 40, 42 and 44, respectively registering with and indicating the notes C sharp, C, B, E flat, A, E, F, F sharp, G and A flat.
The punched template 10, shown in FIG. 2, is now completed for its selected twelve-tone-row. If it is now applied in superimposed position upon the rectangular plate 12, in the manner shown in FIG. 3, with the first hole 22 registering with the printed note B flat in the first or left-hand column on plate 12, each succeeding printed note of the row will be visible through the respective hole 24-44 in the template 10. The punched holes constitute a succession of windows through which the composer can now easily read the notes in the original sequence of the twelve-tone-row and transcribe it on paper.
In the original position of template 20 in which it was punched, and as shown in FIGS. 2 and 3, the upper lefthand corner of template 10 is marked with indicia 46 indicating that this is its original position. The indicia 46 may, for example, consist of the letters ORI to signify "original.
The composer may also achieve the twelve-tone-row manipulations merely by inverting or turning the template 10, or by moving it upwardly or downwardly upon the plate 12.
To obtain a retrograde inversion of the original twelve-tone-row, the composer inverts the template 10 from its original position, as indicated in FIG. 4, the template 10 being turned. 186 in the plane of its front surface. The original left-hand column of squares now becomes the right-hand column, and the first punched hole 22 now becomes the last hole in the sequence. In-
. template 10 will reveal a retrograde inversion.
The inverted template If) is now applied to the plate 12 in the manner shown in FIG. 4a, with the hole 44 (now in the left-hand vertical column of template 10) in registry' with the first note of the original twelvetone-row, namely the note B flat. The rest of the holes 22-42 are in reverse order, and in this position thetemplate 10 reveals to the composer the retrograde inversion, which, as shown constitutes the succession of. notes B flat, B, C, C sharp, D, A, E flat, G, F sharp, F,
E and A flat. The composer can now visually and instantly determine whether or not this retrograde inversion is in the proper sequence in the composition, and if so may transcribe it. If not, he may try different manipulations until the proper one is achieved.
' To obtain an inversion of the original twleve-tonetion will reveal an inversion of the original twelve-tonerow. The hole 22 in this position isstill in the first or left-hand vertical column, but is now in the top row of the column,while' the remaining holes 24-44 are also in their same vertical column, but their positions in the columns are reversed. When the reversed template H is applied to plate 12 in the manner shown in FIG. A, the holes in said template reveal the inverted twelvetone-row by notes in the following sequence: B flat, F sharp, G, A flat, A, F, B, E, E flat, D, C sharp and C.
To reverse the original twelve-tone-row to produce a retrograde, the template in the reversed position of FIGS. 5 and 5A is inverted 180 in the plane of its rear surface in the manner shown in FIG. 6 to bring the indicia 52 to the top of the template, said indicia 52 constituting the letter R to indicate that the template in this position will reveal a retrograde of the original twelve-tone-row. The hole 22 is now at the bottom row of the last or right-hand column, and the hole-44 is in the left-hand column. The template 10 in this position is applied to plate 12 with the hole 44 registering with the first note, B flat, of the original twelve-tone-row as shown in FIG. 6A. The alignment of holes in template 10 now reveals the retrograde consisting of the succession of notes B flat, A., A flat, G, F sharp, B, F, C sharp, D, E flat, E and C.
To obtain transpositions of the original twelve-tonerow, the template 10 in its original position of FIG. 3 is moved vertically upward or downward along the plate 12 in the manner indicated in FIG. 7, until the hole 22 registers with a note other than B flat, the starting note of the original twelve-tone-row. Thus, if the template 10, for example, is moved upwardly along plate 12 by two horizontal rows from its position of FIG. 3, the first hole 22 will register with the note C, and the remaining holes will reveal notes two pitches higher than those of the original twelve-tone-row. In this manner 1 1 different transpositions of the original twelve-tone-row can be attained, the pitches of the original row changing, but the relationship of the successive notes to each other being retained.
In a similar manner, transpositions of the retrograde inversion obtained by the template 10 in the position of FIG. 4A can be achieved, as can transpositions of the inversion of FIG. 5A and the retrograde of FIG. 6A.
It will be appreciated that new variations of the twelve-tone-row may be achieved by use of the modulator through manipulations heretofore unachievable. To produce these variations, the template 10, in any of its positions shown in FIGS. 3, 4A, 5A or 6A, may be turned 90 so that the horizontal rows become the vertical columns. This produces different sequences of the twelve pitches in the scale, and transpositions of any of these sequences can be attained in the manner described above.
FIG. 8 shows a template 60 of somewhat modified form which is provided with a border 62 adjacent the left-hand edge thereof. The border is divided by a continuation of the horizontal lines 16 into a column of blank squares in which a series of notes 64 may be printed to designate a selected scale sequence. In the template 60, illustrated in FIG. 8, the scale sequence is shown by way of example as beginning with the note B flat and ending with the note A. Thus, the user can easily determine the proper row and column in which to punch the successive holes representing the twelvetone-row of his selection. If the twelve-tone-row is the same as that previously described herein, the holes in templte 60 would be punched in the identical positions as the holes 2244 of the template 10 shown in FIG. 2.
In using the modulator in the manner described above the composer by merely turning and rotating the punched template l0 and placing it upon the plate 12 will receive an instant visual depiction of the row manipulation so that he can concentrate on the creative work of selecting the desired sequence of row manipulations to form the complete composition. Such noncreative work as calculating the arrangement of notes in a row manipulation is eliminated. It has been found that the time and brain energy consumed in creating an original composition is reduced an average of 50 percent by use of the modulator.
While a preferred embodiment of the invention has been shown and described herein, it will be obvious that numerous omissions, changes and additions may be made in such embodiment without departing from the spirit and scope of the invention.
What is claimed is:
l. A modulator for visual manipulation of twelvetone-rows of musical pitches, comprising an elongated base plate and a template in superimposed position on said base plate, said base plate having a face with letter names of musical notes arranged in 12 vertical columns thereon, the notes in each column being arranged in chromatic order of scales, with identical notes of said columns arranged in horizontal rows, said template having divisions formed thereon arranged in 12 vertical columns and I2 horizontal rows corresponding in size and spacing to the vertical columns and horizontal rows of said base plate, and windows selectively formed in said template at intersections of said columns and rows such that each row and each column has only one window formed therein, said template being adapted to be turned in the plane of its front surface relative to said base plate to change the position of its edges, and to be reversed relative to said base plate to locate within said windows inversions, retrogrades and retrograde inversions of said selected twelve-tone-row sequence of notes.
2. A modulator according to claim 1 in which the 12 vertical columns of notes on said base plate are spaced apart by equal distances, and the horizontal rows of notes on said base plate are spaced apart by the same distances.
3. A modulator according to claim 2 in which said template is of square shape having four equal edges and is divided into contiguous squares arranged in 12 verti- .ca| columns and I2 horizontal rows.
4. A modulator according to claim 3 in which said base plate is of elongated rectangular shape, the width of said base plate being substantially equal to the length of one of the edges of said template, and the length of said base plate being at least twice the length of one of the edges of said template.
5. A modulator according to claim 4 in which the base plate has at least 24 horizontal rows of notes arranged in said vertical columns in continuous chromatic succession.
6. A modulator according to claim I in which said template has a square area divided into contiguous squares arranged in 12 vertical columns and I2 horizontal rows, and in which the series of vertical columns is bordered by an additional column of 12 squares, and squares of said additional column of 12 squares, the squares of said additional column containing a sequence of respective notes arranged in chromatic or-