United States Patent 3601518

A single reference frequency source is coupled to a series of controlled period multipliers (frequency dividers) for selecting a musical keynote and for producing selected output tones that vary according to extensions of the natural or diatonic scale. The output tone selectors are arranged in a two-dimensional array correlating tonal intervals with spatial relationships.

Application Number:
Publication Date:
Filing Date:
Primary Class:
Other Classes:
84/706, 84/DIG.11, 984/381
International Classes:
G10H5/06; (IPC1-7): G10H5/06
Field of Search:
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US Patent References:
3445578CHIFF AND TONE GENERATOR1969-05-20Cunningham
3443017ELECTRONIC ORGAN SYSTEM1969-05-06Jones
3293561Frequency synthesizer1966-12-20Hegarty et al.
3258677N/A1966-06-28Carruth et al.
2879387Multi-channel phase locked tone converter1959-03-24Kahn

Primary Examiner:
Hirshfield, Milton O.
Assistant Examiner:
Reynolds B. A.
I claim

1. Signal-period multiplying apparatus for a musical instrument comprising:

2. Signal-period multiplying apparatus as in claim 1 wherein:

3. Signal-period multiplying apparatus as in claim 1 for producing a plurality of periodic resultant signals of different periods according to a musical scale comprising:

4. Signal-period multiplying apparatus as in claim 1 which produces discrete signal frequencies according to a musical scale, the apparatus comprising:

5. Apparatus in a musical instrument for producing discrete tones in accordance with a musical scale comprising:

6. Apparatus in a musical instrument for producing discrete tones in accordance with a musical scale comprising:

7. Apparatus as in claim 6 for producing discrete tones in accordance with a musical scale wherein:

8. Apparatus in accordance with claim 6 providing a selectable keynote comprising:

9. Apparatus for a musical instrument comprising:

10. a musical instrument comprising:

11. Apparatus as in claim 10 comprising:

12. Apparatus as in claim 10 comprising:

13. The method of playing music according to a musical scale comprising the steps, performed in selected order, of:


A series of controlled period multiplier circuits (frequency dividers) is coupled to a reference frequency source and each of the multiplier circuits multiplies an applied signal period by one of several selectable integers as selected by control signals applied thereto. This technique is used in an electronic musical instrument to generate selectable musical tones in accordance with both the diatonic musical scale and a music scale described previously by John Redfield (see: J. Redfield, "Music, A Science and an Art"; A. Knopf, Inc., N.Y., 1949). One embodiment of this invention provides a twelve interval per octave extension of both of these scales and also includes means for generating these scales transposed to any selectable keynote. Additional selectable binary period multipliers extend the tonal range over as many octaves as may be desired and a two-dimensional keyboard array facilitates manual playing of the instrument.


FIG. 1 is a simplified diagram of one embodiment of the musical instrument of the present invention;

FIGS. 2a and b are block diagrams of the controlled period multiplier used in the musical instrument of the present invention;

FIG. 3 is a block diagram of the preferred embodiment of the present invention; and

FIG. 4 is a pictorial diagram of the keyboard arrangement in the embodiment of FIG. 3.


The relative frequencies of the tones of the diatonic scale are well known, and the minimum integers representing these frequencies over a little more than an octave range are shown in the following Table 1, column 1. The corresponding periods (i.e., the reciprocals of frequency) are proportional to the minimum integers which are shown in column 3 and which are obtained by dividing 4,320 by the corresponding integer shown in column 1. The integers of column 3 are factored into products of prime factors as shown in column 4. These factors can be regrouped in many different ways, and it has been discovered that the two groupings shown in columns 5 and 6 are particularly attractive because they provide the alternate factor products shown below columns 5 and 6. These simple alternate factor products lead to simple circuits for the generation and control of electrical signals corresponding to the musical tones and they also produce useful new musical scales. ##SPC1##

Referring now to FIG. 1, there is shown the block diagram of one embodiment of the instrument according to the present invention for operation over an octave range of output frequencies or tones using controlled period multipliers 11-15 to provide the alternate factors derived in column 5 of Table 1. Thus, by selectively controlling these controlled period multipliers from control signal source 17 the frequency of the reference signal source 9, as later described herein, is divided down, and seven tonal intervals per octave may be generated at the output 19. The controlled period multipliers as referred to herein and as shown in FIG. 1 are combinations of digital logic elements as shown, for example, in FIG. 2a which receive a periodic input signal and produce a periodic output signal which has an output period that is equal to the period of the periodic input signal multiplied by an integer that is selected by control signals applied to the logic elements. The set of selectable integers chosen for this example is 9 or 8. Elements 8, 10, 12 and 14 are conventional J-K flip-flop circuits such as those commercially available in integrated circuit form designated as type SN7473. When the control signal applied to element 14 is in the low state, the Q output 18 of element 14 is low and the output of gate 22 is high and elements 8, 10 and 12 act as a three-stage binary counter with Pout equal to eight times Pin. On the other hand, if the control signal input is high, the output of gate 22 will go low in response to one of the eight counting states of elements 8, 10 and 12, thereby disabling the input to element 8 for one period of the input signal. On this extra input period, the Q output 18 of element 14 is driven low so that the input to element 8 is reactivated for the next input period. Pout therefore is equal to nine times Pin when the control signal is high.

FIG. 2b shows the symbol used herein to represent a controlled period multiplier with the selectable multiplying integers 9 or 8. The selectable multiplying integers can be changed to 5 or 4 by eliminating element 10 from FIG. 2a and connecting the Q output of element 8 to the clock input of element 12. It should therefore be apparent to persons of ordinary skill in the field that controlled period multipliers with other sets of selectable multiplying integers may readily be designed and constructed in accordance with the principles above. Also, it should be noted that other circuit arrangements for dividing an input frequency by a controllably selected factor may be used as the controlled period multipliers in the present invention (see, for example, "A Variable Counter Design Technique," E. L. Renschler, IEEE Trans. on Computers, July 1968, pages 694 et seq.).

The cascade connection, as shown in FIG. 1, of three controlled period multipliers 11, 13 and 15 of the type shown in FIG. 2 thus provide period multiplication in response to combinations of control signals C1, C2 and C3 applied thereto as shown in the following Table 2. --------------------------------------------------------------------------- Table 2

combined C1 C2 C3 PERIOD MULTIPLIER __________________________________________________________________________ H H H 180 L H H 160 H L H 144 L L H 128 (extra) H H L 135 L H L 120 H L L 108 L L L 96 __________________________________________________________________________

h = control input signal C is high

L = Control input signal C is low

It should be noted that this set includes all of the integers representing the relative periods of the tones Do through Ti in Table 1, and it should also be noted that the configuration of FIG. 1 provides one additional combination of factors, namely 8×4×4, not listed in Table 1. Introduction of this additional tone generated by this combination produces a scale that divides the octave into eight intervals. These intervals, expressed as ratios of successive frequencies from lowest to highest, are: 9/8, 10/9, 16/15, 135/128, 16/15, 10/9, 9/8, and 16/15. This set of eight intervals reduces to the seven-interval diatonic scale if the fourth and fifth intervals are combined (multiplied) and it also reduces to the seven-interval Redfield scale, in the Daleth mode, if the third and fourth intervals are combined. Combining of successive intervals is readily accomplished by not using the encompassed tone.

The factors shown in column 6 of Table 1 can be realized by changing the controlled period multiplier 13 of FIG. 1 to permit selection of the integers 5 or 6. This configuration also produces an eight-interval scale with successive frequency ratios of: 10/9, 81/80, 10/9, 16/15, 9/8, 10/9, 9/8 and 16/15. The diatonic scale is thus produced if the first and second intervals are combined, and the Redfield scale in the Aleph mode is produced if the second and third intervals are combined.

The principles demonstrated thus far are incorporated into the preferred embodiment of the present musical instrument shown in block diagram form in FIG. 3. The scale generator section, as in FIG. 1, consists of controlled period multipliers 31, 33, 35 and 37 that are controlled by the tone selector 30. Multiplier 37 provides one of three multiplying factors which extends the range of this part of the instrument to an octave and a half. Also, multiplier 35 is added to give a scale having 12 intervals per octave. Table 3 below lists the relative periods of the tones of this scale along with one possible assignment of tone names with corresponding frequency ratios and interval names as described in the literature (see, for example, "The International Cyclopedia of Music and Musicians," Oscar Thompson editor, 9th Ed., Dodd, Mead and Co., N.Y. 1964, page 12). --------------------------------------------------------------------------- Table

3 Relative Tone Frequency Interval Period Name Ratio to Do from Do __________________________________________________________________________ 720 Do 1:1 Unison 675 Ru- 16:15 Limma 640 Re 9:8 Major 2nd 600 Mu 6:5 Minor 3rd 576 Mi 5:4 Major 3rd 540 Fa 4:3 Perf. 4th 512 Fi+ 45:32 Between Aug. 4th tg and dim.5th 480 Sol 3:2 Perf. 5th 450 Lu 8:5 Minor 6th 432 La 5:3 Major 6th 400 Tu 9:5 Minor7th 384 Ti 15:8 Major 7th 360 Do' 2:1 Octave __________________________________________________________________________

Unlike the equally tempered 12-tone scale, this scale does not provide for transposing the same scale into different keys, but it does provide a much wider variety of modes. The ability to transpose this scale into different keys is provided by the scale transposer section which consists of multipliers 41, 43 and 45 which are similar to those shown in FIG. 1 and which are controlled by the keynote selector 40. The scale transposer section can be visualized as a means for providing a set of selectable reference signals for the scale generator section where these reference signals in turn form a musical scale as determined by the scale transposer section.

Oscillator 47 provides the periodic signal which is multiplied by the various factors to produce the output tones. An oscillator frequency of 68.4288 MHz. in the instrument of FIG. 3 produces output tones into the third octaves above and below middle C. It is practical to build oscillators and period multipliers operating at 68 M MHz., but it may be economically advantageous to reduce this frequency by eliminating one or more period multipliers such as 41 and selecting equivalent frequencies by using some selectable frequency determining elements in the oscillator circuit 47.

The octave extender section is a series of conventional flip-flop circuits 51, 53, 55 with a gated bypass under the control of range selector 50 which provides for shifting the output of the scale generator in octave steps . The output waveforming circuits consist of a flip-flop circuit 57 for producing a square wave followed by an amplifier 20 which also responds to control unit 58 to gate the signal on and off and to selectively control and amplitude modulate the signal. Control element 48 provides for altering the reference frequency about its nominal value to produce small variations in pitch and to introduce vibrato in the audio signal produced at output 19.

It should be apparent that the controlled period multipliers can be rearranged in any order without altering the output signal and that some of the elementary multipliers could be combined. For example, multipliers 33 and 35 could be combined into a single multiplier with selectable multiplying integers of 16, 20 or 25. In addition, several similar channels of multiplier units 31-37 may be connected to receive reference frequencies, say, from the scale transposer section for producing additional tonal frequencies which can be combined in amplifier 20 to produce more than one tone simultaneously.

In the present embodiment of this invention the control console includes a keyboard for the tone selector 30 consisting of a set of switches arranged in a two-dimensional array, as shown in FIG. 4. The selectors for the tonal frequencies are arranged in rows and columns which need not be orthogonal although they are drawn so for simplicity. The rows are shown horizontally with six selectors per row and with two rows per octave. Within a row the successive selectors, moving from left to right, increase the selected tonal frequency by a Major 2nd alternating with a Minor tone. The columns are shown vertically, and within a column successive selectors, moving from bottom to top, increase the selected tonal frequency by either a Perfect 4th or a Doric 4th (a frequency ratio of 27: 20). Any number of octaves could be included by extending the array of selectors in accordance with the pattern established in FIG. 4.

The "selector vector" from any first selector to any second selector is defined as the vector drawn from the center of the first selector position to the center of the second selector position. Two selector vectors are equal if they have equal lengths and directions, and this equality is independent of positional translation about the pattern of selectors shown in FIG. 4.

FIG. 4 also shows the relative periods of the selectable tones, and the "tonal interval" from any first tone to any second tone is defined as the ratio of the period of the first tone divided by the period of the second tone.

An important property of this set of tonal frequencies combined with this array of selectors is that all pairs of tones having equal tonal intervals also have equal selector vectors. Therefore, if the scale and range of the keyboard permit a melodic pattern or a chord to be translated in pitch then the corresponding fingering pattern will be simply translated in position. This consistent relationship between tonal patterns and geometrical selector patterns, together with the independent operation of keynote selector 40, makes it relatively easy to create and play music on the instrument of the present invention.

A musical instrument constructed in accordance with the present invention is thus ideally suited for playing music in the various modes of the diatonic scale and for developing the musical potential of the extensions of this scale which have been presented herein. The pitch of every tone in every musical key is as accurate as the frequency of the reference oscillator, and an ideal accompaniment for vocal music is provided by these precise tones extending the natural scale of Ptolemy.