Electronic musical instrument with equally spaced binary note codes

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BACKGROUND OF THE INVENTION

This invention relates to an electronic musical instrument, more particularly a device for generating note codes by utilizing equally spaced binary codes.

In a digital electronic musical instrument, for the purpose of producing a musical tone having a frequency corresponding to the tone pitch of a depressed key of a keyboard, a binary code is used to produce a key code signal representing the depressed key.

In the case of an electronic musical instrument having 61 keys, for example, key informations or codes identifying respective ones of the 61 keys (5 octaves plus one key) are generally expressed by standard binary codes as shown in Table I, and 12 tone names are assigned as shown in the following Table II based on this concept.

TABLE I ______________________________________ Data number to be designated Binary code ______________________________________ 1 0000 2 0001 3 0010 4 0011 5 0100 6 0101 7 0110 8 0111 9 1000 10 1001 11 1010 12 1011 13 1100 14 1101 15 1110 16 1111 ______________________________________

TABLE II ______________________________________ Key code Note Binary code of Binary code of Octave name octave data note name data ______________________________________ 1 001 2 010 3 011 4 100 5 101 6 110 C .0000 C.music-sharp. .0001 D .0010 D.music-sharp. .0011 E .0100 F .0101 F.music-sharp. .0110 G .0111 G.music-sharp. .1000 A .1001 A.music-sharp. .1011 B .1011 ______________________________________

In the case of Table II, the note name data representing 12 note names C, C.sup..music-sharp. . . . B assigned to fractional parts (i.e. below radix point) of the key codes and the octave data representing the octaves are assigned to integer portions of the key codes. In order to discriminate 12 tone names four bits are required and to discriminate 6 octaves 3 bits are required.

When respective note names C, C.sup..music-sharp. . . . B are respectively assigned to the first to 12th binary codes ".0000"-".1011" as shown in Table II, the key codes of the chromatic notes in the same octave are expressed by an equal interdigit spacing that is ".0001" and the first to sixth octaves repeat cyclically the binary codes of ".0001"-".1000". However, the interdigit spacing corresponding to one semitone step at a transition of from one octave to the other becomes ".0101". In other words, the spacing between the binary code of the note name B and the binary code of the note name C of the next octave is ".0101", and thus all spacings are not equal.

One method of producing a musical tone from an electronic musical instrument is a method of reading out a waveform memory device. According to this method, sampled amplitude values of a waveform to be produced are prestored in a waveform memory device and the stored values are sequentially and repeatedly read out by an address signal having a frequency determined by the key code thereby forming a musical tone waveform.

To form a read out address signal it has been proposed to regularly and repeatedly accumulate a frequency number signal having a magnitude corresponding to a numeral (hereinafter called frequency number) proportional to the frequency of a tone to be produced so as to form a saw tooth shaped repetitively progressive signal having a frequency corresponding to the magnitude of the frequency number from the accumulated value. Then the repetitive frequency signal is read out and used as the address signal.

Thus, the reading and addressing operation of the waveform memory device is performed in each period of the address signal thereby producing a musical tone signal having a frequency corresponding to the frequency number.

When producing a musical tone according to this method, it is essential to obtain a frequency number signal proportional to the tone pitch, i.e., frequency of each key of the keyboard. In this manner, it is possible to cause respective generated tones to have predetermined pitches corresponding to respective keys. According to the prior art method, however, since the key code signals have been assigned to 12 note names by using standard binary codes having 16 values, when transferring from one octave to the other, the content (value) of the key code can not maintain an equal difference. For the purpose of giving a linear proportional relationship to a portion not having the equal difference, the prior art electronic musical instrument has been constructed as follows:

More particularly, as shown in FIG. 1, there is provided a frequency number signal generator 1 having a ROM capable of storing linear numerical information over the entire tone range of the keyboard. A key code signal KC, containing key codes shown in Table II and formed by a key assignor 4 acting as a depressed key detector and operated by a key switch 3 responsive to a depressed key 2, is applied to the ROM in the frequency number signal generator 1 to act as an address signal.

Then, a numerical value output having a magnitude corresponding to a key designated by the key code signal KC is read out from the ROM in the frequency number signal generator 1 and the output is sent out as a frequency number signal F which has a content regarding the numerical value information (i.e. the frequency numbers) having a linear characteristic over the entire tone range of the keyboard.

The frequency number signal F is multiplied with the output PT of a pitch modifying data generator 5 in a multiplier 6 for applying an effect to the musical tone. The product F.multidot.PT is applied to a accumulator 7 as an input to be accumulated. The accumulator 7 sends its accumulated value to a musical tone wave generator 8 including a waveform memory device to act as a read out address signal. This prior art electronic musical instrument is disclosed in U.S. Pat. No. 3,979,996 dated Sep. 14, 1976 and invented by Tomisawa et al.

In the prior art electronic musical instrument shown in FIG. 1 it is essential to convert a key code signal KC not having a linear equal difference relationship at a portion of the numerical value content into a numerical data information having a linear equal ratio relationship in the frequency number signal generator 1.

While in the circuit shown in FIG. 1, a pitch modifying effect is applied by the multiplier 6, its construction is extremely complicated for effecting addition of a plurality of partial integrations. To simplify the multiplier 6, the frequency number signal generator 1 shown in FIG. 1 has been modified such that it does not directly memorize the linear frequency number F but, rather, memorizes the same after converting it into a logarithmic value log F and applies the logarithmic value log PT of the linear numerical information value PT to the pitch modifying data generator 5. Log PT and log F are added together by an adder sustituted for the multiplier 6 shown in FIG. 1, and its output log F+log PT=log F.multidot.PT is converted by a lagarithm-linear converter, not shown, into a linear numerical value information F.multidot.PT which is applied to the accumulator 7 as an input to the accumulator. This modified electronic musical instrument is disclosed in Chibana et al U.S. Pat. No. 4,215,614 issued Aug. 5, 1980 entitled "Electronic Musical Instruments of Harmonic Wave Synthsizing Type".

As above described, in the prior art waveform memory device read out type digital electronic musical istrument, in order to obtain a frequency number signal F in the form of linear numerical information it is necessary to use a ROM adapted to directly store a plurality of frequency numbers F corresponding to respective tone pitches over the entire tone range of a keyboard after converting the frequency numbers F into logarithmic values. In addition, in order to apply an effect, it is necessary to provide a multiplier of a complicated construction or an adder and a linear-logarithm converting circuit. For this reason, simplification of the entire construction has been limited.

SUMMARY OF THE INVENTION

Accordingly, it is a principal object of this invention to provide an electronic musical instrument utilizing novel equally spaced binary codes.

Another object of this invention is to provide an electronic musical instrument utilizing novel binary codes capable of forming key information or codes representing the number of pairs of linear frequency numbers with an extremely simple construction.

A further object of this invention is to provide an improved electronic musical instrument capable of simplifying the entire construction by forming note codes with a novel binary code.

According to this invention these and other objects can be accomplished by providing an electronic musical instrument comprising means for producing note codes respectively having n (n is positive integer) bits representing juxtaposed notes aligned by a semitone interval step in a musical scale, the note codes to be generated being selected from a binary code table consisting of successively aligned binary values according to an order of alignment of the notes in a musical scale; the binary code table omitting either one of the largest and smallest values to be represented by the lowest m bits (when m is a positive integer smaller than n); means for generating modified note codes for repetitively adding the lowest m bits of each of the generated note codes to further lower order digits below the least significant bit of each note code; and means for producing a signal of a frequency corresponding to the modified note code.

BRIEF DESCRIPTION OF THE DRAWINGS

In the accompanying drawings:

FIG. 1 is a block diagram showing a prior art electronic musical instrument;

FIG. 2 is a block diagram showing one of the electronic musical instrument embodying the invention;

FIG. 3 is a connection diagram showing one example of the frequency converter shown in FIG. 2;

FIG. 4 is a connection diagram showing one example of the pitch modifying signal generator shown in FIG. 2;

FIG. 5 is a graph for explaining the relation between the outputs of the counter and logic circuit shown in FIG. 4 and the variation of the pitch modifying signal;

FIG. 6 is a connection diagram showing the glide control circuit; and

FIG. 7 is a graph for explaining the operation of the glide effect control circuit shown in FIG. 6.

DESCRIPTION OF THE PREFERRED EMBODIMENT

The following embodiment relates to an electronic musical instrument having 61 keys.

The principle of this invention lies in that a cyclically repeated bit portion of binary code data is repeatedly and (substantially) limitlessly added to further lower order digits below the least significant bit of the data to obtain converted code data having a lesser number of equally spaced values than that attainable by normal binary code data.

For example, as shown in the following Table III, where an input binary code data has a value of two bits at its fractional portion, two bit data "00", "01", "10" and "11" are added to the further lower order digits below the least significant values ".00", ".01", ".10" and ".11" respectively.

When the input binary code data have fractional 3 bit values as shown in Table IV, to the further lower orders of the least significant bit of the input binary code data ".000", ".001" . . . ".111" are infinitely added 3 bit data "000", "001" . . . "111" respectively.

In the same manner, where the binary code data are fractional four bit values, as shown in Table V, to the further lower order digits of the least significant orders of the input binary code data ".0000", ".0001", . . . ".1111" are infinitely added four bit data "0000", "0001" . . . "1111" respectively.

TABLE III ______________________________________ Given code Converted code data data Binary values Name ______________________________________ .00 .00 00 00 . . . S31 .01 .01 01 01 . . . S32 .10 .10 10 10 . . . S33 .11 .11 11 11 . . . S34 ______________________________________

TABLE IV ______________________________________ Given code Converted code data data Binary values Name ______________________________________ .000 .000 000 000 . . . S41 .001 .001 001 001 . . . S42 .010 .010 010 010 . . . S43 .011 .011 011 011 . . . S44 .100 .100 100 100 . . . S45 .101 .101 101 101 . . . S46 .110 .110 110 110 . . . S47 .111 .111 111 111 . . . S48 ______________________________________

TABLE V ______________________________________ Given code Converted code data data Binary Value Name ______________________________________ .0000 .0000 0000 0000 . . . S501 .0001 .0001 0001 0001 . . . S502 .0010 .0010 0010 0010 . . . S503 .0011 .0011 0011 0011 . . . . .0100 .0100 0100 0100 . . . . .0101 .0101 0101 0101 . . . . .0110 .0110 0110 0110 . . . . .0111 .0111 0111 0111 . . . . .1000 .1000 1000 1000 . . . . .1001 .1001 1001 1001 . . . . .1010 .1010 1010 1010 . . . . .1011 .1011 1011 1011 . . . S512 .1100 .1100 1100 1100 . . . S513 .1101 .1101 1101 1101 . . . S514 .1110 .1110 1110 1110 . . . S515 .1111 .1111 1111 1111 . . . S516 ______________________________________

When expressed in terms of binary values these converted code data have values each corresponding to the sum of infinite geometrical progressions. Since its common ratio q is smaller than 1, the sum converges as expressed by the following equation

S.infin.=a/(1-q) (1)

where a represents a first term. Expressing each value shown in Table III in terms of a decimal value, since in the first value S31, a=0 and q=0 ##EQU1##

In the second value S32 since a=1/4 (a binary value "0.01" is equal to a decimal 1/4) and q=1/4 ##EQU2##

Furthermore in the third value S33 since a=2/4 (binary "0.10" is equal to decimal 3/4) and q=1/4 ##EQU3##

In the fourth value S34 since a=3/4 and q=1/4 ##EQU4##

Respective values shown in Tables IV and V can be obtained in the same manner. In the case of Table IV, for each of the values S41, S42, S43 . . . S48, since a=0, 1/8, 2/8 . . . 7/8 and q=1/8 the values S41, S42, S43 . . . become 0/7, 1/7, 2/7, . . . 7/7 respectively. In the case of Table V, since a=0, 1/13, 2/13 . . . 15/13 and q=1/16, the values S501, S502, S503 . . . S516 become 0/15, 1/15 . . . 15/15, respectively.

Converged values of respective values thus obtained and shown in Tables III, IV and V are shown in the following Tables VI, VII and VIII.

TABLE VI ______________________________________ Given Converged values of data code converted code data ______________________________________ .00 S31 = 0/3 .01 S32 = 1/3 .10 S33 = 2/3 .11 S34 = 3/3 ______________________________________

TABLE VII ______________________________________ Given code Converged values of data converted code data ______________________________________ .00 S31 = 0/3 .01 S32 = 1/3 .10 S33 = 2/3 .11 S34 = 3/3 ______________________________________

TABLE VIII ______________________________________ Given code Converged values of data converted code data ______________________________________ .0000 S501 = 0/15 .0001 S502 = 1/15 .0010 S503 = 2/15 .0011 S504 = 3/15 .0100 S505 = 4/15 .0101 S506 = 5/15 .0110 S507 = 6/15 .0111 S508 = 7/15 .1000 S509 = 8/15 .1001 S510 = 9/15 .1010 S511 = 10/15 .1011 S512 = 11/15 .1100 S513 = 12/15 .1101 S514 = 13/15 .1110 S515 = 14/15 .1111 S516 = 15/15 ______________________________________

As can be noted from Tables VI, VII and VIII, the converted code data values obtained by infinitely adding 2, 3 or 4 bits to the further lower order digits below the least significant bit of the given code, data shown in Tables III, IV and V are converged values with equal spacings therebetween. However, the given code data shown in Tables III, IV and V vary cyclically as the integers of the bits above the radix point increase, so that the values of the converted code data also repeat cyclically.

Considering now a case wherein two bits are repeatedly and infinitely added to the further lower digits of the least significant bits as shown in Table III, and supposing that where values of fractional 4 bits are given as the input code data as shown in Table IX, 16 values of ".00000000"-".11111111" would be obtained as the converted code data.

TABLE IX ______________________________________ Given Converged code data Converted code data values ______________________________________ .00 00 .00 00 00 00 . . . 0/12 .00 01 .00 01 01 01 . . . 1/12 .00 10 .00 10 10 10 . . . 2/12 .00 11 .00 11 11 11 . . . 3/12 .01 00 .01 00 00 00 . . . 3/12 .01 01 .01 01 01 01 . . . 4/12 .01 10 .01 10 10 10 . . . 5/12 .01 11 .01 11 11 11 . . . 6/12 .10 00 .10 00 00 00 . . . 6/12 .10 01 .10 01 01 01 . . . 7/12 .10 10 .10 10 10 10 . . . 8/12 .10 11 .10 11 11 11 . . . 9/12 .11 00 .11 00 00 00 . . . 9/12 .11 01 .11 01 01 01 . . . 10/12 .11 10 .11 10 10 10 . . . 11/12 .11 11 .11 11 11 11 . . . 12/12 ______________________________________

Considering only the fractional portions of the infinitely repetitive converted code data, the difference between adjacent data, for example a certain value ".XX111111" and an adjacent upper value ".XX000000", are substantially zero, where X does not represent specific values but merely indicates the presence of bits. Suppose now that the code data shown in Table IX vary from ".0011" to ".0100", from ".0111" to ".1000", from ".1011" to ".1100" and from ".1111" to ".0000", theoretically where "1" is added to the least significant bit of a code data ".XX111111 . . . ", the code data would change to ".XX000000 . . . ". However, since the bits of the converted code data continue infinitely, the binary value to be added to the least significant bit is an extremely small value (substantially zero). This is also true for decimal numerals.

In other cases, the variation from one value to the another is a definite value of 1/12 in terms of a decimal number as shown in Table IX, so that the variation between ".XX111111 . . . " to ".XX000000 . . . " can be neglected.

Thus, when the infinitely repetitive converted code data varies frrom ".XX111111 . . . " to ".XX000000 . . . " the expressions of the data vary noticeably, while, the difference in the contents of these two data is substantially zero.

Although in Table IX, the converged values of the converted code data and shown to abruptly vary from "12/12" to "0/12" when the code data changes from ".1111" to ".0000", since the given data ".0000"-".1111" are repeated cyclically it may be considered that the values ".00000000 . . . " and ".11111111 . . . " of the converted data have the same meaning.

In the foregoing description, two bits of a given code data were repetitively added to the next (lower side) of its least significant bit but 3, 4 or more bits can be similarly added cyclically.

Thus, generally stated, the binary values "00000 . . . " and "111111" of the converted code data may be considered substantially equal when one considers their contents.

Of the binary values of the converted code data either one of "111111 . . . " and "000000 . . . " may be omitted. Thus, when n bits are repetitively added, the number of sets of the values of the code data may be reduced to (2.sup.n -1).

With the converted code data of this invention based on this concept, the number of sets of the values becomes 12 as shown in the following Table X by decreasing one for each set of four values, when n=2 as shown in Table IX. With this measure, the interdigit spacings between adjacent values become equal (in the case shown in Table X, 1/12).

TABLE X ______________________________________ Given Converted code Converged code data data values ______________________________________ .0001 .00 01 01 01 . . . 1/12 .0010 .00 10 10 10 . . . 2/12 .0011 .00 11 11 11 . . . 3/12 .0101 .01 01 01 01 . . . 4/12 .0110 .01 10 10 10 . . . 5/12 .0111 .01 11 11 11 . . . 6/12 .1001 .10 01 01 01 . . . 7/12 .1010 .10 10 10 10 . . . 8/12 .1011 .10 11 11 11 . . . 9/12 .1101 .11 01 01 01 . . . 10/12 .1110 .11 10 10 10 . . . 11/12 .1111 .11 11 11 11 . . . 12/12 ______________________________________

According to this invention it is possible to convert a standard binary code data having 16 values of fractional 4 bits into binary code data having 12 values of equal interdigital spacing. These binary code data having 12 values can be used as note data representing 12 note names in one octave. Thus as shown in Table XI, respective note names of C through B of 12 note names are assigned to 12 values obtained from Table X, and 3 bit binary values "001"-"110" representing the octave number are added to the integer portions.

TABLE XI ______________________________________ Converted code data Assigned note Converged values ______________________________________ 001.00010101 C 2 ##STR1## 001.00101010 C.music-sharp. 2 ##STR2## 001.00111111 D 2 ##STR3## 001.01010101 D.music-sharp. 2 ##STR4## 001.01101010 E 2 ##STR5## 001.01111111 F 2 ##STR6## 001.10010101 F.music-sharp. 2 ##STR7## 001.10101010 G 2 ##STR8## 001.10111111 G.music-sharp. 2 ##STR9## 001.11010101 A.music-sharp. 2 ##STR10## 001.11101010 A.music-sharp. 2 ##STR11## 001.11111111 B 2 ##STR12## 010.0010101 C 3 ##STR13## . . . . . . . . . 010.11111111 B 3 ##STR14## . . . . . . . . . 101.00010101 C 6 ##STR15## . . . . . . . . . 101.11111111 B 6 ##STR16## - 110.00010101 C 7 ##STR17## ______________________________________

In the case shown in Table XI, the values of the converted code data have equal spacing. This will be considered from the standpoint of the pitches of the assigned notes. On an average the frequency of the tone of the (k+1)th tone among 12 tones contained in one octave is 2.sup.k/12 times of that of the first tone, and the spacing between tones has a frequency ratio of 2.sup.1/12. More particularly, the pitches of notes C.music-sharp., D . . . , B of each octave are 2.sup.1/12, 2.sup.2/12, 2.sup.3/12 . . . 2.sup.11/12 times of the pitch of the note C, and spacings between tones have a frequency ratio of 2.sup.1/12 times.

The logarithm of the frequency .alpha..sub.k as normalized in ratio of the kth tone is expressed in equation (6) in which 2 is used as the base

log.sub.2 .alpha..sub.k =k/12 (6)

where k=1, 2, . . . 12.

Thus, the result of equation (6) coincides with the converged value shown in Table X.

In equation (6) let us expand the value of k beyond the range of one octave. Thus, as the k increases as k=13, 14, . . . the value of the righthand term of equation (6) increases as a mixed number, and this also coincides with the relationship of the converged values shown in Table XI.

From the foregoing investigation, it can be noted that the converged values shown in Table XI are expressed as logarithms of the frequencies of all notes taking 2 as the base. Thus, the converted code data represent the logarithms of the values (hereinafter termed a note representing value) corresponding to the frequencies of respective notes.

For example, speaking of the code data of note E.sub.3, it can be expressed as

010.01101010

=2(5/12)=2.416=log.sub.2 5.3393 (7)

Accordingly, the note representing value .alpha..sub.E3 can be shown as follows.

.alpha..sub.E3 =5.3393 (8)

On the other hand, the note E4 can be expressed as

011.01101010

=3(5/12)=3.416=log.sub.2 10.6787 (9)

Accordingly, the note representing value .alpha..sub.E can be shown by

.alpha..sub.E4 =10.6787 (10)

Furthermore, note E5 can be expressed as

100.01101010

=4(5/12)=4.416=log.sub.2 21.3574 (11)

Thus, the note representing value .alpha..sub.E5 can be shown by

.alpha..sub.E5 =21.3574 (12)

However, as clearly shown by equations (8), (10) and (12), the ratios between the note representing values .alpha..sub.E3, .alpha..sub.E4 and .alpha..sub.E5 are respectively 2. Thus, as defining

.alpha..sub.E3 =.alpha..sub.o, (13),

then

.alpha..sub.E4 =2.alpha..sub.o (14)

.alpha..sub.E5 =4.alpha..sub.o (15)

This means that .alpha..sub.E3, .alpha..sub.E4 and .alpha..sub.E5 represent the frequency relationships of notes E3, E4 and E5 in an octave relationship.

In the case of note F5 one semitone higher than the note E5

100.011111111

=4(6/12)=4.500=log.sub.2 22.6274

=log.sub.2 (.alpha..sub.E5 .times.1.05946) (16)

where a value 1.05946 means a semitone interval.

When respective notes are assigned to the converted code data shown in Table XI, values corresponding to the respective notes can be obtained with respect to a reference frequency.

As shown in the following Table XII, when the content of the first bit of an integer portion of a key code signal is "1" (that is, when a code data of "001.0000000000" is given), the frequency of the musical tone signal becomes 1200 cents above the reference frequency, whereby a musical signal of a pitch of 1200 cents higher than the reference note would be produced.

On the other hand, respectively when the content of the second bit and the third bit of the integer portion is "1" (that is, when code data of "010.0000000000" and "100.0000000000" is given), a musical tone having a pitch of 1200.times.2.sup.n cents (n=1 and 2 respectively) would be produced, and correspondingly when the content of the first bit, second bit, . . . 10th bit of the fractional portion is "1", that is, respectively when code data of "000.1000000000", "000.0100000000" . . . "000.0000000001" is given, a musical tone having a pitch of 1200.times.2.sup.2 cents (n=-1, -2, . . . -10 respectively) would be produced.

TABLE XII ______________________________________ Key code signal Pitch (in cents) ______________________________________ 100.0000000000 4800 010.0000000000 2400 001.0000000000 1200 000.1000000000 600 000.0100000000 300 000.0010000000 150 000.0001000000 75 000.0000100000 37.5 000.0000010000 18.75 000.0000001000 9.375 000.0000000100 4.6875 000.0000000010 2.34375 000.0000000001 1.171875 ______________________________________

When the content of a key code data increases by "001.0000000000", the frequency of the musical tone increases by one octave (1200 cents). Further, when "000.0001010101" is added to the content of a key code, the frequency of the musical tone increases by a semitone (100 cents), whereas when its complement "111.1110101010" is added (this means a subtraction), the frequency of the musical tone decreases by a semitone (100 cents). In the same manner addition of "000.0000001000" and "000.0000101010" respectively results in the increase of 10 and 50 cents respectively of the frequency of the musical tone.

A vibrato effect may be imparted by adding "000.0000000001" through "000.0000011111" and "111.1111111110" through "111.1111100000" to the content of a key code data, in which case the width of the frequency of the musical tone varies by 1.172 through 36.3 cents.

To impart a glide effect, "111.1110000000" is added to the content of a key code data (this means subtraction of "000.0001111111") and thereafter the addend is gradually increased to "111.1111111111". Then the pitch of the musical tone suddenly decreases by about 150 cents and thereafter gradually restores to the original pitch.

The formation of key codes for an electronic musical instrument based on the principle described above can be realized by a circuit shown in FIG. 2.

The circuit shown in FIG. 2 comprises a key switch group 11 corresponding to sixty-one (61) keys 12. These sixty-one key switches are divided into a plurality of blocks, each of which is sequentially scanned by a key assigner 13. This type of key assigner is disclosed in U.S. Pat. No. 4,148,017 dated Apr. 3, 1978. The blocks are divided into octave units. Thus, notes C2 through B2, C3 through B3, . . . and C6 through B6 are divided into five (first through fifth) blocks whereas note C7 is alloted to the 6th block. The key assigner 13 sequentially scans from the first to 6th blocks to produce a detected block signal BLo consisting of outputs on three output lines. The assigner 13 also scans the key switches 11 corresponding to note names C through B belonging to each block to produce a detected note signal NT.sub.o consisting of outputs on four output lines representing the note name of the depressed key, if any. The detected block signal BLo is expressed by a 3 bit binary value, whereas the detected note signal NTo is expressed by a 4 bit binary value. As shown by the "given code data" in Table X, the detected note signals NTo have contents as if note names C through B were assigned to 12 values of ".0001" through ".1111" remaining after omitting four values of ".0000" ".0100", ".1000" and ".1100" from sixteen standard binary values.

Thus the detected block signal BLo is applied to an adder 14 as an integer bit input. On the other hand, the detected note signal NTo is applied to the adder 14 as a fractional bit input, and moreover its two lowest bits are repeatedly applied to the adder 14 to act as further lower order bits below the least significant bit of the fractional portion of the detected 7-bit code. In this manner 7 bit detected key code signals KCo appear at the output of the key assignor 13, while converted key code signals KC same as the "converted code data" in Table XI appear on the output of the adder 14.

In the circuit shown in FIG. 2, the fractional bit signals inputted to and outputted from the adder 14 comprise 10 bits as shown in Table XIII whereby an approximate mathematical operation of the key code signal is made within a permissible error range. The data shown as the "converted code data" in Table XI are theoretically expressed as infinite geometrical progressions. However, when one considers the influence upon the pitches of respective not