1 7 ARABIC 1620: an ANALYSIS and PROCEDURE for COMPOSING COMPUTER MUSIC THESIS Presented to the Graduate Council of the North Te

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1 7

ARABIC 1620: AN ANALYSIS AND PROCEDURE FOR COMPOSING COMPUTER MUSIC

THESIS

Presented to the Graduate Council of the North Texas State University in Partial Fulfillment of the Requirements

For the Degree of

MASTER OF MUSIC

William Loyd Lott, B. M. Denton, Texas August, 1968 TABLE OF CONTENTS

Page LIST OF TABLES...... 0 . . 0 0 .P

LIST OF ILLUSTRATIONS ...... 0 . V Chapter

I. INTRODUCTION ...... * . . 0 . 0 0 ."1

II. COMPUTER INPUT SPECIFICATIONS. . . . 0 . 0 0 0 4 Tempo Blank: H-Code Note Rest Period

III. REALIZATION PROCEDURES ...... * . . . . 16 The Composition Process The Codification Process The Card Punch Process The Computer-Recording Process The Modification Process

IV. ANALYSIS OF ARABICI1620...... 26

APPENIX. 0 0 0 . . . 0 ...... 0 . 33

BIIBLIOGRAPHY. . 0 0 . 0 . 0 . . 0 ...... 0 40

iii LIST OF TA3LES

Table Page I. Horizontal Interval Frequencies and Percentages ...... 32

iv LIST OF ILLUSTRATIONS

Figure Page

1. Four-mColumn Field. 40 ...... 5 2. Number of Notes, Rhythmic Notation, and Codes Equivalent to One Quarter Note Value..*. .10 3. Substitute Letters for Dotted Notes. . . . . ** 13

4. Substitute Letters for Sharp Notes ...... 13

5. Substitute Letters for Flat Notes...... 14 6. Punching Positions of Digits, Letters, and the Special Character on the IBM Card . . . 19

7. Notation for Reverberation ...... 24

8. Notation for White Noise ...... 24

9. Oblique Modulated Signal Upward...... 24

10. Oblique Modulated Signal Downward...... 24

11. Modulated Signal in Contrary Motion...... 24

12. Original Row and Theme...... 26

13. Original Row in B Section.....*...... 28

14. Design of a Mirrored Exponential Envelope. . . . 28

15. Design Showing Rapid Alternation between Notes to Create Harmony ...... 29 16. The First Three Notes of Channel II in Diminution of Channel III ...... 30

17. Original Row Used As Ostinato...... 30

V CHAPTER I

INTRODUCTION

Computers are used in the music field for generation of sound, for composing music, for analysis of music, and for musicological applications, such as cataloguing a bib liography of music literature. These areas are relatively new aspects of computer usage, and research is being con ducted to stay abreast of current technological advancements.

Avant-grd composers are challenged by new advances in music. Computer-generated music is one of the new trends, but the composer is usually limited in the use of the medium for two reasons: there are no computers to which he may have access, and/or there is not enough knowl edge about computer-generated music. The composer sometimes feels that he must have vast knowledge of the computer be fore he can attempt to use it in musical composition; how ever, a limited amount of investigation of computer-generated music has shown that methods can be codified to the point where great technical knowledge is not required of the com poser.

Arabic 1620 is designed for performance by the Inter national Business Machines 1620 Data Processing System, an electronic digital computer. The computer will generate the sounds, which are recorded onto magnetic tape. In order I 2 to generate sounds from the computer, information from the music is typed onto 80-column cards. The data from the cards are programmed through the computer, which stores this information. An AM radio receiver,1 placed on the computer console, will pick up the electromagnetic radiation emitted by the computer as it executes the program and will transmit through its loudspeaker the musical material that was punched on the IBM input cards. The Richard F. Smiley music program uses an approximation to the equal-tempered chromatic scale, American Standard Pitch, in which A4 (above middle C on the piano keyboard) equals 440 cycles per second.

The computer is used for the generation of the pitches and the durations. Electronic analog equipment should then be used to add dynamics, reverberation, modulation, and filtering, which as of this time, the 1620 computer is un able to perform under the Smiley program.

There are a number of musicians pursuing new musical advancements using computers. Important work in various fields of computer music is being done by the following people: Lejaren A. Hiller, Leonard M. Isaacson, and

1 The radio serves as a monitor so the programmer can hear the musical results.

2 Riehard F. Smiley, "Music Interpreter," abstracted from IBM Systems Reference Library, Catalog of Program for IBM 1620 and 1710 Data Processin Sysems(Hawthorne, New York, 1967)7 p. 107. 3

Robert A. Baker at the University of Illinois; M. V. Mathews and J. L. Divilbiss at the Bell Telephone Laboratories, hurray Hill, New Jersey; James C. Tenny, formerly at Bell Telephone Laboratories and currently at Polytechnic Insti tute of Brooklyn, New York; Arthur Roberts at the Argonne National Laboratory, Argonne, Illinois; Godfrey Winham and Hubert S. Howe at Princeton University; and Yannis Xenakis at Paris, France. This is by no means an exhaustive list, but these are probably the most prominent in the field. 3 Most of the researchers listed above use large, high speed computers. At present, most composers do not have access to these large computer systems. A more practical approach for generating music is to seek a small computer, which should be more commonly available to composers. Such an instrument is the IBI 1620 computer. A primary objective in this study is to gain maximum use of the small computer.

3Compositions-by these specialists include Illiac Suite for Stri Qartet, by Hiller and Isaacson, using an Illiac computer, Copter Cantata, by Hiller and Baker, using an IBt 7090 and CSX-l electronic digital computers, Music 4, by Mathews, Four Stochastic Studies and Ergodos I, by Tenny, MusicT7 Orpheus, and Maestro, by Roberts, using an ASI-210 computer, Music 4B, by Winham and Howe, us ing an IBM 7094, S481 2, Amorsima-Morsima, and Atrees, by Xenakis, using an IBM 7090. CHAPTER II

COLIPUTER INPUT SPECIFICATIONS

The object deck, which consists of cards representing the Smiley computer program, is processed into the memory of the IBM 1620 computer. Following this deck is the input data, which are the actual realization of the musical score. This chapter covers the preparation of the input data, IBM 80-column cards serve as the means for transmitting the information from the musical score into computer storage and language. Each card is divided into segments called fields. For the purpose of generating computer music in this study, four columns consist, of a field, with each card divided into twenty four-column fields. The first column of a field (the left column) is referred to as the octave column; the second as the note column; the third and fourth as the length columns.

A field is a column or columns reserved for the punching of data of a specific nature. The field may consist of from one to eighty columns, depending upon the length of the particular type of information,

4 5

0 L L cN e e t o nn a t g g V e t t e h h

X X X X Fig. 1--Four-column field

The contents of a field may be any one of six classes: tempo, blank, H-code, note, rest, or period. The various classes of fields are distinguished by the interpreter (computer program) on the basis of the contents of the note column (except for tempo fields, about which the interpreter knows in advance).

Tempo

The interpreter requires a tempo for each tune or set of data. This is a six-digit decimal fraction equal to one-fortieth the length of a whole note, in seconds. Nor mally this tempo comes from a tempo field on the input cards. However, if the tempo field on the cards is blank, the programmer must type the tempo with the IBM typewriter.2

The four digits of a tempo field, whether they are already on the input cards or need to be typed, become the four high order digits of the tempo. The low-order digits are filled in as zeros automatically by the interpreter.

2 See the footnote under the Detailed Operating Pro cedure for the IBM 1620 Computer in the Appendix. 6

The first field on the first card of a set of data is interpreted as a tempo field. Should data in the note class be accidentally punched in the first field of the card, a blank IBM card may be inserted ahead of the first input data card. The tempo may then be typed.

The digits, if typed in the tempo field, may range from 0000 to 9999, the former tempo being the COstest pos sible speed and the latter being the 1o*est. If the digits are typed by the IBM 1620 typewriter, as many as six digits can be specified.

Blank If the field is not a tempo field, it is classified according to the contents of the note column. If this column is blank, the field is not processed. The inter preter immediately proceeds to the next field. This provision makes it possible to put one event or line of material on a card, leaving the rest of the fields blank.

Material punched in this manner is easier to read (when it is being corrected) than material whose lines are run together on the card. If a few fields are used and the remainder of the card is blank, the interpreter goes to the next card without any delay. Should there be any blank fields between data on a card, the interpreter will 7

continue reading. It should be noted that the amount of blank space left on a card has no relevancy to the amount of time it takes for the interpreter to read it; nor does it have any bearing on the tempo or length of- the compo sition.

H-Code The interpreter takes its tempo from the first field on the first input card. However, it may be desirable to change the tempo during the composition. This is achieved by means of an H-code. If the interpreter finds an H in the note column, it will treat the next field as a tempo field and will replace its current tempo with the new one. No other information is coded in the H-code class, but it still occupies one field or four columns with the three remaining columns blank (bHbb)Al If there are several H-codes in the input data, the typewriter carriage will return for each tempo to be typed before the computer plays the material. The typewriter will not be needed if the tempi are already typed on the IBM cards following each H-code.

Note Most fields of a musical composition will be of this class. If the note column contains one of the letters A

-he "b" is a symbol representing a blank space. 8 through G, the interpreter will assemble a tone of the musi cal event and will play it during the playing phase.

The pitch of the written note is specified with a modi fication of standard musical notation. In this notation the pitches are divided into octaves with 0 the lowest note in each octave. Each note is given a subscript corresponding to the octave in which it is located. For example, 04 is middle 0 On the piano keyboard, or approximately 270 cycles per second. The note below 04 can be 0 .or B3 . In a note field the first two columns specify the pitch of a note. The octave column specified the octave by the Arabic numerals 0 through 6. The note column specifies the note within the octave by letter, corresponding with the musical notes A through G. The interpreter will accept any note from oto 06, the range of the Model I IBM 1620 computer.4

The duration of each note is specified by the last two columns of the note field. The reciprocal of the length is entered in the length columns, with a leading zero, if necessary. For example , a whole note is coded as 01 in the two length columns of a field; a half note is 02; a quarter note is 04. Any two-digit numeral from 01 to 99 can be entered in these two columns. This is useful in

4 The Smiley program was designed for the 1620 Model I, but it can be modified for the Model II. 9

playing triplets. For example, a triplet pattern of three quarter notes 4 ), which is equivalent intotal time to two quarter notes, is coded as sixth notes (06). One to twenty-four notes can be played by the computer in a total time equivalent to one quarter note. Figure 2

shows the number of notes, the notation, and their cor responding codes which represent the equivalent time of

one quarter note. Notes can be dotted or double-dotted by placing 11 punches5 in the length columns. Each 11-punch corresponds to a dot. For example, a G3 dotted ninety-ninth note can be coded either as 3G99 or as 3G99. To facilitate typing on the card punch machines, the ll-punches may be substi tuted by another letter which gives the same results. Substituting the letters eliminates having to backspace for the ll-punch and reduces keypunch time on the machines.

5The ll-zone punch is one of the twelve punching positions on the IBI cards. By pressing the (-) or -SKIP key on the keypunch machine, the ll-code is punched onto the card. When ll-punches are needed, the numeral or letter is punched and the card is backspaced one column to receive - the ll-punch. The dash (-) will be superim posed on the printed numeral or letter at the top of the card. 10

No. of' Notes Rhythmic Notation Code

1 04

_ _ I 2 08

3 12 N

4 16

5 20

6 24

7 28

8 32

9 36

Fitg. 2--The number of notes, rhythmic notation, and codes equivalent to one quarter note value. 11

Noe of Notes Rhythmic Notation Code

I I I I I I I I0 ~~~aIfl 40 L______- _____

II II k I I 44

I ti-I 12 -1111IT7T 48

13 Moves 11 (1 52

14 -111111g11es 56 1A.

111111I II~ -11111I1I1 -11F1T1J I 15 60

': Jill III I ILj,-1-T-T 16 or V 4V 9 9 0 64

17 fill I111111111 111 68

glum 18 --- I IIIIII I I11 11 I I I I 11111 72 IL A -I 12

No. of Notes Rhythmic Notation Code

19 I I I_II_ II_ IIIII1_ 76

-up

NM I I I a I I I ---- 20 ---- I-a O&f A sf 80

21 84 1, A II li

22 88

23 92 [I!!I!I!1- IL IIIIIIII lii IT tI I i I

24 244r 96964IF 13

Figure 3 lists the letters which may be substituted for the 11-punches in the length columns.

0- =oJ 02= OK 03= OL 04= CM 05= ON 04= 00 04= OP 09= OQ 09= OR Fig. 3--Substitute letters for dotted notes

Notes may be sharped or flatted. A note may be sharped Ip one of two ways: by putting a 11-punch in the octave

column or by substituting a different letter in the octave

column. The substitute letter must correspond to the octave placement as shown in Figure 4. For example, a quarter note F*4 is coded as MF04; using the l-punch, it is coded as 4F04.

Octave Substitute 1 = J 2 K 3 = L 4 M 5 = N

6 - 0 Fig. 4--Substitute letters for sharp notes

To sharpen a note in the 0 octave, it is necessary to type 0, backspace on the card punch machine, and type an

l-punch over the octave column. The result is g. 14

A note can be flatted by putting an li-punch in the note column or by substituting a different letter in the note column for the regular one, as shown in Figure 5.

'Note Sukstitute A- J Bk = 1

DO M E - N

Go P

Fig. 5--Substitute letters for flat notes

For example, a sixteenth note D 2 using the l-punch method is coded as 2B16; a twelfth note Eb5 is coded as 5N12 by the substitute method. Since the computer makes no distinction between en harmonic notes, one method of coding the enharmonic notes is sufficient. For example, Ap4 is exactly the same sound as G; therefore, either the substitute for the flat note

(4J) or the substitute for the sharp note (MG) may be used consistently throughout a composition.

The computer program is limited to a maximum of 2277 notes and rests in any one set of data on a 201 machine.

On a 40K or 60K machine, the program will accomodate an additional 2500 notes per 20K extra memory.

Rest If the note column contains an R, the interpreter will put a rest in the passage. This "rest" is actually a low 15

note or a wavelength slightly less than forty milliseconds. The length of the rest is coded in the same manner as the length of a note. For example, OROM or OR04 represents a dotted quarter note rest.

To eliminate the low note frequency during the rests, a toggle switch on the computer, a telegraph key, or a switch mechanism can be used to prevent the sound from reatihing the tape recorder; however, the sound of the rest will still be monitored through the radio, if it is used. Cutting the relay produces silence on the tape, as indi cated by the VU meter on the tape recorder. The programmer will have to operate the switch for the rests as the com puter is playing the music. The switching must be precise and exactly coordinated with the tempo of the composition.

Period A period (.) in the note column signals the interpreter to stop processing input cards and to proceed to another phase. There are no other numerals or letters before or after the period (b.bb). CHAPTER III

REALIZAT ION PROCEDURES

The procedures discussed in this chapter are the steps

that the composer follows to produce a taped recording of

a computer composition for performance. Each process is an intiggal part leading toward the finished production.

The Composition Process Composing good music is the first important step for generating computer music. After studying the computer input specifications to understand the coding system, the composer must develop ideas and concepts for the composition. Creativity is essential. The composer must have something to say and must select a suitable medium, such as pure com puter music, computer with live performers, piano and com puter, or any other combination. The computer is capable of executing many musical ideas that are not possible with acoustical instruments. The composer must explore the potential of the computer. Melodic material can be played much faster than is humanly possible. The extraordinary variety of rhythm, preciseness, and speed is almost beyond comprehension. Rubato and ac

celerando are easily achieved. Although the 1620 computer plays only one melodic line at a time, harmony may be

16 17

created by rapid alternation of notes. Arhythmic concepts are easily achieved. By studying musical scores, the com poser may develop new ideas for bAa composition.

Along with his ideas and concepts, the composer must decide the type of notation for the composition: graph, chart, or traditional notation. The composer must decide the number of linear materials in the composition; one to several parts can be recorded onto a four-channel tape.

Another possibility is to record as many horizontal lines as needed onto two four-channel tape machines. The per

formance of the latter would be achieved by playing both

tapes simultaneously. To gain computer experience, realizationsA of tra ditional music by other composers may precede the composer's original composition. Practice and experimentation aid in the composer's understanding of the computer's potential. A superb musical composition should be the primary goal for the composer.

*Realization means to transform notes, symbols, graphs, or digits into sound. 2The techniques for generating music from the IB3M 1620 computer were developed by making a computer realization of the J. S. Bach "Little" Fugue in G Minor for organ* This fugue consists of four polyphonic lines which were recorded onto four tape channels from the computer. This study, as well as other exercises, preceded Arabic 1620. 18

The Codification Process

When the composition is completed, the next process is to code every tone, every rhythm, and every event into com puter language according to the input specifications. Through the use of letters, numbers, and symbols on the IBM cards, the computer produces digital signals or tones.3 The codification and card punch procedures may some day be eliminated when a computer is built and perfected to "read" the musical score, translate the notation into computer language, and generate the musical sounds.

The data for the computer should be written horizontally, with eighty bits of information (or less) on one line. At the end of each set of data, a period in the second column of the last field is the signal for the computer to stop processing the input cards. If the period is omitted at the end of each set on the IBM cards, insert, before processing, a final card with a period in the second column. This card may be used for subsequent sets of data.

The input data for Arabic 1620. included in the Ap pendix and is arranged according to channels. Two lines of information represent one card. The spaces between the fields are omitted when the data is typed onto IBM cards.

3Digital signals differ from analog signals. The former signals move rapidly in stairstep progression (LJ m ), whereas analog equipment produces an electrical sweep signal ( ). Both signals achieve the same results as shown in the superimposed illustration ( N).

4 The spaces are used to facilitate the checking of notes. 19

The Card Punch Process

The coded data ae transcribed to punched cards by the IBM 26 Printing Card Punch. These IBM cards, containing the

music data in the form of punched holes, actuate the IBM 1920 computer to perform the composition.

The IBM card is divided into eighty vertical areas

called columns. 5 They are numbered from 1 on the left side

to 80 on the right side of the card. Each column is divided

horizontally into twelve punching positions. The punching positions are designated from the top to the bottom of the

card: one each for the zones 12, 11, and 0, and one each

Digits Letters Chaacter 0 .34%39 ABCDEFGH iJKL 1OPOR 12 Zone 11 Zone ~~0 ~ ~ ~~ ~ ~ ~ ~ ~~~r U 'al 33033003Ela l00 0 b0 UOU 0 l0

34 .6183 3ms. s ns za : 22sn 3332 ea289 4 40 9 4 4.4I3,313331113/J3sa ssaso nu413163138198 1 1 41 111 1 1 1 11 1 1 1111 11111 11 1128 1111111 111 11111 11111111111 11I 11 11 11 111 1111 111.1 11

2 22222222 2222222222222222222222222 2 2 22 22 222222222 2222222 22222 222 2 222 222222 2 2

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

4 444 444 4 4 44 44444 44444 44444 44 4 4 4 4 4 4 4444444 4444444444444444444 4444444444 4444

555 5 5 5 5555 555 5555 5 5555 55 5555 5 5 5555 555555555 5 5 5 5 5 55 5 55 55 5 5555

666666666666666 6 6666666666 6 6 6 6 66666 66 6 6 66 666 6 6 6 6 6 66666 666666

7 7 111177777 7 777777 11 717 7 17777 1777 7771 7771 777717711 1177171111717711

8 8 8 8 8 8 B 8 8 8 8 8 3 88 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 88 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 888 888

99999 99999 99999 99999999999 999999 999 199 9999999999999999999999999999 9999 1 2 J 4 1, 1 18 i. 8 ) VI1 3 2 A021I J 33221A 63 1 . 4 3333 46 , 384 ;4 0 1 S2113 A S 56 51 "8 ' Go6 10 t L 2J'lb b 68 .9!11 I'7 1314 15 16 17 78 79 80

Fig. 6--Punching positions of digits, letters, and the special character on the IBM card.

51BM Systems Reference Library IBM 1620 Fortran (With Format) (San Jose, California, 1963), p. 9. 20

for the digits 1 to 9. Each column of the card is able to accommodate a digit, a letter, or a special character.

Thus the card may contain up to eighty individual pieces of information.

Digits are recorded by punching a single hole in the corresponding digit or zero position of the desired column.

A letter is a combination of one zone punch and one digit punch in the desired colimn as illustrated in Figure 6. Punching of two holes in one column for a letter is auto matic when the corresponding key is pressed. The only special character used in this study is the dash (-). It is punched by pressing the dash key or -SKIP key on the keyboard. The result is an l-punch. It makes no difference if the keyboard is in numeric shift or in alphabetic shift for this special character.

The coded music data is punched by a combination alpha betic and numeric keyboard.

The combination keyboards have the best features of both a typewriter and a numeric keypunch. The letter keys are arranged for operation by the stand ard typewriter touch system, while the digit keys are placed so that a rapid 3-finger touch system can be used. The usual numeric keys on a typewriter have been eliminated; instead, a group of dual purpose keys at the right serves for digit punching as well as letter punching. This permits numeric punching dwith the right hand from the normal home position for alphabetic punching. The touch system for the ten numeric kwys is: index finger for digits 1, 4 and 7; middle finger for digits 2, 5, and 8; and ting finger for digits 0, 3, 6 and 9. The punching of a digit or a letter with any of the combination keys depends on the shift of the key board. For example, pressing the 4-J key punches 21

a 4 when the keyboard is in numeric shift, but a J when in alphabetic shift. This shifting is similar to upper or lower case shifting on a standard typewriter. . . . This section containing the combination keys is readily distinguishable by the blue area of the key plate.

By studying the manual for the card punch machine, a composer may learn to punch his own cards since the process is a relatively easy one for music programs.

The Computer-Recording Process

After the data ha been punched onto IBM cards, the composition is ready to be played and recorded. A detailed operating procedure for the IBX 1620 computer is included in the Appendix. For Arabic 1620 a four-channel tape recorder7 is uti lized to record the composition from the computer. Since the computer generates one melodic line at a time, four channels are used to record the four grand staves of the score. Unlike a four-part Bach fugue in which there would be only four sets of data (one set of cards for each line), Arabic 1620 contains more than twenty sets, since most of the composition contains melodic events. 8

6Reference Manual: IBM 24 Card Punch; IBM 26 Printing Card Punch foughkeepsie, New York, 1965), p. 11. 7 The tape recorder must contain SEL-SYNC, a device to provide synchronization of the musical material. A melodic or musical event is a group of tones heard successively but perceived as one unit. 22

The musical material generated by the computer may be recorded directly from the computer or from an AM radio.

The former method is more desirable since the sound recorded from a radio contains many unnecessary harmonics that pro duce a less desirable sound. If the souwd is recorded onto the tape directly from the computer, the result is a much

"cleaner" production. This process is achievable by making a connection from the E-Time on the computer console through a capacitor (.5 microfarads) and to a spare toggle switch on the computer. The output from the toggle switch is connected to an adapter on a patch cord that leads into the input of the tape recorder. When the toggle switch is up, the ON position, the signals will be recorded. When the switch is OFF or down, the signals are blocked from the recorder but will be heard through the radio speaker. If a radio monitor is not used, a monitoring system should be attached to the outputs Of the tape machine. The composer will use the spare toggle switch to pro vide "rests" on the tape while he reads the score. In addition to operating the toggle switch, the composer must

star* the computer at the precise moment. With the musical

score in a scroll form, crucial page turns are eliminated and the composer is able to read the score in a continuous

linear motion while executing the program. When recording other sets of data sound on sound, a

dominant melodic line on the tape should play through the 23 monitor system and serve as a guide for the entrance of subsequent material. If synchronization is not achieved, the process can be repeated for perfection.

The Modification Process One reason for modifying computer signals is to reduce the metrical, "mechanistic" sound associated with the com puter. This is accomplished by adding dynamics, changes of timbre, reverberation, and modulation. These modifications of the computer signal can be achieved by passing the taped

signals through an analog synthesizer.9 Proper handling of the various modules which make up the synthesizer will produce the desired results. A new system of notationlis utilized to represent the electronic modification. Figure 7 shows the notation for reverberation, and the notation in Figure 8 represents white noise or white sound.

9The analog sound synthesizer used in this process is an Ellis-II Performance System, built by the R. A. Moog Company of Trumansburg, New York. The system consists of the Moog "900 Series" modular instruments plus several special features which adapt these instruments to real time performance. 1 Similar notational practices preceded this study in the author's symphonic composition Eni Rhapsody for Orchestra and Eive Electronic Instruments. 24

Fig. 7--Notation for reverberation

Fig. 8--Notation for white noise

There are several ways of notating modulated signals, as shown in Figures 9, 10, and II. The degree of modu lation may vary from slight to extreme modulation.

Fig. 9--Oblique modulated signal upward

Fig. 10-Oblique modulated signal downward

Fig. Il--Modulated signal in contrary motion 25

Another purpose of modifying tape sounds could be to

achieve envelope control of the signals. The envelope control of attack and decay is related with the aesthetic qualities that most musicians associate with music. When modifying the tape sounds, each channel of the tape recorder may be modified separately, or a combination

of channels may be modified simultaneously. Another poso sibility is to modify all the channels at once, in which case the various channels will be modified alike.

When the modification process is completed, this is the finished composition, and it is ready for performance.

"Envelope is the contour of the change in a signal variable (usually amplitude) as a function of time. CHAPTER IV

ANALYSIS OF ARABIC 1620

Arabic 1620 is an original composition for the IBM 1620 computer. The composition is in ternary form, following the scheme A B A. It may be considered the sum of three single parts, each of which is complete within itself. The two A sections contain melodic materials that maintain a steady tempo, especially the final movement, which drives vigorously to a climactic ending. The contrasting B section consists of melodic events and is more rhapsodic in nature than the two A sections.

Much of the composition is based on twelvemtone tech nique, but it is not restricted to the use of the four forms of the row and their transpositions.

Fig. 12--Original row and theme

26 27

The introduction contains the original row in Channel IV but in a different rhythm from the theme in the A section. After this statement, the melody progresses from two notes per beat to ten notes per beat, giving the effect of in

creasing the tempo. With a gradual crescendo during this

time, a climax is reached before the main theme is announced in Channel I. The theme of A section is composed of all twelve tones. It is followed by a transposition of the original row in a different rhythm. A chromatic descent of two and one-half octaves precedes the next inverted and transposed melodic row in Channel II. There is a transition between sections

A and B in Channels II and IV which incorporate a wide variety of rhythmic patterns.

The B section employs various events performable only by the computer. It is improbable that an orchestral per former would be able to play the events in this section for several reasons: a lack of range on his instrument; the rapidity of the notes, up to twenty-four in one beat; in

sufficient dexterity control; extreme leaps, up to three

octaves. This free and atonal movement utilizes several

forms of the row. Even the original row occurs once, but

in an indiscernible manner. 28

Fig. 13--Original row in B section

The first event in this section represents a mirror inversion and retrograde of the exponential envelope design with an accelerando.

Fig. 14-Design of a mirrored exponential envelope

Harmony on Uhannel I is created by alternating between notes very rapidly. The pattern begins with an interval of a twenty-eighth and moves to a unison C4i. The design is shown in Figure 15.

Another rapid alternation occurs in the B section between the minor second interval in the lowest register of the com puter. These twenty-four notes in one beat will be heard

1 These two lowest notes on the computer are G#0 and A,, which correspond to the lowest note on the piano key beard and a half-step below the keyboard. 29

Fig. 15--Design showing rapid alternation between notes to create harmony, starting wide and moving to unison.

as one low tone. The following event begins on E 4 , repeats with an accelerando, and gradually widens to almost five octaves.

An 45 on Channel I begins very softly in the B section and gradually increases in volume. This note serves as a unifying element. Its penetration may be annoying to the listener, yet it serves another purpose by adding tension to the development leading to the final A section.

The final melodic event of B section forms a transition into the final A section. Channel III begins with triplet quarter notes of the transposed retrograde inversion of the original row. Channel II follows with the same three notes but in diminution, as shown in Figure 16. This transition 30

IL I "Was

Fig. 16--The first three notes of Channel II in dimi nution of Channel III. uses duplets against triplets, triplets against quadruplets and sextuplets, and quadruplets against sextuplets. The rhythmic complexity at the conclusion of B section adds tension and resolves to an ostinato pattern in Channel III based on the first eight notes of the original row.

IW ANN, I v

lip r w

Fig. 17~-Original row used as ostinato

After three beats of the ostinato pattern, the theme appears in its original form on Channel II. When the trans posed row follows the original theme, the ostinato ascends 31 a half step. It then ascends a whole step one beat prior to the entrance of Channel IV, which is a perfect fifth below the melody on Channel II. After six beats in par allel motion, Channels II and IV merge from a one-beat transition into unison for three beats. A chromatic ascent in seconds over four beats contains seven notes in the first beat, eight notes in the second, nine notes in the third, and ten notes in the fourth beat. This ascent resolves to dotted half perfect fourths sfp with a cre scendo, ending fff in octave G's (G2 and G3)* Accidentals in the score affect only the notes they precede. Numerals above notes indicate their duration and are entered in the length columns of the fields. The ratios refer to the number of notes that occur in a certain number of seconds. For example, 12:2 means that there are twelve tones in the space of two seconds. The Roman numerals between the clef signs denote the particular channel. The

Arabic numerals to the left of the braces correspond to the card numbers in the Input Data of the Appendix.

In Arabic 1620, the melodic interval of a minor second occurred most frequently. Table I shows the number of times each melodic interval was used and is interpreted in per centages. The least used interval is the major third, which occurs fourteen times out of 1110 melodic intervals, or

1.3. Many chromatic passages account for the high per centage of minor seconds. 32

TABLE I

HORIZONTAL INTERVAL FREQUENCIES AND PERCENTAGES

NUMber of Times Interval* Interval Was Percentage Used

unison.17 1.5% Minor Second ...... 407 36.7% MTajor Second ...... 92 8.3% 322.9% Minor Third. . . . 3 Major Third...... 14 1.3% Perfect Fourth . . . . - . . 111 10.00% Tritone...... 242 21.8% Perfect Fifth...... 46 4,1% Minor Sixth...... 18 1.6% Major Sixth...... 44 4.0% Minor Seventh...... 2018% Major Seventh...... 67 6.0%

*Compound intervals were reduced to their simple forms. The intervals were also based on their sound--not on their spelling (for example, a diminished seventh sounds as a major sixth). Intervals between quarter rests and larger are not included since the listener is more likely to re tain the intervallic relationship between eighth and six teenth rests.

Most of this analysis has been concerned with melodic material at the expense of harmony. Harmonic structures

in the A sections were written to accompany melodic activity and are somewhat subservient to the melodic line. The usage of vertical intervals is consistent with the usage of horizontal intervals. The five most frequently used melodic intervals also dominate the harmonic structure. APPENDIX

33 DETAIIEJD OPERATING PROCEDURE

FOR THE IBM 1620 COMPUTER

1. Set all console check switches to STOP and set program switch OFF. 2. Load the interpreter (object deck). a. Stop the computer, if it is running, by pressing the SIE or SCE key. b. Press RESET. c. Clear the 1622 read hopper and press NON-PROCESS RUNOUT. Place the object deck in the read hopper (to the right of the 1622) face down. The input data to be played may be placed behind the object deck if desired. d. Press LOAD. e. If only the object deck was placed in the read hopper, the READER NO FEED light will go on with two cards still in the reader. Press READER START.

3. Place an AM radio receiver on the 1620 console either in front of the console check switches or on top of the console. Turn on the radio. Now press START on the console. The interpreter will begin playing middle C (C4). Tune the radio to the position that gives the most desirable tone. If the computer stops playing the note before finishing the tuning, press START again. When the radio is tuned satisfactorily, press STOP/SIE. 4. Phase 1: compile input data. a. Set program switch 1,* and set switch 4 OFF. (Switches 2 and 3 are not used by the interpreter.) bVi Press, in order, INSERT, RELEASE, START on the console.

*Tempo switch option: As explained under the description of tempo fields in Chapter II, at various times the interpreter reads a tempo from the input cards. If the console switch 1 is OFF, the interpreter then goes on to precess the next field. If switch 1 is ON, the program returns the carriage on the typewriter and waits for entry of a new tempo. As the digits of the tempo are entered, they overlay the tempo just read from the tempo fikld. As many as six digits can be specified. If fewer than six are typed in, the low-order digits of the tempo will be the ones read from the tempo field and the two low-order zeros.

34 35 c. If switch 1 is ON, follow the directions under the "tempo switch option" in the footnote for entering the tempo when the carriage on the typewriter is returned. d. If READER NO FEED light comes on, push READER START (after placing the input cards in the reader hopper, if this has not been done previously). (If all the cards of the input data have been read, and the READER NO FEED light goes on, a period was omitted after the last note of the data. Feed through the read hopper another card with a period in column 2.) 5. Phase 2: press START on the console to play the data. 6. Restart procedure: to play the same data again, press START; to process a new set of data or melodic material, follow step 4.

Do t type in the decimal point before the tempo. This will be supplied by the interpreter. The high-order digit may be flagged, but need not be. If more than six digits are typed in, the low-order digits will be ignored. Switch 4 must be OFF before R-S is typed, unless an error was made in typing. If an error was made, turn switch 4 ON, type R-S, turn switch 4 OFF, and retype the tempo. (Note: the digits typed in the second time will overlay the tempo read from the tempo field, as before. They will not overlay the digits typed in the first time. These will be completely ignored.) INPUT DATA OF ARABIC 1620

Channel I

Card 1 4ECJ 2 4A04 4NCOM 4308 4J16 OR16 3316 OR16 LFOM 4EOM 5M12 NF16 CR16 4K08 N0124F12 5012 4GOK 5004 4BOM 4F08 3 NGC8 KD12 NC12 5G12 5D02 4A08 4KOM 4EOK 4 4116 5 6064 5B64 5F64 5E64 4K64 4A64 4P64 4F64 KD04 6 5A44 5N44 5D44 5J44 4B44 5P44 5E44 MA44 5F44 5044 NC44 5G16 CR16 CR08 CR02 0A08 JD09 1E10 1K12 7 2G14 3C16 3D18 LG20 MC22 MF24 5F26 5B32 6032 5B32 5B32 6032 5B32 6032 5B80 2080 5380 2080 5380 8 5380 2080 5B80 2080 5B80 2080 5380 2080 5K84 2E84 5K84 2E84 5K84 2E84 5K84 2E84 5K84 2E84 5K84 9 2E84 5K84 3D88 5E88 3D88 5E88 3D88 5E88 3D88 5E88 3D88 5E88 3D88 4G90 LG90 4G90 LG90 4G90 LG90 4G90 10 LG90 4D9 6 4096 439 6 4096 MC02 OR01 NA01 NA01 NAOJ NA01 NA01 NAGa NAOI NAOJ

Channel II

Card

1 3BOJ 2 LF49 3 4J60 4G60 4P60 4F60 4360 4N60 4360 4M60 4060 3360 3K60 3A60 3J60 3G60 3P60 3F60 3E60 3N60 3D60 4 3M60 3060 2360 2160 2A60 2J60 2060 2P60 2F60 2E60 2N60 2DOM 3J 12 2A12 2N12 2016 OR16 4FOM 3GOM MC16 5 OR16 MF08 4316 OR16 4KO1M 4EOM 4F08 MF1C 4G12 MG14 4A16 MA18 4320 5022 NC24 5D26 ND28 5E30 5F04 5P06 6 5006 MC06 1116 4A04 4E04 LF12 4012 4F12 MF16 4016 4M16 3F16 3E08 4324 4A24 ND24 5A08 5G16 5P16 5F08 7 5B08 5E0Q 5K16 5012 4B12 4F12 4E08 4F48 3048 3F48 LA48 4A48 ND48 5A08 5D0Q NC16 5016 4K16 4FOQ 4DOQ 8 5A16 5E24 5B24 6C24 NFOI 9 3A16 3B16 OR08 OR04 LF16 4016 OR08 OR02 4012 412 4E12 4K20 MF20 4B20 5Y, 20 4020 @0.96 0A9 6 @996 10 0A96 G96 0A9 6 QG96 OA9 6 @996 OA9 6 @0.96 OA9 6 @996 0A96 096 0A9 6 QG96 0A9 6 @0.96 0A9 6 @996 OA9 6 @996

36 37

Card

11 (DUPLICATE) 12 (DUPLICATE) 13 0A96 OG96 0A96 @Q96 OA9 6 OG96 0A96 Q96 0A96 @Q08 OR08 OR02 4E02 4E04 4E06 4E06 4E06 4E08 4E08 4E12 14 T012 4E12 412 4E12 4M12 4E16 4016 4E16 3B16 4E24 3A24 4E24 3G24 4E24 3F24 4E26 3D28 4F30 2A32 4G34 15 2E36 MA38 2D40 NC42 1K44 NF46 JC48 6016 OR16 OR08 OR01 5A12 TD12 5E12 4312 4P12 4012 4Q12 4N12 4112 16 M012 4A12 4G12 4F16 4116 4K16 MD16 4J16 4N16 MC16 4K16 416 4016 4D16 416 4A24 4P24 4F24 4B24 MF24 17 5024 4K24 4F24 MG24 5D24 5M24 4Q24 4Q24 5M24 5024 5F24 MA24 5E24 5F24 5K24 5J24 5D24 ND24 5A24 ORO 18 4A04 4NOM 408 4J16 OR16 3B16 OR16 LFOM 4E04 4K08 4F12 5012 5M12 4GOK 5P16 0R16 5004 4BOM 4F08 5J08 19 5N12 NC12 5G12 5D16 5016 4P16 4F16 3B20 4020 L020 3D20 2Q20 2A04 LDO 3E08 KA08 3A08 4GOM MG08 5012 20 4B12 4K12 4A12 4N12 4012 4J16 4G16 5P16 5E16 5K20 5F20 5020 NC20 5G20 2A28 KA28 2328 3028 L028 3D28 21 LD28 3E32 3F32 LF32 3G32 LG32 3A32 LA32 3B32 4032 MC32 4D36 M36 4E36 436 MP36 4G36 MG36 4A40 MA40 22 I 4B40 5040 NC40 5D40 ND40 5E40 5F40 NF40 5GOK 3G16

Channel III

,Card 1 3A0J 2 5026 51A'26 4Q26 4P26 31326 4E36 3K36 3J36 3P36 3D40 KG40 2B40 3D40 3F40 2B40 3040 2Q40 3D40 KG40 3 K1F0J 4 4EOK 5 5J24 5G24 6024 4B24 NC24 4Q24 3P24 3N24 3A24 2K24 3E24 2N24 OR04 2E32 2A32 3E32 3A32 4E32 4A32 6 5E32 5A32 7 @G01 8 2F64 KF64 3064 L064 3G64 LG64 4D64 MD64 4F04 9 MD16 4A16 OR08 OR04 4J16 4116 OR08 OR02 1F12 4112 4112 5E20 5020 5F20 5G20 5M20 QG96 0A96 OG96 10 OA96 QG96 0A96 QG96 OA9 6 OG96 0A96 QG96 OA96 OG96 OA96 G96 OA96 QG96 0A9 6 OG96 OA96 QQ96 0A96 OG96 11 (DUPLICATE) 12 (DUPLICATE) 13 0A96 OQ96 OA96 QQ96 0A9 6 OG96 OA96 QG96 OA96 GG08 14 5A06 ND06 5E06 4B08 4P08 4008 4K08 408 LG08 mD08 5M08 4G12 4M12 4012 MF12 4A12 4E12 4112 MG12 15 5N12 MA12 4B12 412 N016 5D16 IG16 5F16 4K16 5016 5P16 4316 5E16 51)16 5A16 38

Card 16 5N32 5D32 5J32 4B32 4P32 3E32 KA32 5A32 17 (DUPLICATE) 18 (DUPLICATE) 19 (DUPLICATE 20 DUPLICATE 21 (DUPLICATE 22 DUPLICATE) 23 DUPLICATE) 24 IDUPLICATE) 25 DUPLICATE) 26 DUPLICATE) 27 DUPLICATE) 28 5N32 5D32 5J32 4B32 4P32 3E32 2K32 1A32 OB44 1F44 JF44 KC44 KG44 3D44 4C44 4G44 ND44 5E44 5K44 29 5E32 ND32 A32 5C32 4G32 3F32 2B32 5K32 30 (DUPLICATE 31 (DUPLICATE 32 DUPLICATE) 33 5E32 5N32 5A32 5C32 4G32 3F32 2332 lK32 JC48 lG48 JF48 2q48 KD48 KA48 LG48 4D48 4A48 4E48 4F48 6C48 34 5P32 5F32 5B32 5D32 4A32 3G32 LC32 6C32 35 (DUPLICATE 36 DUPLICATE 37 (DUPLICATE 38 (DUPLICATE) 39 (DUPLICATE) 40 (DUPLICATE) 41 (DUPLICATE) 42 (DUPLICATE) 43 DUPLICATE) 44 DUPLICATE)

Channel IV

Card

1 5A06 51406 4A-06 OR04 OR08 5J08 4312 MF12 5E12 4K16 4F16 4016 4M16 3GO4 OR02 4B08 4F08 4E12 4A12 2 4D12 3J16 2K'16 3N16 3C16 LF20 3G20 L020 2B20 2F20 KF24 L024 KG24 3D24 3C24 3G24 3K28 3E28 LD28 3A28 3 3K28 3E28 4128 3B32 MG 32 MC32 1v32 4A32 432 4G32 1F32 5C36 5D:36 4G36 MG36 5D36 4B36 5E36 NF36 5C36 4 5F40 5K40 5A40 5N40 NC40 5G40 NF40 5B40 5E40 NA40 6C0J 5 4G32 MG32 4A32 432 3G32 MD32 5E32 6032 OR08 5B32 5N32 4K34 4D32 3P32 3C32 2B32 2F32 CR08 CR02 6 MGO2 OR04 5C02 39

Card, 5024 4B24 5F24 NC02 B16 8 4DOM 3B08 3K10 3A12 3J14 3G16 3P18 3F20 3E22 3N24 3D26 3M28 3030 2B04 9 3E04 2006 3D06 3F06 I1G01 4004 41)08 3F08 3112 3A12 1012 4E08 KF48 3048 3F48 LA48 4A48 ND48 5J08 10 5D08 4COM 5P12 4G12 4012 4A16 MD08 MGO8 4K08 4F16 4E08 4316 5002 4E04 4113 4E14 4115 4E16 4M17 4E18 11 4019 4E20 3B22 4E24 3K26 4E28 3A30 4E32 3G34 4E36 3N38 4E40 2B42 4E44 2K46 4E48 2P50 4E52 2D54 4E56 12 IC58 4E60 1J 62 4E64 1F08 13 5D48 MG48 4A48 5E48 3348 3F48 LD48 LA48 MC48 4G48 NF48 6048 14 MG02 15 2DO4 KGOM 2A08 KFO8 3108 400M MC08 D12 4F12 MG12 4A12 4N12 40)12 4J16 4G16 5P16 5E16 5K20 5F20 16 5020 NC20 5G20 2G28 KG28 2A28 KA28 2B28 3028 1028 3D32 LD32 3E32 3F32 LF32 3G32 1G32 3A32 LA36 3336 17 4036 M36 4036 MD36 4E36 4F36 MF36 4G40 MG40 4A40 MA40 4B40 5040 NC40 5D40 1D40 5E40 4DOK 2G16 BIBLIOGRAPHY

IBM Systems Reference Library, IBM 1620 Fortran (With For mat), Form C26-5619-4, San~Jose,~California,~Inter~~ national Business Machines Corporation, 1963. Reference Manual: IBM j Card Punch; IM 26 Printing Card Punch, Edition A24-0520-m3, Poughkeepsie, New York, International Business Machines Corporation, 1965. Smiley, Richard F., "Music Interpreter," abstracted from IBM Systems Reference Library, Catalog of Programs for IBM 1620 and 1710 a Process* Systems, Form C20Ti-3-7,m Hawthorne, New York, International Busi ness Machines Corporation, 1967.