Magic Square Version 4.0 was written in 1985 shortly after I got my Mac and Microsoft Basic as an exercise to teach myself Basic programming. It comes with no warranties, expressed or implied. It has been tested on a Mac Plus and a Mac SE and comes through with flying colors. This program is absolutely free and may be distributed in its original form with no obligation to the author, who retains the copyright. The program was compiled in Microsoft Quick Basic, which explains its rather bloated size. Feedback etc. may be sent to the author: David Rakowski, 51 Big Tree Way, Woodside, CA 94062. Donations, for those so inclined, may be sent to the Music Department, Stanford University, Stanford, CA 94305.
A "magic square" (also sometimes wrongly called a "Babbitt square") is a compositional tool for 12-tone composers. The square presents a visual 12-by-12 matrix based on a 12-tone set such that all 12 possible transpositions of the original set are available reading rows left to right, all 12 possible retrogrades reading rows right to left, all 12 possible inversions reading columns down, all 12 possible retrograde inversions reading columns up. This program will generate, and print, such a 12-by-12 matrix given any set entered by the user.
Magic Square presents two basic screens: the row entry screen and the matrix screen. The following options are available on the row entry screen: Notes may sound or not sound when they are "played" (not sounding is the default); notes may disappear or dim after they are selected (this prevents any tone from being repeated: the default is for notes to disappear); a row may be entered one note at a time or a row from a piece by Babbitt, Bauer, Berg, Schoenberg or Rakowski may be chosen from a menu. As each new note is entered, the row is displayed below the "keyboard;" clicking on the musical notation will play the note displayed where the click is made.
After a complete row is entered, the matrix screen is displayed. One window shows the frequency of melodic intervals (expressed in semitones) in the row. Another window shows the interval vector for the two hexachords of the row (the statistical occurrence of interval classes between any two notes of a hexachord; note that the interval vector is ALWAYS the same for both hexachords of a 12-tone set). The large window displays the matrix with several buttons and a musical notation representation of the set. Clicking on the staff plays the note where the click is made. Clicking anywhere except the first row of the matrix transposes the matrix to that pitch level. Clicking on buttons Row, Retrograde, Inversion, or Retrograde Inv. will play the row representing the particular transformation. Clicking on the M5 button transforms the set by multiplying the pitch class numbers by five (this is equivalent to mapping the chromatic scale to the circle of fifths) and presents a completely new set. Clicking the Copy button puts a PICT version of the set onto the clipboard so it may be put into the scrapbook or into any drawing/painting program. The Sclip button merely shows the contents of the clipboard. The Print Screen button sends a screen dump to an ImageWriter printer, if one is connected. The Print button will print the matrix and the intervallic information, and prompts you for a description of the matrix (such as "My Set" or something equally clever) to appear on the printout.
This program could be useful to undergraduate music students who have to write 12-tone pieces in an otherwise well-meaning class, or to twelve-tone composers looking for relationships between set forms. If none of the above descriptions mean anything to you, there is little you can get out of this program.
