Slope Songs on the HP48

© 1997, Agnes Azzolino, MATHEMATICAL CONCEPTS, inc., Keyport

Using the HP48 you can hear a slope.

Feel free to use this material for nonprofit purposes as long as the source is noted.

The HP48 permits one to hear a slope, other than that of a vertical line, by using the BEEP command - the same beep that sounds on the HP48 when the user makes an error. One may use the notes of one octave, as vertical increments and the duration as horizontal increments to represent slope, the ratio of vertical change to horizontal change.

The slope, a number, is entered on the stack. The SS for "Slope Song" key is pressed. The slope of that number BEEPs its way into the ears of the user.

Before all this happens, the user must prepare the calculator by storing five things: a unit constant for the duration of a note, three vectors of constants for NEGative, ZERo, and POSiTive slopes, and of course SS, the "Slope Song" program.

STEP 1:

To adjust the length the time a note is sounded, N is used. As an initial value store .3 for N. You may adjust this later to suit yourself. STORE .3 AS "N" IN THE HP48.

STEP 2:

The frequency of the notes of the musical scale --

C4 = 262, D4 = 294, E4 = 330, F4 = 349,

G4 = 392, A4 = 440, B4 = 494, C5 = 524

-- must be stored in the calculator as three vectors.

STORE EACH OF THE FOLLOWING VECTORS IN THE HP48.

NEGT = [262 294 330 349 392 440 494 524]

ZER = [262 262 262 262 262 262 262 262]

POST = [524 494 440 392 349 330 294 262]

STEP 3:

The program SS must be stored. The program is printed below and is arranged on lines so that the programming can be read, The program creates a subprogram with its own dummy variables. The subprogram checks, though SIGN, the sign of the variable M, the slope, and evokes the commands SAME and CASE to select the desired list of frequencies. It takes the reciprocal of the slope, dilates it by N, and stores this as the "change in x" value. It BEEPs 8 times - "sings the slope."

STORE THE PROGAM SS.

SS is:

<< DUP 'M' STO Y

<< CASE

Y SIGN 0 SAME THEN

ZER OBJ DROP 1 'M' STO END

Y SIGN 1 SAME THEN

POST OBJ DROP END

Y SIGN -1 SAME THEN

NEGT OBJ DROP M -1 'M' STO END

END >>

M 1/X N 'M' STO

M BEEP M BEEP M BEEP M BEEP

M BEEP M BEEP M BEEP M BEEP >>

STEP 4:

Check MODE to be sure that BEEP is toggled ON rather than toggled OFF.

STEP 5:

Type the desired slope and press the SS key.    MATHEMATICAL CONCEPTS, inc.

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