T.TEMPERED FUN
FILE INFORMATION
FILENAME(S): T.TEMPERED FUN
FILE TYPE(S): PRG
FILE SIZE: 5.9K
FIRST SEEN: 2025-11-30 18:12:17
APPEARS ON: 1 disk(s)
FILE HASH
2095a3a61b50dda312c4217cb1862600cc1d21aed0b2e5909b9e81831535899c
FOUND ON DISKS (1 DISKS)
| DISK TITLE | FILENAME | FILE TYPE | COLLECTION | TRACK | SECTOR | ACTIONS |
|---|---|---|---|---|---|---|
| LOADSTAR 50 S 2 | T.TEMPERED FUN | PRG | Sailor, Ganheden | 25 | 1 | DOWNLOAD FILE |
FILE CONTENT & ANALYSIS
00000000: 00 80 5E 55 3A 43 42 4D 0D 20 20 20 20 20 20 D4 |..^U:CBM. .| 00000010: 20 C5 20 CD 20 D0 20 C5 20 D2 20 C5 20 C4 20 20 | . . . . . . . | 00000020: 20 C6 20 D5 20 CE 0D 0D 20 20 20 20 20 20 20 20 | . . ... | 00000030: 20 42 59 20 D0 41 55 4C 20 D2 2E 20 CD 41 43 48 | BY .AUL .. .ACH| 00000040: 55 4C 41 0D 0D 20 20 20 20 D4 48 4F 55 47 48 20 |ULA.. .HOUGH | 00000050: 49 54 20 4D 41 59 20 4E 4F 54 20 53 45 45 4D 20 |IT MAY NOT SEEM | 00000060: 4F 42 56 49 4F 55 53 20 41 54 0D 46 49 52 53 54 |OBVIOUS AT.FIRST| 00000070: 2C 20 4D 55 53 49 43 20 41 4E 44 20 4D 41 54 48 |, MUSIC AND MATH| 00000080: 45 4D 41 54 49 43 53 20 41 52 45 0D 50 52 41 43 |EMATICS ARE.PRAC| 00000090: 54 49 43 41 4C 4C 59 20 4F 4E 45 20 41 4E 44 20 |TICALLY ONE AND | 000000A0: 54 48 45 20 53 41 4D 45 2E 20 20 D4 48 41 54 27 |THE SAME. .HAT'| 000000B0: 53 0D 57 48 59 20 49 54 27 53 20 4E 4F 20 57 4F |S.WHY IT'S NO WO| 000000C0: 4E 44 45 52 20 54 48 41 54 20 4F 4E 45 20 4F 46 |NDER THAT ONE OF| 000000D0: 20 54 48 45 0D 46 49 52 53 54 20 41 50 50 4C 49 | THE.FIRST APPLI| 000000E0: 43 41 54 49 4F 4E 53 20 4F 46 20 54 48 45 0D 4D |CATIONS OF THE.M| 000000F0: 41 54 48 45 4D 41 54 49 43 41 4C 20 43 41 50 41 |ATHEMATICAL CAPA| 00000100: 42 49 4C 49 54 49 45 53 20 4F 46 20 54 48 45 0D |BILITIES OF THE.| 00000110: 43 4F 4D 50 55 54 45 52 20 57 41 53 20 49 4E 20 |COMPUTER WAS IN | 00000120: 43 52 45 41 54 49 4E 47 20 4D 55 53 49 43 2E 20 |CREATING MUSIC. | 00000130: 20 D4 48 49 53 0D 45 58 43 45 4C 4C 45 4E 54 20 | .HIS.EXCELLENT | 00000140: 50 52 4F 47 52 41 4D 20 41 4C 4C 4F 57 53 20 59 |PROGRAM ALLOWS Y| 00000150: 4F 55 20 54 4F 20 44 4F 0D 54 48 49 4E 47 53 20 |OU TO DO.THINGS | 00000160: 57 49 54 48 20 4E 4F 54 45 53 20 41 4E 44 20 53 |WITH NOTES AND S| 00000170: 43 41 4C 45 53 20 54 48 41 54 0D 50 52 45 2D 43 |CALES THAT.PRE-C| 00000180: 4F 4D 50 55 54 45 52 20 4D 55 53 49 43 49 41 4E |OMPUTER MUSICIAN| 00000190: 53 20 41 4E 44 20 4D 55 53 49 43 41 4C 0D 53 43 |S AND MUSICAL.SC| 000001A0: 48 4F 4C 41 52 53 20 57 4F 55 4C 44 20 48 41 56 |HOLARS WOULD HAV| 000001B0: 45 20 43 55 54 20 4F 46 46 20 54 48 45 49 52 0D |E CUT OFF THEIR.| 000001C0: 45 41 52 53 20 54 4F 20 48 41 56 45 20 42 45 45 |EARS TO HAVE BEE| 000001D0: 4E 20 41 42 4C 45 20 54 4F 20 44 4F 2E 0D 0D 20 |N ABLE TO DO... | 000001E0: 20 20 20 D4 C5 CD D0 C5 D2 C5 C4 20 C6 D5 CE 20 | ........ ... | 000001F0: 4D 41 4B 45 53 20 49 54 20 45 41 53 59 2E 0D 0D |MAKES IT EASY...| 00000200: 20 20 20 20 C2 45 46 4F 52 45 20 C9 20 47 4F 54 | .EFORE . GOT| 00000210: 20 49 4E 54 4F 20 43 4F 4D 50 55 54 45 52 53 2C | INTO COMPUTERS,| 00000220: 20 C9 0D 57 41 53 20 41 20 4D 55 53 49 43 49 41 | ..WAS A MUSICIA| 00000230: 4E 20 41 4E 44 20 4F 43 43 41 53 49 4F 4E 41 4C |N AND OCCASIONAL| 00000240: 20 50 49 41 4E 4F 0D 54 55 4E 45 52 2E 20 20 C9 | PIANO.TUNER. .| 00000250: 20 46 49 52 53 54 20 4C 45 41 52 4E 45 44 20 54 | FIRST LEARNED T| 00000260: 4F 20 54 55 4E 45 20 42 59 0D 45 41 52 20 42 55 |O TUNE BY.EAR BU| 00000270: 54 20 57 48 45 4E 20 54 48 45 20 50 52 49 43 45 |T WHEN THE PRICE| 00000280: 20 4F 46 20 45 4C 45 43 54 52 4F 4E 49 43 0D 54 | OF ELECTRONIC.T| 00000290: 55 4E 45 52 53 20 43 41 4D 45 20 44 4F 57 4E 20 |UNERS CAME DOWN | 000002A0: 54 4F 20 41 20 52 45 41 53 4F 4E 41 42 4C 45 0D |TO A REASONABLE.| 000002B0: 4C 45 56 45 4C 20 28 41 52 4F 55 4E 44 20 31 39 |LEVEL (AROUND 19| 000002C0: 37 35 29 20 C9 20 53 54 41 52 54 45 44 20 55 53 |75) . STARTED US| 000002D0: 49 4E 47 0D 4F 4E 45 20 4F 46 20 54 48 45 4D 20 |ING.ONE OF THEM | 000002E0: 54 4F 20 53 45 54 20 54 48 45 20 54 45 4D 50 45 |TO SET THE TEMPE| 000002F0: 52 41 4D 45 4E 54 20 4F 46 0D 54 48 45 20 46 49 |RAMENT OF.THE FI| 00000300: 52 53 54 2C 20 41 4E 44 20 4D 4F 53 54 20 44 49 |RST, AND MOST DI| 00000310: 46 46 49 43 55 4C 54 2C 20 4F 43 54 41 56 45 0D |FFICULT, OCTAVE.| 00000320: 4F 4E 20 41 20 50 49 41 4E 4F 2E 20 20 C9 54 20 |ON A PIANO. .T | 00000330: 53 45 45 4D 45 44 20 54 4F 20 4D 45 20 54 48 41 |SEEMED TO ME THA| 00000340: 54 20 54 48 45 0D 48 55 4D 41 4E 20 45 41 52 20 |T THE.HUMAN EAR | 00000350: 57 41 53 20 4E 4F 20 4D 41 54 43 48 20 46 4F 52 |WAS NO MATCH FOR| 00000360: 20 41 20 4D 41 43 48 49 4E 45 0D 57 48 45 4E 20 | A MACHINE.WHEN | 00000370: 49 54 20 43 41 4D 45 20 54 4F 20 43 4F 55 4E 54 |IT CAME TO COUNT| 00000380: 49 4E 47 20 56 49 42 52 41 54 49 4F 4E 53 2E 0D |ING VIBRATIONS..| 00000390: 0D 20 20 20 20 C8 4F 57 45 56 45 52 2C 20 54 48 |. .OWEVER, TH| 000003A0: 45 52 45 20 49 53 20 41 20 53 43 48 4F 4F 4C 20 |ERE IS A SCHOOL | 000003B0: 4F 46 0D 54 48 4F 55 47 48 54 20 54 48 41 54 20 |OF.THOUGHT THAT | 000003C0: 53 41 59 53 20 54 48 41 54 20 53 49 4E 43 45 20 |SAYS THAT SINCE | 000003D0: 4D 55 53 49 43 20 49 53 0D 54 4F 20 42 45 20 48 |MUSIC IS.TO BE H| 000003E0: 45 41 52 44 20 42 59 20 48 55 4D 41 4E 20 45 41 |EARD BY HUMAN EA| 000003F0: 52 53 2C 20 54 48 45 20 54 55 4E 49 4E 47 0D 49 |RS, THE TUNING.I| 00000400: 53 20 42 45 53 54 20 41 43 43 4F 4D 50 4C 49 53 |S BEST ACCOMPLIS| 00000410: 48 45 44 20 42 59 20 48 55 4D 41 4E 20 45 41 52 |HED BY HUMAN EAR| 00000420: 53 2E 0D D3 4F 20 C9 20 47 55 45 53 53 20 C9 20 |S...O . GUESS . | 00000430: 53 48 4F 55 4C 44 20 53 41 59 2C 20 41 20 4D 41 |SHOULD SAY, A MA| 00000440: 43 48 49 4E 45 0D 43 41 4E 20 43 4F 55 4E 54 20 |CHINE.CAN COUNT | 00000450: 56 49 42 52 41 54 49 4F 4E 53 20 42 45 54 54 45 |VIBRATIONS BETTE| 00000460: 52 20 54 48 41 4E 20 CD D9 0D 45 41 52 53 2E 0D |R THAN ...EARS..| 00000470: 20 20 20 20 C8 41 56 45 20 59 4F 55 20 45 56 45 | .AVE YOU EVE| 00000480: 52 20 57 4F 4E 44 45 52 45 44 20 57 48 59 20 54 |R WONDERED WHY T| 00000490: 48 45 52 45 0D 41 52 45 20 45 49 47 48 54 20 4E |HERE.ARE EIGHT N| 000004A0: 4F 54 45 53 20 49 4E 20 41 4E 20 4F 43 54 41 56 |OTES IN AN OCTAV| 000004B0: 45 3F 20 20 D7 45 0D 49 4E 53 54 49 4E 43 54 49 |E? .E.INSTINCTI| 000004C0: 56 45 4C 59 20 43 41 4E 20 54 45 4C 4C 20 49 46 |VELY CAN TELL IF| 000004D0: 20 4F 4E 45 20 4E 4F 54 45 0D 48 41 53 20 41 20 | ONE NOTE.HAS A | 000004E0: 46 52 45 51 55 45 4E 43 59 20 4F 46 20 54 57 49 |FREQUENCY OF TWI| 000004F0: 43 45 20 41 4E 4F 54 48 45 52 20 4E 4F 54 45 0D |CE ANOTHER NOTE.| 00000500: 41 4E 44 20 57 45 20 53 41 59 20 54 48 41 54 20 |AND WE SAY THAT | 00000510: 54 48 45 53 45 20 4E 4F 54 45 53 20 41 52 45 20 |THESE NOTES ARE | 00000520: 41 4E 0D 4F 43 54 41 56 45 20 41 50 41 52 54 2E |AN.OCTAVE APART.| 00000530: 20 20 D7 48 45 4E 20 59 4F 55 20 53 49 4E 47 20 | .HEN YOU SING | 00000540: 54 48 45 20 57 4F 52 44 0D 22 D3 4F 4D 45 2D 57 |THE WORD.".OME-W| 00000550: 48 45 52 45 22 20 49 4E 20 54 48 45 20 53 4F 4E |HERE" IN THE SON| 00000560: 47 20 22 CF 56 45 52 20 54 48 45 0D D2 41 49 4E |G ".VER THE..AIN| 00000570: 42 4F 57 22 20 59 4F 55 20 41 52 45 20 53 49 4E |BOW" YOU ARE SIN| 00000580: 47 49 4E 47 20 54 57 4F 20 4E 4F 54 45 53 20 41 |GING TWO NOTES A| 00000590: 4E 0D 4F 43 54 41 56 45 20 41 50 41 52 54 2E 20 |N.OCTAVE APART. | 000005A0: 20 C2 55 54 20 57 48 59 20 41 52 45 20 54 48 45 | .UT WHY ARE THE| 000005B0: 52 45 20 4F 4E 4C 59 0D 45 4C 45 56 45 4E 20 4F |RE ONLY.ELEVEN O| 000005C0: 54 48 45 52 20 4E 4F 54 45 53 20 42 45 54 57 45 |THER NOTES BETWE| 000005D0: 45 4E 20 54 48 45 4D 3F 20 20 D7 48 59 0D 4E 4F |EN THEM? .HY.NO| 000005E0: 54 20 54 45 4E 20 4F 52 20 54 48 49 52 54 45 45 |T TEN OR THIRTEE| 000005F0: 4E 3F 0D 0D 20 20 20 20 D4 C5 CD D0 C5 D2 C5 C4 |N?.. ........| 00000600: 20 C6 D5 CE 20 57 49 4C 4C 20 4C 45 54 20 59 4F | ... WILL LET YO| 00000610: 55 20 48 45 41 52 0D 46 4F 52 20 59 4F 55 52 53 |U HEAR.FOR YOURS| 00000620: 45 4C 46 20 57 48 59 2E 20 20 D7 45 27 52 45 20 |ELF WHY. .E'RE | 00000630: 4E 4F 54 20 55 53 45 44 20 54 4F 0D 4F 44 44 42 |NOT USED TO.ODDB| 00000640: 41 4C 4C 20 54 55 4E 49 4E 47 53 20 41 4E 44 20 |ALL TUNINGS AND | 00000650: 54 48 45 59 20 46 52 41 4E 4B 4C 59 0D 53 4F 55 |THEY FRANKLY.SOU| 00000660: 4E 44 20 42 41 44 2E 20 20 C2 55 54 20 57 45 20 |ND BAD. .UT WE | 00000670: 53 48 4F 55 4C 44 20 52 45 41 4C 49 5A 45 0D 54 |SHOULD REALIZE.T| 00000680: 48 41 54 20 59 45 41 52 53 20 41 47 4F 2C 20 50 |HAT YEARS AGO, P| 00000690: 45 4F 50 4C 45 20 57 4F 55 4C 44 20 43 4F 4E 53 |EOPLE WOULD CONS| 000006A0: 49 44 45 52 0D 57 48 41 54 20 57 45 20 4C 49 53 |IDER.WHAT WE LIS| 000006B0: 54 45 4E 20 54 4F 20 54 4F 44 41 59 20 42 41 44 |TEN TO TODAY BAD| 000006C0: 2E 20 20 CF 55 52 0D 53 45 4E 53 49 42 49 4C 49 |. .UR.SENSIBILI| 000006D0: 54 49 45 53 20 48 41 56 45 20 43 48 41 4E 47 45 |TIES HAVE CHANGE| 000006E0: 44 2E 0D 20 20 20 20 D4 48 45 20 4D 41 4A 4F 52 |D.. .HE MAJOR| 000006F0: 20 43 48 41 4E 47 45 20 43 41 4D 45 20 57 48 45 | CHANGE CAME WHE| 00000700: 4E 20 CA 2E 20 D3 2E 0D C2 41 43 48 20 43 4F 4E |N .. ....ACH CON| 00000710: 56 49 4E 43 45 44 20 4D 41 4E 59 20 4F 46 20 48 |VINCED MANY OF H| 00000720: 49 53 0D 43 4F 4E 54 45 4D 50 4F 52 41 52 49 45 |IS.CONTEMPORARIE| 00000730: 53 20 54 48 41 54 20 48 55 4D 41 4E 53 20 57 4F |S THAT HUMANS WO| 00000740: 55 4C 44 20 47 45 54 0D 55 53 45 44 20 54 4F 20 |ULD GET.USED TO | 00000750: 54 48 45 20 22 45 51 55 41 4C 22 20 54 45 4D 50 |THE "EQUAL" TEMP| 00000760: 45 52 41 4D 45 4E 54 20 48 45 0D 45 53 50 4F 55 |ERAMENT HE.ESPOU| 00000770: 53 45 44 2E 20 20 D4 48 49 53 20 53 43 41 4C 45 |SED. .HIS SCALE| 00000780: 20 57 41 53 20 44 45 56 49 53 45 44 20 42 59 0D | WAS DEVISED BY.| 00000790: 41 20 44 49 53 43 49 50 4C 45 20 4F 46 20 C1 52 |A DISCIPLE OF .R| 000007A0: 49 53 54 4F 54 4C 45 20 4E 41 4D 45 44 0D C1 52 |ISTOTLE NAMED..R| 000007B0: 49 53 54 4F 58 45 4E 55 53 2C 20 42 55 54 20 57 |ISTOXENUS, BUT W| 000007C0: 41 53 20 4E 45 56 45 52 20 41 44 4F 50 54 45 44 |AS NEVER ADOPTED| 000007D0: 0D 55 4E 54 49 4C 20 41 20 4D 55 53 49 43 49 41 |.UNTIL A MUSICIA| 000007E0: 4E 20 4F 46 20 C2 41 43 48 27 53 20 53 54 41 54 |N OF .ACH'S STAT| 000007F0: 55 52 45 0D 52 45 43 4F 4D 4D 45 4E 44 45 44 20 |URE.RECOMMENDED | 00000800: 49 54 2E 0D 0D 20 20 20 20 C2 45 46 4F 52 45 20 |IT... .EFORE | 00000810: C2 41 43 48 20 57 45 53 54 45 52 4E 20 50 45 4F |.ACH WESTERN PEO| 00000820: 50 4C 45 20 55 53 45 44 20 41 0D 22 4A 55 53 54 |PLE USED A."JUST| 00000830: 22 20 54 55 4E 49 4E 47 20 57 48 49 43 48 20 57 |" TUNING WHICH W| 00000840: 41 53 20 42 41 53 45 44 20 55 50 4F 4E 0D 54 48 |AS BASED UPON.TH| 00000850: 45 20 46 41 43 54 20 54 48 41 54 20 54 48 45 20 |E FACT THAT THE | 00000860: 46 4F 55 52 54 48 20 41 4E 44 20 46 49 46 54 48 |FOURTH AND FIFTH| 00000870: 0D 54 4F 4E 45 53 20 4F 46 20 41 20 53 43 41 4C |.TONES OF A SCAL| 00000880: 45 20 48 41 44 20 46 52 45 51 55 45 4E 43 49 45 |E HAD FREQUENCIE| 00000890: 53 20 54 48 41 54 0D 57 45 52 45 20 45 58 41 43 |S THAT.WERE EXAC| 000008A0: 54 4C 59 20 34 2F 33 20 41 4E 44 20 33 2F 32 20 |TLY 4/3 AND 3/2 | 000008B0: 54 48 41 54 20 4F 46 20 54 48 45 0D 52 4F 4F 54 |THAT OF THE.ROOT| 000008C0: 20 4E 4F 54 45 2E 20 20 C9 46 20 C1 20 48 41 44 | NOTE. .F . HAD| 000008D0: 20 41 20 46 52 45 51 55 45 4E 43 59 20 4F 46 0D | A FREQUENCY OF.| 000008E0: 34 34 30 20 48 45 52 54 5A 2C 20 54 48 45 4E 20 |440 HERTZ, THEN | 000008F0: C4 20 57 41 53 20 35 38 36 2E 36 37 20 28 34 34 |. WAS 586.67 (44| 00000900: 30 0D 54 49 4D 45 53 20 34 2F 33 29 20 41 4E 44 |0.TIMES 4/3) AND| 00000910: 20 C5 20 57 41 53 20 36 36 30 20 28 34 34 30 20 | . WAS 660 (440 | 00000920: 54 49 4D 45 53 0D 33 2F 32 29 2E 0D 20 20 20 20 |TIMES.3/2).. | 00000930: D4 48 45 20 43 48 41 52 4D 20 4F 46 20 54 48 49 |.HE CHARM OF THI| 00000940: 53 20 54 55 4E 49 4E 47 20 57 41 53 20 54 48 41 |S TUNING WAS THA| 00000950: 54 0D 41 4E 59 20 53 4F 4E 47 53 20 49 4E 20 54 |T.ANY SONGS IN T| 00000960: 48 45 20 4B 45 59 20 4F 46 20 C1 20 53 4F 55 4E |HE KEY OF . SOUN| 00000970: 44 45 44 0D 47 52 45 41 54 2E 20 20 D4 48 45 20 |DED.GREAT. .HE | 00000980: 50 52 4F 42 4C 45 4D 20 57 49 54 48 20 54 48 49 |PROBLEM WITH THI| 00000990: 53 20 54 55 4E 49 4E 47 0D 57 41 53 20 54 48 41 |S TUNING.WAS THA| 000009A0: 54 20 53 4F 4E 47 53 20 49 4E 20 41 4E 59 20 4F |T SONGS IN ANY O| 000009B0: 54 48 45 52 20 4B 45 59 0D 44 49 44 4E 27 54 20 |THER KEY.DIDN'T | 000009C0: 53 4F 55 4E 44 20 47 52 45 41 54 2E 20 20 C1 53 |SOUND GREAT. .S| 000009D0: 20 41 20 4D 41 54 54 45 52 20 4F 46 0D 46 41 43 | A MATTER OF.FAC| 000009E0: 54 2C 20 54 48 45 59 20 53 4F 55 4E 44 45 44 20 |T, THEY SOUNDED | 000009F0: 4C 4F 55 53 59 2E 20 20 C3 4F 4E 43 45 52 54 53 |LOUSY. .ONCERTS| 00000A00: 0D 49 4E 20 54 48 45 20 4F 4C 44 20 44 41 59 53 |.IN THE OLD DAYS| 00000A10: 20 44 49 44 4E 27 54 20 48 41 56 45 20 54 48 45 | DIDN'T HAVE THE| 00000A20: 0D 4E 4F 4E 2D 53 54 4F 50 20 41 43 54 49 4F 4E |.NON-STOP ACTION| 00000A30: 20 57 45 20 45 4E 4A 4F 59 20 28 4F 52 20 44 45 | WE ENJOY (OR DE| 00000A40: 50 4C 4F 52 45 2C 0D 44 45 50 45 4E 44 49 4E 47 |PLORE,.DEPENDING| 00000A50: 20 55 50 4F 4E 20 59 4F 55 52 20 41 54 54 49 54 | UPON YOUR ATTIT| 00000A60: 55 44 45 29 20 54 4F 44 41 59 0D 42 45 43 41 55 |UDE) TODAY.BECAU| 00000A70: 53 45 20 41 46 54 45 52 20 54 48 45 20 50 49 41 |SE AFTER THE PIA| 00000A80: 4E 49 53 54 20 50 4C 41 59 45 44 20 41 0D 4D 41 |NIST PLAYED A.MA| 00000A90: 53 54 45 52 50 49 45 43 45 20 49 4E 20 C1 2C 20 |STERPIECE IN ., | 00000AA0: 54 48 45 52 45 20 57 41 53 20 41 0D 53 55 42 53 |THERE WAS A.SUBS| 00000AB0: 54 41 4E 54 49 41 4C 20 44 45 4C 41 59 20 57 48 |TANTIAL DELAY WH| 00000AC0: 49 4C 45 20 C9 43 48 41 42 4F 44 20 54 48 45 0D |ILE .CHABOD THE.| 00000AD0: 54 55 4E 45 52 20 54 52 4F 54 54 45 44 20 49 4E |TUNER TROTTED IN| 00000AE0: 20 41 4E 44 20 52 45 54 55 4E 45 44 20 54 48 45 | AND RETUNED THE| 00000AF0: 0D 50 49 41 4E 4F 20 46 4F 52 20 54 48 45 20 4E |.PIANO FOR THE N| 00000B00: 45 58 54 20 53 4F 4E 47 2C 20 57 48 49 43 48 20 |EXT SONG, WHICH | 00000B10: 57 41 53 20 49 4E 0D 54 48 45 20 4B 45 59 20 4F |WAS IN.THE KEY O| 00000B20: 46 20 C3 2E 0D 0D 20 20 20 20 C2 41 43 48 20 43 |F .... .ACH C| 00000B30: 48 41 4E 47 45 44 20 41 4C 4C 20 54 48 41 54 20 |HANGED ALL THAT | 00000B40: 57 48 45 4E 20 48 45 0D 49 4E 53 49 53 54 45 44 |WHEN HE.INSISTED| 00000B50: 20 55 50 4F 4E 20 55 53 49 4E 47 20 C1 52 49 53 | UPON USING .RIS| 00000B60: 54 4F 58 45 4E 55 53 27 0D 22 45 51 55 41 4C 22 |TOXENUS'."EQUAL"| 00000B70: 20 54 45 4D 50 45 52 41 4D 45 4E 54 2E 0D 20 20 | TEMPERAMENT.. | 00000B80: 20 20 D4 48 49 53 20 54 55 4E 49 4E 47 20 44 49 | .HIS TUNING DI| 00000B90: 56 49 44 45 44 20 54 48 45 20 4F 43 54 41 56 45 |VIDED THE OCTAVE| 00000BA0: 0D 49 4E 54 4F 20 54 57 45 4C 56 45 20 45 51 55 |.INTO TWELVE EQU| 00000BB0: 41 4C 20 49 4E 54 45 52 56 41 4C 53 2E 20 20 C5 |AL INTERVALS. .| 00000BC0: 41 43 48 0D 4E 4F 54 45 20 48 41 53 20 41 20 46 |ACH.NOTE HAS A F| 00000BD0: 52 45 51 55 45 4E 43 59 20 54 48 41 54 20 49 53 |REQUENCY THAT IS| 00000BE0: 20 31 2E 30 35 39 34 36 0D 54 49 4D 45 53 20 54 | 1.05946.TIMES T| 00000BF0: 48 45 20 4E 45 58 54 20 4C 4F 57 45 52 20 4E 4F |HE NEXT LOWER NO| 00000C00: 54 45 2E 20 20 31 2E 30 35 39 34 36 0D 49 53 20 |TE. 1.05946.IS | 00000C10: 54 48 45 20 54 57 45 4C 46 54 48 20 52 4F 4F 54 |THE TWELFTH ROOT| 00000C20: 20 4F 46 20 32 2E 0D 0D 20 20 20 20 D7 49 54 48 | OF 2... .ITH| 00000C30: 20 54 48 49 53 20 54 55 4E 49 4E 47 2C 20 54 48 | THIS TUNING, TH| 00000C40: 45 20 4E 4F 54 45 53 20 4F 46 0D 54 48 45 20 53 |E NOTES OF.THE S| 00000C50: 43 41 4C 45 2C 20 50 41 52 54 49 43 55 4C 41 52 |CALE, PARTICULAR| 00000C60: 4C 59 20 54 48 45 20 46 4F 55 52 54 48 0D 41 4E |LY THE FOURTH.AN| 00000C70: 44 20 46 49 46 54 48 20 4F 4E 45 53 2C 20 57 49 |D FIFTH ONES, WI| 00000C80: 4C 4C 20 53 4F 55 4E 44 20 41 20 4C 49 54 54 4C |LL SOUND A LITTL| 00000C90: 45 0D 4F 55 54 20 4F 46 20 54 55 4E 45 2E 20 20 |E.OUT OF TUNE. | 00000CA0: C2 55 54 20 2D 20 41 4E 44 20 54 48 49 53 20 49 |.UT - AND THIS I| 00000CB0: 53 20 54 48 45 0D 52 45 41 53 4F 4E 20 46 4F 52 |S THE.REASON FOR| 00000CC0: 20 55 53 49 4E 47 20 41 4E 20 22 45 51 55 41 4C | USING AN "EQUAL| 00000CD0: 22 0D 54 45 4D 50 45 52 41 4D 45 4E 54 20 2D 20 |".TEMPERAMENT - | 00000CE0: 41 4E 59 20 4B 45 59 20 59 4F 55 20 50 4C 41 59 |ANY KEY YOU PLAY| 00000CF0: 20 49 4E 0D 57 49 4C 4C 20 53 4F 55 4E 44 20 45 | IN.WILL SOUND E| 00000D00: 51 55 41 4C 4C 59 20 4F 55 54 20 4F 46 20 54 55 |QUALLY OUT OF TU| 00000D10: 4E 45 2E 20 20 D4 48 45 0D 41 4D 4F 55 4E 54 20 |NE. .HE.AMOUNT | 00000D20: 54 48 41 54 20 49 54 27 53 20 4F 55 54 20 49 53 |THAT IT'S OUT IS| 00000D30: 20 53 4F 20 53 4D 41 4C 4C 20 54 48 41 54 0D C2 | SO SMALL THAT..| 00000D40: 41 43 48 20 54 48 4F 55 47 48 54 20 57 45 20 43 |ACH THOUGHT WE C| 00000D50: 4F 55 4C 44 20 47 45 54 20 55 53 45 44 20 54 4F |OULD GET USED TO| 00000D60: 20 49 54 2E 0D CF 4E 43 45 20 57 45 20 44 49 44 | IT...NCE WE DID| 00000D70: 2C 20 54 48 45 20 50 49 41 4E 49 53 54 20 43 4F |, THE PIANIST CO| 00000D80: 55 4C 44 20 50 4C 41 59 0D 49 4E 20 41 4E 59 20 |ULD PLAY.IN ANY | 00000D90: 4B 45 59 20 57 49 54 48 4F 55 54 20 48 41 56 49 |KEY WITHOUT HAVI| 00000DA0: 4E 47 20 C9 43 48 41 42 4F 44 20 4F 4E 0D 48 41 |NG .CHABOD ON.HA| 00000DB0: 4E 44 2E 0D 0D 20 20 20 20 D4 48 45 52 45 20 49 |ND... .HERE I| 00000DC0: 53 20 41 20 57 45 41 4C 54 48 20 4F 46 20 49 4E |S A WEALTH OF IN| 00000DD0: 46 4F 52 4D 41 54 49 4F 4E 0D 50 55 42 4C 49 53 |FORMATION.PUBLIS| 00000DE0: 48 45 44 20 4F 4E 20 54 48 45 20 50 48 45 4E 4F |HED ON THE PHENO| 00000DF0: 4D 45 4E 41 20 4F 46 0D 54 55 4E 49 4E 47 53 2C |MENA OF.TUNINGS,| 00000E00: 20 54 45 4D 50 45 52 41 4D 45 4E 54 53 2C 20 41 | TEMPERAMENTS, A| 00000E10: 43 4F 55 53 54 49 43 53 2C 0D 50 48 59 43 48 4F |COUSTICS,.PHYCHO| 00000E20: 2D 41 43 4F 55 53 54 49 43 53 20 41 4E 44 20 50 |-ACOUSTICS AND P| 00000E30: 48 59 53 49 4F 4C 4F 47 59 20 54 48 41 54 0D 57 |HYSIOLOGY THAT.W| 00000E40: 49 4C 4C 20 54 45 4C 4C 20 59 4F 55 20 4D 55 43 |ILL TELL YOU MUC| 00000E50: 48 20 4D 4F 52 45 2E 20 20 D4 48 45 20 41 52 54 |H MORE. .HE ART| 00000E60: 49 43 4C 45 0D 42 59 20 D0 41 55 4C 20 D2 2E 20 |ICLE.BY .AUL .. | 00000E70: CD 41 43 48 55 4C 41 20 49 4E 20 54 48 45 20 C1 |.ACHULA IN THE .| 00000E80: 55 47 55 53 54 0D C9 53 53 55 45 20 4F 46 20 C3 |UGUST..SSUE OF .| 00000E90: 4F 4D 4D 4F 44 4F 52 45 20 CD 41 47 41 5A 49 4E |OMMODORE .AGAZIN| 00000EA0: 45 20 48 41 53 20 41 20 4C 4F 54 0D 4F 46 20 49 |E HAS A LOT.OF I| 00000EB0: 4E 54 45 52 45 53 54 49 4E 47 20 49 4E 46 4F 52 |NTERESTING INFOR| 00000EC0: 4D 41 54 49 4F 4E 20 54 4F 4F 2E 0D 0D 20 20 20 |MATION TOO... | 00000ED0: 20 D4 48 45 20 50 52 4F 47 52 41 4D 20 49 53 20 | .HE PROGRAM IS | 00000EE0: 4D 45 4E 55 2D 44 52 49 56 45 4E 20 53 4F 20 59 |MENU-DRIVEN SO Y| 00000EF0: 4F 55 0D 43 41 4E 20 45 41 53 49 4C 59 20 43 48 |OU.CAN EASILY CH| 00000F00: 4F 4F 53 45 20 54 48 45 20 50 41 52 41 4D 45 54 |OOSE THE PARAMET| 00000F10: 45 52 53 20 46 4F 52 0D 41 4E 59 54 48 49 4E 47 |ERS FOR.ANYTHING| 00000F20: 20 59 4F 55 27 44 20 4C 49 4B 45 20 54 4F 20 48 | YOU'D LIKE TO H| 00000F30: 45 41 52 2E 20 20 C1 4C 4C 20 59 4F 55 0D 48 41 |EAR. .LL YOU.HA| 00000F40: 56 45 20 54 4F 20 44 4F 20 49 53 20 50 52 45 53 |VE TO DO IS PRES| 00000F50: 53 20 41 20 46 45 57 20 4E 55 4D 42 45 52 53 20 |S A FEW NUMBERS | 00000F60: 41 4E 44 0D 59 4F 55 20 43 41 4E 20 43 4F 4D 50 |AND.YOU CAN COMP| 00000F70: 41 52 45 20 54 55 4E 49 4E 47 53 2C 20 43 48 4F |ARE TUNINGS, CHO| 00000F80: 52 44 53 20 41 4E 44 0D 4D 45 4C 4F 44 49 45 53 |RDS AND.MELODIES| 00000F90: 2E 20 20 C2 41 43 48 20 57 4F 55 4C 44 20 48 41 |. .ACH WOULD HA| 00000FA0: 56 45 20 4B 49 4C 4C 45 44 20 46 4F 52 0D 54 48 |VE KILLED FOR.TH| 00000FB0: 49 53 20 50 52 4F 47 52 41 4D 21 0D 0D 0D 0D 0D |IS PROGRAM!.....| 00000FC0: 20 20 20 20 D4 48 45 52 45 20 41 52 45 20 46 49 | .HERE ARE FI| 00000FD0: 56 45 20 54 45 4D 50 45 52 41 4D 45 4E 54 53 2E |VE TEMPERAMENTS.| 00000FE0: 20 20 D4 48 45 0D 54 45 4D 50 45 52 41 4D 45 4E | .HE.TEMPERAMEN| 00000FF0: 54 20 49 53 20 54 48 45 20 4D 45 54 48 4F 44 20 |T IS THE METHOD | 00001000: 4F 46 20 44 49 56 49 44 49 4E 47 0D 54 48 45 20 |OF DIVIDING.THE | 00001010: 4F 43 54 41 56 45 20 49 4E 54 4F 20 50 41 52 54 |OCTAVE INTO PART| 00001020: 53 2E 20 20 D9 4F 55 20 43 41 4E 20 45 56 45 4E |S. .OU CAN EVEN| 00001030: 0D 43 48 4F 53 45 20 59 4F 55 52 20 4F 57 4E 20 |.CHOSE YOUR OWN | 00001040: 54 45 4D 50 45 52 41 4D 45 4E 54 2E 0D 0D 20 20 |TEMPERAMENT... | 00001050: 20 20 CE 45 58 54 20 59 4F 55 20 43 48 4F 4F 53 | .EXT YOU CHOOS| 00001060: 45 20 54 48 45 20 53 43 41 4C 45 20 59 4F 55 0D |E THE SCALE YOU.| 00001070: 57 41 4E 54 20 54 4F 20 48 45 41 52 2E 20 20 C1 |WANT TO HEAR. .| 00001080: 20 42 4F 4F 4B 20 4F 4E 20 48 41 52 4D 4F 4E 59 | BOOK ON HARMONY| 00001090: 20 57 49 4C 4C 0D 54 45 4C 4C 20 59 4F 55 20 41 | WILL.TELL YOU A| 000010A0: 20 4C 4F 54 20 4D 4F 52 45 20 41 42 4F 55 54 20 | LOT MORE ABOUT | 000010B0: 53 43 41 4C 45 53 2E 0D D3 49 4E 43 45 20 54 48 |SCALES...INCE TH| 000010C0: 45 52 45 20 41 52 45 20 54 57 45 4C 56 45 20 48 |ERE ARE TWELVE H| 000010D0: 41 4C 46 2D 54 4F 4E 45 53 20 49 4E 0D 41 4E 20 |ALF-TONES IN.AN | 000010E0: 4F 43 54 41 56 45 2C 20 42 55 54 20 4F 4E 4C 59 |OCTAVE, BUT ONLY| 000010F0: 20 45 49 47 48 54 20 4F 46 20 54 48 45 4D 20 41 | EIGHT OF THEM A| 00001100: 52 45 0D 50 4C 41 59 45 44 20 49 4E 20 41 20 50 |RE.PLAYED IN A P| 00001110: 41 52 54 49 43 55 4C 41 52 20 53 43 41 4C 45 2C |ARTICULAR SCALE,| 00001120: 20 54 48 45 0D 53 43 41 4C 45 20 49 53 20 47 45 | THE.SCALE IS GE| 00001130: 4E 45 52 41 4C 4C 59 20 44 45 54 45 52 4D 49 4E |NERALLY DETERMIN| 00001140: 45 44 20 42 59 0D 57 48 49 43 48 20 45 49 47 48 |ED BY.WHICH EIGH| 00001150: 54 20 4F 46 20 54 48 45 20 54 57 45 4C 56 45 20 |T OF THE TWELVE | 00001160: 41 52 45 20 55 53 45 44 2E 0D CF 52 2C 20 49 46 |ARE USED...R, IF| 00001170: 20 59 4F 55 20 57 49 4C 4C 2C 20 54 48 45 20 46 | YOU WILL, THE F| 00001180: 4F 55 52 20 4E 4F 54 45 53 20 54 48 41 54 0D 41 |OUR NOTES THAT.A| 00001190: 52 45 20 CE CF D4 20 50 4C 41 59 45 44 2E 0D 0D |RE ... PLAYED...| 000011A0: 0D 0D 20 20 20 20 CD C5 CE D5 20 32 20 54 48 45 |.. .... 2 THE| 000011B0: 4E 20 53 48 4F 57 53 20 53 4F 4D 45 20 54 48 49 |N SHOWS SOME THI| 000011C0: 4E 47 53 20 59 4F 55 0D 43 41 4E 20 44 4F 20 57 |NGS YOU.CAN DO W| 000011D0: 49 54 48 20 54 48 49 53 20 53 43 41 4C 45 2E 20 |ITH THIS SCALE. | 000011E0: 20 D9 4F 55 20 43 41 4E 20 48 45 41 52 0D 54 48 | .OU CAN HEAR.TH| 000011F0: 45 20 53 43 41 4C 45 2C 20 48 45 41 52 20 54 48 |E SCALE, HEAR TH| 00001200: 45 20 52 4F 4F 54 20 43 48 4F 52 44 2C 20 50 4C |E ROOT CHORD, PL| 00001210: 41 59 0D 57 49 54 48 20 54 48 45 20 53 43 41 4C |AY.WITH THE SCAL| 00001220: 45 20 42 59 20 50 52 45 53 53 49 4E 47 20 54 48 |E BY PRESSING TH| 00001230: 45 20 4E 55 4D 42 45 52 0D 4B 45 59 53 2C 20 4F |E NUMBER.KEYS, O| 00001240: 52 20 4C 49 53 54 45 4E 20 54 4F 20 D4 57 49 4E |R LISTEN TO .WIN| 00001250: 4B 4C 45 2C 20 D4 57 49 4E 4B 4C 45 0D CC 49 54 |KLE, .WINKLE..IT| 00001260: 54 4C 45 20 D3 54 41 52 20 50 4C 41 59 45 44 20 |TLE .TAR PLAYED | 00001270: 49 4E 20 54 48 45 20 53 43 41 4C 45 20 41 4E 44 |IN THE SCALE AND| 00001280: 0D 54 45 4D 50 45 52 41 4D 45 4E 54 20 59 4F 55 |.TEMPERAMENT YOU| 00001290: 20 43 48 4F 53 45 2E 0D 0D 20 20 20 20 C8 45 41 | CHOSE... .EA| 000012A0: 52 49 4E 47 20 54 48 45 20 53 4F 4E 47 20 57 49 |RING THE SONG WI| 000012B0: 54 48 20 48 41 52 4D 4F 4E 59 20 49 53 0D 49 4E |TH HARMONY IS.IN| 000012C0: 54 45 52 45 53 54 49 4E 47 2C 20 41 4C 54 48 4F |TERESTING, ALTHO| 000012D0: 55 47 48 20 49 54 20 44 4F 45 53 4E 27 54 0D 53 |UGH IT DOESN'T.S| 000012E0: 4F 55 4E 44 20 4E 45 41 52 4C 59 20 41 53 20 47 |OUND NEARLY AS G| 000012F0: 4F 4F 44 20 41 53 20 54 57 4F 20 48 55 4D 41 4E |OOD AS TWO HUMAN| 00001300: 0D 53 49 4E 47 45 52 53 20 57 4F 55 4C 44 20 44 |.SINGERS WOULD D| 00001310: 4F 2E 20 20 CD 41 54 48 45 4D 41 54 49 43 53 20 |O. .ATHEMATICS | 00001320: 49 53 0D 45 41 53 59 20 4F 4E 20 41 20 43 4F 4D |IS.EASY ON A COM| 00001330: 50 55 54 45 52 20 2D 20 49 4E 54 45 4C 4C 49 47 |PUTER - INTELLIG| 00001340: 45 4E 43 45 2C 0D 44 49 53 43 52 49 4D 49 4E 41 |ENCE,.DISCRIMINA| 00001350: 54 49 4F 4E 20 41 4E 44 20 54 41 53 54 45 20 41 |TION AND TASTE A| 00001360: 52 45 0D 49 4E 43 52 45 44 49 42 4C 59 20 44 49 |RE.INCREDIBLY DI| 00001370: 46 46 49 43 55 4C 54 2E 20 20 C8 4F 57 20 43 41 |FFICULT. .OW CA| 00001380: 4E 20 59 4F 55 0D 50 52 4F 47 52 41 4D 20 41 20 |N YOU.PROGRAM A | 00001390: 43 4F 4D 50 55 54 45 52 20 54 4F 20 44 45 43 49 |COMPUTER TO DECI| 000013A0: 44 45 20 49 46 20 41 0D 4E 4F 54 45 20 4F 52 20 |DE IF A.NOTE OR | 000013B0: 48 41 52 4D 4F 4E 59 20 53 4F 55 4E 44 53 20 27 |HARMONY SOUNDS '| 000013C0: 47 4F 4F 44 27 3F 0D 0D 0D 0D 20 20 20 20 D4 52 |GOOD'?.... .R| 000013D0: 59 20 43 48 4F 4F 53 49 4E 47 20 59 4F 55 52 20 |Y CHOOSING YOUR | 000013E0: 4F 57 4E 20 54 45 4D 50 45 52 41 4D 45 4E 54 0D |OWN TEMPERAMENT.| 000013F0: 46 52 4F 4D 20 54 48 45 20 46 49 52 53 54 20 4D |FROM THE FIRST M| 00001400: 45 4E 55 20 41 4E 44 20 44 49 56 49 44 45 20 54 |ENU AND DIVIDE T| 00001410: 48 45 0D 4F 43 54 41 56 45 20 49 4E 54 4F 20 31 |HE.OCTAVE INTO 1| 00001420: 32 30 30 20 49 4E 54 45 52 56 41 4C 53 2E 20 20 |200 INTERVALS. | 00001430: D4 48 45 0D 43 4F 4D 50 55 54 45 52 20 57 49 4C |.HE.COMPUTER WIL| 00001440: 4C 20 50 4C 41 59 20 41 20 53 54 45 41 44 59 20 |L PLAY A STEADY | 00001450: 52 45 46 45 52 45 4E 43 45 0D 4E 4F 54 45 20 41 |REFERENCE.NOTE A| 00001460: 4E 44 20 41 54 20 54 48 45 20 53 41 4D 45 20 54 |ND AT THE SAME T| 00001470: 49 4D 45 20 47 52 41 44 55 41 4C 4C 59 0D 49 4E |IME GRADUALLY.IN| 00001480: 43 52 45 41 53 45 20 41 4E 4F 54 48 45 52 20 4E |CREASE ANOTHER N| 00001490: 4F 54 45 2E 20 20 D4 48 45 20 54 57 4F 20 4E 4F |OTE. .HE TWO NO| 000014A0: 54 45 53 0D 48 45 41 52 44 20 53 49 4D 55 4C 54 |TES.HEARD SIMULT| 000014B0: 41 4E 45 4F 55 53 4C 59 20 57 49 4C 4C 20 50 52 |ANEOUSLY WILL PR| 000014C0: 4F 44 55 43 45 20 41 0D 22 42 45 41 54 22 20 46 |ODUCE A."BEAT" F| 000014D0: 52 45 51 55 45 4E 43 59 20 54 48 41 54 20 47 52 |REQUENCY THAT GR| 000014E0: 41 44 55 41 4C 4C 59 0D 49 4E 43 52 45 41 53 45 |ADUALLY.INCREASE| 000014F0: 53 20 49 4E 20 46 52 45 51 55 45 4E 43 59 20 54 |S IN FREQUENCY T| 00001500: 4F 4F 2E 20 20 D4 48 49 53 0D 22 42 45 41 54 22 |OO. .HIS."BEAT"| 00001510: 20 46 52 45 51 55 45 4E 43 59 20 49 53 20 57 48 | FREQUENCY IS WH| 00001520: 41 54 20 50 49 41 4E 4F 20 54 55 4E 45 52 53 0D |AT PIANO TUNERS.| 00001530: 4C 49 53 54 45 4E 20 46 4F 52 2E 20 20 C9 54 27 |LISTEN FOR. .T'| 00001540: 53 20 53 4F 52 54 20 4F 46 20 41 4E 20 41 55 52 |S SORT OF AN AUR| 00001550: 41 4C 0D 4D 4F 49 52 45 20 50 41 54 54 45 52 4E |AL.MOIRE PATTERN| 00001560: 2C 20 57 48 49 43 48 20 49 53 20 41 20 52 45 53 |, WHICH IS A RES| 00001570: 55 4C 54 41 4E 54 0D 50 41 54 54 45 52 4E 20 46 |ULTANT.PATTERN F| 00001580: 4F 52 4D 45 44 20 42 59 20 54 48 45 20 49 4E 54 |ORMED BY THE INT| 00001590: 45 52 53 45 43 54 49 4F 4E 20 4F 46 0D 54 57 4F |ERSECTION OF.TWO| 000015A0: 20 44 49 46 46 45 52 45 4E 54 20 50 41 54 54 45 | DIFFERENT PATTE| 000015B0: 52 4E 53 2E 0D 0D 0D 0D 0D 20 20 20 20 CE 4F 54 |RNS...... .OT| 000015C0: 49 43 45 20 54 48 41 54 20 49 46 20 59 4F 55 20 |ICE THAT IF YOU | 000015D0: 43 48 4F 4F 53 45 20 41 4E 59 0D 4F 54 48 45 52 |CHOOSE ANY.OTHER| 000015E0: 20 54 45 4D 50 45 52 41 4D 45 4E 54 20 4F 54 48 | TEMPERAMENT OTH| 000015F0: 45 52 20 54 48 41 4E 20 22 45 51 55 41 4C 22 0D |ER THAN "EQUAL".| 00001600: 59 4F 55 27 4C 4C 20 42 45 20 41 53 4B 45 44 20 |YOU'LL BE ASKED | 00001610: 46 4F 52 20 53 48 41 52 50 53 20 4F 52 20 46 4C |FOR SHARPS OR FL| 00001620: 41 54 53 2E 0D C9 4E 20 54 48 45 20 22 45 51 55 |ATS...N THE "EQU| 00001630: 41 4C 22 20 54 45 4D 50 45 52 41 4D 45 4E 54 20 |AL" TEMPERAMENT | 00001640: C1 20 53 48 41 52 50 20 49 53 0D 45 58 41 43 54 |. SHARP IS.EXACT| 00001650: 4C 59 20 54 48 45 20 53 41 4D 45 20 4E 4F 54 45 |LY THE SAME NOTE| 00001660: 20 41 53 20 C2 20 46 4C 41 54 2E 20 20 C9 4E 0D | AS . FLAT. .N.| 00001670: 54 48 45 20 4F 54 48 45 52 20 54 45 4D 50 45 52 |THE OTHER TEMPER| 00001680: 41 4D 45 4E 54 53 2C 20 54 48 45 59 20 41 52 45 |AMENTS, THEY ARE| 00001690: 0D 53 4C 49 47 48 54 4C 59 20 44 49 46 46 45 52 |.SLIGHTLY DIFFER| 000016A0: 45 4E 54 2E 0D 0D 20 20 20 C2 55 54 20 C9 27 56 |ENT... .UT .'V| 000016B0: 45 20 52 41 4D 42 4C 45 44 20 4F 4E 20 57 41 59 |E RAMBLED ON WAY| 000016C0: 20 54 4F 4F 20 4D 55 43 48 2E 0D D4 48 45 20 42 | TOO MUCH...HE B| 000016D0: 45 53 54 20 57 41 59 20 54 4F 20 45 4E 4A 4F 59 |EST WAY TO ENJOY| 000016E0: 20 54 48 49 53 20 50 52 4F 47 52 41 4D 20 49 53 | THIS PROGRAM IS| 000016F0: 0D 54 4F 20 50 4C 41 59 20 57 49 54 48 20 49 54 |.TO PLAY WITH IT| 00001700: 2E 20 20 CD 55 53 49 43 49 41 4E 20 4F 52 20 4E |. .USICIAN OR N| 00001710: 4F 54 2C 0D 59 4F 55 20 43 41 4E 20 4C 45 41 52 |OT,.YOU CAN LEAR| 00001720: 4E 20 41 4E 44 20 48 41 56 45 20 46 55 4E 20 57 |N AND HAVE FUN W| 00001730: 49 54 48 20 49 54 2E 0D 0D 0D C4 C9 D3 CB 20 C6 |ITH IT........ .| 00001740: C9 CC C5 D3 20 D4 C8 C9 D3 20 D0 D2 CF C7 D2 C1 |.... .... ......| 00001750: CD 20 D5 D3 C5 D3 0D 0D D4 C5 CD D0 C5 D2 C5 C4 |. ..............| 00001760: 20 C6 D5 CE 20 20 20 20 20 20 20 D4 2E 20 D4 C5 | ... .. ..| 00001770: CD D0 C5 D2 C5 C4 20 C6 D5 CE 0D 0D 20 20 20 20 |...... ..... | 00001780: 20 20 20 20 2A 2A 2A 2A 20 C5 4E 44 20 4F 46 20 | **** .ND OF | 00001790: D4 45 58 54 20 2A 2A 2A 2A 0D |.EXT ****. |
..^U:CBM. T E M P E R E D F U N..
BY PAUL R. MACHULA.. THOUGH
IT MAY NOT SEEM OBVIOUS AT.FIRST, MUSIC
AND MATHEMATICS ARE.PRACTICALLY ONE AND
THE SAME. THAT'S.WHY IT'S NO WONDER THA
T ONE OF THE.FIRST APPLICATIONS OF THE.M
ATHEMATICAL CAPABILITIES OF THE.COMPUTER
WAS IN CREATING MUSIC. THIS.EXCELLENT
PROGRAM ALLOWS YOU TO DO.THINGS WITH NOT
ES AND SCALES THAT.PRE-COMPUTER MUSICIAN
S AND MUSICAL.SCHOLARS WOULD HAVE CUT OF
F THEIR.EARS TO HAVE BEEN ABLE TO DO...
TEMPERED FUN MAKES IT EASY... BEFO
RE I GOT INTO COMPUTERS, I.WAS A MUSICIA
N AND OCCASIONAL PIANO.TUNER. I FIRST L
EARNED TO TUNE BY.EAR BUT WHEN THE PRICE
OF ELECTRONIC.TUNERS CAME DOWN TO A REA
SONABLE.LEVEL (AROUND 1975) I STARTED US
ING.ONE OF THEM TO SET THE TEMPERAMENT O
F.THE FIRST, AND MOST DIFFICULT, OCTAVE.
ON A PIANO. IT SEEMED TO ME THAT THE.HU
MAN EAR WAS NO MATCH FOR A MACHINE.WHEN
IT CAME TO COUNTING VIBRATIONS... HOW
EVER, THERE IS A SCHOOL OF.THOUGHT THAT
SAYS THAT SINCE MUSIC IS.TO BE HEARD BY
HUMAN EARS, THE TUNING.IS BEST ACCOMPLIS
HED BY HUMAN EARS..SO I GUESS I SHOULD S
AY, A MACHINE.CAN COUNT VIBRATIONS BETTE
R THAN MY.EARS.. HAVE YOU EVER WONDER
ED WHY THERE.ARE EIGHT NOTES IN AN OCTAV
E? WE.INSTINCTIVELY CAN TELL IF ONE NOT
E.HAS A FREQUENCY OF TWICE ANOTHER NOTE.
AND WE SAY THAT THESE NOTES ARE AN.OCTAV
E APART. WHEN YOU SING THE WORD."SOME-W
HERE" IN THE SONG "OVER THE.RAINBOW" YOU
ARE SINGING TWO NOTES AN.OCTAVE APART.
BUT WHY ARE THERE ONLY.ELEVEN OTHER NOT
ES BETWEEN THEM? WHY.NOT TEN OR THIRTEE
N?.. TEMPERED FUN WILL LET YOU HEAR.F
OR YOURSELF WHY. WE'RE NOT USED TO.ODDB
ALL TUNINGS AND THEY FRANKLY.SOUND BAD.
BUT WE SHOULD REALIZE.THAT YEARS AGO, P
EOPLE WOULD CONSIDER.WHAT WE LISTEN TO T
ODAY BAD. OUR.SENSIBILITIES HAVE CHANGE
D.. THE MAJOR CHANGE CAME WHEN J. S..
BACH CONVINCED MANY OF HIS.CONTEMPORARIE
S THAT HUMANS WOULD GET.USED TO THE "EQU
AL" TEMPERAMENT HE.ESPOUSED. THIS SCALE
WAS DEVISED BY.A DISCIPLE OF ARISTOTLE
NAMED.ARISTOXENUS, BUT WAS NEVER ADOPTED
.UNTIL A MUSICIAN OF BACH'S STATURE.RECO
MMENDED IT... BEFORE BACH WESTERN PEO
PLE USED A."JUST" TUNING WHICH WAS BASED
UPON.THE FACT THAT THE FOURTH AND FIFTH
.TONES OF A SCALE HAD FREQUENCIES THAT.W
ERE EXACTLY 4/3 AND 3/2 THAT OF THE.ROOT
NOTE. IF A HAD A FREQUENCY OF.440 HERT
Z, THEN D WAS 586.67 (440.TIMES 4/3) AND
E WAS 660 (440 TIMES.3/2).. THE CHAR
M OF THIS TUNING WAS THAT.ANY SONGS IN T
HE KEY OF A SOUNDED.GREAT. THE PROBLEM
WITH THIS TUNING.WAS THAT SONGS IN ANY O
THER KEY.DIDN'T SOUND GREAT. AS A MATTE
R OF.FACT, THEY SOUNDED LOUSY. CONCERTS
.IN THE OLD DAYS DIDN'T HAVE THE.NON-STO
P ACTION WE ENJOY (OR DEPLORE,.DEPENDING
UPON YOUR ATTITUDE) TODAY.BECAUSE AFTER
THE PIANIST PLAYED A.MASTERPIECE IN A,
THERE WAS A.SUBSTANTIAL DELAY WHILE ICHA
BOD THE.TUNER TROTTED IN AND RETUNED THE
.PIANO FOR THE NEXT SONG, WHICH WAS IN.T
HE KEY OF C... BACH CHANGED ALL THAT
WHEN HE.INSISTED UPON USING ARISTOXENUS'
."EQUAL" TEMPERAMENT.. THIS TUNING DI
VIDED THE OCTAVE.INTO TWELVE EQUAL INTER
VALS. EACH.NOTE HAS A FREQUENCY THAT IS
1.05946.TIMES THE NEXT LOWER NOTE. 1.0
5946.IS THE TWELFTH ROOT OF 2... WITH
THIS TUNING, THE NOTES OF.THE SCALE, PA
RTICULARLY THE FOURTH.AND FIFTH ONES, WI
LL SOUND A LITTLE.OUT OF TUNE. BUT - AN
D THIS IS THE.REASON FOR USING AN "EQUAL
".TEMPERAMENT - ANY KEY YOU PLAY IN.WILL
SOUND EQUALLY OUT OF TUNE. THE.AMOUNT
THAT IT'S OUT IS SO SMALL THAT.BACH THOU
GHT WE COULD GET USED TO IT..ONCE WE DID
, THE PIANIST COULD PLAY.IN ANY KEY WITH
OUT HAVING ICHABOD ON.HAND... THERE I
S A WEALTH OF INFORMATION.PUBLISHED ON T
HE PHENOMENA OF.TUNINGS, TEMPERAMENTS, A
COUSTICS,.PHYCHO-ACOUSTICS AND PHYSIOLOG
Y THAT.WILL TELL YOU MUCH MORE. THE ART
ICLE.BY PAUL R. MACHULA IN THE AUGUST.IS
SUE OF COMMODORE MAGAZINE HAS A LOT.OF I
NTERESTING INFORMATION TOO... THE PRO
GRAM IS MENU-DRIVEN SO YOU.CAN EASILY CH
OOSE THE PARAMETERS FOR.ANYTHING YOU'D L
IKE TO HEAR. ALL YOU.HAVE TO DO IS PRES
S A FEW NUMBERS AND.YOU CAN COMPARE TUNI
NGS, CHORDS AND.MELODIES. BACH WOULD HA
VE KILLED FOR.THIS PROGRAM!..... THER
E ARE FIVE TEMPERAMENTS. THE.TEMPERAMEN
T IS THE METHOD OF DIVIDING.THE OCTAVE I
NTO PARTS. YOU CAN EVEN.CHOSE YOUR OWN
TEMPERAMENT... NEXT YOU CHOOSE THE SC
ALE YOU.WANT TO HEAR. A BOOK ON HARMONY
WILL.TELL YOU A LOT MORE ABOUT SCALES..
SINCE THERE ARE TWELVE HALF-TONES IN.AN
OCTAVE, BUT ONLY EIGHT OF THEM ARE.PLAYE
D IN A PARTICULAR SCALE, THE.SCALE IS GE
NERALLY DETERMINED BY.WHICH EIGHT OF THE
TWELVE ARE USED..OR, IF YOU WILL, THE F
OUR NOTES THAT.ARE NOT PLAYED..... ME
NU 2 THEN SHOWS SOME THINGS YOU.CAN DO W
ITH THIS SCALE. YOU CAN HEAR.THE SCALE,
HEAR THE ROOT CHORD, PLAY.WITH THE SCAL
E BY PRESSING THE NUMBER.KEYS, OR LISTEN
TO TWINKLE, TWINKLE.LITTLE STAR PLAYED
IN THE SCALE AND.TEMPERAMENT YOU CHOSE..
. HEARING THE SONG WITH HARMONY IS.IN
TERESTING, ALTHOUGH IT DOESN'T.SOUND NEA
RLY AS GOOD AS TWO HUMAN.SINGERS WOULD D
O. MATHEMATICS IS.EASY ON A COMPUTER -
INTELLIGENCE,.DISCRIMINATION AND TASTE A
RE.INCREDIBLY DIFFICULT. HOW CAN YOU.PR
OGRAM A COMPUTER TO DECIDE IF A.NOTE OR
HARMONY SOUNDS 'GOOD'?.... TRY CHOOSI
NG YOUR OWN TEMPERAMENT.FROM THE FIRST M
ENU AND DIVIDE THE.OCTAVE INTO 1200 INTE
RVALS. THE.COMPUTER WILL PLAY A STEADY
REFERENCE.NOTE AND AT THE SAME TIME GRAD
UALLY.INCREASE ANOTHER NOTE. THE TWO NO
TES.HEARD SIMULTANEOUSLY WILL PRODUCE A.
"BEAT" FREQUENCY THAT GRADUALLY.INCREASE
S IN FREQUENCY TOO. THIS."BEAT" FREQUEN
CY IS WHAT PIANO TUNERS.LISTEN FOR. IT'
S SORT OF AN AURAL.MOIRE PATTERN, WHICH
IS A RESULTANT.PATTERN FORMED BY THE INT
ERSECTION OF.TWO DIFFERENT PATTERNS.....
. NOTICE THAT IF YOU CHOOSE ANY.OTHER
TEMPERAMENT OTHER THAN "EQUAL".YOU'LL B
E ASKED FOR SHARPS OR FLATS..IN THE "EQU
AL" TEMPERAMENT A SHARP IS.EXACTLY THE S
AME NOTE AS B FLAT. IN.THE OTHER TEMPER
AMENTS, THEY ARE.SLIGHTLY DIFFERENT...
BUT I'VE RAMBLED ON WAY TOO MUCH..THE B
EST WAY TO ENJOY THIS PROGRAM IS.TO PLAY
WITH IT. MUSICIAN OR NOT,.YOU CAN LEAR
N AND HAVE FUN WITH IT....DISK FILES THI
S PROGRAM USES..TEMPERED FUN T. TE
MPERED FUN.. **** END OF TEXT ***
*.
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