T.TEMPERED FUN
FILE INFORMATION
FILENAME(S): T.TEMPERED FUN
FILE TYPE(S): PRG
FILE SIZE: 6.4K
FIRST SEEN: 2025-11-30 18:12:20
APPEARS ON: 1 disk(s)
FILE HASH
2b245c31299a14e1cfc0ad2eb22bd85cd160b10a243eace33c1add476e6a8945
FOUND ON DISKS (1 DISKS)
| DISK TITLE | FILENAME | FILE TYPE | COLLECTION | TRACK | SECTOR | ACTIONS |
|---|---|---|---|---|---|---|
| LOADSTAR 51 S 2 | T.TEMPERED FUN | PRG | Sailor, Ganheden | 25 | 2 | 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 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A |ULA..***********| 00000050: 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A |****************| 00000060: 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A 0D 2A 20 20 D9 |***********.* .| 00000070: 45 53 2C 20 D6 49 52 47 49 4E 49 41 2C 20 54 48 |ES, .IRGINIA, TH| 00000080: 49 53 20 53 41 4D 45 20 50 52 4F 47 52 41 4D 20 |IS SAME PROGRAM | 00000090: 20 2A 0D 2A 20 20 20 20 57 41 53 20 50 55 42 4C | *.* WAS PUBL| 000000A0: 49 53 48 45 44 20 49 4E 20 4C 41 53 54 20 4D 4F |ISHED IN LAST MO| 000000B0: 4E 54 48 27 53 20 20 20 2A 0D 2A 20 20 20 CC CF |NTH'S *.* ..| 000000C0: C1 C4 D3 D4 C1 D2 2E 20 20 C9 54 20 57 41 53 20 |....... .T WAS | 000000D0: 53 45 4E 54 20 54 4F 20 55 53 20 42 59 20 20 2A |SENT TO US BY *| 000000E0: 0D 2A 20 20 C3 4F 4D 4D 4F 44 4F 52 45 20 CD 41 |.* .OMMODORE .A| 000000F0: 47 41 5A 49 4E 45 20 4C 41 53 54 20 4D 4F 4E 54 |GAZINE LAST MONT| 00000100: 48 20 41 4E 44 20 2A 0D 2A 20 57 48 45 4E 20 57 |H AND *.* WHEN W| 00000110: 45 20 47 4F 54 20 57 4F 52 44 20 46 52 4F 4D 20 |E GOT WORD FROM | 00000120: 54 48 45 4D 20 54 48 41 54 20 49 54 20 2A 0D 2A |THEM THAT IT *.*| 00000130: 20 20 48 41 44 20 42 45 45 4E 20 27 42 55 4D 50 | HAD BEEN 'BUMP| 00000140: 45 44 27 20 46 4F 52 20 4F 4E 45 20 52 45 41 53 |ED' FOR ONE REAS| 00000150: 4F 4E 20 20 2A 0D 2A 20 20 20 4F 52 20 41 4E 4F |ON *.* OR ANO| 00000160: 54 48 45 52 2C 20 49 54 20 57 41 53 20 54 4F 4F |THER, IT WAS TOO| 00000170: 20 4C 41 54 45 20 46 4F 52 20 20 2A 0D 2A 20 20 | LATE FOR *.* | 00000180: 20 20 55 53 20 54 4F 20 48 41 4C 54 20 49 54 53 | US TO HALT ITS| 00000190: 20 50 55 42 4C 49 43 41 54 49 4F 4E 20 4F 4E 20 | PUBLICATION ON | 000001A0: 20 20 2A 0D 2A 20 CC CF C1 C4 D3 D4 C1 D2 2E 20 | *.* ......... | 000001B0: 20 D7 45 20 44 45 43 49 44 45 44 20 54 4F 20 52 | .E DECIDED TO R| 000001C0: 45 50 55 42 4C 49 53 48 20 2A 0D 2A 20 49 54 20 |EPUBLISH *.* IT | 000001D0: 53 4F 20 54 48 41 54 20 54 48 49 53 20 49 53 53 |SO THAT THIS ISS| 000001E0: 55 45 20 4F 46 20 CC CF C1 C4 D3 D4 C1 D2 20 20 |UE OF ........ | 000001F0: 2A 0D 2A 20 20 20 57 4F 55 4C 44 20 42 45 54 54 |*.* WOULD BETT| 00000200: 45 52 20 4D 41 54 43 48 20 54 48 45 20 C1 55 47 |ER MATCH THE .UG| 00000210: 55 53 54 20 20 20 20 2A 0D 2A 20 20 20 20 49 53 |UST *.* IS| 00000220: 53 55 45 20 4F 46 20 C3 4F 4D 4D 4F 44 4F 52 45 |SUE OF .OMMODORE| 00000230: 20 CD 41 47 41 5A 49 4E 45 2E 20 20 20 20 2A 0D | .AGAZINE. *.| 00000240: 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A |****************| 00000250: 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A 2A |****************| 00000260: 2A 2A 2A 2A 2A 2A 0D 0D 0D 20 20 20 20 D4 48 4F |******... .HO| 00000270: 55 47 48 20 49 54 20 4D 41 59 20 4E 4F 54 20 53 |UGH IT MAY NOT S| 00000280: 45 45 4D 20 4F 42 56 49 4F 55 53 20 41 54 0D 46 |EEM OBVIOUS AT.F| 00000290: 49 52 53 54 2C 20 4D 55 53 49 43 20 41 4E 44 20 |IRST, MUSIC AND | 000002A0: 4D 41 54 48 45 4D 41 54 49 43 53 20 41 52 45 0D |MATHEMATICS ARE.| 000002B0: 50 52 41 43 54 49 43 41 4C 4C 59 20 4F 4E 45 20 |PRACTICALLY ONE | 000002C0: 41 4E 44 20 54 48 45 20 53 41 4D 45 2E 20 20 D4 |AND THE SAME. .| 000002D0: 48 41 54 27 53 0D 57 48 59 20 49 54 27 53 20 4E |HAT'S.WHY IT'S N| 000002E0: 4F 20 57 4F 4E 44 45 52 20 54 48 41 54 20 4F 4E |O WONDER THAT ON| 000002F0: 45 20 4F 46 20 54 48 45 0D 46 49 52 53 54 20 41 |E OF THE.FIRST A| 00000300: 50 50 4C 49 43 41 54 49 4F 4E 53 20 4F 46 20 54 |PPLICATIONS OF T| 00000310: 48 45 0D 4D 41 54 48 45 4D 41 54 49 43 41 4C 20 |HE.MATHEMATICAL | 00000320: 43 41 50 41 42 49 4C 49 54 49 45 53 20 4F 46 20 |CAPABILITIES OF | 00000330: 54 48 45 0D 43 4F 4D 50 55 54 45 52 20 57 41 53 |THE.COMPUTER WAS| 00000340: 20 49 4E 20 43 52 45 41 54 49 4E 47 20 4D 55 53 | IN CREATING MUS| 00000350: 49 43 2E 20 20 D4 48 49 53 0D 45 58 43 45 4C 4C |IC. .HIS.EXCELL| 00000360: 45 4E 54 20 50 52 4F 47 52 41 4D 20 41 4C 4C 4F |ENT PROGRAM ALLO| 00000370: 57 53 20 59 4F 55 20 54 4F 20 44 4F 0D 54 48 49 |WS YOU TO DO.THI| 00000380: 4E 47 53 20 57 49 54 48 20 4E 4F 54 45 53 20 41 |NGS WITH NOTES A| 00000390: 4E 44 20 53 43 41 4C 45 53 20 54 48 41 54 0D 50 |ND SCALES THAT.P| 000003A0: 52 45 2D 43 4F 4D 50 55 54 45 52 20 4D 55 53 49 |RE-COMPUTER MUSI| 000003B0: 43 49 41 4E 53 20 41 4E 44 20 4D 55 53 49 43 41 |CIANS AND MUSICA| 000003C0: 4C 0D 53 43 48 4F 4C 41 52 53 20 57 4F 55 4C 44 |L.SCHOLARS WOULD| 000003D0: 20 48 41 56 45 20 43 55 54 20 4F 46 46 20 54 48 | HAVE CUT OFF TH| 000003E0: 45 49 52 0D 45 41 52 53 20 54 4F 20 48 41 56 45 |EIR.EARS TO HAVE| 000003F0: 20 42 45 45 4E 20 41 42 4C 45 20 54 4F 20 44 4F | BEEN ABLE TO DO| 00000400: 2E 0D 0D 20 20 20 20 D4 C5 CD D0 C5 D2 C5 C4 20 |... ........ | 00000410: C6 D5 CE 20 4D 41 4B 45 53 20 49 54 20 45 41 53 |... MAKES IT EAS| 00000420: 59 2E 0D 0D 0D 0D 0D 20 20 20 20 C2 45 46 4F 52 |Y...... .EFOR| 00000430: 45 20 C9 20 47 4F 54 20 49 4E 54 4F 20 43 4F 4D |E . GOT INTO COM| 00000440: 50 55 54 45 52 53 2C 20 C9 0D 57 41 53 20 41 20 |PUTERS, ..WAS A | 00000450: 4D 55 53 49 43 49 41 4E 20 41 4E 44 20 4F 43 43 |MUSICIAN AND OCC| 00000460: 41 53 49 4F 4E 41 4C 20 50 49 41 4E 4F 0D 54 55 |ASIONAL PIANO.TU| 00000470: 4E 45 52 2E 20 20 C9 20 46 49 52 53 54 20 4C 45 |NER. . FIRST LE| 00000480: 41 52 4E 45 44 20 54 4F 20 54 55 4E 45 20 42 59 |ARNED TO TUNE BY| 00000490: 0D 45 41 52 20 42 55 54 20 57 48 45 4E 20 54 48 |.EAR BUT WHEN TH| 000004A0: 45 20 50 52 49 43 45 20 4F 46 20 45 4C 45 43 54 |E PRICE OF ELECT| 000004B0: 52 4F 4E 49 43 0D 54 55 4E 45 52 53 20 43 41 4D |RONIC.TUNERS CAM| 000004C0: 45 20 44 4F 57 4E 20 54 4F 20 41 20 52 45 41 53 |E DOWN TO A REAS| 000004D0: 4F 4E 41 42 4C 45 0D 4C 45 56 45 4C 20 28 41 52 |ONABLE.LEVEL (AR| 000004E0: 4F 55 4E 44 20 31 39 37 35 29 20 C9 20 53 54 41 |OUND 1975) . STA| 000004F0: 52 54 45 44 20 55 53 49 4E 47 0D 4F 4E 45 20 4F |RTED USING.ONE O| 00000500: 46 20 54 48 45 4D 20 54 4F 20 53 45 54 20 54 48 |F THEM TO SET TH| 00000510: 45 20 54 45 4D 50 45 52 41 4D 45 4E 54 20 4F 46 |E TEMPERAMENT OF| 00000520: 0D 54 48 45 20 46 49 52 53 54 2C 20 41 4E 44 20 |.THE FIRST, AND | 00000530: 4D 4F 53 54 20 44 49 46 46 49 43 55 4C 54 2C 20 |MOST DIFFICULT, | 00000540: 4F 43 54 41 56 45 0D 4F 4E 20 41 20 50 49 41 4E |OCTAVE.ON A PIAN| 00000550: 4F 2E 20 20 C9 54 20 53 45 45 4D 45 44 20 54 4F |O. .T SEEMED TO| 00000560: 20 4D 45 20 54 48 41 54 20 54 48 45 0D 48 55 4D | ME THAT THE.HUM| 00000570: 41 4E 20 45 41 52 20 57 41 53 20 4E 4F 20 4D 41 |AN EAR WAS NO MA| 00000580: 54 43 48 20 46 4F 52 20 41 20 4D 41 43 48 49 4E |TCH FOR A MACHIN| 00000590: 45 0D 57 48 45 4E 20 49 54 20 43 41 4D 45 20 54 |E.WHEN IT CAME T| 000005A0: 4F 20 43 4F 55 4E 54 49 4E 47 20 56 49 42 52 41 |O COUNTING VIBRA| 000005B0: 54 49 4F 4E 53 2E 0D 0D 20 20 20 20 C8 4F 57 45 |TIONS... .OWE| 000005C0: 56 45 52 2C 20 54 48 45 52 45 20 49 53 20 41 20 |VER, THERE IS A | 000005D0: 53 43 48 4F 4F 4C 20 4F 46 0D 54 48 4F 55 47 48 |SCHOOL OF.THOUGH| 000005E0: 54 20 54 48 41 54 20 53 41 59 53 20 54 48 41 54 |T THAT SAYS THAT| 000005F0: 20 53 49 4E 43 45 20 4D 55 53 49 43 20 49 53 0D | SINCE MUSIC IS.| 00000600: 54 4F 20 42 45 20 48 45 41 52 44 20 42 59 20 48 |TO BE HEARD BY H| 00000610: 55 4D 41 4E 20 45 41 52 53 2C 20 54 48 45 20 54 |UMAN EARS, THE T| 00000620: 55 4E 49 4E 47 0D 49 53 20 42 45 53 54 20 41 43 |UNING.IS BEST AC| 00000630: 43 4F 4D 50 4C 49 53 48 45 44 20 42 59 20 48 55 |COMPLISHED BY HU| 00000640: 4D 41 4E 20 45 41 52 53 2E 0D D3 4F 20 C9 20 47 |MAN EARS...O . G| 00000650: 55 45 53 53 20 C9 20 53 48 4F 55 4C 44 20 53 41 |UESS . SHOULD SA| 00000660: 59 2C 20 41 20 4D 41 43 48 49 4E 45 0D 43 41 4E |Y, A MACHINE.CAN| 00000670: 20 43 4F 55 4E 54 20 56 49 42 52 41 54 49 4F 4E | COUNT VIBRATION| 00000680: 53 20 42 45 54 54 45 52 20 54 48 41 4E 20 CD D9 |S BETTER THAN ..| 00000690: 0D 45 41 52 53 2E 0D 20 20 20 20 C8 41 56 45 20 |.EARS.. .AVE | 000006A0: 59 4F 55 20 45 56 45 52 20 57 4F 4E 44 45 52 45 |YOU EVER WONDERE| 000006B0: 44 20 57 48 59 20 54 48 45 52 45 0D 41 52 45 20 |D WHY THERE.ARE | 000006C0: 45 49 47 48 54 20 4E 4F 54 45 53 20 49 4E 20 41 |EIGHT NOTES IN A| 000006D0: 4E 20 4F 43 54 41 56 45 3F 20 20 D7 45 0D 49 4E |N OCTAVE? .E.IN| 000006E0: 53 54 49 4E 43 54 49 56 45 4C 59 20 43 41 4E 20 |STINCTIVELY CAN | 000006F0: 54 45 4C 4C 20 49 46 20 4F 4E 45 20 4E 4F 54 45 |TELL IF ONE NOTE| 00000700: 0D 48 41 53 20 41 20 46 52 45 51 55 45 4E 43 59 |.HAS A FREQUENCY| 00000710: 20 4F 46 20 54 57 49 43 45 20 41 4E 4F 54 48 45 | OF TWICE ANOTHE| 00000720: 52 20 4E 4F 54 45 0D 41 4E 44 20 57 45 20 53 41 |R NOTE.AND WE SA| 00000730: 59 20 54 48 41 54 20 54 48 45 53 45 20 4E 4F 54 |Y THAT THESE NOT| 00000740: 45 53 20 41 52 45 20 41 4E 0D 4F 43 54 41 56 45 |ES ARE AN.OCTAVE| 00000750: 20 41 50 41 52 54 2E 20 20 D7 48 45 4E 20 59 4F | APART. .HEN YO| 00000760: 55 20 53 49 4E 47 20 54 48 45 20 57 4F 52 44 0D |U SING THE WORD.| 00000770: 22 D3 4F 4D 45 2D 57 48 45 52 45 22 20 49 4E 20 |".OME-WHERE" IN | 00000780: 54 48 45 20 53 4F 4E 47 20 22 CF 56 45 52 20 54 |THE SONG ".VER T| 00000790: 48 45 0D D2 41 49 4E 42 4F 57 22 20 59 4F 55 20 |HE..AINBOW" YOU | 000007A0: 41 52 45 20 53 49 4E 47 49 4E 47 20 54 57 4F 20 |ARE SINGING TWO | 000007B0: 4E 4F 54 45 53 20 41 4E 0D 4F 43 54 41 56 45 20 |NOTES AN.OCTAVE | 000007C0: 41 50 41 52 54 2E 20 20 C2 55 54 20 57 48 59 20 |APART. .UT WHY | 000007D0: 41 52 45 20 54 48 45 52 45 20 4F 4E 4C 59 0D 45 |ARE THERE ONLY.E| 000007E0: 4C 45 56 45 4E 20 4F 54 48 45 52 20 4E 4F 54 45 |LEVEN OTHER NOTE| 000007F0: 53 20 42 45 54 57 45 45 4E 20 54 48 45 4D 3F 20 |S BETWEEN THEM? | 00000800: 20 D7 48 59 0D 4E 4F 54 20 54 45 4E 20 4F 52 20 | .HY.NOT TEN OR | 00000810: 54 48 49 52 54 45 45 4E 3F 0D 0D 20 20 20 20 D4 |THIRTEEN?.. .| 00000820: C5 CD D0 C5 D2 C5 C4 20 C6 D5 CE 20 57 49 4C 4C |....... ... WILL| 00000830: 20 4C 45 54 20 59 4F 55 20 48 45 41 52 0D 46 4F | LET YOU HEAR.FO| 00000840: 52 20 59 4F 55 52 53 45 4C 46 20 57 48 59 2E 20 |R YOURSELF WHY. | 00000850: 20 D7 45 27 52 45 20 4E 4F 54 20 55 53 45 44 20 | .E'RE NOT USED | 00000860: 54 4F 0D 4F 44 44 42 41 4C 4C 20 54 55 4E 49 4E |TO.ODDBALL TUNIN| 00000870: 47 53 20 41 4E 44 20 54 48 45 59 20 46 52 41 4E |GS AND THEY FRAN| 00000880: 4B 4C 59 0D 53 4F 55 4E 44 20 42 41 44 2E 20 20 |KLY.SOUND BAD. | 00000890: C2 55 54 20 57 45 20 53 48 4F 55 4C 44 20 52 45 |.UT WE SHOULD RE| 000008A0: 41 4C 49 5A 45 0D 54 48 41 54 20 59 45 41 52 53 |ALIZE.THAT YEARS| 000008B0: 20 41 47 4F 2C 20 50 45 4F 50 4C 45 20 57 4F 55 | AGO, PEOPLE WOU| 000008C0: 4C 44 20 43 4F 4E 53 49 44 45 52 0D 57 48 41 54 |LD CONSIDER.WHAT| 000008D0: 20 57 45 20 4C 49 53 54 45 4E 20 54 4F 20 54 4F | WE LISTEN TO TO| 000008E0: 44 41 59 20 42 41 44 2E 20 20 CF 55 52 0D 53 45 |DAY BAD. .UR.SE| 000008F0: 4E 53 49 42 49 4C 49 54 49 45 53 20 48 41 56 45 |NSIBILITIES HAVE| 00000900: 20 43 48 41 4E 47 45 44 2E 0D 20 20 20 20 D4 48 | CHANGED.. .H| 00000910: 45 20 4D 41 4A 4F 52 20 43 48 41 4E 47 45 20 43 |E MAJOR CHANGE C| 00000920: 41 4D 45 20 57 48 45 4E 20 CA 2E 20 D3 2E 0D C2 |AME WHEN .. ....| 00000930: 41 43 48 20 43 4F 4E 56 49 4E 43 45 44 20 4D 41 |ACH CONVINCED MA| 00000940: 4E 59 20 4F 46 20 48 49 53 0D 43 4F 4E 54 45 4D |NY OF HIS.CONTEM| 00000950: 50 4F 52 41 52 49 45 53 20 54 48 41 54 20 48 55 |PORARIES THAT HU| 00000960: 4D 41 4E 53 20 57 4F 55 4C 44 20 47 45 54 0D 55 |MANS WOULD GET.U| 00000970: 53 45 44 20 54 4F 20 54 48 45 20 22 45 51 55 41 |SED TO THE "EQUA| 00000980: 4C 22 20 54 45 4D 50 45 52 41 4D 45 4E 54 20 48 |L" TEMPERAMENT H| 00000990: 45 0D 45 53 50 4F 55 53 45 44 2E 20 20 D4 48 49 |E.ESPOUSED. .HI| 000009A0: 53 20 53 43 41 4C 45 20 57 41 53 20 44 45 56 49 |S SCALE WAS DEVI| 000009B0: 53 45 44 20 42 59 0D 41 20 44 49 53 43 49 50 4C |SED BY.A DISCIPL| 000009C0: 45 20 4F 46 20 C1 52 49 53 54 4F 54 4C 45 20 4E |E OF .RISTOTLE N| 000009D0: 41 4D 45 44 0D C1 52 49 53 54 4F 58 45 4E 55 53 |AMED..RISTOXENUS| 000009E0: 2C 20 42 55 54 20 57 41 53 20 4E 45 56 45 52 20 |, BUT WAS NEVER | 000009F0: 41 44 4F 50 54 45 44 0D 55 4E 54 49 4C 20 41 20 |ADOPTED.UNTIL A | 00000A00: 4D 55 53 49 43 49 41 4E 20 4F 46 20 C2 41 43 48 |MUSICIAN OF .ACH| 00000A10: 27 53 20 53 54 41 54 55 52 45 0D 52 45 43 4F 4D |'S STATURE.RECOM| 00000A20: 4D 45 4E 44 45 44 20 49 54 2E 0D 0D 20 20 20 20 |MENDED IT... | 00000A30: C2 45 46 4F 52 45 20 C2 41 43 48 20 57 45 53 54 |.EFORE .ACH WEST| 00000A40: 45 52 4E 20 50 45 4F 50 4C 45 20 55 53 45 44 20 |ERN PEOPLE USED | 00000A50: 41 0D 22 4A 55 53 54 22 20 54 55 4E 49 4E 47 20 |A."JUST" TUNING | 00000A60: 57 48 49 43 48 20 57 41 53 20 42 41 53 45 44 20 |WHICH WAS BASED | 00000A70: 55 50 4F 4E 0D 54 48 45 20 46 41 43 54 20 54 48 |UPON.THE FACT TH| 00000A80: 41 54 20 54 48 45 20 46 4F 55 52 54 48 20 41 4E |AT THE FOURTH AN| 00000A90: 44 20 46 49 46 54 48 0D 54 4F 4E 45 53 20 4F 46 |D FIFTH.TONES OF| 00000AA0: 20 41 20 53 43 41 4C 45 20 48 41 44 20 46 52 45 | A SCALE HAD FRE| 00000AB0: 51 55 45 4E 43 49 45 53 20 54 48 41 54 0D 57 45 |QUENCIES THAT.WE| 00000AC0: 52 45 20 45 58 41 43 54 4C 59 20 34 2F 33 20 41 |RE EXACTLY 4/3 A| 00000AD0: 4E 44 20 33 2F 32 20 54 48 41 54 20 4F 46 20 54 |ND 3/2 THAT OF T| 00000AE0: 48 45 0D 52 4F 4F 54 20 4E 4F 54 45 2E 20 20 C9 |HE.ROOT NOTE. .| 00000AF0: 46 20 C1 20 48 41 44 20 41 20 46 52 45 51 55 45 |F . HAD A FREQUE| 00000B00: 4E 43 59 20 4F 46 0D 34 34 30 20 48 45 52 54 5A |NCY OF.440 HERTZ| 00000B10: 2C 20 54 48 45 4E 20 C4 20 57 41 53 20 35 38 36 |, THEN . WAS 586| 00000B20: 2E 36 37 20 28 34 34 30 0D 54 49 4D 45 53 20 34 |.67 (440.TIMES 4| 00000B30: 2F 33 29 20 41 4E 44 20 C5 20 57 41 53 20 36 36 |/3) AND . WAS 66| 00000B40: 30 20 28 34 34 30 20 54 49 4D 45 53 0D 33 2F 32 |0 (440 TIMES.3/2| 00000B50: 29 2E 0D 20 20 20 20 D4 48 45 20 43 48 41 52 4D |).. .HE CHARM| 00000B60: 20 4F 46 20 54 48 49 53 20 54 55 4E 49 4E 47 20 | OF THIS TUNING | 00000B70: 57 41 53 20 54 48 41 54 0D 41 4E 59 20 53 4F 4E |WAS THAT.ANY SON| 00000B80: 47 53 20 49 4E 20 54 48 45 20 4B 45 59 20 4F 46 |GS IN THE KEY OF| 00000B90: 20 C1 20 53 4F 55 4E 44 45 44 0D 47 52 45 41 54 | . SOUNDED.GREAT| 00000BA0: 2E 20 20 D4 48 45 20 50 52 4F 42 4C 45 4D 20 57 |. .HE PROBLEM W| 00000BB0: 49 54 48 20 54 48 49 53 20 54 55 4E 49 4E 47 0D |ITH THIS TUNING.| 00000BC0: 57 41 53 20 54 48 41 54 20 53 4F 4E 47 53 20 49 |WAS THAT SONGS I| 00000BD0: 4E 20 41 4E 59 20 4F 54 48 45 52 20 4B 45 59 0D |N ANY OTHER KEY.| 00000BE0: 44 49 44 4E 27 54 20 53 4F 55 4E 44 20 47 52 45 |DIDN'T SOUND GRE| 00000BF0: 41 54 2E 20 20 C1 53 20 41 20 4D 41 54 54 45 52 |AT. .S A MATTER| 00000C00: 20 4F 46 0D 46 41 43 54 2C 20 54 48 45 59 20 53 | OF.FACT, THEY S| 00000C10: 4F 55 4E 44 45 44 20 4C 4F 55 53 59 2E 20 20 C3 |OUNDED LOUSY. .| 00000C20: 4F 4E 43 45 52 54 53 0D 49 4E 20 54 48 45 20 4F |ONCERTS.IN THE O| 00000C30: 4C 44 20 44 41 59 53 20 44 49 44 4E 27 54 20 48 |LD DAYS DIDN'T H| 00000C40: 41 56 45 20 54 48 45 0D 4E 4F 4E 2D 53 54 4F 50 |AVE THE.NON-STOP| 00000C50: 20 41 43 54 49 4F 4E 20 57 45 20 45 4E 4A 4F 59 | ACTION WE ENJOY| 00000C60: 20 28 4F 52 20 44 45 50 4C 4F 52 45 2C 0D 44 45 | (OR DEPLORE,.DE| 00000C70: 50 45 4E 44 49 4E 47 20 55 50 4F 4E 20 59 4F 55 |PENDING UPON YOU| 00000C80: 52 20 41 54 54 49 54 55 44 45 29 20 54 4F 44 41 |R ATTITUDE) TODA| 00000C90: 59 0D 42 45 43 41 55 53 45 20 41 46 54 45 52 20 |Y.BECAUSE AFTER | 00000CA0: 54 48 45 20 50 49 41 4E 49 53 54 20 50 4C 41 59 |THE PIANIST PLAY| 00000CB0: 45 44 20 41 0D 4D 41 53 54 45 52 50 49 45 43 45 |ED A.MASTERPIECE| 00000CC0: 20 49 4E 20 C1 2C 20 54 48 45 52 45 20 57 41 53 | IN ., THERE WAS| 00000CD0: 20 41 0D 53 55 42 53 54 41 4E 54 49 41 4C 20 44 | A.SUBSTANTIAL D| 00000CE0: 45 4C 41 59 20 57 48 49 4C 45 20 C9 43 48 41 42 |ELAY WHILE .CHAB| 00000CF0: 4F 44 20 54 48 45 0D 54 55 4E 45 52 20 54 52 4F |OD THE.TUNER TRO| 00000D00: 54 54 45 44 20 49 4E 20 41 4E 44 20 52 45 54 55 |TTED IN AND RETU| 00000D10: 4E 45 44 20 54 48 45 0D 50 49 41 4E 4F 20 46 4F |NED THE.PIANO FO| 00000D20: 52 20 54 48 45 20 4E 45 58 54 20 53 4F 4E 47 2C |R THE NEXT SONG,| 00000D30: 20 57 48 49 43 48 20 57 41 53 20 49 4E 0D 54 48 | WHICH WAS IN.TH| 00000D40: 45 20 4B 45 59 20 4F 46 20 C3 2E 0D 0D 20 20 20 |E KEY OF .... | 00000D50: 20 C2 41 43 48 20 43 48 41 4E 47 45 44 20 41 4C | .ACH CHANGED AL| 00000D60: 4C 20 54 48 41 54 20 57 48 45 4E 20 48 45 0D 49 |L THAT WHEN HE.I| 00000D70: 4E 53 49 53 54 45 44 20 55 50 4F 4E 20 55 53 49 |NSISTED UPON USI| 00000D80: 4E 47 20 C1 52 49 53 54 4F 58 45 4E 55 53 27 0D |NG .RISTOXENUS'.| 00000D90: 22 45 51 55 41 4C 22 20 54 45 4D 50 45 52 41 4D |"EQUAL" TEMPERAM| 00000DA0: 45 4E 54 2E 0D 20 20 20 20 D4 48 49 53 20 54 55 |ENT.. .HIS TU| 00000DB0: 4E 49 4E 47 20 44 49 56 49 44 45 44 20 54 48 45 |NING DIVIDED THE| 00000DC0: 20 4F 43 54 41 56 45 0D 49 4E 54 4F 20 54 57 45 | OCTAVE.INTO TWE| 00000DD0: 4C 56 45 20 45 51 55 41 4C 20 49 4E 54 45 52 56 |LVE EQUAL INTERV| 00000DE0: 41 4C 53 2E 20 20 C5 41 43 48 0D 4E 4F 54 45 20 |ALS. .ACH.NOTE | 00000DF0: 48 41 53 20 41 20 46 52 45 51 55 45 4E 43 59 20 |HAS A FREQUENCY | 00000E00: 54 48 41 54 20 49 53 20 31 2E 30 35 39 34 36 0D |THAT IS 1.05946.| 00000E10: 54 49 4D 45 53 20 54 48 45 20 4E 45 58 54 20 4C |TIMES THE NEXT L| 00000E20: 4F 57 45 52 20 4E 4F 54 45 2E 20 20 31 2E 30 35 |OWER NOTE. 1.05| 00000E30: 39 34 36 0D 49 53 20 54 48 45 20 54 57 45 4C 46 |946.IS THE TWELF| 00000E40: 54 48 20 52 4F 4F 54 20 4F 46 20 32 2E 0D 0D 20 |TH ROOT OF 2... | 00000E50: 20 20 20 D7 49 54 48 20 54 48 49 53 20 54 55 4E | .ITH THIS TUN| 00000E60: 49 4E 47 2C 20 54 48 45 20 4E 4F 54 45 53 20 4F |ING, THE NOTES O| 00000E70: 46 0D 54 48 45 20 53 43 41 4C 45 2C 20 50 41 52 |F.THE SCALE, PAR| 00000E80: 54 49 43 55 4C 41 52 4C 59 20 54 48 45 20 46 4F |TICULARLY THE FO| 00000E90: 55 52 54 48 0D 41 4E 44 20 46 49 46 54 48 20 4F |URTH.AND FIFTH O| 00000EA0: 4E 45 53 2C 20 57 49 4C 4C 20 53 4F 55 4E 44 20 |NES, WILL SOUND | 00000EB0: 41 20 4C 49 54 54 4C 45 0D 4F 55 54 20 4F 46 20 |A LITTLE.OUT OF | 00000EC0: 54 55 4E 45 2E 20 20 C2 55 54 20 2D 20 41 4E 44 |TUNE. .UT - AND| 00000ED0: 20 54 48 49 53 20 49 53 20 54 48 45 0D 52 45 41 | THIS IS THE.REA| 00000EE0: 53 4F 4E 20 46 4F 52 20 55 53 49 4E 47 20 41 4E |SON FOR USING AN| 00000EF0: 20 22 45 51 55 41 4C 22 0D 54 45 4D 50 45 52 41 | "EQUAL".TEMPERA| 00000F00: 4D 45 4E 54 20 2D 20 41 4E 59 20 4B 45 59 20 59 |MENT - ANY KEY Y| 00000F10: 4F 55 20 50 4C 41 59 20 49 4E 0D 57 49 4C 4C 20 |OU PLAY IN.WILL | 00000F20: 53 4F 55 4E 44 20 45 51 55 41 4C 4C 59 20 4F 55 |SOUND EQUALLY OU| 00000F30: 54 20 4F 46 20 54 55 4E 45 2E 20 20 D4 48 45 0D |T OF TUNE. .HE.| 00000F40: 41 4D 4F 55 4E 54 20 54 48 41 54 20 49 54 27 53 |AMOUNT THAT IT'S| 00000F50: 20 4F 55 54 20 49 53 20 53 4F 20 53 4D 41 4C 4C | OUT IS SO SMALL| 00000F60: 20 54 48 41 54 0D C2 41 43 48 20 54 48 4F 55 47 | THAT..ACH THOUG| 00000F70: 48 54 20 57 45 20 43 4F 55 4C 44 20 47 45 54 20 |HT WE COULD GET | 00000F80: 55 53 45 44 20 54 4F 20 49 54 2E 0D CF 4E 43 45 |USED TO IT...NCE| 00000F90: 20 57 45 20 44 49 44 2C 20 54 48 45 20 50 49 41 | WE DID, THE PIA| 00000FA0: 4E 49 53 54 20 43 4F 55 4C 44 20 50 4C 41 59 0D |NIST COULD PLAY.| 00000FB0: 49 4E 20 41 4E 59 20 4B 45 59 20 57 49 54 48 4F |IN ANY KEY WITHO| 00000FC0: 55 54 20 48 41 56 49 4E 47 20 C9 43 48 41 42 4F |UT HAVING .CHABO| 00000FD0: 44 20 4F 4E 0D 48 41 4E 44 2E 0D 0D 20 20 20 20 |D ON.HAND... | 00000FE0: D4 48 45 52 45 20 49 53 20 41 20 57 45 41 4C 54 |.HERE IS A WEALT| 00000FF0: 48 20 4F 46 20 49 4E 46 4F 52 4D 41 54 49 4F 4E |H OF INFORMATION| 00001000: 0D 50 55 42 4C 49 53 48 45 44 20 4F 4E 20 54 48 |.PUBLISHED ON TH| 00001010: 45 20 50 48 45 4E 4F 4D 45 4E 41 20 4F 46 0D 54 |E PHENOMENA OF.T| 00001020: 55 4E 49 4E 47 53 2C 20 54 45 4D 50 45 52 41 4D |UNINGS, TEMPERAM| 00001030: 45 4E 54 53 2C 20 41 43 4F 55 53 54 49 43 53 2C |ENTS, ACOUSTICS,| 00001040: 0D 50 48 59 43 48 4F 2D 41 43 4F 55 53 54 49 43 |.PHYCHO-ACOUSTIC| 00001050: 53 20 41 4E 44 20 50 48 59 53 49 4F 4C 4F 47 59 |S AND PHYSIOLOGY| 00001060: 20 54 48 41 54 0D 57 49 4C 4C 20 54 45 4C 4C 20 | THAT.WILL TELL | 00001070: 59 4F 55 20 4D 55 43 48 20 4D 4F 52 45 2E 20 20 |YOU MUCH MORE. | 00001080: D4 48 45 20 41 52 54 49 43 4C 45 0D 42 59 20 D0 |.HE ARTICLE.BY .| 00001090: 41 55 4C 20 D2 2E 20 CD 41 43 48 55 4C 41 20 49 |AUL .. .ACHULA I| 000010A0: 4E 20 54 48 45 20 C1 55 47 55 53 54 0D C9 53 53 |N THE .UGUST..SS| 000010B0: 55 45 20 4F 46 20 C3 4F 4D 4D 4F 44 4F 52 45 20 |UE OF .OMMODORE | 000010C0: CD 41 47 41 5A 49 4E 45 20 48 41 53 20 41 20 4C |.AGAZINE HAS A L| 000010D0: 4F 54 0D 4F 46 20 49 4E 54 45 52 45 53 54 49 4E |OT.OF INTERESTIN| 000010E0: 47 20 49 4E 46 4F 52 4D 41 54 49 4F 4E 20 54 4F |G INFORMATION TO| 000010F0: 4F 2E 0D 0D 20 20 20 20 D4 48 45 20 50 52 4F 47 |O... .HE PROG| 00001100: 52 41 4D 20 49 53 20 4D 45 4E 55 2D 44 52 49 56 |RAM IS MENU-DRIV| 00001110: 45 4E 20 53 4F 20 59 4F 55 0D 43 41 4E 20 45 41 |EN SO YOU.CAN EA| 00001120: 53 49 4C 59 20 43 48 4F 4F 53 45 20 54 48 45 20 |SILY CHOOSE THE | 00001130: 50 41 52 41 4D 45 54 45 52 53 20 46 4F 52 0D 41 |PARAMETERS FOR.A| 00001140: 4E 59 54 48 49 4E 47 20 59 4F 55 27 44 20 4C 49 |NYTHING YOU'D LI| 00001150: 4B 45 20 54 4F 20 48 45 41 52 2E 20 20 C1 4C 4C |KE TO HEAR. .LL| 00001160: 20 59 4F 55 0D 48 41 56 45 20 54 4F 20 44 4F 20 | YOU.HAVE TO DO | 00001170: 49 53 20 50 52 45 53 53 20 41 20 46 45 57 20 4E |IS PRESS A FEW N| 00001180: 55 4D 42 45 52 53 20 41 4E 44 0D 59 4F 55 20 43 |UMBERS AND.YOU C| 00001190: 41 4E 20 43 4F 4D 50 41 52 45 20 54 55 4E 49 4E |AN COMPARE TUNIN| 000011A0: 47 53 2C 20 43 48 4F 52 44 53 20 41 4E 44 0D 4D |GS, CHORDS AND.M| 000011B0: 45 4C 4F 44 49 45 53 2E 20 20 C2 41 43 48 20 57 |ELODIES. .ACH W| 000011C0: 4F 55 4C 44 20 48 41 56 45 20 4B 49 4C 4C 45 44 |OULD HAVE KILLED| 000011D0: 20 46 4F 52 0D 54 48 49 53 20 50 52 4F 47 52 41 | FOR.THIS PROGRA| 000011E0: 4D 21 0D 0D 0D 0D 0D 20 20 20 20 D4 48 45 52 45 |M!..... .HERE| 000011F0: 20 41 52 45 20 46 49 56 45 20 54 45 4D 50 45 52 | ARE FIVE TEMPER| 00001200: 41 4D 45 4E 54 53 2E 20 20 D4 48 45 0D 54 45 4D |AMENTS. .HE.TEM| 00001210: 50 45 52 41 4D 45 4E 54 20 49 53 20 54 48 45 20 |PERAMENT IS THE | 00001220: 4D 45 54 48 4F 44 20 4F 46 20 44 49 56 49 44 49 |METHOD OF DIVIDI| 00001230: 4E 47 0D 54 48 45 20 4F 43 54 41 56 45 20 49 4E |NG.THE OCTAVE IN| 00001240: 54 4F 20 50 41 52 54 53 2E 20 20 D9 4F 55 20 43 |TO PARTS. .OU C| 00001250: 41 4E 20 45 56 45 4E 0D 43 48 4F 53 45 20 59 4F |AN EVEN.CHOSE YO| 00001260: 55 52 20 4F 57 4E 20 54 45 4D 50 45 52 41 4D 45 |UR OWN TEMPERAME| 00001270: 4E 54 2E 0D 0D 20 20 20 20 CE 45 58 54 20 59 4F |NT... .EXT YO| 00001280: 55 20 43 48 4F 4F 53 45 20 54 48 45 20 53 43 41 |U CHOOSE THE SCA| 00001290: 4C 45 20 59 4F 55 0D 57 41 4E 54 20 54 4F 20 48 |LE YOU.WANT TO H| 000012A0: 45 41 52 2E 20 20 C1 20 42 4F 4F 4B 20 4F 4E 20 |EAR. . 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SHARP I| 00001870: 53 0D 45 58 41 43 54 4C 59 20 54 48 45 20 53 41 |S.EXACTLY THE SA| 00001880: 4D 45 20 4E 4F 54 45 20 41 53 20 C2 20 46 4C 41 |ME NOTE AS . FLA| 00001890: 54 2E 20 20 C9 4E 0D 54 48 45 20 4F 54 48 45 52 |T. .N.THE OTHER| 000018A0: 20 54 45 4D 50 45 52 41 4D 45 4E 54 53 2C 20 54 | TEMPERAMENTS, T| 000018B0: 48 45 59 20 41 52 45 0D 53 4C 49 47 48 54 4C 59 |HEY ARE.SLIGHTLY| 000018C0: 20 44 49 46 46 45 52 45 4E 54 2E 0D 0D 20 20 20 | DIFFERENT... | 000018D0: C2 55 54 20 C9 27 56 45 20 52 41 4D 42 4C 45 44 |.UT .'VE RAMBLED| 000018E0: 20 4F 4E 20 57 41 59 20 54 4F 4F 20 4D 55 43 48 | ON WAY TOO MUCH| 000018F0: 2E 0D D4 48 45 20 42 45 53 54 20 57 41 59 20 54 |...HE BEST WAY T| 00001900: 4F 20 45 4E 4A 4F 59 20 54 48 49 53 20 50 52 4F |O ENJOY THIS PRO| 00001910: 47 52 41 4D 20 49 53 0D 54 4F 20 50 4C 41 59 20 |GRAM IS.TO PLAY | 00001920: 57 49 54 48 20 49 54 2E 20 20 CD 55 53 49 43 49 |WITH IT. .USICI| 00001930: 41 4E 20 4F 52 20 4E 4F 54 2C 0D 59 4F 55 20 43 |AN OR NOT,.YOU C| 00001940: 41 4E 20 4C 45 41 52 4E 20 41 4E 44 20 48 41 56 |AN LEARN AND HAV| 00001950: 45 20 46 55 4E 20 57 49 54 48 20 49 54 2E 0D 0D |E FUN WITH IT...| 00001960: 0D C4 C9 D3 CB 20 C6 C9 CC C5 D3 20 D4 C8 C9 D3 |..... ..... ....| 00001970: 20 D0 D2 CF C7 D2 C1 CD 20 D5 D3 C5 D3 0D 0D D4 | ....... .......| 00001980: C5 CD D0 C5 D2 C5 C4 20 C6 D5 CE 20 20 20 20 20 |....... ... | 00001990: 20 20 D4 2E 20 D4 C5 CD D0 C5 D2 C5 C4 20 C6 D5 | .. ........ ..| 000019A0: CE 0D 0D 20 20 20 20 20 20 20 20 2A 2A 2A 2A 20 |... **** | 000019B0: C5 4E 44 20 4F 46 20 D4 45 58 54 20 2A 2A 2A 2A |.ND OF .EXT ****| 000019C0: 0D |. |
..^U:CBM. T E M P E R E D F U N..
BY PAUL R. MACHULA..***********
***************************.* YES, VIRG
INIA, THIS SAME PROGRAM *.* WAS PUBL
ISHED IN LAST MONTH'S *.* LOADSTAR.
IT WAS SENT TO US BY *.* COMMODORE MA
GAZINE LAST MONTH AND *.* WHEN WE GOT WO
RD FROM THEM THAT IT *.* HAD BEEN 'BUMP
ED' FOR ONE REASON *.* OR ANOTHER, IT
WAS TOO LATE FOR *.* US TO HALT ITS
PUBLICATION ON *.* LOADSTAR. WE DECI
DED TO REPUBLISH *.* IT SO THAT THIS ISS
UE OF LOADSTAR *.* WOULD BETTER MATCH
THE AUGUST *.* ISSUE OF COMMODORE
MAGAZINE. *.************************
**************... THOUGH IT MAY NOT S
EEM OBVIOUS AT.FIRST, MUSIC AND MATHEMAT
ICS ARE.PRACTICALLY ONE AND THE SAME. T
HAT'S.WHY IT'S NO WONDER THAT ONE OF THE
.FIRST APPLICATIONS OF THE.MATHEMATICAL
CAPABILITIES OF THE.COMPUTER WAS IN CREA
TING MUSIC. THIS.EXCELLENT PROGRAM ALLO
WS YOU TO DO.THINGS WITH NOTES AND SCALE
S THAT.PRE-COMPUTER MUSICIANS AND MUSICA
L.SCHOLARS WOULD HAVE CUT OFF THEIR.EARS
TO HAVE BEEN ABLE TO DO... TEMPERED
FUN MAKES IT EASY...... BEFORE I GOT
INTO COMPUTERS, I.WAS A MUSICIAN AND OCC
ASIONAL PIANO.TUNER. I FIRST LEARNED TO
TUNE BY.EAR BUT WHEN THE PRICE OF ELECT
RONIC.TUNERS CAME DOWN TO A REASONABLE.L
EVEL (AROUND 1975) I STARTED USING.ONE O
F THEM TO SET THE TEMPERAMENT OF.THE FIR
ST, AND MOST DIFFICULT, OCTAVE.ON A PIAN
O. IT SEEMED TO ME THAT THE.HUMAN EAR W
AS NO MATCH FOR A MACHINE.WHEN IT CAME T
O COUNTING VIBRATIONS... HOWEVER, THE
RE IS A SCHOOL OF.THOUGHT THAT SAYS THAT
SINCE MUSIC IS.TO BE HEARD BY HUMAN EAR
S, THE TUNING.IS BEST ACCOMPLISHED BY HU
MAN EARS..SO I GUESS I SHOULD SAY, A MAC
HINE.CAN COUNT VIBRATIONS BETTER THAN MY
.EARS.. HAVE YOU EVER WONDERED WHY TH
ERE.ARE EIGHT NOTES IN AN OCTAVE? WE.IN
STINCTIVELY CAN TELL IF ONE NOTE.HAS A F
REQUENCY OF TWICE ANOTHER NOTE.AND WE SA
Y THAT THESE NOTES ARE AN.OCTAVE APART.
WHEN YOU SING THE WORD."SOME-WHERE" IN
THE SONG "OVER THE.RAINBOW" YOU ARE SING
ING TWO NOTES AN.OCTAVE APART. BUT WHY
ARE THERE ONLY.ELEVEN OTHER NOTES BETWEE
N THEM? WHY.NOT TEN OR THIRTEEN?.. T
EMPERED FUN WILL LET YOU HEAR.FOR YOURSE
LF WHY. WE'RE NOT USED TO.ODDBALL TUNIN
GS AND THEY FRANKLY.SOUND BAD. BUT WE S
HOULD REALIZE.THAT YEARS AGO, PEOPLE WOU
LD CONSIDER.WHAT WE LISTEN TO TODAY BAD.
OUR.SENSIBILITIES HAVE CHANGED.. TH
E MAJOR CHANGE CAME WHEN J. S..BACH CONV
INCED MANY OF HIS.CONTEMPORARIES THAT HU
MANS WOULD GET.USED TO THE "EQUAL" TEMPE
RAMENT HE.ESPOUSED. THIS SCALE WAS DEVI
SED BY.A DISCIPLE OF ARISTOTLE NAMED.ARI
STOXENUS, BUT WAS NEVER ADOPTED.UNTIL A
MUSICIAN OF BACH'S STATURE.RECOMMENDED I
T... BEFORE BACH WESTERN PEOPLE USED
A."JUST" TUNING WHICH WAS BASED UPON.THE
FACT THAT THE FOURTH AND FIFTH.TONES OF
A SCALE HAD FREQUENCIES THAT.WERE EXACT
LY 4/3 AND 3/2 THAT OF THE.ROOT NOTE. I
F A HAD A FREQUENCY OF.440 HERTZ, THEN D
WAS 586.67 (440.TIMES 4/3) AND E WAS 66
0 (440 TIMES.3/2).. THE CHARM OF THIS
TUNING WAS THAT.ANY SONGS IN THE KEY OF
A SOUNDED.GREAT. THE PROBLEM WITH THIS
TUNING.WAS THAT SONGS IN ANY OTHER KEY.
DIDN'T SOUND GREAT. AS A MATTER OF.FACT
, THEY SOUNDED LOUSY. CONCERTS.IN THE O
LD DAYS DIDN'T HAVE THE.NON-STOP ACTION
WE ENJOY (OR DEPLORE,.DEPENDING UPON YOU
R ATTITUDE) TODAY.BECAUSE AFTER THE PIAN
IST PLAYED A.MASTERPIECE IN A, THERE WAS
A.SUBSTANTIAL DELAY WHILE ICHABOD THE.T
UNER TROTTED IN AND RETUNED THE.PIANO FO
R THE NEXT SONG, WHICH WAS IN.THE KEY OF
C... BACH CHANGED ALL THAT WHEN HE.I
NSISTED UPON USING ARISTOXENUS'."EQUAL"
TEMPERAMENT.. THIS TUNING DIVIDED THE
OCTAVE.INTO TWELVE EQUAL INTERVALS. EA
CH.NOTE HAS A FREQUENCY THAT IS 1.05946.
TIMES THE NEXT LOWER NOTE. 1.05946.IS T
HE TWELFTH ROOT OF 2... WITH THIS TUN
ING, THE NOTES OF.THE SCALE, PARTICULARL
Y THE FOURTH.AND FIFTH ONES, WILL SOUND
A LITTLE.OUT OF TUNE. BUT - AND THIS IS
THE.REASON FOR USING AN "EQUAL".TEMPERA
MENT - ANY KEY YOU PLAY IN.WILL SOUND EQ
UALLY OUT OF TUNE. THE.AMOUNT THAT IT'S
OUT IS SO SMALL THAT.BACH THOUGHT WE CO
ULD GET USED TO IT..ONCE WE DID, THE PIA
NIST COULD PLAY.IN ANY KEY WITHOUT HAVIN
G ICHABOD ON.HAND... THERE IS A WEALT
H OF INFORMATION.PUBLISHED ON THE PHENOM
ENA OF.TUNINGS, TEMPERAMENTS, ACOUSTICS,
.PHYCHO-ACOUSTICS AND PHYSIOLOGY THAT.WI
LL TELL YOU MUCH MORE. THE ARTICLE.BY P
AUL R. MACHULA IN THE AUGUST.ISSUE OF CO
MMODORE MAGAZINE HAS A LOT.OF INTERESTIN
G INFORMATION TOO... THE PROGRAM IS M
ENU-DRIVEN SO YOU.CAN EASILY CHOOSE THE
PARAMETERS FOR.ANYTHING YOU'D LIKE TO HE
AR. ALL YOU.HAVE TO DO IS PRESS A FEW N
UMBERS AND.YOU CAN COMPARE TUNINGS, CHOR
DS AND.MELODIES. BACH WOULD HAVE KILLED
FOR.THIS PROGRAM!..... THERE ARE FIV
E TEMPERAMENTS. THE.TEMPERAMENT IS THE
METHOD OF DIVIDING.THE OCTAVE INTO PARTS
. YOU CAN EVEN.CHOSE YOUR OWN TEMPERAME
NT... NEXT YOU CHOOSE THE SCALE YOU.W
ANT TO HEAR. A BOOK ON HARMONY WILL.TEL
L YOU A LOT MORE ABOUT SCALES..SINCE THE
RE ARE TWELVE HALF-TONES IN.AN OCTAVE, B
UT ONLY EIGHT OF THEM ARE.PLAYED IN A PA
RTICULAR SCALE, THE.SCALE IS GENERALLY D
ETERMINED BY.WHICH EIGHT OF THE TWELVE A
RE USED..OR, IF YOU WILL, THE FOUR NOTES
THAT.ARE NOT PLAYED..... MENU 2 THEN
SHOWS SOME THINGS YOU.CAN DO WITH THIS
SCALE. YOU CAN HEAR.THE SCALE, HEAR THE
ROOT CHORD, PLAY.WITH THE SCALE BY PRES
SING THE NUMBER.KEYS, OR LISTEN TO TWINK
LE, TWINKLE.LITTLE STAR PLAYED IN THE SC
ALE AND.TEMPERAMENT YOU CHOSE... HEAR
ING THE SONG WITH HARMONY IS.INTERESTING
, ALTHOUGH IT DOESN'T.SOUND NEARLY AS GO
OD AS TWO HUMAN.SINGERS WOULD DO. MATHE
MATICS IS.EASY ON A COMPUTER - INTELLIGE
NCE,.DISCRIMINATION AND TASTE ARE.INCRED
IBLY DIFFICULT. HOW CAN YOU.PROGRAM A C
OMPUTER TO DECIDE IF A.NOTE OR HARMONY S
OUNDS 'GOOD'?.... TRY CHOOSING YOUR O
WN TEMPERAMENT.FROM THE FIRST MENU AND D
IVIDE THE.OCTAVE INTO 1200 INTERVALS. T
HE.COMPUTER WILL PLAY A STEADY REFERENCE
.NOTE AND AT THE SAME TIME GRADUALLY.INC
REASE ANOTHER NOTE. THE TWO NOTES.HEARD
SIMULTANEOUSLY WILL PRODUCE A."BEAT" FR
EQUENCY THAT GRADUALLY.INCREASES IN FREQ
UENCY TOO. THIS."BEAT" FREQUENCY IS WHA
T PIANO TUNERS.LISTEN FOR. IT'S SORT OF
AN AURAL.MOIRE PATTERN, WHICH IS A RESU
LTANT.PATTERN FORMED BY THE INTERSECTION
OF.TWO DIFFERENT PATTERNS...... NOTI
CE THAT IF YOU CHOOSE ANY.OTHER TEMPERAM
ENT OTHER THAN "EQUAL".YOU'LL BE ASKED F
OR SHARPS OR FLATS..IN THE "EQUAL" TEMPE
RAMENT A SHARP IS.EXACTLY THE SAME NOTE
AS B FLAT. IN.THE OTHER TEMPERAMENTS, T
HEY ARE.SLIGHTLY DIFFERENT... BUT I'VE
RAMBLED ON WAY TOO MUCH..THE BEST WAY T
O ENJOY THIS PROGRAM IS.TO PLAY WITH IT.
MUSICIAN OR NOT,.YOU CAN LEARN AND HAV
E FUN WITH IT....DISK FILES THIS PROGRAM
USES..TEMPERED FUN T. TEMPERED FU
N.. **** END OF TEXT ****.
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