PIAGUI IV SCALE

The best option on piano tuning.

P = 1,05707299111

W= 1,06425952555

------27,5 A Key Nº 1

xP= 29,06950 =Bb

xW= 30,93750 =B PIAGUI IV (HZ)

xP= 32,70319 =C Keyboard Tone Frequencies.

xP= 34,56966 =C#

xW= 36,79109 =D

xP= 38,89087 =Eb

xP= 41,11049 =E The optimal 88 tuned frequencies will be

xW= 43,75223 =F given in the coming days.

xP= 46,24930 =F#

xP= 48,88888 =G Enjoy the harmony and brilliance

xW= 52,03046 =Ab of the Piagui IV chords.

xP= 55 =A

xP= 58,13901 =Bb MIDDLE

xW= 61,87500 =B OCTAVE

xP = 65,40637 130,81278 C 261,62556 523,25113 1046,50226 xP = C#

xP = 69,13931 138,27862 C# 276,55731 553,11463 1106,22927 xW= D

xW= 73,58217 147,16434 D 294,32876 588,65752 1177,31504 xP = Eb

xP= 77,78172 155,56345 Eb 311,12698 622,25396 1244,50793 xP = E

xP= 82,22096 164,44192 E 328,88393 657,76786 1315,53572 xW= F

xW= 87,50444 175,00888 F 350,01785 700,03571 1400,07142 xP = F#

xP= 92,49860 184,99716 F# 369,99442 739,98884 1479,97769 xP = G

xP= 97,77777 195,55555 G 391,11111 782,22222 1564,44444 xW= Ab

xW= 104,06093 208,12186 Ab 416,24372 832,48745 1664,97490 xP = A

xP= 110 220 A 440 880 1760 xP = Bb

xP= 116,27803 232,55605 Bb 465,11211 930,22423 1860,44846 xW= B

xW= 123,75 247,5 B 495 990 1980 xP = C

xP= 130,81278 261,62556 2C 523,25113 1046,50226 2093,00452 xP = C#

These are the theoretical tone frequencies before the

needed adjustments that must be done due to the C# 2212,45855 xW=D

imperfections of the ear of man. Once the corrections D 2354,63008 xP =Eb

in all the keys but the middle octave are done, a list of Eb 2489,01587 xP =E

the tuned frequencies establishes the optimal data E 2631,07145 xW=F

to be attained by measuring the pitches already tuned F 2800,14285 xP =F#

by means of an electronic frequency counter. The tuned F# 2959,95538 xP=G

frequency list makes that the tunings by ear of the next G 3128,88888 xW=Ab

keyboard instruments are replaced by frequency Ab 3329,94980 xP =A

measurements of the piano strings. This method A 3520 xP =Bb

reduces the time of tunings, simplifies them Bb 3720,89693 xW=B

considerably and gives accurate results. B 3960 xP =C

.................................................................Key Nº 88 C 4186,00904 Hz

Mario Pizarro

Lima, August 27,2008

< piagui@ec-red.com >