--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote/asked:

> Andreas, my dear fellow, I am most interested in knowing what truly
> exceptional super-human auditory capability you posses which allows
> you, upon hearing them, to tell a 704 cent fifth from a 700 cent
> fifth. They both beat extremely slowly by exactly the same amount.
> Have you got some sort of advanced technology in your ears, perhaps a
> harmonic Babelfish or some such?
>
Dear Paul,

nothing of all that presupmtions,
except of tuning for example on my own acoustic-piano
-as precisely as i can do that-
in the following circle of tempered 5ths:

A2 = 221 A442Hz, that's 120Metronome-Beats/min sharper above 440Hz
E4 = E331 e662 (<663 := 3*A2)
B0 = 31 62 124 248 B496 b992 (<993:=3*E4)
rem:
B0=31Hz is the lowest pitch on 5string doublebass
or the second whithe key on a modern piano, without inharmonicity
F#2 = 93 := 3*B0
C#4 = C#279 := 3*F#2
G#5 = 837 := 3*C#4
Eb3 = 158 Eb314 eb628 1256 2512 (>2151 := 3*G#5) ~+0.7Cents wide 5th
Bb4 = B471 := 3*Eb3
F4 = F353 f706 1412 (<1413 := 3*Bb4)
C5 = (33 66 132 264 528 <) 529 1058 (<1059 := 3*F4)
G2 = 99 := 3*33
D2 = 37 74 148 D296 (<297 := 3*G2)
A3 = 221 (<222 111 := 3*D2)

that's in acending order over the usual 2 tuning octaves in
http://www.xs4all.nl/~huygensf/scala/scl_format.html

!Sparschuh442wideFrench5th.scl
!
! relative deviations in the circle of 5ths, beginning from:
! 442Hz=A 662:663 E 992:993 B F# C# G#
inbetween the "french"5th G#-Eb 2512:2511 =~0.7Cents widend sharper
! Eb Bb 1412:1413 F 1058:1059 C 528:529 G 296:297 D 221:222 A=442Hz
! and with all other 5ths JI-pure or narrow flattend.
12
!
! that yields the concrete absolute pitches on the keys, starting from
! 264.5Hz C4 http://en.wikipedia.org/wiki/Middle_C
! 279 C#
! 314 Eb
! 331 E
! 353 F
! 372 F#
! 396 G
! 416.5 G#
! 442 A that's exactly 2Hz above: http://en.wikipedia.org/wiki/A440
! 471 Bb
! 496 B
! 523Hz c5 http://en.wikipedia.org/wiki/Tenor_C
558/523 ! c#
592/523 ! d
628/523 ! eb
662/523 ! e (5:4)*(2652:2645) ~4.6 Cents sharper above 5/4 JI 3rd
706/523 ! f (4:3)*(1059:1058) ~1.6 Cents sharper above 4/3 JI 4th
744/523 ! f#
792/523 ! g (3:2)*(528:529) ~3.3Cents flattend up than 3/2 JI 5th
884/523 ! a
942/523 ! bb
992/523 ! b
2/1 ! 1058Hz c6 http://en.wikipedia.org/wiki/Soprano_C
!
!

After a while in retuning and playing in that again and again:
Sooner or later,
most professional tuners become aware about the
different quality of the wide-"french"5th against
all others narrow-well ones.

Question:
How does that sound on yours piano?

Next step:
Once if you have mastered the above one and:
if you do also prefer A4=416Hz
-the modern pseudo-historically "Cammer-thone"-
then you should try out:
http://www.wegscheider-orgel.de/html/artikel.php?filename=artikel.php&tabname=Ar\
tikel&sz=22&Unterpunkt=H.C.%A0Snerha%A0und%A0die%A0Bachstimmung
with an even even about 3 times
smaller wide 5th inbetween G#-Eb
of the merely tiny deviation:

702,2276...Cent -701,9550...Cent = ~+0,2726..Cents wider than 3/2 JI.

that's even
about less than 7-times smaller
against Brad's alleged PC^(1/12) of ~+2Cents

Jsut try it out!
A.S.