Johnny's assertions about W-III, on harpsichord

A few days ago, excusing himself from reading my analysis, Johnny wrote:

> How academic. I sing Werckmeister III tuning, as I sing Harry
> Partch Li Po Songs. What you call lumpy I find dramatic. Do you fully > realize that this List includes all manner of different tuning
> systems. In recent years I have explored polymicrotonality. You could > say I have the stretched ears that George Ives hoped for his son
> Charles. I don't see how your writing how something sounds bad trumps > my hearing that same something sounding good.

All righty...this exercise is principally for Johnny, but also for Andreas and anyone else who wants to listen along.

For one who allegedly "sings" W-III and who has promoted it for many years, this should be a piece of cake. Can you recognize W-III reliably, on harpsichord, playing core repertoire from the late 17th and early 18th century? I have set up some listening examples.

Here's the introduction:
http://listserv.albany.edu:8080/cgi-bin/wa?A2=ind0806&L=hpschd-l&D=1&T=0&O=D&P=27073

There are four pieces of music in different keys, and each piece is played three times. The harpsichord, the performer (me), and the microphone are all held constant; the only thing changing here is the temperament. There are three different temperaments for comparison:

- Normal W-III.

- W-III with three notes deliberately knocked off-spot by about 5 cents each, to hear what difference that makes.

- My all-purpose experimental temp for this music of c1700, having moved 7 of the 12 notes off W-III's spots.

The sequence of presentation is a mystery, within each triple play of a composition. That's the exercise. Listen closely, and decide which is which.

Within each set of three performances, Johnny, which one is normal W-III? And in the altered version, which three notes have moved, and in which direction(s)? Of the unique beauties that you claim are present in W-III, as you encourage your non-keyboard colleagues to perform "in" W-III, which features are most important to help you discern this temperament specifically against others? (How do you know when your ensemble has succeeded or failed?)

For Andreas: in the altered version, where three notes have been knocked off-spot from W-III, please tell us *exactly* where you hear the several 707-cent 5ths or 4ths. Where are these wide ones within the circle of 5ths? (Or, if you can't pick them out at all reliably here, what's your objection to the sound of 704-cent 5ths elsewhere?)

For anyone: what adjectives would you use to characterize the differences in mood, within each set of three performances? What melodic and harmonic clues tip off the presence of W-III...and, is that necessarily a virtue, on harpsichord?

And now, to the examples....

Part 1 (F major and E minor):
http://www.youtube.com/watch?v=PPSuUGCXgXE

Part 2 (Eb major and G minor):
http://www.youtube.com/watch?v=SKyf_HSHVOo

Enjoy,
Brad Lehman

If you can remember, I did a similar listening test a while back

/tuning/topicId_69224.html#69224

I think I took the files down, but I remember the results--everybody
failed. And, for those who have them, everybody failed to even
recognize their own favorite 'pet temperaments'.

I've before and since remained a skeptic of any claims whatsoever
about the special qualities of any well-temperament. In use, in actual
music, they are all so close to each other as to be interchangable.

Sitting on a triad while tuning up for several seconds, that's a
different story, but let's not delude ourselves as to the difference
between tuning an instrument and playing actual music.

Still, have this test here, I'm curious to see the results....I'm
always for putting words to 'the test'.

-A.

--- In tuning@yahoogroups.com, Brad Lehman <bpl@...> wrote:
>
> A few days ago, excusing himself from reading my analysis, Johnny wrote:
>
> > How academic. I sing Werckmeister III tuning, as I sing Harry
> > Partch Li Po Songs. What you call lumpy I find dramatic. Do you
fully
> > realize that this List includes all manner of different tuning
> > systems. In recent years I have explored polymicrotonality. You
could
> > say I have the stretched ears that George Ives hoped for his son
> > Charles. I don't see how your writing how something sounds bad
trumps
> > my hearing that same something sounding good.
>
>
> All righty...this exercise is principally for Johnny, but also for
> Andreas and anyone else who wants to listen along.
>
> For one who allegedly "sings" W-III and who has promoted it for many
> years, this should be a piece of cake. Can you recognize W-III
> reliably, on harpsichord, playing core repertoire from the late 17th
and
> early 18th century? I have set up some listening examples.
>
> Here's the introduction:
>
http://listserv.albany.edu:8080/cgi-bin/wa?A2=ind0806&L=hpschd-l&D=1&T=0&O=D&P=27073
>
> There are four pieces of music in different keys, and each piece is
> played three times. The harpsichord, the performer (me), and the
> microphone are all held constant; the only thing changing here is the
> temperament. There are three different temperaments for comparison:
>
> - Normal W-III.
>
> - W-III with three notes deliberately knocked off-spot by about 5 cents
> each, to hear what difference that makes.
>
> - My all-purpose experimental temp for this music of c1700, having
moved
> 7 of the 12 notes off W-III's spots.
>
> The sequence of presentation is a mystery, within each triple play of a
> composition. That's the exercise. Listen closely, and decide which is
> which.
>
> Within each set of three performances, Johnny, which one is normal
> W-III? And in the altered version, which three notes have moved,
and in
> which direction(s)? Of the unique beauties that you claim are present
> in W-III, as you encourage your non-keyboard colleagues to perform "in"
> W-III, which features are most important to help you discern this
> temperament specifically against others? (How do you know when your
> ensemble has succeeded or failed?)
>
> For Andreas: in the altered version, where three notes have been
knocked
> off-spot from W-III, please tell us *exactly* where you hear the
several
> 707-cent 5ths or 4ths. Where are these wide ones within the circle of
> 5ths? (Or, if you can't pick them out at all reliably here, what's
your
> objection to the sound of 704-cent 5ths elsewhere?)
>
> For anyone: what adjectives would you use to characterize the
> differences in mood, within each set of three performances? What
> melodic and harmonic clues tip off the presence of W-III...and, is that
> necessarily a virtue, on harpsichord?
>
>
> And now, to the examples....
>
> Part 1 (F major and E minor):
> http://www.youtube.com/watch?v=PPSuUGCXgXE
>
> Part 2 (Eb major and G minor):
> http://www.youtube.com/watch?v=SKyf_HSHVOo
>
>
> Enjoy,
> Brad Lehman
>

--- In tuning@yahoogroups.com, Brad Lehman <bpl@...> wrote:

> All righty...this exercise is principally for Johnny, but also for
> Andreas and anyone else who wants to listen along.
...
>
> For Andreas: in the altered version, where three notes have been
knocked
> off-spot from W-III, please tell us *exactly* where you hear the
several
> 707-cent 5ths or 4ths. Where are these wide ones within the circle of
> 5ths? (Or, if you can't pick them out at all reliably here, what's
your
> objection to the sound of 704-cent 5ths elsewhere?)
>
>
Hi Brad & all others lovers of his wide"French"-5ths hypothesis,

Johnny also disagrees with Brad's hypothesis in:
/tuning/topicId_77237.html#77284
quote:
"My instincts agree with Andreas's;
Bach's fifths were flatted in only one direction from just."

So thinks also too
M.Zapf's & K.Brigs in their's reinterpretation (May 2003):
http://keithbriggs.info/bach-wtc.html

But here my new proposal inbetween 2 others modern "Bach"-tunings:

1. Tom Dent's A4=419Hz reinterpretation of "squiggle"(Sept. 1999)
http://f1.grp.yahoofs.com/v1/EMtjSBdDLKZenwXKL3g47vURgGdMST8RbE8t_v0Qk2vomRsmHmEkPAruVkHuEJP6ulPx-wG95MVU6lEp6FDVq3SEJwcSCw/sparsgraph.txt

2. Kristian's A4=416Hz
http://www.wegscheider-orgel.de/html/artikel.php?filename=artikel.php&tabname=Artikel&sz=22&Unterpunkt=H.C.%A0Snerha%A0und%A0die%A0Bachstimmung
vomRsmHmEkPAruVkHuEJP6ulPx-wG95MVU6lEp6FDVq3SEJwcSCw/sparsgraph.txt

Presented as double inequality for the 12 absolute-pitches inbetween:

Tom Dent's 419Hz "squiggle" >= new-proposal 418Hz >= Wegscheider 416Hz

compare that 3 ones in chromatically order:

c' 250 > 249.5 < 248.7 at 'middle-C4'
C# 264 = 264 < 262.279688...
D: 280 = 280 < 278
Eb 297 > 296 > 295.111111...
E: 314 > 312 > (311,25 = 311+1/4)
F: 333.5> 333 > 332
F# 352 > 351 > 349,70625
G: 374 = 374 > 372.05
G# 396 > 394.75> 393,419531...
A: 419 > 418 > 416 > neo-"Baroque" modern 'Cammer-Thone' ~415Hz
Bb 445 > 444 > (442.66666... = 442+2/3)
B: 470 > 468 > 466.275
c" 500 > 499 > 497.4 at 'tenor-C5'

!Sparschuh418ib_Wegscheider_Dent.scl
12
Inbetween K.Wegscheider416Hz(June2003) and T.Dent419Hz(September2006)
!
1059/998 ! C# 529.5'tenor-C#5'/499
560/499 ! D
592/499 ! Eb
624/499 ! E (5:4)*(2496:2495) ~0.7 Cents wider than an 5/4 JI 3rd
666/499 ! F (4:3)*(999:998) ~1.7 Cents wider than an 4/3 JI 4th
702/499 ! F#
748/499 ! G (3:2)*(1496:1497)~-1.2 Cents narrower than an 3/2 JI 5th
1579/998 ! G# 789.5/499
836/499 ! A5 that's an octave above the absolute A4=418Hz reference
888/499 ! Bb
936/499 ! B
2/1 ! C6 = 998 'sopran-C6'
!

That proposal meets even Johnny demands
due to satisfying Sorge's condition:
All 5ths in that become barely tempered down in one direction
by the following 7 epimoric ratios lowered inbetween the 5ths,
that do amout totally an PC=3^12/2^19

499Hz=C5 1496:1497 G 560:561 D 209:210 A 208:209 E B F# C#...
C# 3158:3159 G# 4736:4737 Eb Bb F 998:999 C5=499Hz

or as expanded cycle of a dozen duodecimes 3:2 and
19-times octaves 2:1 down:

C5 = 499 'tenor-C5'
G2 = 187 374 748 1496 (<1497 := 3*C5)
D2 = 70 140 280 560 (<561 := 3*G2)
A3 = (13 26 52 104 208<) 209 (<210 := 3*D2)
E1 = 39 := 3*13
B2 = 117 := 9*13
F#4 = 351 :=27*13
C#6 = 1059 :=81*13
G#6 = 1579 3158 (<3159 := 243*13)
Eb1 = 37 74 148 296 592 1184 2368 4736 (<4737 := 3*G#6)
Bb2 = 111 := 3*Eb1
F4 = 333 := 3*Bb2
C5 = 499 998 (<999 := 3*F4)

if you posseses by change an todays modern
http://en.wikipedia.org/wiki/Harpsichord
that meets even:
"Tuning Pitch in nowadays' practice is taken often at a=415 Hz, a
semitone below modern standard concert pitch of a=440 Hz."
or more precisely:
http://en.wikipedia.org/wiki/Piano_key_frequencies
# "48 gb/b2/ab-b2 Gb/4/Ab-4 ~415.305..."

when calculated from an theoretically 12-EDO step downwards:
440 / 2^(1/12) = ~415.304698...

with even 2 different keyboards for 2 independent 8-foot stops
then try to tune in practice on the one hand:
Wegscheider416Hz
versus on the other manual
Dent419Hz.

After that unify that both versions in one instrument
by synchonizing them to the above procedure into
the new intermediate tuning, in order to get rid of
'objections' against Wegscheider's broade-"French"5th.

Who in that group here dares to tune that new
another 'Bach' on his/hers own 415Hz instument?

No warranty garanteed for what happens then!

Yours Sincerely
A.S.

--- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@...>
wrote:
>
> --- In tuning@yahoogroups.com, Brad Lehman <bpl@> wrote:
>
I don't know abot others, here, Andreas, but I am not even gonna try
to unravel what you might trying to say until you stop doing several
rediculous things:

(1) Peppering you posts with endless wiki links for really stupid
things, like middle C or piano keyboard frequencies.

(2) Start using just ONE clear and easy to understand method for
indicating temperaments. All that scala mismash and wierd stuff like
multiplying frequencies by 3 instead of 1,5 just makes it all not
worth the time.

Try being simple and clear for just once. Maybe you've really got
something to say, who knows? At the moment it just looks like the
ravings of a madman.

Ciao,

P

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

Hi Paul,
> Start using just ONE clear and easy to understand method for
> indicating temperaments.
Simply consider all given values there
as frequencies in Hz of absolute pitches,
that are subjects of 3 possible sequential operations:

Algorithm for synchroneous well-temperaments:
1. Step 19-times an octaves down, by halfing the pitch-frequency
2. Go 12 times to partial 3:1, by multipying with facor 3.
occasional
3. Decrement frequncy by -1Hz down, when intend tempering flattend.

but only if you insist in "wide-5ths" then allow also too:
(4. Increment by +1Hz upwards, for an sharper "French"-5th.)

Comeback condition:
Choose the chain of flow in the operation sequence
so that the circle of a dozen 5ths returns back to the initial
start after 12times 3:1 and 19times 1:2 while fitting the
decrements so, that they yield an distribution of the PC=3^12:2^19
into
http://en.wikipedia.org/wiki/Superparticular_ratio
s.

> All that scala mismash and wierd stuff like
> multiplying frequencies by 3 instead of 1,5 just makes it all not
> worth the time.

That ratio of 3/2 = 1.5 arises operationally from taking the
quotient of the 3rd partial (3:1) over an octve (2:1),
when realting that both overtones #2 and #3 to theirs fundamental
(1:1) base.

http://en.wikipedia.org/wiki/Harmonic_series_(music)
"...allowed wavelengths are 1/2, 1/3, 1/4, 1/5, 1/6, etc. times of the
fundamental."

but on strings there never appear 2/3 = 1:(3/2) due to the lack of
http://en.wikipedia.org/wiki/Subharmonics
in pianos:
http://www.sfu.ca/sonic-studio/handbook/Subharmonic.html
"Subharmonics do not normally occur in natural sounds, although the
subharmonic f/2 may be generated by the cone of a LOUDSPEAKER."

That makes an 5th (3:2 = 1.5) less fundamental than the ratio
inbetween the overtones 3:1 and 2:1 within the harmonic series.

Hence an 5th is composed by an
division of an 12th (3:1) as nominator
over an octave (2:1) as denominator by the calculation

(3:2) := (3:1):(2:1)

In other words:
any 5th (3:2) consists terms of
http://en.wikipedia.org/wiki/Harmonic
as composed of the difference of an '12th'-'8th'.
"3 just perfect fifth P8 + P5 1902.0 702.0"
when both do refer to the same (1:1) base or
http://en.wikipedia.org/wiki/Fundamental_frequency

hope that helps,
why i do prefer the multiplication by the "harmoic" factor 3
in order to stay wihin the partial-series.

Even Brad understood that in his:
http://www-personal.umich.edu/~bpl/larips/bachtemps.html
"...in the line of fifths A-E-B-F#-C#-G#-D#-Bb-F-C-G-D-A to reduce the
next note by 1 Hz, i.e. introducing a beat rate of 1 per second
against the preceding fifth. The fifths F#-C#-G#-D# and D-A are kept
pure. The other eight are adjusted by different geometric amounts,
based on the superparticular ratios described in his algorithm.
(Arithmetically, it amounts to subtracting 1 Hz from the top of most
of the columns, in his chart, wherever there are values in
parentheses.)"...

Brad contiues or the experts:
"Sparschuh's mathematical algorithm resembles the classic unproven
"Collatz Conjecture" from 1937, except that Sparschuh's iterated
function uses (3n-1) rather than (3n+1). [And see Eric Roosendaal's
3x+1 web site, along with this page by Frits Beukers demonstrating and
comparing the numerical sequences....]"

Yours Sincerely
A.S.

Yours Sincerely
A.S.