Re:The real Lehman tuning, Re: Here is the Excel worksheet I have work

Andreas wrote :

> The Lehman temperament is of modern design. It is, like the one > designed by the late Herbert Anton Kellner...."

There are many temperaments, considered historical, that are defined by fifths lowered by equal portions of commas.
Can you precise in a few words what's more precisely of "modern design" in Lehman's, and what would be instead of "ancient design" in your sense - or rather possibly used by J.S.Bach as plausible tuning techniques in comparison ?

> Many thanks Oz,
> for clearing what Brad's instruction's really do mean:
>
> !Lehman_Yarman.scl
> Bradley Lehman's ratios, compiled from 'instructions' by Ozan Yarman
> 12
> !
> 8926735/8435236 ! 1200*ln(8926735/8435236)/ln(2) = ~98.0449991...C
> 2907629/2596260 ! 1200*ln(2907629/2596260)/ln(2) = ~196.089998...C
> 8495647/7152031 ! 1200*ln(8495647/7152031)/ln(2) = ~298.044999...C
> 6837827/5451757 ! 1200*ln(6837827/5451757)/ln(2) = ~392.179997...C
> 12177389/9112438 ! 1200*ln(12177389/9112438)/ln(2)= ~501.955001...C
> 8926735/6326427 ! 1200*ln(8926735/6326427)/ln(2) = ~596.089998...C
> 3285409/2195225 ! 1200*ln(3285409/2195225)/ln(2) = ~698.044999...C
> 4613353/2909514 ! 1200*ln(4613353/2909514)/ln(2) = ~798.044999...C
> 2299792/1372105 ! 1200*ln(2299792/1372105)/ln(2) = ~894.134997...C
> 1419143/797367 ! 1200*ln(1419143/797367 )/ln(2) = ~998.044999...C
> 15193459/8075767 ! 1200*ln(15193459/8075767)/ln(2)=~1094.135......C
> 2/1
> !
> ![eof]

If a tuning integrates one or more loops between several notes (is it the case here ?), or even equal divisions of a comma, the fact that it can be modelized through very high numbers seems to me as a very relative indication of the "meaning" of the tuning.
The only thing we can presume is that Bach was not using such complex ratios - but was he using numbers at all ?
He could have use some advanced loop techniques and yet without the need to calculate any ratio.

On the other hand, if a temperament can be modeled correctly with relatively low numbers it is an indication of possibly simple equal or proportional beating, and therefore tuning-by-ear techniques.
The only thing we can say, apart from all other considerations, is that Lehman does not demonstrates it.
- - - - - - - - - - - - -
Jacques Dudon

--- In tuning@yahoogroups.com, Jacques Dudon <fotosonix@...> wrote:

> There are many temperaments, considered historical,
> that are defined by fifths lowered by equal portions of commas.

In deed Jacques,

> Can you precise in a few words what's more precisely of "modern
> design" in Lehman's,

"modern design" in that sense means any subdivisions of the
Pythagorean-Comma" = 3^12/2^19 into logarithmically-equidistant partitions of the seizes

PC^(1/n)

with any integral n€N, as modern generalizations
of Simon Stevin's classical case of n=12.

> and what would be instead of "ancient design" in
> your sense -
I overtook that from J.P. Kirnberger
http://harpsichords.pbworks.com/f/Kirn_1871.html
that meets almost yours on critique:
Quote:
"Da die Logarithmen für die meisten Musikanten Böhmische Dörfer sind, ohnerachtet sie bei der Musik wenig oder gar keinen Nutzen schaffen, so ist es nach meinem Sinn, auch deutlicher, sich durch bekannte Rechnungsart auszudrücken. Die gleichschwebende Temperatur ist schlechterdings ganz verwerflich, nur in diesem Fall nothwendig zu verstehen, um die Bände einer Theorbe, Laute oder solcher ähnlicher Instrumente als Psalter, Zitter u. s. w. recht zu legen, weil eine Temperatur ausser dieser Art jeder Seite ihr Recht nicht thut. Alle bisher herausgekommenen gleichschwebenden Temperaturen sind doch nicht vollkommen gleichschwebend, werden es auch in Ewigkeit nicht werden. Obgleich die grossen Mathematiker Zahlen von 200000 und darüber angenommen haben und dennoch sehr verschiedene Intervalle gleiches Namens vorbrachten, bei alle dem zufrieden waren, wenn eine grosse Terz gegen die andere um 50000 differirte, welches man doch mit wenigen Zahlen viel genauer haben kann,....

then Kirnberger conludes his letter, judgeing about 12-ET

....Mit dieser Materie von Temperaturen werde ich Sie niemals belästigen. Ich muss auch ganz nicht mehr daran gedenken, weil ich viele Jahre damit die Zeit verdorben habe. Damals, wo ich ging und standte, rechnete ich immer: es ist eine Arbeit für einen Baugefangenen oder für einen Menschen ohne Genie.
"

"Since the logarithms for most musicians strange Bohemian villages, notwithstanding contadictional to the music, they create only little or no benefit, it is more to my taste, to express the prportions by well-known rational calculation. The equal temperament is absolutely completely reprehensible, only in some case necessary to exhibt the the frets of the theorbo, lute, or such similar instruments as a psaltery, zither and so on, because only in a temperature of that type, each step should have the same seize. Hitherto all previously outcomes of so called "evenly temperatures" do not match exactly quite the logarithmically equal temperament, they are barely approximations with tiny deviations from equal. It will also be in eternity, however precisely fine one wants to choose the precision in accuracy. Although such large numbers above 200000 had been tried out in vain in order to gain that fiction. And mathematicians have adopted them and brought forward yet very different intervals of the same name, where were all the content if a major third differs from the other to 50,000, which nobody needs to have more accurately ,....

then Kirnberger conludes his letter, judgeing about 12-ET

.... With this matter of temperatures
(logarithmically equal supartitions of the PC)
I will never bother you. ,Also I don't want to be remember
of that, want to get rid of that, because I have ruined so many years time. Once at that now passed timem, everyhere I stood or went, I I was always occupied by even deeper calculations [of that 12-ET] : it is a job for a prisoner in a gulag or for a man without genius."

I.m.h.o, even today that still true:
Probably Bach's Master-Pupul would condemn Keller's & Lehman's
needless attempts in the same way.

>... or rather possibly used by J.S.Bach as plausible tuning
> techniques in comparison ?...
...as for instance Werckmeister's "septenarian" technique.

>
>
> If a tuning integrates one or more loops between
> several notes (is it the case here ?),
> or even equal divisions of a comma, the fact that
> it can be modelized through very high numbers seems to me as a
> very relative indication of the "meaning" of the tuning.

Agreed, the higher here the numbers, the less probable the proposal.

> The only thing we can presume is that Bach was not using
> such complex
> ratios - but was he using numbers at all ?

At least when counting bars in the scores of his compositions.

> He could have use some advanced loop techniques and yet without
> the need to calculate any ratio.

For considering such "loops" attend and consider the circle in the
right hand of Bach's favorite cousin:
http://upload.wikimedia.org/wikipedia/commons/a/ad/Walther-Johann-Gottfried-01.jpg
http://en.wikipedia.org/wiki/Johann_Gottfried_Walther
"...he was the famous composer's cousin."
Walther overtook that symbolic compass from his teacher
Werckmeister. Walther translated Wercksmeister's gothic medivial
number-symbolism into the state of the art in 1708.
He made 14 transcriptions of concertos by Albinoni, Gentili, Taglietti, Giuseppe Torelli, Vivaldi and Telemann.
"

Ruth Tatlow reports, that the two cousins often made
jokes about the the number 41 on occasions when the
lage Bach familiy clan had theirs regular family celebrations.
Alike for instance that JSB considered his cousin JGW twice
more musically capable gifted then himself,
because 82=JGW would be the double-time of 41=JSB.

One possible answer could be among many others:
/tuning/topicId_88725.html#89114

>
> On the other hand, if a temperament can be modeled correctly with
> relatively low numbers it is an indication of possibly simple
> equal or proportional beating,

Exactly.

> and therefore tuning-by-ear techniques.

Alike in the Jena [1706) tuning-competion
inbetween Johann-Nikolaus-Bach versus Neidhardt:

http://books.google.de/books?id=G-pG77pmlp4C&pg=PA85&lpg=PA85&dq=johann-nikolaus-bach+neidhardt+tuning+competition&source=bl&ots=WtyoEGO5_Q&sig=2uCkvmBft6t6viEfUhNj7-Q6MPA&hl=de&ei=9X3-S5L8EYaX_QbxxYzYCw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBYQ6AEwAA#v=onepage&q&f=false

> The only thing we can say,
> apart from all other considerations, is
> that Lehman does not demonstrates it:

Fully agreed!
Byond over and above of that:
As far as I know at the moment
-within the large community of serious musicologists-
all the leading experts in Baroque-Tuning
do strictly dismiss that "botched" attempt alike
the late Kellner's one, due to the drawback of an
all to much 'modern-design'.

Concise conclusion:
So not!
Ad acta.

bye
A.S.

Andreas wrote :

> (Jacques) :
> > There are many temperaments, considered historical,
> > that are defined by fifths lowered by equal portions of commas.
>
> In deed Jacques,
>
> > Can you precise in a few words what's more precisely of "modern
> > design" in Lehman's,
>
> "modern design" in that sense means any subdivisions of the
> Pythagorean-Comma" = 3^12/2^19 into logarithmically-equidistant
> partitions of
> the seizes
>
> PC^(1/n)
>
> with any integral n€N, as modern generalizations
> of Simon Stevin's classical case of n=12.

...So, if I follow you, WerckmeisterIII, IV, V would be of "modern
design" ??

> > and what would be instead of "ancient design" in
> > your sense -
> I overtook that from J.P. Kirnberger
> http://harpsichords.pbworks.com/f/Kirn_1871.html
> that meets almost yours on critique:
> Quote:
> "Da die Logarithmen für die meisten Musikanten Böhmische Dörfer
> sind,
> ohnerachtet sie bei der Musik wenig oder gar keinen Nutzen
> schaffen, so ist es
> nach meinem Sinn, auch deutlicher, sich durch bekannte Rechnungsart
> auszudrücken. Die gleichschwebende Temperatur ist schlechterdings
> ganz
> verwerflich, nur in diesem Fall nothwendig zu verstehen, um die BÃ
> ¤nde einer
> Theorbe, Laute oder solcher ähnlicher Instrumente als Psalter,
> Zitter u. s. w.
> recht zu legen, weil eine Temperatur ausser dieser Art jeder Seite
> ihr Recht
> nicht thut. Alle bisher herausgekommenen gleichschwebenden
> Temperaturen sind
> doch nicht vollkommen gleichschwebend, werden es auch in Ewigkeit
> nicht werden.
> Obgleich die grossen Mathematiker Zahlen von 200000 und darüber
> angenommen
> haben und dennoch sehr verschiedene Intervalle gleiches Namens
> vorbrachten, bei
> alle dem zufrieden waren, wenn eine grosse Terz gegen die andere um
> 50000
> differirte, welches man doch mit wenigen Zahlen viel genauer haben
> kann,....
>
> then Kirnberger conludes his letter, judgeing about 12-ET
>
> ....Mit dieser Materie von Temperaturen werde ich Sie niemals belÃ
> ¤stigen. Ich
> muss auch ganz nicht mehr daran gedenken, weil ich viele Jahre
> damit die Zeit
> verdorben habe. Damals, wo ich ging und standte, rechnete ich
> immer: es ist eine
> Arbeit für einen Baugefangenen oder für einen Menschen ohne Genie.
> "
>
> "Since the logarithms for most musicians strange Bohemian villages,
> notwithstanding contadictional to the music, they create only
> little or no
> benefit, it is more to my taste, to express the prportions by well-
> known
> rational calculation. The equal temperament is absolutely completely
> reprehensible, only in some case necessary to exhibt the the frets
> of the
> theorbo, lute, or such similar instruments as a psaltery, zither
> and so on,
> because only in a temperature of that type, each step should have
> the same
> seize. Hitherto all previously outcomes of so called "evenly
> temperatures" do
> not match exactly quite the logarithmically equal temperament, they
> are barely
> approximations with tiny deviations from equal. It will also be in
> eternity,
> however precisely fine one wants to choose the precision in
> accuracy. Although
> such large numbers above 200000 had been tried out in vain in order
> to gain that
> fiction. And mathematicians have adopted them and brought forward
> yet very
> different intervals of the same name, where were all the content if
> a major
> third differs from the other to 50,000, which nobody needs to have
> more
> accurately ,....
>
> then Kirnberger conludes his letter, judgeing about 12-ET
>
> .... With this matter of temperatures
> (logarithmically equal supartitions of the PC)
> I will never bother you. ,Also I don't want to be remember
> of that, want to get rid of that, because I have ruined so many
> years time. Once
> at that now passed timem, everyhere I stood or went, I I was always
> occupied by
> even deeper calculations [of that 12-ET] : it is a job for a
> prisoner in a gulag
> or for a man without genius."
>
> I.m.h.o, even today that still true:
> Probably Bach's Master-Pupul would condemn Keller's & Lehman's
> needless attempts in the same way.
>
>
> >... or rather possibly used by J.S.Bach as plausible tuning
> > techniques in comparison ?...
> ...as for instance Werckmeister's "septenarian" technique.

... interesting point of view.

> (Jacques) :
> > If a tuning integrates one or more loops between
> > several notes (is it the case here ?),
> > or even equal divisions of a comma, the fact that
> > it can be modelized through very high numbers seems to me as a
> > very relative indication of the "meaning" of the tuning.
>
> Agreed, the higher here the numbers, the less probable the proposal.

Hmm... I agree with that too (as I said later), but that's not
exactly what I meant here. By "very relative" I meant that the number
of digits are not so much significant of what the temperament really
does. If we put aside his indications (that seem unprecise anyway), I
am certain that you or me could do an improvment of Lehman's with
much lower numbers than those. The problem is rather that we are not
interested !

> > The only thing we can presume is that Bach was not using
> > such complex
> > ratios - but was he using numbers at all ?
>
> At least when counting bars in the scores of his compositions.

Probably, and in rhythmic/melodic patterns, too ! :)

> > He could have use some advanced loop techniques and yet without
> > the need to calculate any ratio.
>
> For considering such "loops" attend and consider the circle in the
> right hand of Bach's favorite cousin:
> http://upload.wikimedia.org/wikipedia/commons/a/ad/Walther-Johann-
> Gottfried-01.j\
> pg
> http://en.wikipedia.org/wiki/Johann_Gottfried_Walther
> "...he was the famous composer's cousin."
> Walther overtook that symbolic compass from his teacher
> Werckmeister. Walther translated Wercksmeister's gothic medivial
> number-symbolism into the state of the art in 1708.
> He made 14 transcriptions of concertos by Albinoni, Gentili,
> Taglietti, Giuseppe
> Torelli, Vivaldi and Telemann.
> "
>
> Ruth Tatlow reports, that the two cousins often made
> jokes about the the number 41 on occasions when the
> lage Bach familiy clan had theirs regular family celebrations.
> Alike for instance that JSB considered his cousin JGW twice
> more musically capable gifted then himself,
> because 82=JGW would be the double-time of 41=JSB.
>
> One possible answer could be among many others:
> /tuning/topicId_88725.html#89114
>
>
> >
> > On the other hand, if a temperament can be modeled correctly with
> > relatively low numbers it is an indication of possibly simple
> > equal or proportional beating,
>
> Exactly.
>
> > and therefore tuning-by-ear techniques.
>
> Alike in the Jena [1706) tuning-competion
> inbetween Johann-Nikolaus-Bach versus Neidhardt:
>
> http://books.google.de/books?id=G-
> pG77pmlp4C&pg=PA85&lpg=PA85&dq=johann-nikolaus\
> -bach+neidhardt+tuning
> +competition&source=bl&ots=WtyoEGO5_Q&sig=2uCkvmBft6t6viEf\
> UhNj7-Q6MPA&hl=de&ei=9X3-
> S5L8EYaX_QbxxYzYCw&sa=X&oi=book_result&ct=result&resnum\
> =1&ved=0CBYQ6AEwAA#v=onepage&q&f=false
>
>
> > The only thing we can say,
> > apart from all other considerations, is
> > that Lehman does not demonstrates it:
>
> Fully agreed!
> Byond over and above of that:
> As far as I know at the moment
> -within the large community of serious musicologists-
> all the leading experts in Baroque-Tuning
> do strictly dismiss that "botched" attempt alike
> the late Kellner's one, due to the drawback of an
> all to much 'modern-design'.
>
> Concise conclusion:
> So not!
> Ad acta.
>
> bye
> A.S.

Thanks !
- - - - - - -
Jacques

--- In tuning@yahoogroups.com, Jacques Dudon <fotosonix@...> wrote:
>
> > Andreas wrote :
> > PC^(1/n)
> Jacques replied :
> ...So, if I follow you, WerckmeisterIII, IV, V would be of "modern
> design" ??

Salut Jaques,
that depends on which (re)interpretation of Werckmeister #3
one chooses. For some possible variants see my meassage:
/tuning/topicId_73833.html#74576
as for instance Daniel G. Tuerck's [1806] monochord stringlenths:

C 8192
# 7776
D 7331
# 6912
E 6540
F 6144
# 5832
G 5480
# 5184
A 4905
# 4608
C 4096

!Tuerck_s_W3.scl
Daniel Gottlob Tuerck's [1806] Werckmeister #3 compiled by A.Sparschuh
! by converting the monochord-stringlengths into ratio
12
!
! 1/1 ! C 8192
256/243 ! C# 7776
8192/7331 ! D 7331
32/27 ! Eb 6912
2048/1635 ! E 6540
4/3 ! F 6144
1024/729 ! F# 5832
1024/685 ! G 5480
128/81 ! G# 5184
8192/4905 ! A 4905
16/9 ! Bb 4608
2/1 ! C' 4096
!
![eof]

Attend here the unequal distribution of the involved 5ths:

C 2048/2055 G 21920/21993 D 14662/14715 A - E - B...
...B 2180/2187 F# - C# - G# - D# - A# - F - C

that's in Cent-units:

C ~-5.91cent ~G~ 5.76cent ~D~ 6.25cent ~A - E - B...
~ 5.55cent ~ F# - C# - G# - D# - A# - F - C

which shown that all that four ones are different in seize,
instead of the modern PC^(1/4), on that you do refer.

>>> ...(Jacques) or rather possibly used by J.S.Bach as plausible
>>> tuning techniques in comparison ?...
> > ...(Andreas)..for instance Werckmeister's "septenarian" technique.
> ...(Jacques)...interesting point of view.

Because I considered even Tuerck's numbers as to high in range,
see for my own lower nubers than Tuerck that I found in my:
/tuning/topicId_68023.html#68047
in order to distribute four superparticular ratios over
Werckmeister's 'eight-pure-5ths- specification:
C ~ G ~ D ~ A - E - B ~ F# - C# - G# - Eb - Bb - F - C

Concise solution:
C 6560/6561 G 204/205 D 152/153 A - E - B...
...B 512/513 F# - C# - G# - Eb - Bb - F - C

or when expanded into absolute-ptich frequencies:

273.375 C_4 : ((17))2187:= 3^7
410 G_4 : (17*3=51,102,204<)205,410,820,1640,3280,6560(<6561:= 3^8)
306 D_4 : (19,38,76,152<)153:= 17*9
456 A_4 : 57:= 19*3
342 E_4 : 171:= 19*9
256.5 B_4 : (1,...,512<)513:= 19*27
384 F#4 : 3
288 C#4 : 9
432 G#4 : 27
324 Eb4 : 81
486 Bb4 : 243
364.5 F_4 : 729:= 3^6
273.375 C_4 : 2187:= 3^7

that's in chromatique ascending pitch order

pitch | name | ratio
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
273.375 C_4 1/1
288 C#4 256/243
306 D_4 272/243
324 Eb4 32/27
342 E_4 304/243
364.5 F_4 4/3
384 F#4 1024/729
410 G_4 3280/2187 Bach's coeval Cammer-tone ~410cps
432 G#4 128/81
456 Hz A_4 1216/729 Bach's coeval Choir-tone ~456cps
486 Bb4 16/9
513 B_4 152/81
546.75 C_5 2/1

The absolute-pitches in 41-limit "Monzo"s prime-number decomposition:

273.375 C_4 = |-3,7>
288 C#4 = |5,2>
306 D_4 = |1,2,0,0,0,0,1> = |1,2>*17
324 Eb4 = |2,4>
342 E_4 = |1,2,0,0,0,0,0,1> = |1,2>*19
364.5 F_4 = |-1,6>
384 F#4 = |7,1>
410 G_4 = |2,0,1,0,0,0,0,0,0,0,0,0,1> = |2,0,1>*41 !JSB!
432 G#4 = |4,3>
456 Hz A_4 = |3,1,0,0,0,0,0,1> = |3,1>*19
486 Bb4 = |1,5>
513 B_4 = |0,3,0,0,0,0,0,1> = 19*3^3
546.75 C_5 = |-2,7>

or in scala normalized ratios

!Sp41limW3.scl
Sparschuh's 41-limit Werckmeister #3 interpretation for J.S.Bach
12
!
256/243 ! C# |8,-5> the Pythagorean-Limma
272/243 ! D |4,-5,0,0,0,0,1> = |4,-5>*17
32/27 ! Eb |5,-3>
304/243 ! E |1,-5,0,0,0,0,0,1> = |1,-5>*19
4/3 ! F |2,-1>
1024/729 ! F# |10,-6>
3280/2187 ! G |4,-7,1,0,0,0,0,0,0,0,0,0,1> = |4,-7,1>*41 !JSB!
128/81 ! G# |-7,4>
1216/729 ! A |6,-6,0,0,0,0,0,1> = |6,-6>*19
16/9 ! Bb |4,-2>
152/81 ! B |3,-4,0,0,0,0,0,1> = |3,-4>*19
2/1
!
![eof]

Enjoy Bach's organ-music especially in that one.
Hence now, it's up to the experts to consider how
'authentic' or even 'originally'
they want do deem that as apt for Bach.

> (Jacques:) Probably, and in rhythmic/melodic patterns, too ! :)
Verly likely not only there,
but also inbetween the beating of the 5ths an 3rds.

I.m.h.o,
A. Werckmeister, J.G.Walther and J.S.Bach used
something close to the above tuning, or perhaps even
exactly the same ratios, as an 41-limit refinement of the predecessor:

http://groenewald-berlin.de/text/text_T126.html

"Andreas Reinhard, [1604] - Abraham Bartulus, [1614]"
'Benutzt werden die fünf Quotienten':
"By using the five quotients":
16/15, 17/16, 18/17, 19/18 und 20/19:
almost at the same positions.

Walther remarked in a letter that his teacher Werckmeister once donated him the works of Reinhard & Bartulus when he was W's student
in Halberstadt, in order to study from that how to tune an well-temperament...

au revoir, bye bye à bientôt
Andy

Let's straighten out this thread, which has been apparently almost 100% a (possibly deliberate?) mis-representation of my principles.

My hypothesis is not a mathematical one. It is musical! It presents an easy method to tune harpsichords WITHOUT DOING ANY CALCULATIONS. All of this stuff with ratios, and with the mathematical values of the commas, is IRRELEVANT. It is not even necessary to count beats, to get the work done at the instrument! The grumbling about the mathematics is a series of red herrings put up by people disinclined to accept my work, because it doesn't match their own expectations.

The discussion of "number symbolism", numerology, etc, etc, is also irrelevant to my research and musical practices. There is nothing cabalistic in my methods, or in my hypothesis: where I suggest that Bach likely *did* this same physical task at his own instruments, to get them suitably into tune, and he drew a straightforward picture of what he knew and did. I take Bach's drawing as a step-by-step diagram, a schematic to get the job done.

No calculations. No assignment of putative meaning to any numbers. Just learn this listening skill and this physical tuning skill, do this procedure in a couple of minutes, and be done. That is the hypothesis. I have done it myself more than 300 times now, over the past several years, and there is certainly nothing difficult about it. It is a practical musical skill to practice and master, like anything else one learns in music.

> > > The only thing we can say,
> > > apart from all other considerations, is
> > > that Lehman does not demonstrates it:

Lehman allegedly does not demonstrate what? (Maybe we've lost some context on what "it" is?) There are CDs of musical examples, with relevant compositions by Bach. There are YouTube videos showing directly how to tune my hypothetical Bach temperament by ear, without any calculations. There are papers explaining all the musical and historical points that have informed and tested the hypothesis. There are three very long FAQ pages on the web site. There are lecture notes and slides from multiple presentations at different universities. There are *also* many pages where I present mathematical models and some beat rates, for those who are interested in such things, but the math and the beats are not necessary to the basic theory.

I don't believe that Bach himself would have cared about any of the tuning math, either. There were many more important musical tasks and other responsibilities to get done.

Here are some other tasks that are easy to do with a little bit of training and practice, but which look prohibitively difficult if it all has to be reduced to mathematical measurements -- down to the tiniest scrutiny of distances, angles, rotations, velocity, acceleration, and functional modeling:

- Tie a shoe.

- Watch a moving bird through a telescope.

- Throw a ball to hit a target.

- Sing a melody such as "Twinkle, Twinkle Little Star", and end accurately on the same note where it started.

- Walk up the stairs.

Criticize my musical and historical hypothesis on quibbles about ratios? That's absurd and pointless. We might as well reject the sequential muscular motions of swallowing a drink of water, because it's too hard to model it all accurately enough using a system of polar-coordinate equations.

Brad Lehman

--- In tuning@yahoogroups.com, "bplehman27" <bpl@...> wrote:

> My hypothesis .... is IRRELEVANT....
> is a series of red herrings...
> ....because ...
everything else than Lehman's reinterpretation of older prior works
>... it doesn't match...
his personal
>... own expectations.
> I take Bach's drawing as a step-by-step diagram, a schematic to
> get the job done.
Long before you Zapf & Briggs [May 2003] did already so earlier in
http://keithbriggs.info/bach-wtc.html
and also
http://www.mobbsearlykeyboard.co.uk/KWMamplificationofEMAug05letter.htm

> That is the hypothesis:
> I have done it myself more than 300 times now, over the past
> several years, and there is certainly nothing difficult about it.

That wishful thinking consists barely in:
http://en.wikipedia.org/wiki/Begging_the_question

Concluding blatant from over 300-times successful repetition over and over some years, doesn't convert a-posteriori yours selfproclaimed wild speculations invention into J.S.Bachs alleged "original" tuning-instructions. Argueing in such an way

> > > > The only thing we can say,
> > > > apart from all other considerations, is
> > > > that Lehman does not demonstrates it:
In deed,
because:
Not even a historically possible starting note is given.

> There are CDs of musical examples,
> with relevant compositions by Bach.
What does proof the existence of such CDs?

> There are YouTube videos showing directly how to tune my
> hypothetical Bach temperament by ear, without any calculations.
Fine, that you are able to do yours own modern invention so well.
But what has that to do with J.S.Bach practice over two centuries ago?

> There are papers explaining all the musical and historical points
> that have informed and tested the hypothesis.
Who tested that, except the well known "Caveat lector"
peer-review editor?
That means nothing, except that there happened eclatant:
http://en.wikipedia.org/wiki/Peer_review_failure

> I don't believe that Bach himself would have cared about any of the > tuning math, either.

With joy I take the first time to my knowledge that
untenable superstition should now be only your personal belief.

> There were many more important musical tasks and other
> responsibilities to get done.
Agreed.

>
> Here are some other tasks that are easy to do with a little bit of > training and practice, but which look prohibitively difficult if it > all has to be reduced to mathematical measurements --

Quest:
Have you ever asked yourself why do you always just get into this particular difficulty?

> down to the tiniest scrutiny of distances, angles, rotations,
> velocity, acceleration, and functional modeling:
Why do you try to do so?

>
> - Tie a shoe.
If you can not do that,
simply wear slippers or shoes with velcro-closure.
>
> - Watch a moving bird through a telescope.
If you insist to watch birds with that aid:
Then take the telescope "upside-down" as
wide-angle-les in reverse direction.

>
> - Throw a ball to hit a target.
Then you better play handball,
instead of tuning harpsichords.

>
> - Sing a melody such as "Twinkle, Twinkle Little Star", and end
> accurately on the same note where it started.
That's one of the first lessons for my undergraduate-students
in conservatory. Highly recommended in oder to improve
the stability of absolute-pitch.

>
> - Walk up the stairs.
If the elevator is defect.

>...That's absurd and pointless...

Good final word!

bye
Andy