Another Bach tuning comparison

One of the things about well-temperaments is that you can't get much of a feel for the difference between them without playing in all the keys, especially the more remote ones. Some of them are pretty bad in C# major! But intermediate keys, in this case C minor, can be harder to judge. See what you think of these. (Keep in mind I'm not a professional pianist...)

http://home.comcast.net/~teamouse/fugue2a.mp3
http://home.comcast.net/~teamouse/fugue2b.mp3
http://home.comcast.net/~teamouse/fugue2c.mp3
http://home.comcast.net/~teamouse/fugue2d.mp3

One of these is tuned in Werckmeister III. Can you tell which one? Which of these scales "feel" right for Bach and which are less appropriate? (You can guess what the other scales are if you like, but for now I'll keep them a mystery.)

All of these were rendered from the identical MIDI file using the rgc:audio z3ta+ and scales from the Scala archive. For additional comparison you can check these versions out:

http://home.comcast.net/~teamouse/fugue2e.mp3
http://home.comcast.net/~teamouse/fugue2f.mp3
http://home.comcast.net/~teamouse/fugue2g.mp3

My personal experience is that Werckmeister III is a perfectly good tuning for Bach, but I'm open to other possibilities, and a few of the alternatives sound good as well. For a more extreme test, try the C# major prelude from WTC I...

[ Attachment content not displayed ]

Apparently nobody read my post about ABX.

-Carl

Had it for years, someone put up the link on a recording forum IIRC.

It's a great confidence builder.

--- In tuning@yahoogroups.com, "David Bowen" <dmb0317@...> wrote:
>
> A few months back I downloaded a program called winabx that
allows you to
> do A/B comparisons of two sound files. The program randomly
selects one of
> the two files as the X and it's the listener's job to identify the
X as
> either A or B given as many replays of A, B, and X as the listener
needs.
> The program lets you know when you have achieved a statistically
significant
> success rate. I would suggest that the first step is getting ones
ears tuned
> up to the point where they can tell the difference between files in
> different tunings and then worry about actually identifying the
tunings.
>
> David Bowen
>

Interesting, four examples feels kind of overwhelming today, but
anyway, a first reaction without thinking: they're all different in
character, more so than in Carl's example. And different in overall
pitch. 2c sounds sour, and 2d, sweet.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> One of the things about well-temperaments is that you can't get
much of
> a feel for the difference between them without playing in all the
keys,
> especially the more remote ones. Some of them are pretty bad in C#
> major! But intermediate keys, in this case C minor, can be harder
to
> judge. See what you think of these. (Keep in mind I'm not a
professional
> pianist...)
>
> http://home.comcast.net/~teamouse/fugue2a.mp3
> http://home.comcast.net/~teamouse/fugue2b.mp3
> http://home.comcast.net/~teamouse/fugue2c.mp3
> http://home.comcast.net/~teamouse/fugue2d.mp3
>
> One of these is tuned in Werckmeister III. Can you tell which one?
Which
> of these scales "feel" right for Bach and which are less
appropriate?
> (You can guess what the other scales are if you like, but for now
I'll
> keep them a mystery.)
>
> All of these were rendered from the identical MIDI file using the
> rgc:audio z3ta+ and scales from the Scala archive. For additional
> comparison you can check these versions out:
>
> http://home.comcast.net/~teamouse/fugue2e.mp3
> http://home.comcast.net/~teamouse/fugue2f.mp3
> http://home.comcast.net/~teamouse/fugue2g.mp3
>
> My personal experience is that Werckmeister III is a perfectly
good
> tuning for Bach, but I'm open to other possibilities, and a few of
the
> alternatives sound good as well. For a more extreme test, try the
C#
> major prelude from WTC I...
>

> http://home.comcast.net/~teamouse/fugue2a.mp3
> http://home.comcast.net/~teamouse/fugue2b.mp3
> http://home.comcast.net/~teamouse/fugue2c.mp3
> http://home.comcast.net/~teamouse/fugue2d.mp3
>
> One of these is tuned in Werckmeister III. Can you tell which one?

2c sounds like meantone.

Beyond that, it's harder. 2a is perhaps ET, and
2b and 2d some sort of well temperaments.

> Which of these scales "feel" right for Bach and which are
> less appropriate?

2c sounds wrong for Bach. 2b is maybe my favorite. But
the differences between b/d are basically too subtle for me
to report on without ABX.

> For a more extreme test, try the C#
> major prelude from WTC I...

One of the few 5-voice pieces Bach ever wrote.

-Carl

> Interesting, four examples feels kind of overwhelming today, but
> anyway, a first reaction without thinking: they're all different in
> character, more so than in Carl's example. And different in overall
> pitch. 2c sounds sour, and 2d, sweet.

Whatever the sourness of meantone Bach is caused by (and I'd
like to know), it doesn't seem to bother Gene.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:

> > Herman: For a more extreme test, try the C#
> > major prelude from WTC I...
>
> Carl: One of the few 5-voice pieces Bach ever wrote.

Carl, surely you mean the _fugue_ in c# *minor*. The prelude is
basically a two-vioced composition, and the fugue for that one is
3-voiced.

-A.

Herman, all,

I finally listened to these each once....not 'e' 'f' and 'g', though, yet.

I'll take a stab and say that 'd' was WerckIII--it didn't sound all
that bad to me, although I know this piece well, and I recognized the
Ab-C thirds were wide-ish sounding, which is why I would guess that
this is a tuning where Ab-C was somewhere near Pythagorean...hence my
choice of this being WerckIII. 'c', I agree with Carl, was probably
some kind of meantone, and didn't work for Bach. My response to the
first two, 'a' and 'b', was that they were quite similar. I might have
to listen again closer to hear real differences--whatever they were
were too subtle to me on one hearing.

BTW, Herman---the quality of the mp3s was terrible---I had all sorts
of noise---was that me, or all the files really poor (i.e.
low-bitrate)? Also, if you are not a professional pianist, and you
played that in live realtime, kudos, they would indicate you have a
decent technique, but I would say they are rather expressionless....Or
did you take a bland sequence of the net, or step sequence them in, etc.?

Cheers,
Aaron.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> One of the things about well-temperaments is that you can't get much of
> a feel for the difference between them without playing in all the keys,
> especially the more remote ones. Some of them are pretty bad in C#
> major! But intermediate keys, in this case C minor, can be harder to
> judge. See what you think of these. (Keep in mind I'm not a
professional
> pianist...)
>
> http://home.comcast.net/~teamouse/fugue2a.mp3
> http://home.comcast.net/~teamouse/fugue2b.mp3
> http://home.comcast.net/~teamouse/fugue2c.mp3
> http://home.comcast.net/~teamouse/fugue2d.mp3
>
> One of these is tuned in Werckmeister III. Can you tell which one?
Which
> of these scales "feel" right for Bach and which are less appropriate?
> (You can guess what the other scales are if you like, but for now I'll
> keep them a mystery.)

> > > Herman: For a more extreme test, try the C#
> > > major prelude from WTC I...
> >
> > Carl: One of the few 5-voice pieces Bach ever wrote.
>
> Carl, surely you mean the _fugue_ in c# *minor*. The prelude is
> basically a two-vioced composition, and the fugue for that one is
> 3-voiced.

Yes, sorry. -Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > Interesting, four examples feels kind of overwhelming today, but
> > anyway, a first reaction without thinking: they're all different in
> > character, more so than in Carl's example. And different in overall
> > pitch. 2c sounds sour, and 2d, sweet.
>
> Whatever the sourness of meantone Bach is caused by (and I'd
> like to know), it doesn't seem to bother Gene.

Eh? I haven't even commented on this example. As for my own testing of
the hypothesis of meantone tuning for WTC1, that involves moving the
meantone compass to correspond to the key. Since the harmony sticks
inside of a translated compass, you don't get a bunch of sour notes.

> > Whatever the sourness of meantone Bach is caused by (and I'd
> > like to know), it doesn't seem to bother Gene.
>
> Eh? I haven't even commented on this example. As for my own testing of
> the hypothesis of meantone tuning for WTC1, that involves moving the
> meantone compass to correspond to the key. Since the harmony sticks
> inside of a translated compass, you don't get a bunch of sour notes.

But your testings still sounded sour to me, and to a friend.

-Carl

I simply adore that one. Very gloomy, so menacing...

----- Original Message -----
From: "Aaron Krister Johnson" <aaron@dividebypi.com>
To: <tuning@yahoogroups.com>
Sent: 17 Ocak 2007 �ar�amba 20:20
Subject: [tuning] Re: Another Bach tuning comparison

> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > > Herman: For a more extreme test, try the C#
> > > major prelude from WTC I...
> >
> > Carl: One of the few 5-voice pieces Bach ever wrote.
>
> Carl, surely you mean the _fugue_ in c# *minor*. The prelude is
> basically a two-vioced composition, and the fugue for that one is
> 3-voiced.
>
> -A.
>
>
>

Aaron Krister Johnson wrote:
> Herman, all,
> > I finally listened to these each once....not 'e' 'f' and 'g', though, yet.
> > I'll take a stab and say that 'd' was WerckIII--it didn't sound all
> that bad to me, although I know this piece well, and I recognized the
> Ab-C thirds were wide-ish sounding, which is why I would guess that
> this is a tuning where Ab-C was somewhere near Pythagorean...hence my
> choice of this being WerckIII. 'c', I agree with Carl, was probably
> some kind of meantone, and didn't work for Bach. My response to the
> first two, 'a' and 'b', was that they were quite similar. I might have
> to listen again closer to hear real differences--whatever they were
> were too subtle to me on one hearing.
> > BTW, Herman---the quality of the mp3s was terrible---I had all sorts
> of noise---was that me, or all the files really poor (i.e.
> low-bitrate)? Also, if you are not a professional pianist, and you
> played that in live realtime, kudos, they would indicate you have a
> decent technique, but I would say they are rather expressionless....Or
> did you take a bland sequence of the net, or step sequence them in, etc.?

I don't recall what speed I played it (it was an old file I had lying around), but it probably wasn't full speed. And I was obviously playing to the beat of the metronome if I look at the MIDI file, which explains why it sounds expressionless. Probably not the best way to play Bach!

The bit rate is pretty low to save space, but there shouldn't have been much noise. I don't hear any noise when I play them -- nothing I can hear over the noise of my computer fan, at any rate. There's a bit of what sounds like an echo effect, which it turns out is an unintended release of the envelope that's slower than what I was intending.

> http://home.comcast.net/~teamouse/fugue2a.mp3
> http://home.comcast.net/~teamouse/fugue2b.mp3
> http://home.comcast.net/~teamouse/fugue2c.mp3
> http://home.comcast.net/~teamouse/fugue2d.mp3
>
> One of these is tuned in Werckmeister III. Can you tell which one?
> Which of these scales "feel" right for Bach and which are less
> appropriate?

All four of these sounded skippy when played on my rather slow
system. Yesterday I couldn't get c and d to play at all. But, I
gave them another try today and got through them without *too* many
dropouts.

None of them "feel" right for Bach, to me. Both a and b are semi-
decent, not obnoxious, and I've heard a lot worse; a is better than b.

Example c is from another planet. I really liked it, just for the
exoticism, but I wouldn't consider using it seriously for this
piece. :)

Example d is obviously the Werckmeister; obvious as early as the 5th
note (the Ab approached from G, and the Ab being way too low
melodically as is its wont in WerckIII)...and that's before any of
the harmony comes in, which makes it even more obnoxious later. Ugh.

Yes?

Brad Lehman (all of these deliberately without putting much thought
into it, but going on listening impression and first instincts)

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

> Example d is obviously the Werckmeister; obvious as early as the 5th
> note (the Ab approached from G, and the Ab being way too low
> melodically as is its wont in WerckIII)...and that's before any of
> the harmony comes in, which makes it even more obnoxious later. Ugh.

As I wrote earlier, I would have to agree with you that example 'd' is
WerckIII. I have less a hatred than you about the melodic effect, but
I have to say, like you, I definately prefer WTs for Bach that have
mellower thirds than Pythagorean.

-A.

I agree that Werckmeister III is the fourth one. I also noticed that you
have used the frequeny 261.626 hz for middle C.

As for appropriateness, 2a is fine, 2b is a little unbalanced (C-Eb is a
little awry), 2c is meantonish and completely improper in the case of this
particular fugue, 2d sounds very nice.

2e seems to exhibit severe problems in simple keys, 2f did not appeal to me
very much as it sounds edgy, 2g is psychedelic! but quite improper for Bach
in my opinion.

Oz.

----- Original Message -----
From: "Herman Miller" <hmiller@IO.COM>
To: <tuning@yahoogroups.com>
Sent: 17 Ocak 2007 �ar�amba 5:24
Subject: [tuning] Another Bach tuning comparison

> One of the things about well-temperaments is that you can't get much of
> a feel for the difference between them without playing in all the keys,
> especially the more remote ones. Some of them are pretty bad in C#
> major! But intermediate keys, in this case C minor, can be harder to
> judge. See what you think of these. (Keep in mind I'm not a professional
> pianist...)
>
> http://home.comcast.net/~teamouse/fugue2a.mp3
> http://home.comcast.net/~teamouse/fugue2b.mp3
> http://home.comcast.net/~teamouse/fugue2c.mp3
> http://home.comcast.net/~teamouse/fugue2d.mp3
>
> One of these is tuned in Werckmeister III. Can you tell which one? Which
> of these scales "feel" right for Bach and which are less appropriate?
> (You can guess what the other scales are if you like, but for now I'll
> keep them a mystery.)
>
> All of these were rendered from the identical MIDI file using the
> rgc:audio z3ta+ and scales from the Scala archive. For additional
> comparison you can check these versions out:
>
> http://home.comcast.net/~teamouse/fugue2e.mp3
> http://home.comcast.net/~teamouse/fugue2f.mp3
> http://home.comcast.net/~teamouse/fugue2g.mp3
>
> My personal experience is that Werckmeister III is a perfectly good
> tuning for Bach, but I'm open to other possibilities, and a few of the
> alternatives sound good as well. For a more extreme test, try the C#
> major prelude from WTC I...
>
>

Sorry about the sound quality of the original files. I got rid of the release problem with the envelopes (the slight "echo" effect after the notes) and used a slightly better quality setting for the mp3 compression. Hopefully the new versions will be easier to compare. More notes to follow. If you don't want to know which version is the ET version, save this message and come back to it later.

.

...

.

.

...

.

.

...

.

.

...

.

.

> http://home.comcast.net/~teamouse/fugue2a.mp3
> http://home.comcast.net/~teamouse/fugue2b.mp3
> http://home.comcast.net/~teamouse/fugue2c.mp3
> http://home.comcast.net/~teamouse/fugue2d.mp3
> > One of these is tuned in Werckmeister III. Can you tell which one? Which > of these scales "feel" right for Bach and which are less appropriate? > (You can guess what the other scales are if you like, but for now I'll > keep them a mystery.)

As you've probably guessed by now, fugue2c is definitely NOT any kind of well temperament. The other three of these are well-temperaments.

> All of these were rendered from the identical MIDI file using the > rgc:audio z3ta+ and scales from the Scala archive. For additional > comparison you can check these versions out:
> > http://home.comcast.net/~teamouse/fugue2e.mp3
> http://home.comcast.net/~teamouse/fugue2f.mp3
> http://home.comcast.net/~teamouse/fugue2g.mp3

And the ET version is ... fugue2e! As you've probably guessed if you listened to the others, fugue2g is another one of those ... scales that isn't a well-temperament. That leaves fugue2f as ... you guessed it, another well-temperament.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
> > http://home.comcast.net/~teamouse/fugue2a.mp3
> > http://home.comcast.net/~teamouse/fugue2b.mp3
> > http://home.comcast.net/~teamouse/fugue2c.mp3
> > http://home.comcast.net/~teamouse/fugue2d.mp3
> >
> > One of these is tuned in Werckmeister III. Can you tell which
one? Which
> > of these scales "feel" right for Bach and which are less
appropriate?
> > (You can guess what the other scales are if you like, but for now
I'll
> > keep them a mystery.)

I'll cast my vote for 2b.

> > http://home.comcast.net/~teamouse/fugue2e.mp3
> > http://home.comcast.net/~teamouse/fugue2f.mp3
> > http://home.comcast.net/~teamouse/fugue2g.mp3
>
> And the ET version is ... fugue2e!

Much as I hate to say it, I don't think 2e is the worst choice.

Greetings,

Actually, I almost hate to draw attention to this link. As if we've not had enough bitter fighting. Here's a page that will be of interest:

http://www.polettipiano.com/Pages/pag1engpaul.html

All best wishes for a peaceful world and list,

Gordon Rumson

--- In tuning@yahoogroups.com, Gordon Rumson <rumsong@...> wrote:
>
> Greetings,
>
> Actually, I almost hate to draw attention to this link. As if we've
> not had enough bitter fighting. Here's a page that will be of
interest:
>
> http://www.polettipiano.com/Pages/pag1engpaul.html

Werckmeister sometimes seems to mean Didymus comma and sometimes
Pythagoras comma when he says "comma", but we can conclude from this
that he favors having no fifths flatter than 1/8 Pythagorean comma, and
assumes some might be pure but never sharp. We want the average
flatness to be 1/12 Pythagoran comma, which means we could have eight
fifths flat by 1/8 Pythagorean comma and four pure fifths and fit these
prescriptions. So if we have eight fifths of 699 cents and four of 702
cents to play with, what can we come up with? I could check to see if
that fits some known historical temperaments but maybe someone knows.

One thing for sure, it doesn't fit Werckmeister3--that has four fifths
flat by 1/4 Pythagoran comma and eight pure fifths instead. In fact,
the temperaments we've mostly been discussing are too irregular for
Werckmeister, according to this.

Hi Herman,

> > http://home.comcast.net/~teamouse/fugue2a.mp3
> > http://home.comcast.net/~teamouse/fugue2b.mp3
> > http://home.comcast.net/~teamouse/fugue2c.mp3
> > http://home.comcast.net/~teamouse/fugue2d.mp3
> >
> > One of these is tuned in Werckmeister III. Can you tell
> > which one? Which of these scales "feel" right for Bach
> > and which are less appropriate?
>
> As you've probably guessed by now, fugue2c is definitely
> NOT any kind of well temperament. The other three of these
> are well-temperaments.
//
> > http://home.comcast.net/~teamouse/fugue2e.mp3
> > http://home.comcast.net/~teamouse/fugue2f.mp3
> > http://home.comcast.net/~teamouse/fugue2g.mp3
>
> And the ET version is ... fugue2e!

Why'd you have to tell us so close to where we have to
download the files?

I didn't listen to this second group of files the first
time I tried this test. I can definitely hear that 2e
is ET. Though if I remember the timbre you were using
before, I might not have detected it then.

2f is very interesting. What is it?

2g sounds sour.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> Hi Herman,
>
> > > http://home.comcast.net/~teamouse/fugue2a.mp3
> > > http://home.comcast.net/~teamouse/fugue2b.mp3
> > > http://home.comcast.net/~teamouse/fugue2c.mp3
> > > http://home.comcast.net/~teamouse/fugue2d.mp3
> > >
> > > One of these is tuned in Werckmeister III. Can you tell
> > > which one? Which of these scales "feel" right for Bach
> > > and which are less appropriate?
> >
> > As you've probably guessed by now, fugue2c is definitely
> > NOT any kind of well temperament. The other three of these
> > are well-temperaments.
> //
> > > http://home.comcast.net/~teamouse/fugue2e.mp3
> > > http://home.comcast.net/~teamouse/fugue2f.mp3
> > > http://home.comcast.net/~teamouse/fugue2g.mp3
> >
> > And the ET version is ... fugue2e!
>

If 'd' is really 'WIII' (or even if it isn't!) then I don't think it
comes off at all badly. Ab-C doesn't serve as a point of rest - but
the way the piece is composed, it needn't.

However, 'b' has some chords in odd places that seem pretty harsh even
in passing and I wouldn't go for it. Sure 'b' isn't old Werckie?

I'm astonished at the rhythmic regularity of the playing! I'd almost
have thought it synthesized, except for the gradations in dynamic.

'c' is pleasantly strange (must be properly-spelled meantone) sounding
almost like a doo-wop group, not a keyboard at all; 'g' unpleasantly
strange (badly-spelled meantone?).

~~~T~~~

And now for the results.

> http://home.comcast.net/~teamouse/fugue2a.mp3

2a is perhaps ET (Carl Lumma)
Both a and b are semi-decent, not obnoxious, and I've heard a lot worse; a is better than b. (Brad Lehman)
2a is fine (Ozan Yarman)

! sorge3.scl
!
Georg Andreas Sorge, 1758 12
!
96.09000
196.09000
298.04500
394.13500
4/3
596.09000
698.04500
798.04500
894.13500
998.04500
1096.09000
2/1

I did some tests of my own with Winamp in shuffle mode before putting these samples up, and I consistently misidentified this one as ET. I wondered if anyone else would have the same reaction.

> http://home.comcast.net/~teamouse/fugue2b.mp3

2b and 2d some sort of well temperaments. 2b is maybe my favorite. But
the differences between b/d are basically too subtle for me
to report on without ABX. (Carl Lumma)
2b is a little unbalanced (C-Eb is a little awry) (Ozan Yarman)
I'll cast my vote for 2b. (Gene Ward Smith)

! werck3.scl
!
Andreas Werckmeister's temperament III (the most famous one, 1681)
12
!
256/243
192.18000
32/27
390.22500
4/3
1024/729
696.09000
128/81
888.26999
16/9
1092.18000
2/1

And here it is. Interesting how mixed the reactions were; I guess this isn't one of Werckmeister's better keys.

> http://home.comcast.net/~teamouse/fugue2c.mp3

2c sounds sour (Cameron Bobro)
2c sounds like meantone. 2c sounds wrong for Bach. (Carl Lumma)
'c', I agree with Carl, was probably some kind of meantone, and didn't work for Bach (Aaron Krister Johnson)
Example c is from another planet. (Brad Lehman)
2c is meantonish and completely improper in the case of this particular fugue (Ozan Yarman)

! duodene.scl
!
Ellis's Duodene : genus [33355] 12
!
16/15
9/8
6/5
5/4
4/3
45/32
3/2
8/5
5/3
9/5
15/8
2

What surprised me when I tried this is that I was expecting something totally horrible, but it actually ended up better than I was expecting! Obviously something Bach would never have used, but interesting in a way.

> http://home.comcast.net/~teamouse/fugue2d.mp3

2d [sounds] sweet (Cameron Bobro)
2b and 2d some sort of well temperaments (Carl Lumma)
I'll take a stab and say that 'd' was WerckIII (Aaron Krister Johnson)
Example d is obviously the Werckmeister (Brad Lehman)
I agree that Werckmeister III is the fourth one (Ozan Yarman)
2d sounds very nice (Ozan Yarman)

! young.scl
!
Thomas Young well temperament (1807), also Luigi Malerbi nr.2 (1794)
12
!
256/243
196.09000
32/27
392.18000
4/3
1024/729
698.04500
128/81
894.13500
16/9
1090.22500
2/1

I was surprised at first how easy it was to confuse Young with Werckmeister, since the two are quite different. But looking at the Scala files, you can see that they actually share quite a few notes.

And for the bonus examples:

> http://home.comcast.net/~teamouse/fugue2e.mp3
2e seems to exhibit severe problems in simple keys (Ozan Yarman)
Much as I hate to say it, I don't think 2e is the worst choice. (Gene Ward Smith)

(This is equal temperament.)

> http://home.comcast.net/~teamouse/fugue2f.mp3
2f did not appeal to me very much as it sounds edgy (Ozan Yarman)

! kirnberger3.scl
!
Kirnberger 3: 1/4 synt. comma (1744)
12
!
135/128
193.15686
32/27
5/4
4/3
45/32
696.57843
405/256
889.73529
16/9
15/8
2/1

> http://home.comcast.net/~teamouse/fugue2g.mp3
2g is psychedelic! but quite improper for Bach in my opinion. (Ozan Yarman)

! super_12.scl
!
Most equal superparticular 12-tone scale 12
!
16/15
17/15
6/5
19/15
4/3
64/45
68/45
8/5
76/45
16/9
17/9
2/1

Hi herman
Most equal superparticular 12-tone scale is based on 45-ADO and you can see this scale in VISUAL TEMPERAMENT ANALYZER:
http://240edo.googlepages.com/Bach-45-ADO.xls

Shaahin Mohajeri

Tombak Player & Researcher , Microtonal Composer

My web site?? ???? ????? ?????? <http://240edo.googlepages.com/>

My farsi page in Harmonytalk ???? ??????? ?? ??????? ??? <http://www.harmonytalk.com/mohajeri>

Shaahin Mohajeri in Wikipedia ????? ?????? ??????? ??????? ???? ???? <http://en.wikipedia.org/wiki/Shaahin_mohajeri>

________________________________

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of Herman Miller
Sent: Sunday, January 21, 2007 12:12 AM
To: tuning@yahoogroups.com
Subject: Re: [tuning] Another Bach tuning comparison

And now for the results.

> http://home.comcast.net/~teamouse/fugue2a.mp3 <http://home.comcast.net/~teamouse/fugue2a.mp3>

2a is perhaps ET (Carl Lumma)
Both a and b are semi-decent, not obnoxious, and I've heard a lot worse;
a is better than b. (Brad Lehman)
2a is fine (Ozan Yarman)

! sorge3.scl
!
Georg Andreas Sorge, 1758

12
!
96.09000
196.09000
298.04500
394.13500
4/3
596.09000
698.04500
798.04500
894.13500
998.04500
1096.09000
2/1

I did some tests of my own with Winamp in shuffle mode before putting
these samples up, and I consistently misidentified this one as ET. I
wondered if anyone else would have the same reaction.

> http://home.comcast.net/~teamouse/fugue2b.mp3 <http://home.comcast.net/~teamouse/fugue2b.mp3>

2b and 2d some sort of well temperaments. 2b is maybe my favorite. But
the differences between b/d are basically too subtle for me
to report on without ABX. (Carl Lumma)
2b is a little unbalanced (C-Eb is a little awry) (Ozan Yarman)
I'll cast my vote for 2b. (Gene Ward Smith)

! werck3.scl
!
Andreas Werckmeister's temperament III (the most famous one, 1681)
12
!
256/243
192.18000
32/27
390.22500
4/3
1024/729
696.09000
128/81
888.26999
16/9
1092.18000
2/1

And here it is. Interesting how mixed the reactions were; I guess this
isn't one of Werckmeister's better keys.

> http://home.comcast.net/~teamouse/fugue2c.mp3 <http://home.comcast.net/~teamouse/fugue2c.mp3>

2c sounds sour (Cameron Bobro)
2c sounds like meantone. 2c sounds wrong for Bach. (Carl Lumma)
'c', I agree with Carl, was probably some kind of meantone, and didn't
work for Bach (Aaron Krister Johnson)
Example c is from another planet. (Brad Lehman)
2c is meantonish and completely improper in the case of this particular
fugue (Ozan Yarman)

! duodene.scl
!
Ellis's Duodene : genus [33355]

12
!
16/15
9/8
6/5
5/4
4/3
45/32
3/2
8/5
5/3
9/5
15/8
2

What surprised me when I tried this is that I was expecting something
totally horrible, but it actually ended up better than I was expecting!
Obviously something Bach would never have used, but interesting in a way.

> http://home.comcast.net/~teamouse/fugue2d.mp3 <http://home.comcast.net/~teamouse/fugue2d.mp3>

2d [sounds] sweet (Cameron Bobro)
2b and 2d some sort of well temperaments (Carl Lumma)
I'll take a stab and say that 'd' was WerckIII (Aaron Krister Johnson)
Example d is obviously the Werckmeister (Brad Lehman)
I agree that Werckmeister III is the fourth one (Ozan Yarman)
2d sounds very nice (Ozan Yarman)

! young.scl
!
Thomas Young well temperament (1807), also Luigi Malerbi nr.2 (1794)
12
!
256/243
196.09000
32/27
392.18000
4/3
1024/729
698.04500
128/81
894.13500
16/9
1090.22500
2/1

I was surprised at first how easy it was to confuse Young with
Werckmeister, since the two are quite different. But looking at the
Scala files, you can see that they actually share quite a few notes.

And for the bonus examples:

> http://home.comcast.net/~teamouse/fugue2e.mp3 <http://home.comcast.net/~teamouse/fugue2e.mp3>
2e seems to exhibit severe problems in simple keys (Ozan Yarman)
Much as I hate to say it, I don't think 2e is the worst choice. (Gene
Ward Smith)

(This is equal temperament.)

> http://home.comcast.net/~teamouse/fugue2f.mp3 <http://home.comcast.net/~teamouse/fugue2f.mp3>
2f did not appeal to me very much as it sounds edgy (Ozan Yarman)

! kirnberger3.scl
!
Kirnberger 3: 1/4 synt. comma (1744)
12
!
135/128
193.15686
32/27
5/4
4/3
45/32
696.57843
405/256
889.73529
16/9
15/8
2/1

> http://home.comcast.net/~teamouse/fugue2g.mp3 <http://home.comcast.net/~teamouse/fugue2g.mp3>
2g is psychedelic! but quite improper for Bach in my opinion. (Ozan Yarman)

! super_12.scl
!
Most equal superparticular 12-tone scale

12
!
16/15
17/15
6/5
19/15
4/3
64/45
68/45
8/5
76/45
16/9
17/9
2/1

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
>
>
> If 'd' is really 'WIII' (or even if it isn't!) then I don't think it
> comes off at all badly. Ab-C doesn't serve as a point of rest - but
> the way the piece is composed, it needn't.
>
> However, 'b' has some chords in odd places that seem pretty harsh even
> in passing and I wouldn't go for it. Sure 'b' isn't old Werckie?
>
> I'm astonished at the rhythmic regularity of the playing! I'd almost
> have thought it synthesized, except for the gradations in dynamic.
>
> 'c' is pleasantly strange (must be properly-spelled meantone) sounding
> almost like a doo-wop group, not a keyboard at all; 'g' unpleasantly
> strange (badly-spelled meantone?).
>
> ~~~T~~~

For once I'm feeling pretty smug ... only regret that I didn't have
the courage to contradict everyone else and say outright, 'd' is
smoother than 'b', therefore 'd' must be something-like-Young and 'b'
must be WIII.

What made me wince in 'b' (though it took repeated listenings to pin
down) was the G minor passage near the middle of the piece: the glut
of 1/4-Pythagorean-comma flat fifths, plus impure thirds, must be the
problem. Young in G minor is considerably better.

Thanks to Herman for listenable and interesting samples!

~~~T~~~