Wreckmeister explained

The ordinary septimal meantone temperament, which represents 5 by four
meantone fifths and 7 by ten fifths up and three octaves down is the
temperament one gets by combining 81/80 with 126/125, or equivalently,
81/80 with 225/224.
What happens if we let 81/80 fend for itself a little and concentrate on
the 126/125 (or 225/224?)

An equal temperament very well suited to 126/125 is, believe it or not,
108-et. If we take a Fokker block based on the
12-et commas 36/35, 81/80, and 126/125 and temper it via the 108-et, we
get a 126/125-tempered scale with very nice
properties, one of which is that it can serve as a temperament. The scale
is
[0, 11, 17, 28, 35, 45, 52, 63, 73, 80, 91, 97], and its circle of
seven-step intervals is
[63, 62, 63, 63, 62, 63, 67, 62, 63, 63, 62, 63]. This gives us eight
fifths equal to the common 12-et fifth, and four very flat but still
usable fifths, and one sharp wolf. The result *on average* is about
2/7-comma meantone, but it really is quite different, with a great many
intervals and chords quite accurately tuned. This is what I called
Wreckmeister B.

Similarly, if we take the Ellis duodene and temper it by the 72-et, we
get
[0, 7, 12, 19, 23, 30, 35, 42, 49, 53, 61, 65]; it has a 7-step circle
[42, 42, 41, 42, 42, 42, 44, 42, 42, 42, 41, 42]. This has 9 12-et
fifths, and two very, cheesy, very very flat fifths, and a sharp wolf. On
average, it is about 3/13 comma meantone, but it is even farther from
being average. However, it *does* do the 225/224 thing very well, and has
many 72-et tuned chords and intervals. It can, more or less, be
considered a temperament.

Finally, what about Wreckmeister A? This is the block which is three
major triads by four minor triads square, tempered by the 108-et. The
scale is [0, 7, 21, 28, 35, 45, 56, 63, 73, 80, 91, 101], and the 7-step
circle is
[63, 66, 59, 63, 66, 63, 59, 66, 63, 63, 62, 63]. While I called this a
temperament also, I was not being serious; but it *can* be used as a
retuning. What gets me about it is that the results can be very
interesting, as in my Beethoven quartet example, which really sends me.
Maybe I'm just weird, but it seems to have some kind of mojo going that
other retunings I've tried don't.

--- In tuning@y..., Gene W Smith <genewardsmith@j...> wrote:

> This gives us eight
> fifths equal to the common 12-et fifth, and four very flat but still
> usable fifths, and one sharp wolf.

that's thirteen altogther. in a twelve-tone tuning?
>
> Finally, what about Wreckmeister A? This is the block which is three
> major triads by four minor triads square,

did you mean "thirds" rather than "triads"?

> Maybe I'm just weird, but it seems to have some kind of mojo going
that
> other retunings I've tried don't.

well, cheers to that! everyone seems to have different ideas
about 'mojo', though. for example, joe monzo really liked the ravel
pavane in 64-equal, while that retuning appealed very little to me.
ah well, vive la difference!

p.s. i bet at least one person is going to see "Wreckmeister" and
miss the pun, simply reading "Werckmeister". perhaps if you altered
the second part of the name as well, in an equally clever way . . .

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
> p.s. i bet at least one person is going to see "Wreckmeister" and
> miss the pun, simply reading "Werckmeister".

Pays to read carefully, huh?! I was going to say something to Gene's original post, but thought someone else would be more clever. In any event, Gene, I think you really must enjoy your weekends, because that's when your humor seems to come out the most!

I only listened to the 2nd msg's piece, which was the Nutcracker excerpt. And that one, sadly, didn't seem to work for me, temperment-wise...

Cheers,
Jon

Gene,

I noticed the spelling and realised it was a pun, particularly since
you borrrowed my idea about ancient tuning documents found on the
bottom of the sea. :-) That's ok since we decided not to use that one
re the saggital notation.

However, I'm disappointed that the midi files are not in fact retuned,
at least for me, nor apparently for Jon Szanto.

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
> However, I'm disappointed that the midi files are not in fact
> retuned, at least for me, nor apparently for Jon Szanto.

Dave! Maybe it came out wrong in my typing, but the Nutcracker excerpt was *certainly* retuned for me. It didn't vary too much from 12tET, and I have to say that my ears couldn't tell me what the point of the retuning was, but it was _not_ (unless I was halucinating) in 12tET anymore...

Cheers,
Jon

--- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
> --- In tuning@y..., Gene W Smith <genewardsmith@j...> wrote:
>
> > This gives us eight
> > fifths equal to the common 12-et fifth, and four very flat but still
> > usable fifths, and one sharp wolf.
>
> that's thirteen altogther. in a twelve-tone tuning?

Does't add up very well, I agree. Actually, it's seven good fifths, four flat ones and the wolf.

> > Finally, what about Wreckmeister A? This is the block which is three
> > major triads by four minor triads square,
>
> did you mean "thirds" rather than "triads"?

'Fraid so. By the way, does the thirds by thirds block have a name?

> > Maybe I'm just weird, but it seems to have some kind of mojo going
> that
> > other retunings I've tried don't.

> well, cheers to that! everyone seems to have different ideas
> about 'mojo', though. for example, joe monzo really liked the ravel
> pavane in 64-equal, while that retuning appealed very little to me.
> ah well, vive la difference!

Give it a listen and see what you think.

--- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:

> However, I'm disappointed that the midi files are not in fact retuned,
> at least for me, nor apparently for Jon Szanto.

Yow. Listen to the Wreckmeister A examples, in particular
groups.yahoo.com/group/tuning/files/Gene/temperaments/wreck15a.mid
I sounds pretty retuned to me.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "dkeenanuqnetau" <d.keenan@u...> wrote:
>
> > However, I'm disappointed that the midi files are not in fact
retuned,
> > at least for me, nor apparently for Jon Szanto.
>
> Yow. Listen to the Wreckmeister A examples, in particular
> groups.yahoo.com/group/tuning/files/Gene/temperaments/wreck15a.mid
> I sounds pretty retuned to me.

To me too.

But when I click on the "Download" buttons at the end of the posts
that had attachments, the pieces there sounded quite normal.
Nevermind.

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "emotionaljourney22" <paul@s...> wrote:
> > --- In tuning@y..., Gene W Smith <genewardsmith@j...> wrote:

> > > Finally, what about Wreckmeister A? This is the block which is
three
> > > major triads by four minor triads square,
> >
> > did you mean "thirds" rather than "triads"?
>
> 'Fraid so. By the way, does the thirds by thirds block have a name?

if you give the set of 12 ratios in a few different transpositions,
we can ask manuel and monz to check their lists . . .

> Give it a listen and see what you think.

the second bach worked much better for me than the first. neither was
of delaubenfels-like satisfaction level for me, though. perhaps you
could shoot the midi sequence at john so we can get a direct
comparison? (i heard a wrong note and a missing note in the sequence,
though . .. )

>the second bach worked much better for me than the first.

Bach? What did I miss? I heard only the Waldstein and the
Op. 132. And the file marked 15 was another copy of the 132.

>neither was of delaubenfels-like satisfaction level for me, though.

That's for certain.

>(i heard a wrong note and a missing note in the sequence,
>though . .. )

Which one?

-Carl

--- In tuning@y..., Carl Lumma <carl@l...> wrote:

> >(i heard a wrong note and a missing note in the sequence,
> >though . .. )
>
> Which one?
>
> -Carl

the sequences attached here:

/tuning/topicId_37171.html#37171

>>>the second bach worked much better for me than the first.
>>
>>Bach? What did I miss?
>
>a two-part invention, i think the same one that they used to use for
>the commodore-64 commercial (ancient history).

Oh, I was looking in the Files section. And I just learned that
the Op. 132 is quartet #15, so no mistake in the file names there.

>>>(i heard a wrong note and a missing note in the sequence,
>>>though . .. )
>>
>>Which one?
>>
>>-Carl
>
>the sequences attached here:
>
>/tuning/topicId_37171.html#37171

Gene, I thought you'd know better than to use attachments to a mailing
list!

It's #13 in Amin. There seems to be a missing note at 0:59, and there's
also one missing from the right hand in the 2nd bar (though maybe this is
part of an alternate version?). Where's the wrong note?

-Carl