"Warped Canon" page is up!

http://www.io.com/~hmiller/music/warped-canon.html

I put up a web page with all my retunings of the Pachelbel Canon. Some of
them work out better than others, but they're all at least interesting. I
think the endless repetition of the familiar harmonic progression allows me
to become accustomed to the quirks of the different tunings over time.

I have a number of different categories of scales on the page. First, both
3-limit and 5-limit JI. Then the near-JI scales (34-, 41-, 53-, and 72-TET
so far), which sound very similar to the JI version (as you might expect).
Then, a sampling of meantone scales (equal and non-equal), which also sound
the way you'd expect.

After the meantone scales, I grouped together the multiples of 5-TET in one
group and the multiples of 7-TET in another. I expected some similarities
between the members of each of these groups, but I'm not sure if it
actually turns out that way. This will take a bit of careful listening.

After that is a grab bag of all the equal scales that don't fit into any of
the other categories. I'm going to see if I can figure out any kind of
pattern to them. The 8-TET version is in a category all by itself, since
the 16/15 vanishes, reducing the 8 distinct notes of the canon down to a
pentatonic scale! It has such a unique sound that I decided to revoice it
with mallet instruments and other percussive sounds. I think this neglected
scale deserves more attention.

Finally, I tried a few non-octave scales: Bohlen-Pierce, 88-CET, and a
7-limit JI scale (1/1 28/25 6/5 5/4 7/5 3/2 25/16 42/25 7/4). I stretched
the octaves of the original to 3/1 for the BP version, 1584 cents for the
88-CET version, and shrunk them to 7/4 for the 7-limit non-octave version.
They certainly have a unique sound, but I'm not sure how well they work out
for this piece. I'll have to try listening to them a few times to make
sense of them.

--
see my music page ---> ---<http://www.io.com/~hmiller/music/index.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
@io.com email password: thing till they were sure it would offend no body,
\ "Subject: teamouse" / there would be very little printed." -Ben Franklin

Hi Herman,

> http://www.io.com/~hmiller/music/warped-canon.html

> I put up a web page with all my retunings of the Pachelbel Canon. Some of
> them work out better than others, but they're all at least interesting. I
> think the endless repetition of the familiar harmonic progression allows me
> to become accustomed to the quirks of the different tunings over time.
...

> pattern to them. The 8-TET version is in a category all by itself, since
> the 16/15 vanishes, reducing the 8 distinct notes of the canon down to a
> pentatonic scale! It has such a unique sound that I decided to revoice it
> with mallet instruments and other percussive sounds. I think this neglected
> scale deserves more attention.

Great! Went to the 8-tet canon first and it is Wonderful!!

I think it is the first piece I've ever heard in 8-tet.

Robert

--- In tuning@y..., Herman Miller <hmiller@I...> wrote:
> http://www.io.com/~hmiller/music/warped-canon.html

You still haven't answered my question (though I might be able to hear the answer when I'm in a
place where I can listen to these). In the 5-limit JI version, and the JI-like ETs, did you use a
fixed subset, or did you allow two comma-separated versions for one or more notated notes? I
found that a fixed JI subset was unacceptable when I tried to play the piece on my keyboard --
but I'll have to listen to what you did.
>
> After that is a grab bag of all the equal scales that don't fit into any of
> the other categories. I'm going to see if I can figure out any kind of
> pattern to them. The 8-TET version is in a category all by itself, since
> the 16/15 vanishes, reducing the 8 distinct notes of the canon down to a
> pentatonic scale!

Wouldn't this happen in 5-tET as well? Also, did you have a strict set of rules for retuning the
piece to various tunings, or did you subjectively decide what to do in each tuning? If the former,
what was the set of rules you used?

Anyway, this reminds me of something both John Chalmers and I independently did a long
time ago. The Macintosh used to (maybe still does) come with a sample BASIC program
which plays a Bach piece (that famous cantata in 3/4 time). It was very easy to modify the sizes
of tone, diatonic semitone, and chromatic semitone in this program. I've discussed various
people's reactions to various retunings of the piece in the past . . .

Fantastic!

Thanks for the effort Robert!

GZ

Robert Walker wrote:

> Hi Herman,
>
> > http://www.io.com/~hmiller/music/warped-canon.html
>
> > I put up a web page with all my retunings of the Pachelbel Canon. Some of
> > them work out better than others, but they're all at least interesting. I
> > think the endless repetition of the familiar harmonic progression allows me
> > to become accustomed to the quirks of the different tunings over time.
> ...
>
> > pattern to them. The 8-TET version is in a category all by itself, since
> > the 16/15 vanishes, reducing the 8 distinct notes of the canon down to a
> > pentatonic scale! It has such a unique sound that I decided to revoice it
> > with mallet instruments and other percussive sounds. I think this neglected
> > scale deserves more attention.
>
> Great! Went to the 8-tet canon first and it is Wonderful!!
>
> I think it is the first piece I've ever heard in 8-tet.
>
> Robert
>
>
>
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On Mon, 11 Jun 2001 01:38:39 -0000, "Paul Erlich" <paul@stretch-music.com>
wrote:

>--- In tuning@y..., Herman Miller <hmiller@I...> wrote:
>> http://www.io.com/~hmiller/music/warped-canon.html
>
>You still haven't answered my question (though I might be able to hear the answer when I'm in a
>place where I can listen to these). In the 5-limit JI version, and the JI-like ETs, did you use a
>fixed subset, or did you allow two comma-separated versions for one or more notated notes?

I figured that John deLaubenfels' analysis would have answered it. But to
be more specific, all the retuned versions (except the non-octave ones) use
a fixed subset based on this lattice:

B F# C#
C G D A E

If the tuning has a good approximation of 5/4 and 3/2, and is 5-limit
consistent, I plug in those values. In other cases, I try a couple of
different values and pick the one that I like the best. (In the case of
13-TET, there were two different tunings that seemed about as good -- or
bad, as the case may be.)

>> After that is a grab bag of all the equal scales that don't fit into any of
>> the other categories. I'm going to see if I can figure out any kind of
>> pattern to them. The 8-TET version is in a category all by itself, since
>> the 16/15 vanishes, reducing the 8 distinct notes of the canon down to a
>> pentatonic scale!
>
>Wouldn't this happen in 5-tET as well? Also, did you have a strict set of rules for retuning the
>piece to various tunings, or did you subjectively decide what to do in each tuning? If the former,
>what was the set of rules you used?

I didn't try scales with less than 7 notes, although I guess 5-TET might be
a good candidate.

I gradually figured out a set of rules for doing the retuning, but there
are still a number of exceptions. Once I decide on the size for the major
third, fifth, and octave (or their equivalents), the rest follows
automatically. If the best major third and minor third add up to be the
same as the best fifth, I usually just use those if there isn't a good
reason not to. If not, I pick whichever interval is closest to just and try
out a few different sizes for the other intervals. In some cases, I had
previous experience with the scale (such as 20-TET), which helped me to
decide what to do with the triads. (I used Graham Breed's Midiconv program
to do the retuning.)

On Mon, 11 Jun 2001 01:12:00 -0400, Herman Miller <hmiller@IO.COM> wrote:

>I didn't try scales with less than 7 notes, although I guess 5-TET might be
>a good candidate.

I added 5-TET and 6-TET versions to the page. Besides these, I also added a
number of other interesting scales:

5-limit JI *minor* (watch out for the comma-sized step in the melody!)
7-limit JI subminor
Starling temperament (major 3rd = 388 cents, fifth = 700 cents)
1/7-comma meantone with 1/7-comma stretched octaves
Tempered version of the Bohlen-Pierce scale

--
see my music page ---> ---<http://www.io.com/~hmiller/music/index.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
@io.com email password: thing till they were sure it would offend no body,
\ "Subject: teamouse" / there would be very little printed." -Ben Franklin