Pachelbel's Canon sounds great in any tuning!

Okay, that might be a bit of an exaggeration. But it occurred to me as I
was listening to a recording of Pachelbel's Canon that the harmonic
progression doesn't have any comma pumps, making it a perfect candidate for
5-limit JI tuning. So I did a MIDI arrangement:

http://www.io.com/~hmiller/midi/canonj5.mid

Sounds pretty nice, doesn't it? Then I started playing around with some
more unusual tunings. The usual meantone scales sounded good, as expected.
Scales with good approximations to 5-limit JI (like 34- and 72-equal) also
work out well. The 7-limit approximations of 22-equal added a nice flavor.
Even 15-equal sounded good, in contrast to what most music not specifically
written for it does when played in 15! So I tried it in 23-equal, thinking
it would bring out some more discordant harmonies (which it did), but it
still didn't sound really bad, just different. Even warped 11- and 13-equal
versions at least sounded somewhat pleasant and the harmonic progressions
were still recognizable, although the melodic lines started to get really
bent into strange forms.

I haven't tried non-octave scales yet; I figure they'd probably break
everything into dissonance. But I'm thinking of doing retuned versions in a
variety of different temperaments and putting them up on a "Warped Canon"
page. Any suggestions for tunings that might sound interesting?

--
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

Herman,

--- In tuning@y..., Herman Miller <hmiller@I...> wrote:
> Okay, that might be a bit of an exaggeration.

Especially to anyone in a string quartet (or married to someone who
is) or similar group that have played the Canon x million number of
times at weddings and would like to dig up Pachelbel and kill him all
over again!!! <g>

Cheers,
Jon

On 6/9/01 10:05 PM, "Herman Miller" <hmiller@IO.COM> wrote:

> So I tried it in 23-equal, thinking
> it would bring out some more discordant harmonies (which it did), but it
> still didn't sound really bad, just different.

Well first I have to agree with your subject line.

Some classical pieces are seemingly
so rich with a kind of universal content,
that they'll pretty much sound good anywhere.

And I just wanted to sympathize,
I too thought something would sound wrong in 23,
and it really didn't sound too bad.

Marc

Well, just to come back at 90 degrees, if not 180, from your post, I
downloaded your sequence & threw it at my adaptive methods. I was
surprised to find a COFT somewhat different from yours, and even more
surprised that I'm showing full adaptive tuning to recover a significant
amount of "pain" as compared to COFT.

I peeked at your tuning and found a chain of fifths C-G-D-A-E, with
major thirds B-F#-C# hanging off G-D-A. Compared with my COFT calc:

Note Y'r bend My bend
---- -------- -------
C 0.00 +9.04
C# -7.81 -9.14
D +3.91 +4.91
Eb [not present]
E +7.81 +4.27
F [not present]
F# -9.77 -9.45
G +1.95 +4.90
Ab [not present]
A +5.86 +5.06
Bb [not present]
B -11.72 -9.59

Here's some other numbers I calc:

12-tET spring pain: 3260328.670
Werckmeister III spring pain: 3018434.278
Kirnberger III spring pain: 2473325.368
Thomas Young spring pain: 2413627.936
31 from Abb to C : spring pain: 683277.667
31 from Ebb to G : spring pain: 6394656.071
31 from Bbb to D : spring pain: 17273475.749
31 from Fb to A : spring pain: 25846847.329
31 from Cb to E : spring pain: 26278757.117
31 from Gb to B : spring pain: 19075442.233
31 from Db to F# : spring pain: 8498523.856
31 from Ab to C# : spring pain: 530817.728
31 from Eb to G# : spring pain: 530817.728
31 from Bb to D# : spring pain: 530817.728
31 from F to A# : spring pain: 530817.728
31 from C to E# : spring pain: 530817.728
31 from G to B# : spring pain: 683277.667
31 from D to F##: spring pain: 6394656.071
31 from A to C##: spring pain: 17273475.749
COFT Total spring pain: 221203.167
After relaxing, Total spring pain: 107687.775

N spring Pain Strength RMS cents dev.
Vertical 8223 77284.246 47491.342 1.804
Horizontal 6088 13528.589 268300.821 0.318
Melodic 1818 782.513 40.907 6.185
Grounding 6096 16092.426 15098.679 1.460

Ideal melodic semitone: 115.0399 cents.
Ideal melodic tone: 194.1110 cents.
Bend range applied: -12.9397 to 14.1791

I'm using 5-limit tuning-file-free targets with fairly rigid vertical
springs. All the "31" numbers are equivalent to 1/4-comma meantone.
Note that the absence of 4 notes in the circle of fifths means that
five consecutive meantone ranges all have the same pain sum (530817).
I don't yet have the means to evaluate the bends you chose (not that you
_asked_ me to! Just for my own interest...).

I'm showing adaptive pain of 107687, half of COFT (221203). Given the
simplicity of this piece, this surprises me!

Looking forward to your wild tunings...

JdL

Hi John,

I enjoyed Herman's Pachelbel's canon in j.i. too.

Would be interesting to hear your COFT and adaptive tunings of
it as well.

> Looking forward to your wild tunings...

So am I!

I've also been enjoying the other music on
http://www.io.com/~hmiller/music/index.html

I've bookmarked it and will keep coming back.

:-)

Robert

--- In tuning@y..., Herman Miller <hmiller@I...> wrote:
> Okay, that might be a bit of an exaggeration. But it occurred to me as I
> was listening to a recording of Pachelbel's Canon that the harmonic
> progression doesn't have any comma pumps, making it a perfect candidate for
> 5-limit JI tuning.

Actually, I tried this and I thought it sounded _terrible_ in any _fixed_ 5-limit JI tuning.
You must be allowing at least one of the pitches to vary by a comma (I can't listen to your
sequence right now).

So I did a MIDI arrangement:
>
> http://www.io.com/~hmiller/midi/canonj5.mid

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
>
> Looking forward to your [Herman's] wild tunings...
>
> JdL

Me too . . . and I'd like to hear the one you did that you referred to in this message . . . the
5-limit tuning-file-free one with rigid vertical springs. Can you put that up somewhere?

On Sun, 10 Jun 2001 09:46:30 -0600, "John A. deLaubenfels"
<jdl@adaptune.com> wrote:

>I peeked at your tuning and found a chain of fifths C-G-D-A-E, with
>major thirds B-F#-C# hanging off G-D-A. Compared with my COFT calc:
>
>Note Y'r bend My bend
>---- -------- -------
> C 0.00 +9.04
> C# -7.81 -9.14
> D +3.91 +4.91
> Eb [not present]
> E +7.81 +4.27
> F [not present]
> F# -9.77 -9.45
> G +1.95 +4.90
> Ab [not present]
> A +5.86 +5.06
> Bb [not present]
> B -11.72 -9.59

The vast difference between your C and mine isn't surprising, as C natural
is a very uncommon note in the canon. I considered using the C a minor
third above A, but I have a slight preference for 16/9 in a dominant
seventh chord (in 5-limit at least). I think the reason your E is a little
flatter than mine is that there are a few E's in the melody against a G in
the bass at one point. That might also explain in part why your G is a
little sharper than mine.

>I'm showing adaptive pain of 107687, half of COFT (221203). Given the
>simplicity of this piece, this surprises me!

The harmonic progression is simple, but there are some intricacies in the
melody/counterpoint that could explain the improvement with adaptive
tuning. Have you tried 7-limit?

[I wrote:]
>>I peeked at your tuning and found a chain of fifths C-G-D-A-E, with
>>major thirds B-F#-C# hanging off G-D-A. Compared with my COFT calc:
>>
>>Note Y'r bend My bend
>>---- -------- -------
>> C 0.00 +9.04
>> C# -7.81 -9.14
>> D +3.91 +4.91
>> Eb [not present]
>> E +7.81 +4.27
>> F [not present]
>> F# -9.77 -9.45
>> G +1.95 +4.90
>> Ab [not present]
>> A +5.86 +5.06
>> Bb [not present]
>> B -11.72 -9.59

[Herman Miller wrote:]
>The vast difference between your C and mine isn't surprising, as C
>natural is a very uncommon note in the canon. I considered using the C
>a minor third above A, but I have a slight preference for 16/9 in a
>dominant seventh chord (in 5-limit at least). I think the reason your E
>is a little flatter than mine is that there are a few E's in the melody
>against a G in the bass at one point. That might also explain in part
>why your G is a little sharper than mine.

I'm posting an interval analysis of the sequence over on tuning-math.

/tuning-math/message/207

Yes, I show C being pushed up by A and, to a lesser extent, by E; it's
pushed down mainly by G. I show E being pushed up by A and C#, and
down by G and B. And G is pushed up by E and down by D. Just as you
say.

[JdL:]
>>I'm showing adaptive pain of 107687, half of COFT (221203). Given the
>>simplicity of this piece, this surprises me!

[Herman:]
>The harmonic progression is simple, but there are some intricacies in
>the melody/counterpoint that could explain the improvement with
>adaptive tuning. Have you tried 7-limit?

Haven't tried 7-limit, but I don't think it'll make too much difference,
because the piece has very few tritones in it. I'll run it now and see
if I'm right! Uhhh, no, I'm wrong! The tritones have more influence
than I realized. Adaptive pain recovery is still very good, however.

I've downloaded your many variants, and look forward to hearing them.
Thanks for doing this!

JdL