Yahoo Tuning Groups Ultimate Backup tuning Warped Canon page updated!

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

I added a few new JI retunings -- using different warped harmonies like
3:4:5 and 7:9:11 as a substitute for the major triads. I also moved the
"alternative" orchestrations to a section at the bottom of the list and
uploaded new 5-TET and 8-TET versions in the original orchestration. All of
the midis have been updated to use the reed organ and harp instead of the
accordion and marimba. The biggest addition is a description of the various
tunings and how they are mapped to the original scale. I hope this answers
some of the questions.

--
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

🔗jpehrson@rcn.com

--- In tuning@y..., Herman Miller <hmiller@I...> wrote:

/tuning/topicId_25255.html#25255

> http://www.io.com/~hmiller/music/warped-canon.html
>
> I added a few new JI retunings -- using different warped harmonies
like
> 3:4:5 and 7:9:11 as a substitute for the major triads. I also moved
the
> "alternative" orchestrations to a section at the bottom of the list
and
> uploaded new 5-TET and 8-TET versions in the original
orchestration. All of
> the midis have been updated to use the reed organ and harp instead
of the
> accordion and marimba. The biggest addition is a description of the
various
> tunings and how they are mapped to the original scale. I hope this
answers
> some of the questions.
>

Thanks so much, Herman, for this update and, especially, for the
explanations which look very helpful...!

________ _______ _______
Joseph Pehrson

🔗jpehrson@rcn.com

--- In tuning@y..., jpehrson@r... wrote:

/tuning/topicId_25255.html#25257

> --- In tuning@y..., jpehrson@r... wrote:
>
> /tuning/topicId_25255.html#25256
>
> I guess I have one final short question on the Herman
> Miller's "Warped Canon" page...
>
> How is this process done technically, again? How do you get your
> sound card to do all these retunings? Do you feed it pitch bend
> information some way... I'm a little mystified by this...
>

Sorry... Herman, I just remembered that you use Graham Breed's
MIDICONV program to do that... forgot about it...

______________ _______ _____
Joseph Pehrson

🔗carl@lumma.org

🔗monz <joemonz@yahoo.com>

> ----- Original Message -----
> From: <carl@lumma.org>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, June 17, 2001 12:16 AM
> Subject: [tuning] Re: Warped Canon page updated!
>

> The warped canons are the best meantone comparo ever. Herman,
> it would be great if you add 69-tET, as this is extremely close
> to meta-meantone.

I agree with Carl. Herman, this page is really a terrific resource.
I'm glad to see that you've added explanatory comments.
Please allow them to grow. In fact, it would be nice to have
a list of links to tuning list posts that people have submitted
about their experiences of listening to this page.

With my recent interest in retuning Mozart's G-minor Symphony,
I'd love to hear a 55-TET version. And how about 171-TET?
This has been advocated by Martin Vogel and Paul Erlich, and
I've never heard it.

-monz
http://www.monz.org
"All roads lead to n^0"

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

🔗jpehrson@rcn.com

--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_25255.html#25264

> >
> I agree with Carl. Herman, this page is really a terrific
resource.
> I'm glad to see that you've added explanatory comments.
> Please allow them to grow. In fact, it would be nice to have
> a list of links to tuning list posts that people have submitted
> about their experiences of listening to this page.
>

In my opinion, that might make it a little too "chatty...", but
certainly links to CONCEPTS of the various tunings or, at least, to
the Monz dictionary definitions pages would be welcome...

It certainly would make an excellent FAQ centerpiece, if the FAQ ever
gets going again...

______ ______ _________
Joseph Pehrson

🔗Alison Monteith <alison.monteith3@which.net>

🔗Herman Miller <hmiller@IO.COM>

On Sun, 17 Jun 2001 02:38:52 -0000, jpehrson@rcn.com wrote:

>How is this process done technically, again? How do you get your
>sound card to do all these retunings? Do you feed it pitch bend
>information some way... I'm a little mystified by this...

It's just MIDI with pitch bend. Midiconv puts the pitch bends at the
beginning of each note, according to the values specified in the tuning
file. The pitch bend is assumed to be set to plus or minus 2 semitones. So
in effect, each semitone is divided into 4,096 steps of 0.0244 cents.
That's fine enough resolution in theory, but individual MIDI devices such
as PC sound cards may actually have much coarser resolution.

🔗Herman Miller <hmiller@IO.COM>

On Sun, 17 Jun 2001 07:16:22 -0000, carl@lumma.org wrote:

>The warped canons are the best meantone comparo ever. Herman,
>it would be great if you add 69-tET, as this is extremely close
>to meta-meantone.

Added.

>Also, I'm having trouble understanding why you picked the
>mapping to 88CET. Could you elaborate?

I wanted a consonant interval near the octave to substitute for the octave,
so I picked one that's equivalent to 5/2 - 2.31 cents. The 88CET "octave"
is 32 cents sharp. I also wanted consonant intervals for the other notes in
the triad that had roughly the same proportions as the original major
triad. The notes I chose result in a chord that approximates 1/(10:7:6:4).
But there are other possibilities as well. I just now tried 4:6:7:10, and
that seems to work fine, although the melody is a little bent.

🔗Herman Miller <hmiller@IO.COM>

On Sun, 17 Jun 2001 00:29:13 -0700, "monz" <joemonz@yahoo.com> wrote:

>With my recent interest in retuning Mozart's G-minor Symphony,
>I'd love to hear a 55-TET version. And how about 171-TET?
>This has been advocated by Martin Vogel and Paul Erlich, and
>I've never heard it.

Okay, I added those. The 171-TET probably won't sound any different from
just, since the errors are less than half a cent, but if you look at the
pitch bends in a MIDI editor you can see that they *are* different. Maybe
if I ever get around to doing a Csound version I'll be able to perceive a
difference, but I doubt it. The 55-TET is a nice meantone, similar to the
1/6-comma meantone I used for the Ultima VI music.

🔗carl@lumma.org

>>The warped canons are the best meantone comparo ever. Herman,
>>it would be great if you add 69-tET, as this is extremely close
>>to meta-meantone.
>
> Added.

Great! Can anybody hear a difference between this and LucyTuning?
Prefer it (or not) to golden meantone (very close to Erlich's
optimal meantone)?

I can't hear the diff. between 69 and Lucy until the last chord,
which beats more prominantly in Lucy, at about the same rate.
The final chord beats much faster in golden -- something which
I don't like.

>>Also, I'm having trouble understanding why you picked the
>>mapping to 88CET. Could you elaborate?
>
>I wanted a consonant interval near the octave to substitute for
>the octave, so I picked one that's equivalent to 5/2 - 2.31 cents.

As I suspected. Have you tried treating the 7:4 as an octave?
The triad could then use the 3:2 and the neutral or minor third.

>But there are other possibilities as well. I just now tried
>4:6:7:10, and that seems to work fine, although the melody is
>a little bent.

Cool! Say, could you re-post that post where you show how to
make a midiconv tuning file? I can't seem to find it. I tried
midiconv once, but couldn't get it to work. It's obviouly a
powerful tool... you'll be quite busy around here if you're the
only one who knows how to use it!

-Carl

🔗carl@lumma.org

🔗Herman Miller <hmiller@IO.COM>

🔗Jon Szanto <JSZANTO@ADNC.COM>

Herman!

--- In tuning@y..., Herman Miller <hmiller@I...> wrote:
> I wrote the sound drivers and tuned them to 21 notes of 1/6-comma
> meantone (the diatonic scale plus sharps and flats).

Excellent!! This is "microtonality slipped in the back door" at it's
finest. Boy, if ever there was a way to get new tunings into people's
heads/ears, here is a fine way. I've also thought that it would be
great if composers/musicians could get some of the animated series
that still play on Saturday morn, etc., into microtonality you could
infuse it in the ears while they are still accepting of new things.

Very cool insight, thanks!

Cheers,
Jon

🔗Herman Miller <hmiller@IO.COM>

On Sun, 17 Jun 2001 18:06:15 -0000, carl@lumma.org wrote:

>Cool! Say, could you re-post that post where you show how to
>make a midiconv tuning file? I can't seem to find it. I tried
>midiconv once, but couldn't get it to work. It's obviouly a
>powerful tool... you'll be quite busy around here if you're the
>only one who knows how to use it!

The easiest way is just to list the pitches of the notes as fractions of an
octave. That's the way I usually use the tuning files. For example:

! 12 from Chopi 7-note xylophone scale
notes 12
0 0.0
1 0.1516
2 0.1516
3 0.292
4 0.292
5 0.444
6 0.589
7 0.589
8 0.729
9 0.729
10 0.87
11 0.87
12 1.005

The only reason I used 12 notes in that tuning file is that the input MIDI
file is in 12-TET. The final note gives the size of the octave. I made an
approximation of the Chopi xylophone scale that averaged out some of the
differences between the octaves so that I could repeat it and extend it
over the range of MIDI input.

For most of the canons, to save time, I used the "coords" feature to
specify the size of three intervals (the octave, fifth, and third) and
define each of the pitches in the scale based on these intervals. For
example, the note D is an octave down and two fifths up, so its line reads
"-1 2 0" (-1 octave, +2 fifths, +0 thirds). Here's a repeat of that 15TET
tuning file I posted earlier:

! 12 from 15TET
coords 3
octave 1.0
fifth 0.6
third 0.333333333
notes 12
0 0 0 0 ! C
1 -2 3 1 ! C#
2 -1 2 0 ! D
3 2 -3 0 ! Eb
4 0 0 1 ! E
5 1 -1 0 ! F
6 -1 2 1 ! F#
7 0 1 0 ! G
8 -2 4 1 ! G#
9 1 -1 1 ! A
10 2 -2 0 ! Bb
11 0 1 1 ! B
12 1 0 0 ! C

🔗carl@lumma.org

🔗David J. Finnamore <daeron@bellsouth.net>

Herman Miller wrote:

> >Also, I'm having trouble understanding why you picked the
> >mapping to 88CET. Could you elaborate?
>
> I wanted a consonant interval near the octave to substitute for the octave,
> so I picked one that's equivalent to 5/2 - 2.31 cents. The 88CET "octave"
> is 32 cents sharp.

Gasp! Are you saying you treated 88 CET as if it were an octave repeating tuning? I hope not.
There is no octave. If all the tones in the piece, from lowest to highest, don't lie on a single
string, each 88 cents apart, then IMO it's not 88 CET.

I really enjoyed (and am enjoying) the whole page, though. I posted a number of
stream-of-consciousness style reactions to them on Spiritual Tuning. If anyone's interested, I
consolidate them, edit it a little and repost over here. One of the most curious things is that my
Siamese cat, who generally ignores music altogether, seems to LOVE the Canon in 10 ED2! When I play
it, she comes from anywhere in the house to sit in my lap at the computer until it's done. Then she
goes back to the window sill, or whatever she was up to at the moment. She offers no noticeable
response to any of the others. Very strange.

My personal favorite so far is the 72 ED2 version, only slightly more than the 5-limit JI. I used
it several times to "heal me up" from some of the ones that irritated me in some way, such as 15
ED2, which literally made my cavities ache. I also discovered through this listening exercise that
there are quite a few very pretty ETs that have gotten very little press here in the four years I've
been around, most notably 27 and 33. So they may not be "consistent in the whatever limit."
They're beautiful.

--
David J. Finnamore
Nashville, TN, USA
http://personal.bna.bellsouth.net/bna/d/f/dfin/index.html
--
"Always take skeptics with a grain of salt." - Kris Peck

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., "David J. Finnamore" <daeron@b...> wrote:
>
> Gasp! Are you saying you treated 88 CET as if it were an octave
repeating tuning? I hope not.
> There is no octave. If all the tones in the piece, from lowest to
highest, don't lie on a single
> string, each 88 cents apart, then IMO it's not 88 CET.

That's just silly, David. Herman used a subset of 88 CET -- what's
wrong with that?

> I also discovered through this listening exercise that
> there are quite a few very pretty ETs that have gotten very little
press here in the four years I've
> been around, most notably 27

Margo Schulter and I have talked about 27 quite a bit.

> and 33.

33 can be seen as a pretty extreme meantone (26 + 7) -- I'm not sure
if Herman used it this way or some other way -- should be clear from
listening.

> So they may not be "consistent in the whatever limit."

If an ET (like 33) isn't consistent in the 5-limit, there is more
than one equally interesting way to map the Pachelbel Canon to it.

By the way, Herman, 22-tET is consistent through the 11-limit, not
just the 9-limit.

> They're beautiful.

You can say that again. That Tempered BP version -- wow.

🔗David J. Finnamore <daeron@bellsouth.net>

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., "David J. Finnamore" <daeron@b...> wrote:
> >
> > Gasp! Are you saying you treated 88 CET as if it were an octave
> repeating tuning? I hope not.
> > There is no octave. If all the tones in the piece, from lowest
to
> highest, don't lie on a single
> > string, each 88 cents apart, then IMO it's not 88 CET.
>
> That's just silly, David. Herman used a subset of 88 CET -- what's
> wrong with that?

I didn't say there was anything *wrong* with it. My "gasp" needed a
smiley face after it, didn't it? Oh, wait a minute. I think I see
the source of confusion. I didn't mean that the pitches of the piece
have to make up a consective 88 cent set, which is what I literally
said (unintentionally). That must be what you were protesting
as "silly" which it certainly is, so thanks for catching it.

If you take a subset of 88 CET and make it repeat at some interval
other than a multiple of 88 cents, that's fine but it's not 88 CET
anymore. Pitches in different registers won't be related the same
way, right? That's what I took Herman to mean. Like, if I take 12
consecutive pitches of 100 CET, repeat them at 1150 cents, and use
them for a piece that spans more than an octave, it's not 12t-ET. It
might be a perfectly fine tuning for something but I would need to
clarify that it's a special hybrid tuning.

> > I also discovered through this listening exercise that
> > there are quite a few very pretty ETs that have gotten very
little
> press here in the four years I've
> > been around, most notably 27
>
> Margo Schulter and I have talked about 27 quite a bit.

Oh, good. Probably recently? I haven't followed this list closely
for the past two months or so. I'm getting back into the swing now.

> 33 can be seen as a pretty extreme meantone (26 + 7) -- I'm not
sure
> if Herman used it this way or some other way -- should be clear
from
> listening.

Probably. The release of Herman's page happened to nearly coincide
with Marc Jones suggesting I explore the nearest set to 33 in 50. In
the process, I also explored 33 a little, not necessarily as a
meantone, and found it delightfully colorful. Maybe I'll have some
pieces to share in a few weeks or months. :-)

> > So they may not be "consistent in the whatever limit."
>
> If an ET (like 33) isn't consistent in the 5-limit, there is more
> than one equally interesting way to map the Pachelbel Canon to it.

That's a nice way to say it.

David

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., "David J. Finnamore" <daeron@b...> wrote:

> If you take a subset of 88 CET and make it repeat at some interval
> other than a multiple of 88 cents, that's fine but it's not 88 CET
> anymore.

True! But Herman didn't do that.

> That's what I took Herman to mean. Like, if I take 12
> consecutive pitches of 100 CET, repeat them at 1150 cents, and use
> them for a piece that spans more than an octave, it's not 12t-ET.

Right. You must have misunderstood Herman. He used the "7/4", not
the "2/1", as the equivalence interval for the 88CET version --
right, Herman?

🔗Paul Erlich <paul@stretch-music.com>

Herman, these statements on your page are not quite correct:

"The original BP scale is represented as a sequence of ratios from a
base pitch: 1/1 27/25 25/21 9/7 7/5 75/49 5/3 9/5 49/25 15/7 7/3
63/25 25/9 3/1. The 3/1 interval serves as the equivalent of the
octave for this scale. There is also a tempered version of the BP
scale (originally discovered by Kees van Prooijen), based on dividing
the 3/1 into 13 equal steps of 146.3 cents each."

The JI scale above was due to Bohlen, not Pierce. The tempered scale
was discovered independently by both Bohlen and Pierce. I'm not sure
if Kees also discovered it independently . . . if so, he probably
didn't precede Bohlen. Kees does, however, put forth a "BP major
scale" constructed from 3:5:7 "major triads". What would the canon
sound like with this construction instead of the 5:7:9 construction??

🔗Herman Miller <hmiller@IO.COM>

On Mon, 18 Jun 2001 20:47:23 -0000, "Paul Erlich" <paul@stretch-music.com>
wrote:

>The JI scale above was due to Bohlen, not Pierce. The tempered scale
>was discovered independently by both Bohlen and Pierce. I'm not sure
>if Kees also discovered it independently . . . if so, he probably
>didn't precede Bohlen.

Maybe I misinterpreted this paragraph from the Bohlen-Pierce site:

"At about the same time a paper was published that containes the
equal-tempered version of the BP scale, next to that of numerous others, in
a rather encoded form [6]. Its author, Kees van Prooijen², a software
engineer and music theorist, had independently arrived at this result when
searching for equal-tempered scales that satisfy consonance with higher
harmonics, but he decided to keep it concealed until further investigation.
Only many years later he finally lifted the veil [16]."

I've made a preliminary update to the description on the canon page, but
I'll need some time to sort out the details.

🔗David J. Finnamore <daeron@bellsouth.net>

🔗carl@lumma.org

🔗Herman Miller <hmiller@IO.COM>

🔗Paul Erlich <paul@stretch-music.com>

🔗Herman Miller <hmiller@IO.COM>

On Fri, 22 Jun 2001 20:26:10 -0000, "Paul Erlich" <paul@stretch-music.com>
wrote:

>How about a 56-tET version, since Graham talks about 56-tET on his
>diachismic page? It's not quite near-just, but it's certainly
>close . . .

Hmm ... I didn't really "get" diaschismic scales before, but I took another
look at the page, and I think I have a better understanding of them now. I
went through my list of ET's less than 100 to figure out which ones were
diaschismic, and it looks like there's about as many of them as schismic
scales. There are some interesting tunings here. 56-TET sounds very nice.
Its minor sevenths aren't quite low enough to put them in the category of
tunings that suggest 7-limit harmony, but they still sound pretty good. A
bit of the 5-limit goodness of 34 and the 7-limit goodness of 22 (since 56
= 22 + 34). 32-TET also falls into this category, and one of the tunings I
previously tried for 32-TET (not the one that originally ended up on the
page) happens to fit the diaschismic tuning. The 17-limit-consistent 58-TET
is also diaschismic!

I added a section on diaschismic tunings and put up the new 32-TET and
56-TET retunings. See what you think.

🔗Paul Erlich <paul@stretch-music.com>

🔗Gary Morrison <mr88cet@austin.rr.com>

I finally got a chance to read over this thread, and check out Herman's MIDI-file examples of
rendering Pachelbel's canon in various tunings. I have a few thoughts on the topic, especially as
it relates to the rendering in 88CET.

First of all, that's a nice web page for comparing various tunings. I think the best part is its
comprehensiveness with respect to the large number of tunings it compares. Good work, Herman!

I'm not so sure about the usage of 88CET, though. He took an intriguing approach, and the results
are interesting, but I'm not sure how successful to think it turned out. Or more accurately, I
think his solution to the concept of proportionally mapping traditional harmony and melody
simultaneously to 88CET seems reasonable, but I have to wonder how realistic a concept that is in
the first place. As I understand it, Herman drew an analogy between 5:2 and the octave. He then
found chords spanning that 5:2 that are roughly proportionally spaced to the usual major chord.
Later did roughly the same with 7:4. Not surprisingly, the harmonies end up sounding very alien.

I certainly don't have anything against alien harmony, but I find that such alien harmonies need
to be carefully selected, rather than being constrained by an existing score. Also, when most of
the links on that web page lead to comparatively subtle variations on a theme (literally and
figuratively), the entirely alien harmony could turn some people off. Now, I have found that that
approach works for melody alone, but with harmony, the results can get rather horrendous very
quickly.

There may be a more meaningful solution, although it would take more work.

Amazingly enough (it surprised me anyway), it is possible to render a fair approximation to
traditional harmony in 88CET, provided that you can control the vertical voicing of each chord.
That is perhaps outside of the intent of this web page, that intent probably being to hear how
varying only the tuning system, without changing the music itself, affects the music. Still, if
we are allowed to choose the voicing of the chords, you can produce traditional triadic and
seventh-chord harmonies in 88CET. The trick being to take advantage of the 4:6:7:10 structure,
and then let tendency tones resolve in the traditional manner. You end up with a wandering tonic
in many cases, and some of the chords using supramajor thirds instead of major, or subminor
instead of minor. Still, as strange as the results sound, they do pretty much present the same
sensation to listeners as the traditional harmony. I've even managed to pull off chromatically
altered chords, like Neapolitans.

The really wild part of this sort of harmonization is that it's entirely relative to previous
harmony. In traditional 12-toned harmony, if the melody you're trying to harmonize contains an E
in the key of C major, you know that it's scale degree 3, and thus you immediately know what the
possible traditional harmonizations are for it. In this sort of traditional harmonization in
88CET though, how that pitch is interpreted is entirely dependent upon the chords before it.
Because of the wandering tonics, a given pitch could end up producing the sensation and function
of scale degree 4 as easily as scale-degree 3. You can't tell until you flesh out the harmony
leading up to it.

Now rendering a fixed harmony in that manner and also simultaneously rendering a fixed melody I
suspect would prove a lot more difficult to accomplish, and matching a bass line would probably
make it yet more difficult still. It may be possible though.

🔗carl@lumma.org

> I'm not so sure about the usage of 88CET, though. He took an
> intriguing approach, and the results are interesting, but I'm not
> sure how successful to think it turned out. Or more accurately,
> I think his solution to the concept of proportionally mapping
> traditional harmony and melody simultaneously to 88CET seems
> reasonable, but I have to wonder how realistic a concept that
> is in the first place. As I understand it, Herman drew an
> analogy between 5:2 and the octave. He then found chords
> spanning that 5:2 that are roughly proportionally spaced to the
> usual major chord. Later did roughly the same with 7:4. Not
> surprisingly, the harmonies end up sounding very alien.

Herman specifies the tunings for the canons by tuning approximate
4:5:6:8's in the score to something else. In the first 88CET
version, he chose a subharmonic 4:6:7:10 chord. For the second
version he used a harmonic 4:6:7:10 chord. For the 7:4 version,
the chord was 36:44:54:63. Your summary is basically correct,
except Herman didn't stretch and contract the triad proportionally
with the octave, he just tried to find consonant intervals to
map triads to. With the tool he's using to make these midi files,
I can't think of a better approach.

> Amazingly enough (it surprised me anyway), it is possible to render
> a fair approximation to traditional harmony in 88CET, provided that
> you can control the vertical voicing of each chord.

This makes sense, but I don't think midiconv can do it.

> The really wild part of this sort of harmonization is that it's
> entirely relative to previous harmony. In traditional 12-toned
> harmony, if the melody you're trying to harmonize contains an E
> in the key of C major, you know that it's scale degree 3, and
> thus you immediately know what the possible traditional
> harmonizations are for it. In this sort of traditional
> harmonization in 88CET though, how that pitch is interpreted is
> entirely dependent upon the chords before it. Because of the
> wandering tonics, a given pitch could end up producing the
> sensation and function of scale degree 4 as easily as scale-degree
> 3. You can't tell until you flesh out the harmony leading up to
> it.

Sounds like somebody would be able to produce a pretty rippin'
warped canon!

-Carl