My friend's stretch tuning problem

I have a friend who plays Chapman Stick, a guitar-like fretted
instrument with a bass guitar scale length and 5 1/4 octave range.
He recently began "stretch-tuning" his Stick in a manner that
approximates piano-stretch tuning. He does this by tuning it to 12t-
ET then detuning the lowest bass strings and tuning the highest
melody strings sharp. For reference he has been using a stretch-
tuning chart for the Fender Rhodes at:

http://www.fenderrhodes.org/rhodes/manual/fig5-4.gif

Because the frets are equally spaced to 12t-ET, he has to compromise
by detuning his bass strings to some middle cents value between the
recommended offset from 12t-ET for the lowest note on the string and
the recommended offset for the highest note he is going to use on
that string. He is using 3 cents as a fudge factor as he doesn't
hear a difference for adjustments of 3 cents or less.

I asked him why he is going through all this trouble and he said that
there are two main issues:

1. By himself he perceives the lowest and highest strings as being
out of tune. For example, he doesn't like the 3rds, perceiving them
as being too flat.

2. Without the pseudo stretch tuning he finds himself out of tune
with his dual-guitarist (a guy who plays dual guitars using pianistic
tapping). The guitarist is also tuning to 12t-ET via tuner and
making fine tuning adjustments afterwards to one or more strings.

I suggested to him that one or more of the following is going on:

1. Guitars are out of tune in relation to Stick.
2. Stick intonation and other setup parameters (truss rod, etc.) are
messed up.
3. He and the guitarist are both starting to hear the out-of-tuneness
of 12t-ET.

We sort of eliminated #1 in that he and the guitarist do in fact use
the same tuner when recording. #2 cannot be verified either way as I
am not there to check out his Stick. Quite frankly, he has far more
guitar and Stick experience than I do, especially professional
gigging and recording, so he probably does not suffer from #2.

Which leaves #3. I imagine the prospect of abandoning 12t-ET must
frighten my friends, having played that domain literally since
childhood. Is this pseudo stretch-tuning a workable compromise, at
least until they work up the courage to switch to something like 31t-
ET? :)

Is stretch tuning a form of meantone, well temperament, or neither?

Look forward to your help,
Paolo

Paolo asks:
>>Is stretch tuning a form of meantone, well temperament, or neither? >>

Greetings,
"Stretch" is the term given for the cumulative effect of tuning octaves
one from another. The upper partials of a vibrating string are slightly
higher than their ideal ratios would have it, so the upper string of an
octave is tuned by syncronizing its fundamental with the second partial of
the lower note. This partial, being slightly higher than double the
fundamental, causes the upper note of the octave to be slightly sharper than
double the lower note. As you accumulate octaves, the effect increases.
On a Steinway D, C88 is approx. 38 cents sharper than the mathematical
exact placement.
The same phenomenom causes the bass strings on a piano to get increasingly
flatter in regards to absolute octaves. Studio musicians usually use an
electronic tuner without knowing what stretch is. I tune the bass sharp
enough to quell the bass players griping, but not so sharp that I lose my
reinforcement.
The temperaments are an entirely different matter,(though the Steinway
Hall tuners tend toward sharping the first octave out of the middle, creating
a pure fifths temperament with a lot of stretch. The thirds and octaves
begin to sound pretty "active" with this tuning, though the fifths are really
clean.
Regards,
Ed Foote RPT

Wow! I simply can't believe the synchronicity that's been
happening between my work and some of the posts to this list
lately!

I've never done any deep study of stretch tuning until this
week, have been wanting to make a webpage about a particular
article I have on one stretch-tuning, and just spent most of
today working on it, when along comes Paolo asking this!

--- In tuning@egroups.com, phv40@h... wrote:
> http://www.egroups.com/message/tuning/13304
>
> ... Is this pseudo stretch-tuning a workable compromise, at
> least until they work up the courage to switch to something
> like 31t-ET? :)
>
> Is stretch tuning a form of meantone, well temperament, or neither?

I can't give any info on the Stick, but just in general on
stretch tunings.

First, I'll preface my response with a tuning classification
devised here last year that some of us liked. 12-tET and 31-tET
would both be considered an EDO - 'equally divided 8ve' - under
this classification.

In answer to your first question, I'd say that based on some
experiments I've read about, a stretch tuning may actually be
more acoustically 'in tune' than 12-tET, 31-tET, or even JI!

(I'll be sending the basic contents of that webpage in my next
post, so you'll see what I'm talking about.)

As to the second question: I'm mostly a JI guy, so others who
know more about meantones and well-temperaments should comment,
but I'd say (without much reflection) that stretch tunings
really aren't either of those... meantones are sort of the
opposite, a 'compressed' tuning, and well-temperaments have
various-sized intervals scattered in more complex patterns
around the '8ve'. Meantones and well-temperaments are both
UDO - 'unequally divided 8ve'.

Stretch tunings are generally *non-'8ve'*, because all intervals,
including the '8ves', are stretched.

They can be equal-temperaments (EDNO - 'equally-divided non-8ve',
as in the upcoming post I'll be sending next), based on dividing
some other interval instead of the 2/1; or they can be unequal
(UDNO - 'unequally divided non-8ve', as in most recommended
piano tunings, which are close to 12-tET near 'middle-C', but
diverge farther and farther away as they approach the extremes
of the keyboard.

I suppose it's possible that a stretch tuning could also be
a UDO - 'unequally divided 8ve', but that doesn't seem to work
to me. ...?

Stretch tunings seem to work especially well on pianos, because
the piano timbre has stretched harmonics. There are specific
recommended stretch tunings programmed into the expensive
electronic piano-tuners for specific brands and models of
pianos, based on that particular instrument's timbre.

(I don't know the details - more knowledgeable - and I would
presume more affluent - piano tuners on the list will have
to comment.)

I made a webpage last year exploring some ideas Charles Ives
had about using stretch tunings based on 48-tET ('1/8-tones'):
http://www.ixpres.com/interval/monzo/ives/48tet.htm

These were stretched more than any other I've ever seen; in
other words, Ives was not looking for something approaching
perceived consonance, as in most other stretch tunings; he
was simply looking for a very different-sounding scale which
still exhibited the tetrachordal properties familiar from the
12-tET diatonic scale.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:

http://www.egroups.com/message/tuning/13318

>
> I made a webpage last year exploring some ideas Charles Ives
> had about using stretch tunings based on 48-tET ('1/8-tones'):
> http://www.ixpres.com/interval/monzo/ives/48tet.htm
>

Wow. Talk about STRETCHING! Joe, there is something wrong with this
page... the html code. The font size is HUGE. STRETCHED. I hope
you can do something about it, 'cause I can't read it...
___________ ____ __ __ __
Joseph Pehrson

Joseph Pehrson wrote:

> --- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:
>
> http://www.egroups.com/message/tuning/13318
>
> >
> > I made a webpage last year exploring some ideas Charles Ives
> > had about using stretch tunings based on 48-tET ('1/8-tones'):
> > http://www.ixpres.com/interval/monzo/ives/48tet.htm
> >
>
> Wow. Talk about STRETCHING! Joe, there is something wrong with this
> page... the html code. The font size is HUGE. STRETCHED. I hope
> you can do something about it, 'cause I can't read it...

Both in Netscape and IEx there are ways to reduce and expand
the font size.

In Netscape Ctrl+[ for amaller fonts, Ctrl+] for bigger fonts.

--
* D a v i d B e a r d s l e y
* 49/32 R a d i o "all microtonal, all the time"
* http://www.virtulink.com/immp/lookhere.htm

--- In tuning@egroups.com, David Beardsley <xouoxno@v...> wrote:

http://www.egroups.com/message/tuning/13323

>
> Both in Netscape and IEx there are ways to reduce and expand
> the font size.
>
> In Netscape Ctrl+[ for amaller fonts, Ctrl+] for bigger fonts.
>

Thanks, David! One learns something every day... admittedly
sometimes not much, but *SOMETHING.* Great. Now I read this article.
I think I had just subscribed to the list about that time, and was
getting "oriented." I missed a careful read of this one.

Wow. This is a great article, and another Monzo extravaganza. I
always *particularly* love when he includes AUDIBLE MUSICAL
examples... Extremely interesting.

This Ives quote:

http://www.ixpres.com/interval/monzo/ives/48tet.htm

> The other intervals are uneven - some way out from a simple
> ratio [as] 2/1 - for instance 261/712 etc. This, at first,
> seemed very disturbing, - but when the ears have heard more and
> more (and year after year) of uneven ratios, one begins to feel
> that the use, recognition, and meaning (as musical expression)
> of intervals have just begun to be heard and understood. The
> even ratios have been pronounced the true basis of music,
> because man limits his ear, and not because nature does. The
> even ratios have one thing that got them and has kept them in
> the limelight of humanity - and one thing that has kept the
> progress to wider and more uneven ratios very slow - (it is said
> [that] for the power of man's ear to stand up against the
> comparatively uneven 3rds, [when used] to the very even octaves
> and 5ths, was a matter of centuries) - in other words, consonance
> has had a monopolistic tyranny, for this one principal reason:
> - it is *easy* for the ear and mind to use and know them - and
> the more uneven the ratio, the harder it is. The old fight of
> evolution - the one-syllable, soft-eared boys are still on too
> many boards, chairs, newspapers, and concert stages!
>

I take to mean that Ives was really in support of *UNEQUAL*
scale-step sizes. Perhaps he would have liked Just Intonation
scales, then....

I love the ending of this paragraph (Dan Stearns/Ives type stuff).
__________ ___ __ _
Joseph Pehrson

--- In tuning@egroups.com, "Joseph Pehrson" <
josephpehrson@c...> wrote:> This Ives quote:
>
> http://www.ixpres.com/interval/monzo/ives/48tet.htm
>
> > The other intervals are uneven - some way out from a simple
> > ratio [as] 2/1 - for instance 261/712 etc. This, at first,
> > seemed very disturbing, - but when the ears have heard more and
> > more (and year after year) of uneven ratios, one begins to feel
> > that the use, recognition, and meaning (as musical expression)
> > of intervals have just begun to be heard and understood. The
> > even ratios have been pronounced the true basis of music,
> > because man limits his ear, and not because nature does. The
> > even ratios have one thing that got them and has kept them in
> > the limelight of humanity - and one thing that has kept the
> > progress to wider and more uneven ratios very slow - (it is said
> > [that] for the power of man's ear to stand up against the
> > comparatively uneven 3rds, [when used] to the very even octaves
> > and 5ths, was a matter of centuries) - in other words, consonance
> > has had a monopolistic tyranny, for this one principal reason:
> > - it is *easy* for the ear and mind to use and know them - and
> > the more uneven the ratio, the harder it is. The old fight of
> > evolution - the one-syllable, soft-eared boys are still on too
> > many boards, chairs, newspapers, and concert stages!
> >
>
> I take to mean that Ives was really in support of *UNEQUAL*
> scale-step sizes. Perhaps he would have liked Just Intonation
> scales, then....

On the contrary, I take this as expressing disdain for the
simple harmonic ratios of just intonation, and saying
nothing about step sizes. Read it again and pay
attention to what he's saying about the relatively
painful introduction of consonant thirds into music at
the end of the Medieval period. He's talking about JI
ratios, not logarithmic interval-size ratios.

Joseph Pehrson wrote,

> I take to mean that Ives was really in support of *UNEQUAL*
scale-step sizes.

Uneven step sizes would seem to be in sync with much of what Ives
wrote about nature and repetition: "Nature loves analogy and hates
repetition. Botany reveals evolution, not permanence"... as a clearer
example of where he's going musically with this line of thought, he
also wrote, "some claim for Tchaikowsky that his clarity and coherence
of design is unparalleled....That depends, it seems to us, on how far
repetition is an essential part of clarity and coherence....If nature
is not enthusiastic about explanation, why should Tchaikowsky be?"

> Perhaps he would have liked Just Intonation scales, then....

Well I think the quote that you cite is probably stickin' it to simple
JI ratios as much as it's doing anything else! But in every instance
that I've read where he does this he's always consistent in his
"argument"... it's always directed at the reflexive "ease" of
concordance, and the, as he saw it, unfortunate/predictable results of
this as regards the "evolutionary" acceptance and integration of more
discordant possibilities. I find his anti-JI arguments to only be so
by "teleological association" so to speak... so I actually think --
despite his often shrill comments to the contrary! -- that he would
have been open to JI in the broader sense... that too would be
consistent with much of what he wrote as I see it.

Several months ago one of my teeth and I departed company in a
nightmarish episode, but all was not lost, and I was apparently
visited by the tooth fairy... anyway, this "tooth fairies algorithm"
converted O/U series into uniquely articulated fractions of an octave,
in other words it mimicked their contracting or expanding stepwise
superparticular ratios. This would be a good, if odd, way to approach
scales with uneven step sizes for someone whose not particularly
interested in the consistency of their vertical JI approximations.

- dan

--- In tuning@egroups.com, "Paul Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/13337

> >
> > I take to mean that Ives was really in support of *UNEQUAL*
> > scale-step sizes. Perhaps he would have liked Just Intonation
> > scales, then....
>
> On the contrary, I take this as expressing disdain for the
> simple harmonic ratios of just intonation, and saying
> nothing about step sizes. Read it again and pay
> attention to what he's saying about the relatively
> painful introduction of consonant thirds into music at
> the end of the Medieval period. He's talking about JI
> ratios, not logarithmic interval-size ratios.

Oh sure. I got that on the "re-read." I guess I was confusing his
description with the "uneven" scale steps of his examples...

I believe the reason I didn't read this post... in fact I remember
now... is the fact that there was a formatting problem with the
webpage on the screen, and I didn't know about the "ctrl +["

I hope Monz fixes this viewing problem and places this page in a
readily-accessible place, since I found it quite interesting...
especially with the sound examples!

However, the step sizes of these Ives' "stretched" scales seem
vaguely logarithmic, yes?? Or is that wrong. (??)
_____________ ___ _
Joseph Pehrson

--- In tuning@egroups.com, "D.Stearns" <STEARNS@C...> wrote:

http://www.egroups.com/message/tuning/13339

[Ives}
> he
> also wrote, "some claim for Tchaikowsky that his clarity and
coherence of design is unparalleled....That depends, it seems to us,
on how far repetition is an essential part of clarity and
coherence....If nature is not enthusiastic about explanation, why
should Tchaikowsky be?"
>
This, Dan, is undoubtedly my "quote of the day!"
_________ ____ __ __ _
Joseph Pehrson

Joseph Pehrson wrote:
> http://www.egroups.com/message/tuning/13322
>
> --- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:
>
> http://www.egroups.com/message/tuning/13318
>
> >
> > I made a webpage last year exploring some ideas Charles Ives
> > had about using stretch tunings based on 48-tET ('1/8-tones'):
> > http://www.ixpres.com/interval/monzo/ives/48tet.htm
> >
>
> Wow. Talk about STRETCHING! Joe, there is something wrong with
> this page... the html code. The font size is HUGE. STRETCHED.
> I hope you can do something about it, 'cause I can't read it...

Thanks for pointing this out to me, Joe. I normally use Microsoft
Internet Explorer, and all my webpages look fine in that browser,
but I've had this 'stretch' problem with several of my pages
when viewed thru Netscape Navigator. It's been fixed - in fact,
I reformatted the text so it looks a lot better in both browsers.

(someday I'll get around to using Finale to make a real musical
illustration to replace that crude ASCII one...)

-monz
http://www.ixpres.com/interval/monzo/homepage.html

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:

http://www.egroups.com/message/tuning/13377

>
> Thanks for pointing this out to me, Joe. I normally use Microsoft
> Internet Explorer, and all my webpages look fine in that browser,
> but I've had this 'stretch' problem with several of my pages
> when viewed thru Netscape Navigator. It's been fixed - in fact,
> I reformatted the text so it looks a lot better in both browsers.

http://www.ixpres.com/interval/monzo/ives/48tet.htm

It's a great page, and that's the reason I didn't view it last year!
Thanks for fixing it!

Joe
_________ ___ __ _ _
Joseph Pehrson

--- In tuning@egroups.com, "Joseph Pehrson" wrote:
> http://www.egroups.com/message/tuning/13350
>
> However, the step sizes of these Ives' "stretched" scales seem
> vaguely logarithmic, yes?? Or is that wrong. (??)

Joe, I think Dan Stearns hit the nail right on the head with
his comments here:
http://www.egroups.com/message/tuning/13339

Ives was railing against: the *complacency* of simply accepting
low-integer JI because of its consonance and *ruling out*
other types of intervals.

He was interested in an expansion of pitch resources, and
certainly wanted dissonant relationships and structures to
deal with, to accomodate new musical gestures he wanted to
put into his compositions.

Except for the stretched Pythagorean scale I present at the end
of my webpage, all other scales *do* contain logarithmic steps,
because they're all based on ETs.

The important point, which I mention in the webpage but perhaps
didn't stress strongly enough, is that these scales all exhibit
the same kind of tetrachordal similarity that is familiar to
'academic' Euro-centric music and theory. Ives's point was that
even tho the actual pitches are weird (to someone familiar only
with 12-tET/JI/meantone), the *structure* of the scales is
easily recognizable, which thus makes them useful for his
compositional purposes.

-monz
http://www.ixpres.com/interval/monzo/homepage.html