Yahoo Tuning Groups Ultimate Backup makemicromusic Re: Report on low-EDO experiments on guitar

Dave,

-----Original Message-----
> .... So rather than wait till the thread grows cold, I'm
> sending this preliminary report to you now. YA
...

That's brilliant, Ya! And thanks for a good laugh too.
[YA] Glad you enjoyed it, Dave!

Yes. You'll get the most notes farthest from 12-equal if your stretch
or compression factor is a noble number, of the form

1 + (n+1)*phi
-------------
1 + n*phi

Where n is a whole number and phi is (sqrt(5)+1)/2.
-- Dave
[YA] The most? How do you figure that? (If the answer is
just plain mathematical, please make any detailed repply on
tuning-math rather than drive the non-maths people crazy.)
I mean, it's plausible that phi would be involved, but why that
particular form?

Regards,
Yahya

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🔗Dave Keenan <d.keenan@...>

--- In MakeMicroMusic@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...>
wrote:
>
> Dave,
>
> -----Original Message-----
> > .... So rather than wait till the thread grows cold, I'm
> > sending this preliminary report to you now. YA
> ...
>
> That's brilliant, Ya! And thanks for a good laugh too.
> [YA] Glad you enjoyed it, Dave!
>
> Yes. You'll get the most notes farthest from 12-equal if your stretch
> or compression factor is a noble number, of the form
>
> 1 + (n+1)*phi
> -------------
> 1 + n*phi
>
> Where n is a whole number and phi is (sqrt(5)+1)/2.
> -- Dave
> [YA] The most? How do you figure that? (If the answer is
> just plain mathematical, please make any detailed repply on
> tuning-math rather than drive the non-maths people crazy.)
> I mean, it's plausible that phi would be involved, but why that
> particular form?

I admit that "the most notes farthest from 12-equal" is a pretty vague
specification. I don't really want to spend the time to go into it.

I think I've overstated the case for these noble numbers. Although
they are the simplest succesive noble numbers beginning with phi and
getting progressively closer to 1, they will not be the only bad
stretch/compression factors nor will they be the worst, but they will
be local maxima of badness (by most reasonable definitions of badness
in approximating 12-EDO). I note that the badness of 11-EDO and
13-EDO, in approximating 12-EDO, does not derive from any relationship
to phi.

-- Dave

🔗Yahya Abdal-Aziz <yahya@...>

Dave,

That's cool! I just thought that maybe there was
some deep connection I ws missing ...

Regards,
Yahya

-----Original Message-----
...
I admit that "the most notes farthest from 12-equal" is a pretty vague
specification. I don't really want to spend the time to go into it.

-- Dave

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🔗Yahya Abdal-Aziz <yahya@...>

Hi all,

Posting a conversation I had with Paul Erlich
on how I didn't actually GET any low-EDO ...!

Regards,
Yahya

------------------------------------------------

Ouch!

Now you've pointed that out, I see it ... :-)

What interesting _alternate tunings_ I got
with my movable bridge!

I suppose that the "11-EDO" I got wouldn't
have been very far away from true 11-EDO,
but even the "10-EDO" would have been
significantly distorted.

An ideal 12-EDO guitar has frets that give
frequencies F*2^(n/12) for some base
frequency F, and n = 0, 1, 2 ...

That implies that the vibrating string lengths
are L*2^(-n/12), for length L corresponding
to frequency F.

Moving the bridge closer to the nut by an
amount M provides a series of lengths
L*2^(-n/12) - M.

Clearly these are not the same as
(L-M)*2^(-n/p), which are the p-EDO
lengths for a total length (L-M).

In my experiments, M/L = p/12. Then the
relative error of the fret distance from
the nut for p-EDO is
RE(n;p) = (2^(-n/12) - p/12 - (1-p/12)*2^(-n/p)) / (1-p/12)*2^(-n/p))

Writing w=2^(-1/(12*p)),
RE(n;p) = (w^(n*p) - p/12 - (1-p/12)*w^(n*12)) / ((1-p/12)*w^(n*12))

In particular, for 9-EDO,
w=2^(-1/108), w^9=2^(-1/12), w^12=2^(-1/9) and
RE(n;9) = (w^(n*9) - 3/4 - (1/4)*w^(n*12)) / ((1/4)*w^(n*12)).

Using the Windows XP Power Toy Calculator,
a graph of this looks much like a graph of -log(n).
(No surprise.) It gave these relative errors for
the first few frets -
RE(n;1) = -0.1624166
RE(n;2) = -0.3425502
RE(n;3) = -0.5419107
RE(n;4) = -0.7621310
RE(n;5) = -1.0049762

A long way from the real thing ...

Regards,
Yahya

PS For all the above equations in ASCII, E&OE!
It's hard to keep the picture clear, I find, unless
I write equations with sub- and super-scripts. YA

-----Original Message-----
From: Paul Erlich
Sent: Wednesday 18 May 2005 9:31 am

Hello Yahya,

>So the results above don't
> accurately represent 10-EDO, 10.5-EDO or 11-EDO, do they?
> Except on one string at a time.

Not even on one string at a time, I'm afraid. If you'd like me to go
through the math with you, I'd be happy to.

> And yes, 9-EDO IS weird - especially melodically. I hardly know how
> to make a tune in it.

I *love* 9-equal melodically. My paper suggests a few ways of thinking
about 9-equal. Including the one you ended up detailing -- the
Augmented system. Also the Mavila system is relevant here. But of
course your guitar wasn't producing 9-equal, even on a single
string . . .

Looking forward to hearing from you,
Paul

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🔗Yahya Abdal-Aziz <yahya@...>

Hans,

My approximate 10-EDO has, alas, been thoroughly
discredited, by myself! (Following a broad hint from
Paul Erlich, who told me I didn't even get EDO on one
string, let alone on all of them.)

I did work out what the tuning errors in this system
were, and published them on this list. The funny thing
is that, for small movements of the bridge, this process
does indeed create playable scales. That is, they're
acceptable, melodically, but how useful the chord
harmonies are is another matter ...

I posted the relevant message to this list on 18 May
2005.

As to good ideas for tuning the open strings, can I
point you to a paper on "Optimising JI guitar designs
using linear microtemperaments" by Dave Keenan, 2003,
and recently revised. It's available at -
http://dkeenan.com/Music/MicroGuitar.pdf

This is mostly about where to place the frets so that one
can bend notes as usual, but also considers factors which
makes more chords playable.

There are so many alternate open-string tunings for guitars.
I guess that one of the more important considerations
must be how dense or open you want your chord sonorities
to be. If you tune in alternating fifths and fourths, you have
relatively open and wide chords, with only two intervals to the
octave; while you can tune if you like, using different thirds and
fourths, so that you get three or four intervals to the octave,
in relatively close and narrow chords.

The closer structures also require less hand movement to reach
a given interval, useful for quick melodic fingering. Quite a few
trade-offs to consider, I think.

Let's know how your 5- and 10- note music turns out. How close
does it SEEM to being an EDO scale?

Regards,
Yahya

-----Original Message-----

--- In MakeMicroMusic@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...>
wrote:
>
> Here's my report on some simple experiments on a guitar. (If
> you're
> past this stage, there's probably not much new in it for you.) I'm
> pleased to say they were non-destructive esperiments, and can easily
> be repeated without any real expense.

> When I got the guitar, I saw I could easily slip a pen underneath
> the strings to act as a movable bridge, and tension it by jamming a
> thin bit of plastic (actually, the handle of a pink feather duster!)
> under one end. The pen was a cheap gel one, with an almost straight
> plastic barrel, from K-Mart. A ball-point would do just as well.
>
> Success! In no time, I was picking out "tunes" in my approximate
> 11-EDO.

I tried this out yesterday - and it worked! He he, excellent idea -
and very convenient to my current interest in 5-TET and 10-TET!

Interesting detail: the canonical adaptation of standard guitar tuning
to 10-TET yields a completely regular result, i.e. all strings are one
fourth apart (the irregularity of the major third between the g and
the b string vanishes).

But the fingerings in 5-TET are indeed a little boring... Any good
ideas around for alternative tunings of the strings of a 10-TET
guitar?

Maybe I will try dadgad next time...
--
Hans Straub

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🔗hstraub64 <hstraub64@...>

--- In MakeMicroMusic@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@m...>
wrote:
>
>
> Hans,
>
> My approximate 10-EDO has, alas, been thoroughly
> discredited, by myself! (Following a broad hint from
> Paul Erlich, who told me I didn't even get EDO on one
> string, let alone on all of them.)
>
> I did work out what the tuning errors in this system
> were, and published them on this list. The funny thing
> is that, for small movements of the bridge, this process
> does indeed create playable scales. That is, they're
> acceptable, melodically, but how useful the chord
> harmonies are is another matter ...
>
> I posted the relevant message to this list on 18 May
> 2005.
>

Yes, I saw that, and also Dave Keenan's reply to my post.
Pity :-(

>
> Let's know how your 5- and 10- note music turns out. How close
> does it SEEM to being an EDO scale?
>

I tried mainly 5-EDO, and it seemed not that bad to me. It was just a
short try, though, and I did not listen that intently...
I also did not go up to the very high frets (which I do not like that
much anyway). So next time I might try what Dave Keenan wrote about
tuning the fifth fret to a half octave...

Regards,

Hans Straub

🔗daniel_anthony_stearns <daniel_anthony_stearns@...>

well it's my opinion that 10 or 11 or 13EDO or not, if moving the
bridge to the east or the west sounds good, then good is good
and "accuracy" is a nose around the neck of the MMM
moniker.......hell, maybe it even sounds better than the intended or
wished-for tuning ,who knows unless we get in there and make
micromusic the focus and tuning experiments a minority
interest.......after all, this isn't the MTS (make tunning
experiments) forum,wink.

--- In MakeMicroMusic@yahoogroups.com, "hstraub64" <hstraub64@t...>
wrote:
> --- In MakeMicroMusic@yahoogroups.com, "Yahya Abdal-Aziz"
<yahya@m...>
> wrote:
> >
> >
> > Hans,
> >
> > My approximate 10-EDO has, alas, been thoroughly
> > discredited, by myself! (Following a broad hint from
> > Paul Erlich, who told me I didn't even get EDO on one
> > string, let alone on all of them.)
> >
> > I did work out what the tuning errors in this system
> > were, and published them on this list. The funny thing
> > is that, for small movements of the bridge, this process
> > does indeed create playable scales. That is, they're
> > acceptable, melodically, but how useful the chord
> > harmonies are is another matter ...
> >
> > I posted the relevant message to this list on 18 May
> > 2005.
> >
>
> Yes, I saw that, and also Dave Keenan's reply to my post.
> Pity :-(
>
> >
> > Let's know how your 5- and 10- note music turns out. How close
> > does it SEEM to being an EDO scale?
> >
>
> I tried mainly 5-EDO, and it seemed not that bad to me. It was just
a
> short try, though, and I did not listen that intently...
> I also did not go up to the very high frets (which I do not like
that
> much anyway). So next time I might try what Dave Keenan wrote about
> tuning the fifth fret to a half octave...
>
> Regards,
>
> Hans Straub

🔗Kraig Grady <kraiggrady@...>

one of the reason i always favored frets that run completely across the fret board is that it give the user ample access to alternative tunings ofth open strings. This has work well for Rod Poole BTW who is always puylling new thing out of his tuning this way. Much is to be said by placing somwething in front of the player that allows them to 'Stumble' into something by accident.
daniel_anthony_stearns wrote:

>well it's my opinion that 10 or 11 or 13EDO or not, if moving the >bridge to the east or the west sounds good, then good is good >and "accuracy" is a nose around the neck of the MMM >moniker.......hell, maybe it even sounds better than the intended or >wished-for tuning ,who knows unless we get in there and make >micromusic the focus and tuning experiments a minority >interest.......after all, this isn't the MTS (make tunning >experiments) forum,wink.
>
>
> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

🔗daniel_anthony_stearns <daniel_anthony_stearns@...>

agreed ,and a moveable bridge on a standard guitar is like a free
micronirvana saying, "come inside and see the world anew!" btw, nose
=noose .

--- In MakeMicroMusic@yahoogroups.com, Kraig Grady <kraiggrady@a...>
wrote:
> one of the reason i always favored frets that run completely across
the
> fret board is that it give the user ample access to alternative
tunings
> ofth open strings. This has work well for Rod Poole BTW who is
always
> puylling new thing out of his tuning this way. Much is to be said
by
> placing somwething in front of the player that allows them
to 'Stumble'
> into something by accident.
>
>
> daniel_anthony_stearns wrote:
>
> >well it's my opinion that 10 or 11 or 13EDO or not, if moving the
> >bridge to the east or the west sounds good, then good is good
> >and "accuracy" is a nose around the neck of the MMM
> >moniker.......hell, maybe it even sounds better than the intended
or
> >wished-for tuning ,who knows unless we get in there and make
> >micromusic the focus and tuning experiments a minority
> >interest.......after all, this isn't the MTS (make tunning
> >experiments) forum,wink.
> >
> >
> >
> >
>
> --
> Kraig Grady
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
> The Wandering Medicine Show
> KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

🔗Carl Lumma <ekin@...>

🔗Yahya Abdal-Aziz <yahya@...>

Thanks, Dan!

I agree entirely. You might say,
if it sounds like music, then it IS music.

Regards,
Yahya

-----Original Message-----
Date: Sun, 05 Jun 2005 04:45:20 -0000
From: "daniel_anthony_stearns" <daniel_anthony_stearns@...>

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