Eight Post...

It seems that the initial (email) gaffes and confusions that preceded me and
(my wife) Deb having separate email addresses (not to mention the most
rudimentary notion of what the hell we were doing!), are still proliferating
in awkward (and somewhat embarrassing� though no doubt well deserved!)
manifestations�

These eight post were conceived to be �shared��Anything else was not. My
apologies for being such a pestilent�

Dan Stearns

__________________________________________________________

No. 1
"Natural, reasonable, and inherently pleasing"�or not.

In the TUNING digest 1607 (topic No. 16), Carl Lumma wrote:

"�Partch would have been greatful for the DX7. He who says otherwise is a
gentleman and... an academic."

While I'm not an academic (or can I claim to be the �gentleman� so depicted
in this context), I am reasonably certain that I don�t really know much
about this or that "would have been" of someone I never knew� Partch may
very well have been grateful for the DX7�I don�t know (and wouldn�t much
care to hazard a guess). But I will offer a personal point of view or two,
to which (I am fairly certain) someone else is bound to have some heartfelt
objections�

It is my humble opinion that the more unforgettable characteristics of
Partch�s music (assuming that the actual music created carries with it
something distinct from the ideologies that buttress it) are tied a lot
tighter to the creation and implementation of new instruments, than they are
the advancement of a tuning that happened to resolutely embrace aural
causation� And though the tuning the instruments the ideologies (the man and
the music) all seem inseparable to me now...

I for one am pretty darn thankful someone was seduced by carpentry!

Would the �inimical leer� that permeates much of his writing on the subject
tuning have lost a bit of its punch (or charm) had his radical and spirited
MUSIC not shined so brilliantly? I (for whatever that�s worth) certainly
would have found the shrillness of the intonation reform minded rhetoric
nearly unendurable had the music been some underwhelming, imaginatively
anemic quotidian�"Natural, reasonable, and inherently pleasing" or not.

Would one with alternative tuning inclinations truly find an unanticipated
audio encounter with an instrument such as Ivor Darreg�s Megalyra any less
�impressive� or �interesting� were it tuned to (and played in) 12
equidistant divisions of the octave? Would the same go for a DX7...? Or to
put another way: Does a compilation like EMI�s 1st �GRAVICHORDS, WHIRLIES
AND PYROPHONES� make a better �argument� for the design and implementation
of interesting new instruments than a compilation like the tuning forums �A
MICROTONAL MUSIC EXPERIENCE� does for the design and implementation of
interesting new tunings?

In the end I would suppose that the �divinity' is either there, or it ain�
t�quite regardless of whether it is in the gross tactical bone and marrow of
the procedure (or it ain�t)� and ultimately that it�s more or less for each
to say�

As if its not clear by now�I profoundly disagree with many of the
ideological declarations of the [arch] remedial minded �intonationalist��

"For me Partch's message about primitive man is important, and not so nearly
as important as his contribution to tuning in music." [C. Lumma TUNING
digest 1607]

I tend to see the systemic components of music* as a varied lot of
inspiriting, and metaphorically speaking�enclitic understandings�put into
their determinant position by the successful (and influential) realization
of their MUSIC�

But that is not exactly why I wrote, so I guess I�ve run out my "personal
point of view or two� " Intonation and music are not the same� Having said
as much I would hope not to hie to my grave having said, "therefore;
mutually exclusive�"

Respectfully,
D�Stearns

*Be those components the beneficial advancements of causal understanding� of
de-occulting literatim, of pendular oscillations and galvanic skin responses
et-al��where natural phenomena obeys blind necessity�� Or be they some
remarkable detachments from the physically exact�"at what cross-purpose the
world is dreamt"�
__________________________________________________________

No. 2
+ 4th + 4th + 4th + 3rd + 4th in 17 EDO

If you wanted to carry through the conventional open string configuration of
+ 4th + 4th + 4th + 3rd + 4th in 17 EDO*� you would first have to decide
what pitch you wanted to call home (i.e. a �1/1� reference pitch). While
this is obviously your decision to make (and though most chromatic cents
examples are rendered C - C�), I�m going to suppose that the �1/1� reference
pitch will be a common guitar like choice, such as A [and that we�re calling
the 5th string the A string].

As a + 4th = + 7/17ths of an octave; 7/17ths of an octave would equal the
7th
fret of your A string� so:

A @ 0/17 (+ 7th fret = )
D @ 7/17(+ 7th fret = )
G @ 14/17

Assuming that we�re calling 6/17ths of an octave (at 423.9/17 cents) a major
third (as opposed to a 5/17ths at 352.16/17 cents) then:

G @ 14/17(+ 6th fret = )
B @ 3/17 (+ 7th fret = )
E @ 10/17

To tune the low E (6th string) you would fret the 10th fret of the A [5th
string] and tune your open low E string to it [an octave lower, as opposed
to a unison].

All this should lead to an open string subset of 17 EDO that �looks like� A
@ 0 cents, D @ 494 and 2/17 cents, G @ 988 and 4/17 cents, B @ 1411 and
13/17 cents, E @ 1905 and 15/17 cents, and finally going back and tuning the
low E down a 17 EDO fifth to -705 and 15/17 cents.

E = 706
A = 0
D = 494
G = 988
B = 212
E = 706

Respectfully,
D�Stearns

*As far as acronyms go, {E}quidistant {D}ivision of the {O}ctave�s� EDO,
certainly seems (to me) a rather colorless creation (immanently indisposed
as it is to the oddly resonant charm of {T}one {E}qual {T}emperament�s�TET),
but I do believe it 'better says' what (I believe) 'needs saying'� and as
such I feel somewhat obligated to continue to pretend I like it (and
apologize for saying so).
__________________________________________________________

No. 3
A Quick and Dirty [10]<11< >12< >13< >14< >15<

Back when I was working at a music store (MacDuff�s Music around `93 -
`95*), I would often borrow a miscellany of inexpensive gear to use
overnight on recordings I was working on...

One of my favorites was an old Kay jumbo acoustic with a moveable bridge.

By moving the bridge back to the tailpiece I was able to push the octave up
to the 15th fret.** By moving the bridge all the way up to the soundhole I
was able to pull the octave back to the very brink of the 10th fret� While
the first procedure would cause some �choking out�, and latter, a fairly
unfriendly �action��both these problems were relatively easy to work around.

So in one very inexpensive guitar I was able to achieve a quick and dirty***
[10]<11< >12< >13< >14< >15<**** EDO acoustic microtonal instrument�

Though I�ve longed for a more reliable and more playable version of this
guitar ever since� No small part of the beauty here is that the Kay was
accessible to an utter financial nonentity such as myself!

Respectfully
Dan Stearns

*MacDuff�s Music was a small �Moms and Pops� type shop on rt. 9 in
Shrewsbury Massachusetts that died an elongated, piecemeal death of fiscal
dissipation. (Seven years after the Daddy�s franchise opened shop two doors
down.)

**This is entirely contingent on the guitar being a jumbo.

***While the setup and tuning time was certainly not instant; it was indeed
�quick�... And no matter what you did to this particular guitar (short of a
major overhaul), any intonation was going to be �dirty�.

****You could also stop the bridge incrementally between 11 - 15... a good
ways before 11... and a bit after 15.
__________________________________________________________

No. 4
JI and the Insolvent Guitarist

This is a DIY* method I�ve used to experiment with ratio tunings** that
require fretlets (i.e. individual stops that rest under a single string). As
this is meant to address both the desire to try a lot of differing ratio
scenarios, and an inability to afford anything vaguely resembling a real JI
custom job�

Any guitar costing upwards of 75$ should be immediately and permanently
dislodged from this discussion: tout-de-suite! (I used a 35$ Zim-Gar nylon
string�)

Mini-staples, or staple tots are the rather enfeebled munitions of miniature
staplers. They were also ratio stops on the Zim-Gar.

A couple of forewarnings gleaned from trial and tribulation:

1) You will certainly benefit from some reliable form of pitch reference
(such as a tunable keyboard***). For it has been my experience that the
intentional accuracy of (mathematically precise) string ratios fluctuate
quite a bit more than one might anticipate - especially on inexpensive
guitars.

2) Before you start taking the strings off (or loosening the string tension)
to start tapping in the faux fretlets, you might want to lightly mark the
entire horizontal run of the strings down the fingerboard to best
approximate where the fretlets should sit (as the strings fan out from the
nut to the bridge).

3) To fine-tune and (fine) mark the intervals, I bend a paper clip at the
shoulder and (with the guitar lying on its back) slide the straight section
under the string. This serves the dual purpose of being both [potentially�]
very precise, and ready-made for making a straight line.

4) With the greatest of care (and the most tolerant of temperaments!), the
mini-staples will hammer straight into the fretboard. But as this is
somewhat akin to Kwai Chang walking on rice paper, sooner or later your
bound to start twisting, buckling, and crumpling a few of them over� With a
combination of luck, will, and practice, attempt to discourage them from
folding towards the headstock or the soundhole� If they have crumpled within
earshot of their destination: Start hammering. This will smooth out (smash
in) any crimps or crinkles.

5) I found that stopping heptads**** and other perhaps less ambitious tuning
scenarios,***** makes the process of pulling them all out and sanding down
the damage (so you can start all over again******), a far less dispiriting
devoir.

Respectfully,
Dan Stearns

*Perhaps "Did It Myself" (dim indeed!) is more appropriate here, as I�m not
so sure this (Neanderthal) method constitutes the soundest advise�
Nevertheless�It does work.

**I�ve also used this to �freely� stop intervals of my own liking. (Tuned by
listening until I found something I deemed �attractive��)

***I also tune the adjacent open string to a unison of the open string I�m
marking ratios for, as it seems to me that I can sometimes �hear� the
interval �better� against a 1/1 of the same (timbre) species. But this is
really a rather limited sort of double-check that won�t help you much in
distinguishing a 15/14 from a 16/15, and as 1/15th or 1/16th the distance
from the nut to the saddle may or may not stop a 15/14 or a 16/15... the use
of a reliable pitch reference is highly desirable.

****The last tuning I used on the (now deceased) Zim-Gar was the main tuning
(1/1, 8/7, 9/7, 7/5, 32/21, 12/7, 27/14, 2/1) I was using to rework an older
arrangement I had done of Lowell Mason�s �Work For the Night is Coming�.
This tuning is featured in the second verse. (In a sort of polymodal style,
where the guitars take G as the 1/1, and the tenor holds D as the 1/1; G, A,
B, C#, D, E, F#, G and D, E, F#, G#, A, B, C#, D respectfully.) The guitar
was tuned:

E @ 12/7 (+ 4/3 =)
A @ 8/7 (+ 4/3 =)
D @ 32/21 (+ 21/16 =)
G @ 1/1 (+ 9/7 =)
B @ 9/7 (+ 4/3 =)
E @ 12/7

*****However it is possible (hit or miss, as sometimes the dips and bends of
the neck coincide with your desires and sometimes they don�t) to place stops
quite close to each other� In fact I�d say as close as your probably apt to
�fret�. (Which is somewhat different than �play�, as on a fretless guitar
you can very subtly roll your finger to achieve wonderfully infinitesimal
gradations of pitch inflection.)

******As you may want to reutilize some of the same intervals (of which the
octave row would serve as an obvious example), before you start extracting
the staples, it�s best to have some idea of what you would like to try
[fret] next.

Ps�Should your fretboard cleave in half and your truss rod roll to the
floor� I reserve the right to deny ever having written any of this.
__________________________________________________________

No. 5
WHERE F + f = O

A (factitious*) "two and only two sizes" for every 1 - ? edO�

If "d" = division (any so defined equidistant {d}ivision of the octave), "F"
= 7 (a {F}ifth), "f" = 5 (a {f}ourth), and "O" = 12 (an {O}ctave), and you
take the arithmetic means of f[d] and F[d] and use them as a �median� F/f @
7.1/35 and 4.34/35: (f � O x F) + (F � O x F)/(f � O x f) + (F � O x f)�

And if d = (d � O) X F/(d � O) X f, (d � O) X F = {[(d � O) X F] � (O X F)}/
{[(d � O) X F] � (O X f ), and (d � O) X f = {[(d � O) X f ] � (O X F)}/{[(d
� O) X f ] � (O X f )}, you could use ({[(d � O) X F] � (O X F)} + {[(d � O)
X F] � (O X f )) and ([(d � O) X f ] + {[(d � O) X f ] � (O X f )} as
{H}orizontal and {v}ertical {c}oordinates on a I�IV�V triad square where the
first (root), third and fifth of the I, IV and V, delineate the 1st�3rd�5th,
4th�6th�8th, and 5th�7th�(9th - 7) of a + w + w + h + w + w + w + h diatonic
heptad�

And if Hc 1, 2 and vc 1, 2 are �literally� represented as decimal
fractions/mixed decimals where:

0 = the one of the tonic (the d 1st)
0 + {[(d � O) X F] � (O X F)} = the third of the tonic (the d 3rd)
0 + {[(d � O) X F] � (O X F)} + {[(d � O) X f] � (O X F)} = the fifth of the
tonic (the d H5th)

0 + [(d � O) X f ] = the one of the subdominant (the d 4th)
0 + [(d � O) X f ] + {[(d � O) X F] � (O X F)} and {[(d � O) X F] � (O X F)}
+ [(d � O) X f ] = the third of the subdominant (the d 6th)
0 + [(d � O) X f ] + {[(d � O) X F] � (O X F)} + {[(d � O) X f] � (O X F)}
and {[(d � O) X F] � (O X F)} + {[(d � O) X f] � (O X F)} + [(d � O) X f ] =
the fifth of the subdominant (the d 8th)

0 + [(d � O) X f ] + {[(d � O) X f] � (O X f )} = the one of the dominant
(the d v5th)
0 + [(d � O) X f ] + {[(d � O) X f] � (O X f )} + {[(d � O) X F] � (O X F)}
and {[(d � O) X F] � (O X F)} + [(d � O) X f ] + {[(d � O) X f] � (O X f )}
= the third of the dominant (the d 7th)
0 + [(d � O) X f ] + {[(d � O) X f] � (O X f )} + {[(d � O) X F] � (O X F)}
+ {[(d � O) X f] � (O X F)} - d and {[(d � O) X F] � (O X F)} + [(d � O) X
f] � {(O X F) + [(d � O) X f ]} + {[(d � O) X f] � (O X f )} - d = the fifth
of the dominant (the d 2nd)

Then an internally consistent representation (representation being the key
word here, least this all be some manner of numeric sophistry) of diatonic
seconds should be achieved from rounding off the decimal fractions/mixed
decimals of �w�w�h�w�w�w�h�** to the nearest integer.

Respectfully,
Dan Stearns

*Factitious seems (to me) to be one of those words that is pretty tightly
wrapped round a singular connotation... and as such I feel (no doubt
unnecessary) obliged to qualify it here: "formed by or adapted to an
artificial or conventional standard" [Webster�s Ninth New Collegiate
Dictionary pg. 444, 2a]

**Actually this should be: + Lw + Sw + Lh + Sw + Lw + Lw + Sh, as there
would be both a {L}arge and {S}mall diatonic �half-step�, and a {L}arge and
{S}mall diatonic �whole-step� derived from a sort of �ordinal interval�
where the arithmetic mean of F + f squared = [(+ Lw + Sw + Lh + Sw + Lw + Lw
+ Sh) � (v5 - H5)], and d is always comprised of mF + mf squared (4,900
�ordinal intervals�) arranged + 841 + 840 + 349 + 840 + 841 + 841 + 348�
Eventually the integer representations of the w and h diatonic seconds will
round L up or S down one digit; When�? I do not know� But I suspect it would
be well beyond any 'utilitarian' representation of d. (The first equidistant
division of the octave to demarcate the integers of w and h is 3-edO, at 1
and 0.)
__________________________________________________________

No. 6
TRUE THROUGH 102

"...Eventually the integer representations of the w and h diatonic seconds
will round L up or S down one digit; When�? I do not know� But I suspect it
would be well beyond any 'utilitarian' representation of d..."

(102 v5 - 102 H5) X 841 = 18 Lw
(102 v5 - 102 H5) X 840 = 17 Sw

[�137 = + 24 + 23... 172 = + 30 + 29... ]

(176 v5 - 176 H5) X 349 = 13 Lh
(176 v5 - 176 H5) X 348 = 12 Sh

At which point tedium and delirium broke my will to carry on...

Respectfully,
Dan Stearns
______________________________________________________

No. 7
GP

From the time Joe Gore joined the GP editorial staff (in the mid to late `80
�s?) up until his dwindling involvement, gradual departure� and GP�s
inevitable changing of the editorial guard (mid `90�s?), Guitar Player
Magazine was both the most �radical� and the most broad based of the
commercial guitar mags� Whether or not GP�s current (timid) editorial stance
is a repercussion of the magazines previous editorial incarnation, I do not
know� My guess would be that whatever the editorial posture; now is not the
easiest of times to be pushing a guitar magazine out the door and off the
newsstand.

As far as Liona Boyd�s intonation comments are concerned; I would say that
they are just about what I would expect�

Before the widespread advent of the Internet it took more than a cursory
dabble of individual interest and effort to acquire more than a
misunderstood misunderstanding of say, Harry Partch and quartertones� And
while I think there�s little doubt that a present day electronic �cursory
dabble� should give one a fighting chance of an improved grasp of intonation
and tuning possibilities (and that this is no doubt a good thing!)� I think
the real point is that while a vast majority of guitarist are at some point
or another consciously irritated by the B (�s) in a G chord, the F# in a D
etc., etc., they have neither the congenital inclination of individual
interest and effort or (perhaps more importantly), the READY-MADE resources
to address the �problem��

I think that (for better or worse*) the Buzz Feiten tuning system** will
continue to get �rave reviews� as it �addresses� these �problems� with a
bare minimum of intrusion into the overall individual + instrument + music
'dynamic'***�

Respectfully,
Dan Stearns

*I myself have never tried one�

**Or anything �like it�.

***Not to mention the momentum of industry backing!

JOIN THE INTONATION REVOLUTION!
Washburn is proud to offer the Buzz Feiten Tuning System on all of our USA
Electric Guitars. The Buzz Feiten Tuning System� makes Washburn Electric
Guitars in tune from top to bottom. Our guitars sound pleasant at any fret,
in any chord shape without compromising your playing style. Convince
yourself by playing and comparing the new Washburn USA electrics EXCLUSIVELY
featuring the Buzz Feiten System�. [Taken from a Washburn promotional
peroration at WWW.WASHBURN.COM]

__________________________________________________________

No. 8
For Neil

>Go get 'em Neil! I'll try to do the same.

Amen!

Microtonality is indeed a much better place for the consistent (and
fundamentally practical) work and focus of people like Neil Haverstick�

Sincerely,
Dan Stearns

Mr. Stearns I have to agree w/ Wonder boy Carl . I think that Hp would have loved
any "instrument" tunable to His satisfaction. he was diasppointed that he never
got a good crack at the Arp monster 2500. So I think WbC is on the mark. And I
think (having played the wonderful Cosmolyra that yes the novelty would wear off
after a while as just a spinning table guitar. Kind of like (sorry John) The
Starrboard-which provided two weeks of absolute fun then I began to want those
note underneath the frets.

Dan Stearns wrote:

> From: "Dan Stearns" <stearns@capecod.net>
>
> It seems that the initial (email) gaffes and confusions that preceded me and
> (my wife) Deb having separate email addresses (not to mention the most
> rudimentary notion of what the hell we were doing!), are still proliferating
> in awkward (and somewhat embarrassing� though no doubt well deserved!)
> manifestations�
>
> These eight post were conceived to be �shared��Anything else was not. My
> apologies for being such a pestilent�
>
> Dan Stearns
>
> __________________________________________________________
>
> No. 1
> "Natural, reasonable, and inherently pleasing"�or not.
>
> In the TUNING digest 1607 (topic No. 16), Carl Lumma wrote:
>
> "�Partch would have been greatful for the DX7. He who says otherwise is a
> gentleman and... an academic."
>
> While I'm not an academic (or can I claim to be the �gentleman� so depicted
> in this context), I am reasonably certain that I don�t really know much
> about this or that "would have been" of someone I never knew� Partch may
> very well have been grateful for the DX7�I don�t know (and wouldn�t much
> care to hazard a guess). But I will offer a personal point of view or two,
> to which (I am fairly certain) someone else is bound to have some heartfelt
> objections�
>
> It is my humble opinion that the more unforgettable characteristics of
> Partch�s music (assuming that the actual music created carries with it
> something distinct from the ideologies that buttress it) are tied a lot
> tighter to the creation and implementation of new instruments, than they are
> the advancement of a tuning that happened to resolutely embrace aural
> causation� And though the tuning the instruments the ideologies (the man and
> the music) all seem inseparable to me now...
>
> I for one am pretty darn thankful someone was seduced by carpentry!
>
> Would the �inimical leer� that permeates much of his writing on the subject
> tuning have lost a bit of its punch (or charm) had his radical and spirited
> MUSIC not shined so brilliantly? I (for whatever that�s worth) certainly
> would have found the shrillness of the intonation reform minded rhetoric
> nearly unendurable had the music been some underwhelming, imaginatively
> anemic quotidian�"Natural, reasonable, and inherently pleasing" or not.
>
> Would one with alternative tuning inclinations truly find an unanticipated
> audio encounter with an instrument such as Ivor Darreg�s Megalyra any less
> �impressive� or �interesting� were it tuned to (and played in) 12
> equidistant divisions of the octave? Would the same go for a DX7...? Or to
> put another way: Does a compilation like EMI�s 1st �GRAVICHORDS, WHIRLIES
> AND PYROPHONES� make a better �argument� for the design and implementation
> of interesting new instruments than a compilation like the tuning forums �A
> MICROTONAL MUSIC EXPERIENCE� does for the design and implementation of
> interesting new tunings?
>
> In the end I would suppose that the �divinity' is either there, or it ain�
> t�quite regardless of whether it is in the gross tactical bone and marrow of
> the procedure (or it ain�t)� and ultimately that it�s more or less for each
> to say�
>
> As if its not clear by now�I profoundly disagree with many of the
> ideological declarations of the [arch] remedial minded �intonationalist��
>
> "For me Partch's message about primitive man is important, and not so nearly
> as important as his contribution to tuning in music." [C. Lumma TUNING
> digest 1607]
>
> I tend to see the systemic components of music* as a varied lot of
> inspiriting, and metaphorically speaking�enclitic understandings�put into
> their determinant position by the successful (and influential) realization
> of their MUSIC�
>
> But that is not exactly why I wrote, so I guess I�ve run out my "personal
> point of view or two� " Intonation and music are not the same� Having said
> as much I would hope not to hie to my grave having said, "therefore;
> mutually exclusive�"
>
> Respectfully,
> D�Stearns
>
> *Be those components the beneficial advancements of causal understanding� of
> de-occulting literatim, of pendular oscillations and galvanic skin responses
> et-al��where natural phenomena obeys blind necessity�� Or be they some
> remarkable detachments from the physically exact�"at what cross-purpose the
> world is dreamt"�
> __________________________________________________________
>
> No. 2
> + 4th + 4th + 4th + 3rd + 4th in 17 EDO
>
> If you wanted to carry through the conventional open string configuration of
> + 4th + 4th + 4th + 3rd + 4th in 17 EDO*� you would first have to decide
> what pitch you wanted to call home (i.e. a �1/1� reference pitch). While
> this is obviously your decision to make (and though most chromatic cents
> examples are rendered C - C�), I�m going to suppose that the �1/1� reference
> pitch will be a common guitar like choice, such as A [and that we�re calling
> the 5th string the A string].
>
> As a + 4th = + 7/17ths of an octave; 7/17ths of an octave would equal the
> 7th
> fret of your A string� so:
>
> A @ 0/17 (+ 7th fret = )
> D @ 7/17(+ 7th fret = )
> G @ 14/17
>
> Assuming that we�re calling 6/17ths of an octave (at 423.9/17 cents) a major
> third (as opposed to a 5/17ths at 352.16/17 cents) then:
>
> G @ 14/17(+ 6th fret = )
> B @ 3/17 (+ 7th fret = )
> E @ 10/17
>
> To tune the low E (6th string) you would fret the 10th fret of the A [5th
> string] and tune your open low E string to it [an octave lower, as opposed
> to a unison].
>
> All this should lead to an open string subset of 17 EDO that �looks like� A
> @ 0 cents, D @ 494 and 2/17 cents, G @ 988 and 4/17 cents, B @ 1411 and
> 13/17 cents, E @ 1905 and 15/17 cents, and finally going back and tuning the
> low E down a 17 EDO fifth to -705 and 15/17 cents.
>
> E = 706
> A = 0
> D = 494
> G = 988
> B = 212
> E = 706
>
> Respectfully,
> D�Stearns
>
> *As far as acronyms go, {E}quidistant {D}ivision of the {O}ctave�s� EDO,
> certainly seems (to me) a rather colorless creation (immanently indisposed
> as it is to the oddly resonant charm of {T}one {E}qual {T}emperament�s�TET),
> but I do believe it 'better says' what (I believe) 'needs saying'� and as
> such I feel somewhat obligated to continue to pretend I like it (and
> apologize for saying so).
> __________________________________________________________
>
> No. 3
> A Quick and Dirty [10]<11< >12< >13< >14< >15<
>
> Back when I was working at a music store (MacDuff�s Music around `93 -
> `95*), I would often borrow a miscellany of inexpensive gear to use
> overnight on recordings I was working on...
>
> One of my favorites was an old Kay jumbo acoustic with a moveable bridge.
>
> By moving the bridge back to the tailpiece I was able to push the octave up
> to the 15th fret.** By moving the bridge all the way up to the soundhole I
> was able to pull the octave back to the very brink of the 10th fret� While
> the first procedure would cause some �choking out�, and latter, a fairly
> unfriendly �action��both these problems were relatively easy to work around.
>
> So in one very inexpensive guitar I was able to achieve a quick and dirty***
> [10]<11< >12< >13< >14< >15<**** EDO acoustic microtonal instrument�
>
> Though I�ve longed for a more reliable and more playable version of this
> guitar ever since� No small part of the beauty here is that the Kay was
> accessible to an utter financial nonentity such as myself!
>
> Respectfully
> Dan Stearns
>
> *MacDuff�s Music was a small �Moms and Pops� type shop on rt. 9 in
> Shrewsbury Massachusetts that died an elongated, piecemeal death of fiscal
> dissipation. (Seven years after the Daddy�s franchise opened shop two doors
> down.)
>
> **This is entirely contingent on the guitar being a jumbo.
>
> ***While the setup and tuning time was certainly not instant; it was indeed
> �quick�... And no matter what you did to this particular guitar (short of a
> major overhaul), any intonation was going to be �dirty�.
>
> ****You could also stop the bridge incrementally between 11 - 15... a good
> ways before 11... and a bit after 15.
> __________________________________________________________
>
> No. 4
> JI and the Insolvent Guitarist
>
> This is a DIY* method I�ve used to experiment with ratio tunings** that
> require fretlets (i.e. individual stops that rest under a single string). As
> this is meant to address both the desire to try a lot of differing ratio
> scenarios, and an inability to afford anything vaguely resembling a real JI
> custom job�
>
> Any guitar costing upwards of 75$ should be immediately and permanently
> dislodged from this discussion: tout-de-suite! (I used a 35$ Zim-Gar nylon
> string�)
>
> Mini-staples, or staple tots are the rather enfeebled munitions of miniature
> staplers. They were also ratio stops on the Zim-Gar.
>
> A couple of forewarnings gleaned from trial and tribulation:
>
> 1) You will certainly benefit from some reliable form of pitch reference
> (such as a tunable keyboard***). For it has been my experience that the
> intentional accuracy of (mathematically precise) string ratios fluctuate
> quite a bit more than one might anticipate - especially on inexpensive
> guitars.
>
> 2) Before you start taking the strings off (or loosening the string tension)
> to start tapping in the faux fretlets, you might want to lightly mark the
> entire horizontal run of the strings down the fingerboard to best
> approximate where the fretlets should sit (as the strings fan out from the
> nut to the bridge).
>
> 3) To fine-tune and (fine) mark the intervals, I bend a paper clip at the
> shoulder and (with the guitar lying on its back) slide the straight section
> under the string. This serves the dual purpose of being both [potentially�]
> very precise, and ready-made for making a straight line.
>
> 4) With the greatest of care (and the most tolerant of temperaments!), the
> mini-staples will hammer straight into the fretboard. But as this is
> somewhat akin to Kwai Chang walking on rice paper, sooner or later your
> bound to start twisting, buckling, and crumpling a few of them over� With a
> combination of luck, will, and practice, attempt to discourage them from
> folding towards the headstock or the soundhole� If they have crumpled within
> earshot of their destination: Start hammering. This will smooth out (smash
> in) any crimps or crinkles.
>
> 5) I found that stopping heptads**** and other perhaps less ambitious tuning
> scenarios,***** makes the process of pulling them all out and sanding down
> the damage (so you can start all over again******), a far less dispiriting
> devoir.
>
> Respectfully,
> Dan Stearns
>
> *Perhaps "Did It Myself" (dim indeed!) is more appropriate here, as I�m not
> so sure this (Neanderthal) method constitutes the soundest advise�
> Nevertheless�It does work.
>
> **I�ve also used this to �freely� stop intervals of my own liking. (Tuned by
> listening until I found something I deemed �attractive��)
>
> ***I also tune the adjacent open string to a unison of the open string I�m
> marking ratios for, as it seems to me that I can sometimes �hear� the
> interval �better� against a 1/1 of the same (timbre) species. But this is
> really a rather limited sort of double-check that won�t help you much in
> distinguishing a 15/14 from a 16/15, and as 1/15th or 1/16th the distance
> from the nut to the saddle may or may not stop a 15/14 or a 16/15... the use
> of a reliable pitch reference is highly desirable.
>
> ****The last tuning I used on the (now deceased) Zim-Gar was the main tuning
> (1/1, 8/7, 9/7, 7/5, 32/21, 12/7, 27/14, 2/1) I was using to rework an older
> arrangement I had done of Lowell Mason�s �Work For the Night is Coming�.
> This tuning is featured in the second verse. (In a sort of polymodal style,
> where the guitars take G as the 1/1, and the tenor holds D as the 1/1; G, A,
> B, C#, D, E, F#, G and D, E, F#, G#, A, B, C#, D respectfully.) The guitar
> was tuned:
>
> E @ 12/7 (+ 4/3 =)
> A @ 8/7 (+ 4/3 =)
> D @ 32/21 (+ 21/16 =)
> G @ 1/1 (+ 9/7 =)
> B @ 9/7 (+ 4/3 =)
> E @ 12/7
>
> *****However it is possible (hit or miss, as sometimes the dips and bends of
> the neck coincide with your desires and sometimes they don�t) to place stops
> quite close to each other� In fact I�d say as close as your probably apt to
> �fret�. (Which is somewhat different than �play�, as on a fretless guitar
> you can very subtly roll your finger to achieve wonderfully infinitesimal
> gradations of pitch inflection.)
>
> ******As you may want to reutilize some of the same intervals (of which the
> octave row would serve as an obvious example), before you start extracting
> the staples, it�s best to have some idea of what you would like to try
> [fret] next.
>
> Ps�Should your fretboard cleave in half and your truss rod roll to the
> floor� I reserve the right to deny ever having written any of this.
> __________________________________________________________
>
> No. 5
> WHERE F + f = O
>
> A (factitious*) "two and only two sizes" for every 1 - ? edO�
>
> If "d" = division (any so defined equidistant {d}ivision of the octave), "F"
> = 7 (a {F}ifth), "f" = 5 (a {f}ourth), and "O" = 12 (an {O}ctave), and you
> take the arithmetic means of f[d] and F[d] and use them as a �median� F/f @
> 7.1/35 and 4.34/35: (f � O x F) + (F � O x F)/(f � O x f) + (F � O x f)�
>
> And if d = (d � O) X F/(d � O) X f, (d � O) X F = {[(d � O) X F] � (O X F)}/
> {[(d � O) X F] � (O X f ), and (d � O) X f = {[(d � O) X f ] � (O X F)}/{[(d
> � O) X f ] � (O X f )}, you could use ({[(d � O) X F] � (O X F)} + {[(d � O)
> X F] � (O X f )) and ([(d � O) X f ] + {[(d � O) X f ] � (O X f )} as
> {H}orizontal and {v}ertical {c}oordinates on a I�IV�V triad square where the
> first (root), third and fifth of the I, IV and V, delineate the 1st�3rd�5th,
> 4th�6th�8th, and 5th�7th�(9th - 7) of a + w + w + h + w + w + w + h diatonic
> heptad�
>
> And if Hc 1, 2 and vc 1, 2 are �literally� represented as decimal
> fractions/mixed decimals where:
>
> 0 = the one of the tonic (the d 1st)
> 0 + {[(d � O) X F] � (O X F)} = the third of the tonic (the d 3rd)
> 0 + {[(d � O) X F] � (O X F)} + {[(d � O) X f] � (O X F)} = the fifth of the
> tonic (the d H5th)
>
> 0 + [(d � O) X f ] = the one of the subdominant (the d 4th)
> 0 + [(d � O) X f ] + {[(d � O) X F] � (O X F)} and {[(d � O) X F] � (O X F)}
> + [(d � O) X f ] = the third of the subdominant (the d 6th)
> 0 + [(d � O) X f ] + {[(d � O) X F] � (O X F)} + {[(d � O) X f] � (O X F)}
> and {[(d � O) X F] � (O X F)} + {[(d � O) X f] � (O X F)} + [(d � O) X f ] =
> the fifth of the subdominant (the d 8th)
>
> 0 + [(d � O) X f ] + {[(d � O) X f] � (O X f )} = the one of the dominant
> (the d v5th)
> 0 + [(d � O) X f ] + {[(d � O) X f] � (O X f )} + {[(d � O) X F] � (O X F)}
> and {[(d � O) X F] � (O X F)} + [(d � O) X f ] + {[(d � O) X f] � (O X f )}
> = the third of the dominant (the d 7th)
> 0 + [(d � O) X f ] + {[(d � O) X f] � (O X f )} + {[(d � O) X F] � (O X F)}
> + {[(d � O) X f] � (O X F)} - d and {[(d � O) X F] � (O X F)} + [(d � O) X
> f] � {(O X F) + [(d � O) X f ]} + {[(d � O) X f] � (O X f )} - d = the fifth
> of the dominant (the d 2nd)
>
> Then an internally consistent representation (representation being the key
> word here, least this all be some manner of numeric sophistry) of diatonic
> seconds should be achieved from rounding off the decimal fractions/mixed
> decimals of �w�w�h�w�w�w�h�** to the nearest integer.
>
> Respectfully,
> Dan Stearns
>
> *Factitious seems (to me) to be one of those words that is pretty tightly
> wrapped round a singular connotation... and as such I feel (no doubt
> unnecessary) obliged to qualify it here: "formed by or adapted to an
> artificial or conventional standard" [Webster�s Ninth New Collegiate
> Dictionary pg. 444, 2a]
>
> **Actually this should be: + Lw + Sw + Lh + Sw + Lw + Lw + Sh, as there
> would be both a {L}arge and {S}mall diatonic �half-step�, and a {L}arge and
> {S}mall diatonic �whole-step� derived from a sort of �ordinal interval�
> where the arithmetic mean of F + f squared = [(+ Lw + Sw + Lh + Sw + Lw + Lw
> + Sh) � (v5 - H5)], and d is always comprised of mF + mf squared (4,900
> �ordinal intervals�) arranged + 841 + 840 + 349 + 840 + 841 + 841 + 348�
> Eventually the integer representations of the w and h diatonic seconds will
> round L up or S down one digit; When�? I do not know� But I suspect it would
> be well beyond any 'utilitarian' representation of d. (The first equidistant
> division of the octave to demarcate the integers of w and h is 3-edO, at 1
> and 0.)
> __________________________________________________________
>
> No. 6
> TRUE THROUGH 102
>
> "...Eventually the integer representations of the w and h diatonic seconds
> will round L up or S down one digit; When�? I do not know� But I suspect it
> would be well beyond any 'utilitarian' representation of d..."
>
> (102 v5 - 102 H5) X 841 = 18 Lw
> (102 v5 - 102 H5) X 840 = 17 Sw
>
> [�137 = + 24 + 23... 172 = + 30 + 29... ]
>
> (176 v5 - 176 H5) X 349 = 13 Lh
> (176 v5 - 176 H5) X 348 = 12 Sh
>
> At which point tedium and delirium broke my will to carry on...
>
> Respectfully,
> Dan Stearns
> ______________________________________________________
>
> No. 7
> GP
>
> >From the time Joe Gore joined the GP editorial staff (in the mid to late `80
> �s?) up until his dwindling involvement, gradual departure� and GP�s
> inevitable changing of the editorial guard (mid `90�s?), Guitar Player
> Magazine was both the most �radical� and the most broad based of the
> commercial guitar mags� Whether or not GP�s current (timid) editorial stance
> is a repercussion of the magazines previous editorial incarnation, I do not
> know� My guess would be that whatever the editorial posture; now is not the
> easiest of times to be pushing a guitar magazine out the door and off the
> newsstand.
>
> As far as Liona Boyd�s intonation comments are concerned; I would say that
> they are just about what I would expect�
>
> Before the widespread advent of the Internet it took more than a cursory
> dabble of individual interest and effort to acquire more than a
> misunderstood misunderstanding of say, Harry Partch and quartertones� And
> while I think there�s little doubt that a present day electronic �cursory
> dabble� should give one a fighting chance of an improved grasp of intonation
> and tuning possibilities (and that this is no doubt a good thing!)� I think
> the real point is that while a vast majority of guitarist are at some point
> or another consciously irritated by the B (�s) in a G chord, the F# in a D
> etc., etc., they have neither the congenital inclination of individual
> interest and effort or (perhaps more importantly), the READY-MADE resources
> to address the �problem��
>
> I think that (for better or worse*) the Buzz Feiten tuning system** will
> continue to get �rave reviews� as it �addresses� these �problems� with a
> bare minimum of intrusion into the overall individual + instrument + music
> 'dynamic'***�
>
> Respectfully,
> Dan Stearns
>
> *I myself have never tried one�
>
> **Or anything �like it�.
>
> ***Not to mention the momentum of industry backing!
>
> JOIN THE INTONATION REVOLUTION!
> Washburn is proud to offer the Buzz Feiten Tuning System on all of our USA
> Electric Guitars. The Buzz Feiten Tuning System� makes Washburn Electric
> Guitars in tune from top to bottom. Our guitars sound pleasant at any fret,
> in any chord shape without compromising your playing style. Convince
> yourself by playing and comparing the new Washburn USA electrics EXCLUSIVELY
> featuring the Buzz Feiten System�. [Taken from a Washburn promotional
> peroration at WWW.WASHBURN.COM]
>
> __________________________________________________________
>
> No. 8
> For Neil
>
> >Go get 'em Neil! I'll try to do the same.
>
> Amen!
>
> Microtonality is indeed a much better place for the consistent (and
> fundamentally practical) work and focus of people like Neil Haverstick�
>
> Sincerely,
> Dan Stearns
>
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