# Analysis



## Battle_of_Marathon

*Example*:


5a) What is the *minimum number of frets * necessary to reproduce all of the millions of chords and all of the millions of scales formable upon the guitar fretboard?


5b) By what method( i.e. mechanical procedure) can we arrive at the solution to Part (a) above.



*RESEARCH*


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## Battle_of_Marathon

*Welcome to The Analysis*

Welcome.

Chances of someone here solving this problem is very very low.
It is not because you are stupid.
It is because the tools which exist presently within your so-called Guitar Theory is simply not powerful enough to permit a solution to such a simple, important question!

To solve this problem we'll need a new concept:

the concept of an *E-diagonal *line.


So let's first define this extremely important Concept of E-diagonal.



*RESEARCH*


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## suttree

well, the easy answer is 12 frets, anything over that point becomes an octave repetition of the lower chord, and although the timbre changes, the chord itself doesn't. but since timbre and shading are such a vital part of guitar chording, then the answer is basically infinity, but since we physically can't play on a guitar with much more than 36 frets (can't finger the notes well enough), i'll go with 36.

QED


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## devnulljp

Tell it to this guy:








What is that? 32 frets on the sky guitar? 



Battle_of_Marathon said:


> Welcome.
> Chances of someone here solving this problem is very very low.
> It is not because you are stupid.


correct...it is because the question, if that's what it is, is completely amorphous and opaque...what is the sound of one hand clapping/bordering on timecube territory.
Keep waiting for the sales pitch... 

I still think Battle_of_Marathon sounds like a Michael Moorcock creation...










...or a figment of Gene Ray's imagination


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## Battle_of_Marathon

Things will fall into place.
No need to bother too too much.

*Definition*:
(of fretpitch)

A *fretpitch *is the intersection of a string and a fret.



*Definition*:
(of E-diagonal)

Let be *given* an arbitrarily chosen "pitch"(ie. 'fretpitch') upon the guitar fretboard. *The set *
which contains all the fretpitches of this fretboard which has a pitch
*equal to the given pitch *is called The *E-diagonal of *this given pitch.


Example:

Ed(Low-E) = Low-E

since there is only 1 Low-E upon the surface of the quite mysterious guitar fretboard. Ha.



*RESEARCH*


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## Battle_of_Marathon

*Away we go!*

We are now quite well equipped to tackle problems

5a) and 5b).


Let's Go!


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## Battle_of_Marathon

*A much shorter proof*

If we were to introduce yet 1 more definition, the length of our proof could easily be cut in half.

i.e. the definition of *a pitchwise exhaustive set *of fretpitches upon the guitar fretboard.

But let's do without this definition for now.

We the long route take. Ha.


*Research*


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## geezer

I've never had much time for people who talked like they were intellectuals but didn't make any sense.


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## keeperofthegood

I think you are heading to using multi spacing layouts of the frets by string. I've seen it done on experimental instruments. 

Though when you talk set theory and finding the most common element set that you are also talking about extracting the matrix root of the the note set that when applied against itself will derive all the other notes (multiplication expansion).

Hyper math is fun, especially applied to real life items


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## Battle_of_Marathon

*Go!*

This proof _can be started upon any pitch(ie. fretpitch) _of the guitar fretboard.
But les's start it on Low-E....we'll save some work this way.


*Proof*:


1) So we are given the guitar fretboard with at least 12 frets.
2) Choose the Low-E pitch(fretpitch).
3) Stay on Low-E.
4) Choose the next fretpitch up....an f on fret# 1.
5) Choose the next fretpitch up....f#
6) Choose the next fretpitch up....g
7) Choose the next fretpitch up....g#

The 5 fretpitches chosen thus far each have a pitch which occurs nowhere-else upon the given guitar fretboard. Their E-diagonals consists each of a single '*point*'....of a single fretpitch. They are their own E-diagonals.

So! 
These fretpitches MUST belong to the minimal collection of frets that we seek!

*WHY*!?


*Hint*: think about what happen if they do not belong! Ha.


*This proof is continued at Proof-Continuation (1) below*.



*Research*


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## Battle_of_Marathon

*Sorry...no Math here*

Yeah.
I know.
On first exposure The Analysis tends to make you think Mathematics.

The Analysis is far from Math...as you may eventually see.

*Notice*: That in our proof, thus far, absolutely no Math has been used!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

The word "set" belonged to Language before it belonged to 'Math'.
By 'set' we simply mean 'a collection' of objects!
Etc..


In my biased opinion, The Analysis is higher than Math!
It will be proved to be more general than Math one day; i hope. Ha. Take that.


Don't think Mathematics.
Think *Fretboard Analysis*!
It ushers in Two New Kingdoms.


*Research*


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## Battle_of_Marathon

*I wonder*

I really wonder if anybody here, keen, has yet realized *why?* 'its' called an E-diagonal boy!? Ha.


*Research*


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## fraser

battle of marathon- 490 bc
10,000 greeks defeated 20,000 persians on the plains of marathon.
6,400 persian dead, 192 greeks dead.
cool- thanks for that, you made me revisit something that had been misplaced in my head

research


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## suttree

jroberts said:


> If you're talking about chords and not voicings, it would definitely be less than 12. I haven't done the math, but I would think around 5 should give you the ability to do any possible combination of notes on a 6 string guitar. Maybe fewer than 5.


hmmm you're right, i think. i had been working on the need for the highest octave (the high e string), but since you re-worded it i do believe you're right. but then is there really that many chords (not voicings)?


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## Wheeman

Battle_of_Marathon said:


> I really wonder if anybody here, keen, has yet realized *why?* 'its' called an E-diagonal boy!? Ha.


Because if you take the vector of [fret, string] it would take [2, 2] to get to the next E. So there, thats why its called an an "E-Diagonal". It should be more like "Pitch-Diagonal" because thats the case with the E and A strings.

And you can't say that this is "far from math". There is math behind everything from the pitches, fret distance, and much more. You have tried to strip some of the math aspects out of it, while still using math terms.


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## Battle_of_Marathon

*Chords.....Voicings*

Yeah.
Thanks for helping us solve this problem guys.

I can't really spend too much time now...The wife keeping me real busy boi...she doesn't like to see me having free time!...i love her and everything...but she doesn't like to see me having free time...Ha...Fancy that!

Aannnanannnnyway...

*Yes*.

*Essentially we do mean voicings*!!!
You guys are correct.

But!

A voicing too is a chord!!!

Each voicing has its own identity!

Not because of Timber, and Tone and stuff!!!!!!!!!!!!!!!!!!!
(even though that is true...)

But more-so Because each fretpitch *has a DISTINCT LOCATION in a SPACE*!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!


So, voicing( x ) is a totally totally totally different and unique entity than voicing( y ) if they are not located at the 'same place'.

Note: This is not the same situation in Music Theory!

In a Music Theory x and y are essentially the same entity!!!!


And it is this Spacial Property (i.e. location) of fretpitches which help to make
Fretboard Analysis (i.e. Guitar Theory) quite quite different than Music Theory.


So, if we are talking Music Theory...Yes... x = y.

Fretboard Analysis..... x no equal y.


Trust us!
Its Fretboard Analysis that you seek!
Not Music Theory!

Music Theory essentially comes to an end.
The Analysis has no end!


O boi.
Wife!!!

Gotta scram!!.....no time to check for errors. Ha.

(thanks for not kicking us off your site yet guys!)


*Research*


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## Battle_of_Marathon

*Close to 5*

O Yeah!!

The answer is close to 5.

A little more thinking and i'm positive that you'll see the answer.

But check out The Method we use to arrive at the answer!
Because it is very useful all-over-the-bloody-place. Ha.


*Research*


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## Battle_of_Marathon

*The Analysis!*

So far, we essentially have introduced 2 new Concepts.

1) concept of fretpitch

2) concept of E-diagonal

Neither belong to Mathematics nor to Music Theory.

They belong to the brand New Science of Fretboard Analysis.

This new science issues 2 New Kingdoms:

We are living in the One now(some of us), and we know where to look for the Other.


*RESEARCH*


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## Battle_of_Marathon

*Proof-Continuation (1)*

*Proof-Continuation (1):*

Well, these 5 fretpitches MUST belong to the minimal collection of frets that we seek BECAUSE if they don't, since their pitches have *no other occurence* anywhere on the given fretboard, any chord/scale which uses one of these fretpitches *will not be reproducible * within our minimal number of frets.




8) We are still on the Low-E.....on fret#4
9) The next fretpitch up has 2 'points' on its E-diagonal
10) Choose the one on fret# 0....i.e. the open A-string

So if the A on fret# 5 on the Low-E *is used* in some arbitrary chord/scale formable upon the guitar fretboard, then we will have "a representative" of it in our minimal number of frets.

...think of sliding the pitch along its E-diagonal into our minimal set of frets.
...or, as She told us, "the *pitch is pushed *along its E-diagonal....."We can pull the pitch back along its E-diagonal...*a Pullback*"
...*Pushouts and Pullbacks*!

You see the chords and scales as being STATIC OBJECTS quietly sleeply on the surface of the rectangle, Don't Ya!!!!!!!!

Yeah.
Even i.
I use to see it so too!

Then She show us how to see.
Ha.
Fancy that.



We can kill this important proof right here and now if we're boring you guys.

But! Me!!?
I absolutely love this stuff.
This New Science!

Someone who is a little keen and not too sleepy can surely see into the rest of the proof by now, i'm certain.



*RESEARCH*


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## Battle_of_Marathon

*Side:*

*Side*:

That *a fretpitch* is an intrinsically* dual* object.

It is a thing which is essentially composed of 2 things:

1) it is *a pitch*

2) this pitch is associated with *a place*


They are stuck together.Ha.
There was a wedding too.
Food was good.
Me took some cake home in a brown paper bag.
Good cake.
Cake good.


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## Battle_of_Marathon

*Proof-Continuation (2)*

*Proof-Continuation (2): *


11) So we are on the A-string fret# 0 
12)  Choose the next fretpitch up.....a#


But! Look!
There exist 2 points(fretpitches, nodes, particle containers, etc...Ha.) on the E-diagonal of *this a#*!...In #12) just above, we chose the one on the A-string. *So!* If _the other one _ is used in some arbitrary chord/scale formable on the guitar fretboard, its pitch can easily be captured by a fretpitch within our minimal number of frets *by* pulling-back its pitch along its E-diagonal!

...until the pitch lands in our zone of interest...ie. our minimal number of frets. 


*RESEARCH*


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## Battle_of_Marathon

*Ok!!*

OK!!

Stop playing games with me guys.

Surely! one of you guitar people here can easily(and quite smoothly too even) bring us safely to a proof-completion right here-and-now?!!!!!

The rest of this important proof is just repetition...and a bloody waste of paper too Even Steven!

...basically, we're taking all of the fretpitches of the guitar-fretboard and pulling them back along their E-diagonals.

...when this is done, the solution to 5a) and 5b) is right there staring us in a face. Ha.


Research


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## Starbuck

methinks someone may have had the brown acid!


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## Battle_of_Marathon

*Me no spoon-feed nobody!*

Actually ya know what!?
Since i know that you people here, my brothers in It All, are not stupid people(for guitar people can't be stupid people), and that you must at least be seeing by now at least the path of the proof-completion, Me!?...me i'm just gonna wrap up this here quite important proof with just a few stupid remarks('Cause me not spoon-feed quite smart people):




*a)* We used 3 New Concepts in the proof

1...concept of fretpitch
2...concept of the E-diagonal
3...concept of a Pushout (which we didn't define)

These 3 belong not to Mathematics, not to Music Theory, but only to the Brand new Science of Fretboard Analysis(which She gave us recently).


*b) * Everybody simply MUST know what an E-diagonal is!!!!!!!!!!!!!!!!!!!!
It is proving itself to be the very foundation of Guitar Theory.


*END of PROOF*


*Andy Fake*
Director of Advanced Research
*THE ROMAN EMPIRE*


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## Battle_of_Marathon

*Answer to 5a)*

The answer to 5a) is a fraction:



*4 and 5/6*


Which is indeed very close to 5.

So the two persons above who agreed that the answer was 5 was indeed quite correct afterall. Ha. Fancy that.


To see why we get the fraction 5/6 think of the *B-string*. Ha.



*Research*


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## Battle_of_Marathon

*$700.00*

Roberts ol'chap.
U gi me $700 me win you a trip to Cuba in de middle O Feburary.

$200?.....a trip to Irac.

$100?.....trip to nowhere.


Aaaannaannnnaaananway...


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## Battle_of_Marathon

*Solution to the Ming's Problem!*

*Definition*:
(of a *Ming Line*)

A ming line is *'a chromatic path' * starting on the Low-E fretpitch and going all the way up to the highest 'note' on the given guitar fretboard.


Simple.
Fretboard Analysis is simple.
Yet very very very far-reaching.


*MING's PROBLEM*: 

Given a guitar fretboard, exactly how many Ming Lines are there?



So Ming's Problem is asking in how many ways can we climb chromatically from Low-E to the highest 'note' on a guitar fretboard?


*Research*


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## Battle_of_Marathon

*Very very very very very Big Number!!*

The solution to this problem will give us a feel for how bloody 'complex' the peaceful looking fretboard there really is!

Things are happening there!
Lots of things!
There really is no time to be bored!


The whole whole whole solution rests on the Concept *of E-diagonal*.


*Research*


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## Jeff Flowerday

One of these threads is enough! I've combined it into one.

Please don't spew your babble on other theory threads!

Thanks,
Jeff


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## NOS Gary

Jeez, MarathonMan, just shaddap and play yer guitar - if you actually own one!sdsre


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## greco

Paul said:


> I've been playing musical instruments for over 30 years. I've got post secondary education in music. I'm not a full time professional musician, but I do know more about the language of music than most of the general public, and many casual musicians.
> 
> After re-reading all of BoM's posts, I now know less than I did before.
> 
> There are only 12 notes....how hard can it be?


Thanks Paul...given that I have memorized the 12 notes, I now feel better knowing that I have a fighting chance.

Dave


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## Wheeman

greco said:


> Thanks Paul...given that I have memorized the 12 notes, I now feel better knowing that I have a fighting chance.
> 
> Dave


What are they again? A, Bb, B, C, Db, D, Eb...?


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## guitarman2

Wheeman said:


> What are they again? A, Bb, B, C, Db, D, Eb...?


Hey!!! There's no F'n G.


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## GuyB

guitarman2 said:


> Hey!!! There's no F'n G.


Maybe his fingers got all MINGled... after trying the ming with the twang on a diagonal... phew !


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## Wheeman

guitarman2 said:


> Hey!!! There's no F'n G.


Hehe, its like the joke: "Why is 6 afraid of 7? Because 7, 8, 9!" Try saying it out-loud if it doesn't make sense right away.


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## RIFF WRATH

whew.........I finally figured it out, but now I have all these diagonal lines all over the fret board...shouldn't of used the charpie.........took me awhile, so I'm keeping it a secret, you figure it out for yourself....hint......consume a few alcoholic beverages, use a large magnifying glass, and stare down the fretboard towards the bridge, with adequate illumination at the tailstock.....you have to really concentrate and slowly tilt the guitar from right to left........for you lefties, tilt from left to right.............works best if you place the guitar on a flat surface at eye level, trust me, after a few attempts the guitar(s) are too frigin heavy to hold up to the light with 1 hand......warning works best on a fender as the gibson bodies deflect the light at obtuse angles....


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## shad

Battle_of_Marathon said:


> The answer to 5a) is a fraction:
> 
> 
> 
> *4 and 5/6*
> 
> 
> Which is indeed very close to 5.
> 
> So the two persons above who agreed that the answer was 5 was indeed quite correct afterall. Ha. Fancy that.
> 
> 
> To see why we get the fraction 5/6 think of the *B-string*. Ha.
> 
> 
> 
> *Research*


I sort of figured this had to do with the B-string but I still don't get it, shouldn't the fraction be 4/5 ? I guess that your bafflegab must have me baffled. Ha yourself!


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