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Author Topic:  S10 E9 Tempering
William Johnson


From:
Statesboro, Georgia, USA
Post  Posted 8 Feb 2005 11:47 pm    
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I have always seen many different thoughts on what strings should be tempered and how much? All the star players have there own preferred temper.

ya'll help me out here.

IF the E and B strings are tuned straight up to 440, then why shouldn't there be ONE most perfect tempered tuning (assuming the pedal steels are built the same)? so why does this NOT seem to be the way it is? If all other things are constant, why wouldn't the F# always be -11 (not sure what cents flat i used) or so? i understand certain freqs 'beat' off of each other, etc., but in theory everyone should do the same thing, the same way if all other is equal, correct?

i guess the answer may be as simple as nothing is perfect!

anyway, I WONDER HOW MANY DIFFERENT E9 TEMPERS WE ARE USING JUSTS ON THS FORUM???

IS MY THOERY ALL CONFUSED OR WHAT? HELP?

i you don't mine, enter in your common E9 temper.

OK, now, the Petersosn VS-II has a stored tempered tuning for E9 and C6. thats easy enough to do, but HOW did they chose their values?

this should be interesting.

peace,

billy


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William Johnson (Billy)
Grievous Angel Productions
Statesboro, GA. 30461 USA
www.grievousangelpro.com
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Larry Bell


From:
Englewood, Florida
Post  Posted 9 Feb 2005 5:23 am    
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why is there more than one method of tuning?
Because people have their own opinion on what sounds in tune to them.

If you want to see how we all tune, search the forum. Search terms like 'equal temperament' and 'just intonation' will give you enough to read to keep you busy for a week or more.

Mine is on my website if you're interested.

------------------
Larry Bell - email: larry@larrybell.org - gigs - Home Page
2003 Fessenden S/D-12 8x8, 1969 Emmons S-12 6x6, 1971 Dobro, Standel and Peavey Amps

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David Doggett


From:
Bawl'mer, MD (formerly of MS, Nawluns, Gnashville, Knocksville, Lost Angeles, Bahsten. and Philly)
Post  Posted 9 Feb 2005 10:03 am    
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Billy, there is a semantic problem we need to address before this goes any further. By "tempered" you seem to mean a deviation from the straight up meter reading (0 cents, or 440 hz). This is common usage among guitar players and steelers who tune to hand-held electronic tuners, but it is completely backwards from the way the rest of the music world uses these terms. The straight up meter reading is already tempered. The true harmonic tuning based on the physics of string vibrations (and also the way our ears naturally perceive harmony) is Just Intonation (JI). If you take the tonic from a meter or tuning fork and tune the rest of an open chord by ear, you will get very close to the JI intervals, depending on how good your ear is. However, this tuning causes problems for fixed-pitch instruments such as pianos and guitars. Therefore, various compromised tempering methods have been developed over the centuries to make these instruments playable. The common one that is programmed into the "straight up" reading of electronic tuning meters is equal temper (ET).

So if you start with the straight up position and adjust from it by ear (or by counting beats), then you started with a tempered tuning and are adjusting back to JI. If you start with a JI tuning, and adjust toward the straight up meter, then you are tempering. Many steelers just call it tempering no matter which direction your adjustments go. But other musicians might be confused by this loose use of the term. So let's just call our tweaks moving away from straight up "adjustments" or "tweaks", rather than tempering.

Back in December I posted a theoretical JI tuning for E9/B6 Universal. Strings 1 through 9 also work for single neck E9, if you take the low D string tuning from LKR. The thread is titled "JI intonation for E9/B6 Universal." I show the copedent transposed to C9 (I'm an old piano player who thinks in the key of C better than in the key of E), and show the proper meter readings in terms of straight up 440 and deviations from it. It can easily be converted to cents with the factor that a difference of 1 hz = 4 cents. But because of cabinet drop, you may not be able to directly take these theoretical readings and use them. The way I deal with cabinet drop is to measure how much drop I get on my E strings when I activate the AB pedals. On my Zum this drops the Es 1 hz (4 cents). Therefore, in order to keep both my open pedal intonation, and my pedals-down intonation as close as possible to straight up 440 on my tonics, I split the difference. For tuning in the key of E, I tune my open Es 1/2 hz (2 cents) sharp of straight up, and I tune all the open strings likewise compared to the theoretical readings in my chart (the chart readings are in relation to straight up 440, regardless of key). I tune my pedaled As (strings 3 and 6) 1/2 hz (2 cents) flat of straight up, and I tune all the pedaled stops in the A chord the same way. In other words, I would need to create a new chart and add 1/2 hz to all open strings, and subtract 1/2 hz from all pedal and knee stops. You need to measure the cabinet drop on your guitar to arrive at your own chart.

Hope this helps. This is more complicated to explain than it is to actually do. I just take my Es from a meter, adding 1/2 hz, and tune everything else by ear. I tune strings 1 and 2 by ear using the open 5th string B as the tonic.

If I want to tune my stops, I take the pedal-down A from a meter tuning 1/2 hz flat of straight up. Then I tune the rest of the A chord by ear. I tune the C# chord (A pedal and F lever) so that the F lever stop matches the open strings by ear. I tune the C pedal stops by ear to match the B pedal stops. If you tune your open F# string (7) to that chord, it will not be quite right for the 2nd or 9th scale note with the open E chord. I tune it by ear to match the E chord. On my C pedal I raise string 8 to F#, and match that stop by ear to the rest of the B,C-pedaled chord (it is an octave below the pedaled 4th string.

The above method gives a theoretical JI tuning, tempered only for cabinet drop. The open chord and AB-pedaled chord tonics are both within 1/2 hz (2 cents) of straight up. The A,F C# chord is 3 1/2 hz, or 14 cents flat at the nut, and so has to be played slightly above the fret with the bar, and should be avoided at the nut.

[This message was edited by David Doggett on 09 February 2005 at 10:09 AM.]

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William Johnson


From:
Statesboro, Georgia, USA
Post  Posted 9 Feb 2005 10:39 am    
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thats very interesting as i am an (was) electrical engineer by schooling and trade adn have had a bunch of physicss so i follow some of what you are saying at that level (music theory at that level is also interesting to me but have not stufied it too much).

a question: i always thought or was told pianos and acoustiuc quuitars are tempered? so are you saying that all the many strings in a piano are tuned straight 440??? i always thought that quitars are tempered instruments also; that is why the lower bridge on better guiatrs have an adjustable lower bridge or either the top bridge or nut has to be adjustable???

did i get another concept confused?

again, what determines if an instrument is considered temtper or not?

NOW, what about the Peterson VS-II? what method does it offer as it's E9 basic tuning (does it not come with a basic E9/C6 tunigs stored in it? i understand of cousrse you can store your chosen tunings also.)?

later,
Billy


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William Johnson (Billy)
Grievous Angel Productions
Statesboro, GA. 30461 USA
www.grievousangelpro.com
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Greg Vincent


From:
Folsom, CA USA
Post  Posted 9 Feb 2005 12:36 pm    
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Billy,

Staight 440 IS tempered. That's the point Dave D. makes in his first paragraph above. -GV
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Larry Bell


From:
Englewood, Florida
Post  Posted 9 Feb 2005 12:58 pm    
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Any tuning that ISN'T beatless is tempered. Strict Just Intonation (e.g., thirds 14 cents flat) is the only 'untempered' tuning. Some of us who have wrestled with it for 30 years consider it 'ill tempered'.

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Larry Bell - email: larry@larrybell.org - gigs - Home Page
2003 Fessenden S/D-12 8x8, 1969 Emmons S-12 6x6, 1971 Dobro, Standel and Peavey Amps

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William Johnson


From:
Statesboro, Georgia, USA
Post  Posted 9 Feb 2005 12:59 pm    
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OK, that lost me. how is one note or frequency tempered? to what?

past that my me again!

billy


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William Johnson (Billy)
Grievous Angel Productions
Statesboro, GA. 30461 USA
www.grievousangelpro.com
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Larry Bell


From:
Englewood, Florida
Post  Posted 9 Feb 2005 1:13 pm    
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Tempering is variation (+ or -) from beatless, just intonation which, by definition is NOT tempered. On your tuner, it will read -14 cents.

If you tune your 3rd E9 string to the 4th fret harmonic on the 4th string such that there are no beats, that is just intonation and is NOT tempered.

If, instead you choose to tune your 3rd and 4th strings STRAIGHT UP (440) on the tuner, this is a TEMPERED tuning. It is EQUAL TEMPERAMENT -- all strings tuned to A=440.

Go to my website and check out the information on tuning. Click the link below.

------------------
Larry Bell - email: larry@larrybell.org - gigs - Home Page
2003 Fessenden S/D-12 8x8, 1969 Emmons S-12 6x6, 1971 Dobro, Standel and Peavey Amps

[This message was edited by Larry Bell on 09 February 2005 at 01:14 PM.]

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William Johnson


From:
Statesboro, Georgia, USA
Post  Posted 9 Feb 2005 1:14 pm    
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So, when i use by new Peterson VS-II what method or school of thught am i going to use?

where can get a copy of David's tuning method taht he posted? on this site i guess.

are ya'll saying also that on a guitar every string is techically turned straight up to 440? but wasn't it also stated that electronics tuners are pre-tempered? so in reality, we tune theh guitar tempered t o fit the real world? i may have that mixed up!

again, explain how a 440 tone by itseld is tempered? i thought 'tempering' implied adjusted to sound 'pleasant' to humans ears when other notes played with it. is this all wrong?

wow, i might go work on upgrading the opamps in my recording console now to feel back in control!

keep throwing it at me - i'll get somwething good out if this i promise.

Maybe my concept is correct, just my definitions of terms is wrong.

Billy



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William Johnson (Billy)
Grievous Angel Productions
Statesboro, GA. 30461 USA
www.grievousangelpro.com
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Larry Bell


From:
Englewood, Florida
Post  Posted 9 Feb 2005 1:17 pm    
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Tuning EACH STRING to the A440 STANDARD produces a TEMPERED TUNING. It is EQUAL TEMPERAMENT -- all notes are the same distance apart. That system is based on mathematically dividing the octave into 12 segments (semitones or half steps). JUST INTONATION is based on the vibrational nodes of the string, which occur at fractions of the string. They don't work out the same.

------------------
Larry Bell - email: larry@larrybell.org - gigs - Home Page
2003 Fessenden S/D-12 8x8, 1969 Emmons S-12 6x6, 1971 Dobro, Standel and Peavey Amps

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William Johnson


From:
Statesboro, Georgia, USA
Post  Posted 9 Feb 2005 1:49 pm    
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OK. it was mostly a use of terms. i undertand. I just did not consider straight up 400 tempered, but using the term 'Equal Temptered' i see that as i was what i was trying to say or think. I was using "tempered" as meaning "Just Intonation". i understand that.

are ya'll saying that on pianos and guitars each note is tuned straight up to 440? OK, but way are PSG 'tweaked' in order to make a chord sound pleasnat to the human ear?

thanks,
Billy


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William Johnson (Billy)
Grievous Angel Productions
Statesboro, GA. 30461 USA
www.grievousangelpro.com
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Larry Bell


From:
Englewood, Florida
Post  Posted 9 Feb 2005 2:00 pm    
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Why are pedal steels often tweaked?
because that's what some people -- but not others -- choose to do

Buddy Emmons, Weldon Myrick, and many others tune pretty close to 440 for EVERYTHING

Paul Franklin, Lloyd Green, and many others tune pretty close to JUST INTONATION

Others tune somewhere in between. That's what I choose to do (my thirds are about 4 cents flat instead of 0 or 14 and my F's turn out about 12 cents flat instead of 0 or 2Cool. That's just what works for me.

They all play in tune and it sounds just great. It's just another one of those little personal preferences (tubes or solid state; Ford or Chevy) that contributes to a player's personality.

I'll say it again:
It doesn't matter a hill of beans how you TUNE as long as you PLAY IN TUNE.

Pianos are not tuned to A=440 for each note. Some electronic keyboards are -- most these days offer several choices of temperament. Acoustic pianos are 'stretch tuned'.
Quote:
Stretch tuning is a procedure widely followed by the piano tuning profession. It recognizes a phenomenon of the human ear whereby tones in the upper range of a keyboard will sound "flat" even though they are calibrated with extreme precision. Fortunately for all, a consensus has long since been agreed upon as to the exact amount of stretching. A piano so tuned creates the impression of great tonal brilliance.
http://www.badrat.com/rhodes/manual/ch5.html
(there are many other reference on the net as well)


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Larry Bell - email: larry@larrybell.org - gigs - Home Page
2003 Fessenden S/D-12 8x8, 1969 Emmons S-12 6x6, 1971 Dobro, Standel and Peavey Amps

[This message was edited by Larry Bell on 09 February 2005 at 02:05 PM.]

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Greg Vincent


From:
Folsom, CA USA
Post  Posted 9 Feb 2005 2:23 pm    
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Equal Temperament allows a piano to play acceptably in all keys. In the key of C the E note would sound sweetest if it were about 14 cents flat. So... you could tune all the E keys of your piano 14 cents flat to get that ideal major third interval in the key of C. Great, but then what if you want to play in the key of E??? The root note E will be flat. See the problems that start to crop up?

On the steel we'd just sneak the bar up on that E to sharpen it and bring it into tune. Can't do that on a piano --or a guitar for that matter. They are what is called "fixed pitch" instruments, so if they want to play in all keys, they need to compromise and tune using Equal Temperament, a.k.a. "straight up 440" --needle straight up on all notes.

Steelers aren't bound by Equal Temperament, which why the instrument can have such a lyrical sweetness to it.

Pianos use Equal Temperament, but owing to the range of the instrument, the upper register has to be sharpened somewhat and the lower register has to be flattened somewhat to sound in tune, due to the imperfect way a string creates harmonics. This has nothing to do with how the octave is tempered.

Guitars use Equal Temperament, but owing to the sharpening of a string's pitch when it is fretted, the bridge needs to be angled a little bit because this sharpening effect is most prominent on the thicker, tighter strings. This again has nothing to do with how the octave is tempered.

-GV
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David Doggett


From:
Bawl'mer, MD (formerly of MS, Nawluns, Gnashville, Knocksville, Lost Angeles, Bahsten. and Philly)
Post  Posted 9 Feb 2005 2:43 pm    
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Billy, I find that very few guitarists actually play equal temper according to their meters. Most will start by tuning all the strings to the meter. The old way without a meter was to tune the low E with a tuning fork, piano or harmonica, then tune each string to the next lower string at the 5th fret. Those are both ET methods. But many guitarists will not leave things like that. They will play the tonic chord for the next song and tweak by ear to make it sound sweet. Whether they realize it or not, they have then moved closer to JI and away from ET. This works pretty well for related keys and using simple chords. for example, if you tune your E chord by ear, it will work pretty good for the main chords of that key and the key of A. But if you switch to the key of G or C, you will need to retweak things to make the chords in those keys sound good. Most guitarists I play with are constantly retuning that way between songs. If they don't refer back to the meter occassionally, they can drift pretty far away from 440.
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Greg Vincent


From:
Folsom, CA USA
Post  Posted 9 Feb 2005 2:44 pm    
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Quote:
Fortunately for all, a consensus has long since been agreed upon as to the exact amount of stretching


???

The amount of stretching required varies from piano to piano. The shorter strings of an upright will create sharper, less accurate overtones and so will require a more stretched tuning to sound in tune than the longer strings of a 6' grand. A 9' grand will create even more accurate overtones and require less stretch tuning. That is why they are the most desirable. -GV
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William Johnson


From:
Statesboro, Georgia, USA
Post  Posted 9 Feb 2005 3:07 pm    
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OK. now i understand. it is a manner of how you say it anD what Terms yOu are using.

actually (before being a happy player) guitars, pianos and pedal steels are all 'tweaked', 'tempered' (if used losely in defintion), ET or JI after its all said an done in oreder to make it sound AS SWEET AS POSSIBLE.

OK, that's kinda what what i understood even though i did learn about some new terms like 'Just Intonation (JI)' and 'Equally Tempered (ET)'. One aspect is more theoretical and the other is what makes it work for human being's hearing and concept of pleasure.

OK, . . . what tuning method does the Peterson VS-II use? doesn't it come with a E9 and C6 tuning stored in it?

thanks,
Billy


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William Johnson (Billy)
Grievous Angel Productions
Statesboro, GA. 30461 USA
www.grievousangelpro.com
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Larry Bell


From:
Englewood, Florida
Post  Posted 9 Feb 2005 3:38 pm    
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C'mon Greg
What did you expect from a website called badrat.com???


------------------
Larry Bell - email: larry@larrybell.org - gigs - Home Page
2003 Fessenden S/D-12 8x8, 1969 Emmons S-12 6x6, 1971 Dobro, Standel and Peavey Amps

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Greg Vincent


From:
Folsom, CA USA
Post  Posted 9 Feb 2005 4:00 pm    
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Quote:
it is a manner of how you say it and what terms you are using.


Of course!

With this subject, it's critical to use the correct terms and to understand them clearly. Otherwise you can create confusion and that's how a lot of misinformation gets spread around.

We can really screw up beginners if we continue to misuse the term "tempered tuning". Getting guitar bridges and the stretch tuning of a piano all mixed up in this issue just makes things worse.

Sorry, the misuse and misunderstanding of the term "tempered tuning" is one of my pet peeves --brings out the worst of my temperament!

-GV

[This message was edited by Greg Vincent on 09 February 2005 at 04:08 PM.]

[This message was edited by Greg Vincent on 09 February 2005 at 04:09 PM.]

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William Johnson


From:
Statesboro, Georgia, USA
Post  Posted 9 Feb 2005 6:46 pm    
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that's cool. i learned a lot from this discussion.

i just got amy VS-II a hur ago and it talks about the same stuff we talked about. the VS-II and a stored E9 tah came from BG, Emmons, Jeff Neuman and others. NOT one note on the E9 tuning is straight up 440!

later,
Billy


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William Johnson (Billy)
Grievous Angel Productions
Statesboro, GA. 30461 USA
www.grievousangelpro.com
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Eric West


From:
Portland, Oregon, USA, R.I.P.
Post  Posted 9 Feb 2005 6:59 pm    
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So nobody twists it around again:

quote:
My apologies for not explaining up front Bill, but I do tune everything ET. Compensation is what I had to deal with tuning the old way but now it’s a thing of the past. I may go a cent or so flat in some cases but strictly to handle temp changes under certain conditions.
Also when I hear a JI steel third in a ET track, flat is the only word I can come up with. -Buddy Emmons-



GV.

You bring up my point exactly, and why I've expressed my exasperation at this "Beatless Tuning".

New Students.

Not only is it straight out of the Barque period, and was scrapped because it could not be played with other instruments that weren't tuned exactly the same, playing prearranged songs and agreed apon intervals...

Beginners show up wondering how to tune their instruments.

What then?

The answers they get aren't any better than the answers they give people that have been playing straight up to a tuner for a quarter of a century or more. They just seem to include a few less challenges, insults, and snide remarks. They just remain a little less rebutted. ad the new students are confused, excuse themselves politely and go away with no clear answer. It's worse if they take some of these complicated "systems" or rubegoldbergation to heart, and try to put them into use playing with instruments that do not tune that way.

To Billy.

Buddy Emmons, Weldon Myrick, Bill Stafford from what I remember and a host of others tune all their strings and changes to where the needle is exactly in the middle of whatever indicator is exactly zero.

Do yourself a favor. Tune the way they do.

Give yourself a base from which to branch out. Experiment with intonation "issues" a good couple years later, if at all.

Tuning to the most famous "Just Intonation" chart puts one of your changes 28 cents out between two of your most common changes your F lever and your 10th and 5th strings, a common combination. To "Compensate with the bar" between the two offending notes on the 4th and fifth strings would take a slant of about 30 degrees, and you wouldn't be able to play a third string with the two.

Read the latest "anybody else tune straight up 440" thread, and you'll have a better understanding. The above tuning chart and it's glaring mismatch are covered.

Buddy Emmons comments are on one of the threads linked to in the FAQ post of the "Forum Feedback".

His comments are twisted by some in these threads to say that he does change some of his tunings. That's not correct. Read his original comments.

You may indeed "make it hard" for yourself. Many of us did or do.

Just don't start off with a bunch of nonsense that makes it "impossible".

As you can see by reading the "anybody else tune straight up 440" post, the nonsense starts soon enough.

Heres my iron clad simple tuning system.

I tune straight up to the middle of the tuner. All changes, all strings.

I do this because that's how the most common instruments I play with tune.

So does Buddy Emmons, though his reasons I can't speak for. Maybe he's getting hard of hearing.

I don't have any problem explaining, defending or suggesting it.

I started out playing that way because I didn't know aby different.

When I first heard of people detuning their guitars to be "more in tune" I thought it was a joke. This was after I'd played about 20 years, and a couple thousand gigs.

Then when I found out so many people, including some pretty important steel players tuned that way, I stopped laughing.

When people try to suggest that new students tune "that way" with one half baked explanation or another, I go farther than that I'm afraid.

It's my own shortcoming.

At this point, I'm convinced that there IS enough information in these threads to point a new student to a locgical, informed, and simple conclusion.

And Billy, I hope you do.

It's a great instrument.



EJL

[This message was edited by Eric West on 09 February 2005 at 07:09 PM.]

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Larry Bell


From:
Englewood, Florida
Post  Posted 9 Feb 2005 7:15 pm    
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Eric,
Just curious
Do Paul Franklin and Lloyd Green sound out of tune to you?

------------------
Larry Bell - email: larry@larrybell.org - gigs - Home Page
2003 Fessenden S/D-12 8x8, 1969 Emmons S-12 6x6, 1971 Dobro, Standel and Peavey Amps

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William Johnson


From:
Statesboro, Georgia, USA
Post  Posted 9 Feb 2005 7:16 pm    
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Eric,

when you tune straight up, does it not sound dis-chorded? mine always did! do you touch up each string a needed? it always sounded pretty rought playing alone!

Billy


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William Johnson (Billy)
Grievous Angel Productions
Statesboro, GA. 30461 USA
www.grievousangelpro.com
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Eric West


From:
Portland, Oregon, USA, R.I.P.
Post  Posted 9 Feb 2005 7:28 pm    
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Larry.

Does Buddy Emmons sound out of tune to you?

As for Mr Green, I'll be talking to him next week. I'll ask him how he sounds to him.

I'm not going to tell him how I tune until I get him to sign my guitar, if indeed he will be so kind.



Billy.

I have no problem telling you that my tuning in my basement, I might "temper" a little, but mostly I'm not that in tune, due to ending up tuning it up or down to match a recording I'm trying to cop licks off of.

When I have a friend that plays guitar or piano come over I out of courtesy, tune the same way they do. Straight up to a good digital tuner.

On a Bandstand with bandstand volumes, chords with the "proper amont of beats" in them to me, sound the purest, and most in tune with other instruments that I play with.

It has worlds to do with your own confidence, and bar movement. The longer you hone it with bandstand experience, the better it will get. I don't mean "using vibrato", but making your playing more "fluid", and "deliberate". Straight up tuning, to me helps the most with the "deliberate" part.

You may certainly tune any way you wish.

All I can tell you, is that if you start trying to get chords sounding like they "don't have any beats", you are going down a very complicated path. Even within your own instrument.

When you get on the bandstand, and play with instruments that are tuned very differently, things change. That's when the "problems" are not that easily explained away. Some people get to the point that they don't have to. Some aren't that lucky.

It might take years to figure out why.

More than that, or answers to inane "Does Jerry Byrd sound good enough?" baiting, I'm not falling for.

I've put in more then a hundred pages answering every question, taking every piece of bait, and doing research that I thought I'd never in a million years be doing.

This all without ever demeaning anybody elses playing, recordings, or claiming to be something that I'm not.

I'm a well worn bar/club player with lots of experience, and references.

I don't owe anybody any more writing on the subject. I have other things to do.

My explanations are really simple.

I myself would hate to be the one trying to rebut them.

But then, I'm not in that postition.

If you want to get a good handle on it though Bill, you've got a lot of reading to do.

I'm confident that "it's all in here'.

Look up the "tuning posts" in the FAQ on the Feedback Page to start with if you're serious.



EJL

[This message was edited by Eric West on 09 February 2005 at 08:25 PM.]

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Donny Hinson

 

From:
Glen Burnie, Md. U.S.A.
Post  Posted 9 Feb 2005 8:51 pm    
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Billy, while everyone else has offered rather technical explanations, I'll give you my own "Will Rogers" version.

Any temper chart is based on perception, and different people have different perceptions of the same thing.

"Tempering" a pedal steel tuning is a compromise based on many factors. The reason many player's charts do not agree is that they base them on their own "personal perception". That "personal perception" is based not only on how they "hear" the notes, but on how those notes are created. When you add differing guitars (differing string lengths and "cabinet drop" effects), different string types and guages, differing amounts of bar pressure and picking forces, and different environmental factors (a chart which works fine when it's 60 degrees is "out" when it's 85 degrees), you begin to see why there are so many different "recipes" out there to get the good (in tune) sound. Using someone else's "temper chart" in tuning your own rig may result in results that are far from perfect. As a matter of fact, "temper tuning" is pretty far from perfect, to start with!

Also, an interesting sidelight is that an out-of-tune guitar can be played to sound in-tune", and an in-tune guitar can certainly be played to sound out-of-tune.

Or, as one steeler interestingly put it..."Once the bar hits the strings, all bets are off".

The moral of the story:
Forget numbers, and just tune it 'til it sounds good. After all, that's the whole idea, isn't it?

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BIAB Styles
Ray Price Shuffles for Band-in-a-Box
by Jim Baron