Nice reference for the Math & Science folk re Octave based stepped tone systems.

Example:
If we need two parallel lines 3ft. long and 2 inches apart and we draw them and they are precise enough for our application, we might refer to them as being perfect. But, if we extend the lines out to one mile and they are 1/64" closer together, they are not parallel.

But, who does not already know this? ...so it is with just about everything in this thread.

The poignancy of your calculations of that which might be considered perfect, reflects the same notion that all is well if a player resorts to following tuning charts to the letter. I'll maintain an opinion, that is quite the opposite, from where you have taken a stand, with terminology, such as perfect, or exactness. Many things in life are perfect, that is, they cannot be improved in shape or form. A red rose is a fine example. Can you imagine telling a florist that its beauty falls short of YOUR expectations?

I wouldn't want it to be said that that I've disregarded a reply, where Tommy White is mentioned. I still have the business card that Tommy gave to me in Hindsdale, Ma.,
back in the eighties. You must remember that we're not discussing total sound here, or a blend of five or six stringed instruments, with 40 strings vibrating together, sometimes with pitiful chord inversions. While the "wild cowboys race through town", firing into the air, and taking potshots at my terminology, such as the contextualized term of "perfection" in tuning, I have this to say. According to Webster, "PERFECT" has been referred to as that which "satisfies all requirements". The methods of tuning a steel guitar, are preposterous, to put it mildly.
Without doubt, we all enjoy playing steel guitar in a band situation. The next time you set up the steel at home, and check the tuning, after a 3-4 hour "gig", you may realize that all the raves and reviews from patrons, were received
while playing an imperfectly tuned instrument. I know from experience, that the 3rd G# string is rarely "on the money" throughout an evening of entertainment. This may help to explain why Tommy White sounds great in tune or out of tune. BTW, it is a very rare occasion to enjoy Tommy's playing on stage at the Opry, due to poor sound management, and I do mean poor!!

Bill H.

quote:

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I know from experience, that the 3rd G# string is rarely "on the money"

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What I'm saying is that there is not a POINT where your guitar is in tune. There is a RANGE of frequencies that are acceptable to YOUR ear. That says nothing about someone else's ears. They may be more or less discriminating. I've always advocated moving from JI, as close to ET as you can tolerate, but I hear players who tune ALL OVER THE MAP who sound in tune with the other musicians with whom they are playing.

How / to what standard do you tune your 3rd E9 string, Bill?

Perfection is in the eyes and ears of the beholder. My wife is a florist and she will tell you that a rose is not a rose is not a rose. Some red roses are "more perfect" than others!

Tuning "perfection" is in the ear of the beholder. It is more art than science. We may strive for what we individually perceive as perfection but we never reach it. If it were science and could be reduced to a simple procedure that conforms to the laws of physics and sound pleasant, we would all do it the same way! The steel guitar and the human ears along with the brain that does the processing are imperfect. I don't worry about it too much. I tune my guitar as best I can knowing full well that the moment I lay the bar on those strings there are an infinite amount of imperfect "out of tune" notes available between the frets. I estimate on any given day I find 6,376,928 of them!

Terry Edwards
Fessy D-10 (more in tone than in tune)

"On the money" is the equivalent of you not reaching for your tuners to make adjustments, because you like what you hear after playing a tough 4 hour booking. "On the money" is likened to a gratifying blend of harmonic tones when played as triads. "On the money" is referenced when your 4th, 6th, and 8th strings are reasonably harmonic when the E-F lever is applied with the "A" pedal. I'm really not prepared to believe that the inconvenience of the usual day by day touch-ups, is a procedure that you've managed to find a way to avoid. The definition of a guitar string should include, a sensitive spring wire that will only react properly in an environment that remains unchanged. Goodness knows, that will never happen. I cited the 3rd G# string because, unlike the 6th string, slight pitch changes are not as detectable. Therefore, a player may not realize immediately, that he is playing flat or sharp, where the 3rd is used. The discovery will be made by the use of the electronic tuner, the following day. Some players who do not trust the fickle string, will spend every spare moment retuning. This can become very distracting to both band and fans.

Where in the confused state of lost in the forest, of look alike forestland, did you ever find this multitude of irrelevant jargon? After scanning the site offered in your reply, it appears that it must represent years of gathering notes, and paraphrasing unproven theories by scholarly individuals, who have embarked on a lifetime of studies.
The information given, may further the confused state of musical pitches, and how they affect music appreciation. I prefer to enjoy a system that works well, and one that doesn't tempt me to enter into unrelated studies.

Bill H.

[This message was edited by Bill Hankey on 18 September 2003 at 03:52 AM.]

My wife and I visit the beautiful Stanley Park, in Westfield, Ma. a few times each year. When the roses are in full bloom, they number in the thousands. I try to decide which one is the most beautiful; to no avail. Such is the case of applying for support, in the recognizable difficulties, of trying to label a properly tuned steel guitar. The merry chases through the brambles of questionable entries, has at least produced some stimulation of thought.

http://www.physics.brown.edu/Studies/Demo/waves/demo/3b6010.htm

A beat frequency of 2-3 b/s may be acceptable to some .. but,

When I would set up these boxes (and oscilloscope) and adjust for 2 b/s ... the "Stop !! Mr. A ... Stop!!! , we get the picture" ... could be heard down the hall.

Of course I didn't stop there ... 3 b/s, 4 b/s ... by 7 b/s I had students actually running out of class

Beats ... they are not for everyone

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

To JD Sauser ... from the "other thread" which got locked up before I could respond

Beats are caused by the interference between two waves that have similar amplitudes but slightly different frequencies.

When the two waves are added together ... a resultant wave is formed ... its' frequency will be the average of the frequencies of the two parent waves.

However ... the two parent frequencies will sometimes reinforce each other and sometimes cancel each other out.

This will produce a variation in sound amplitude in the resultant wave.

The frequency of the amplitude variation will be equal to the difference of the two frequencies (f1-f2). This is called the Beat Frequency.

[This message was edited by Rick Aiello on 18 September 2003 at 10:45 AM.]

I have said this before on the Forum, but we might wonder why symphony orchestras don't tune and play ET. Perhaps some steelers who tune everything "A 440" ET don't realize that A 440 is the ONLY NOTE that orchestras tune with a tuner. The strings, which are all fretless, tune their other strings to A in fifths by ear. This avoids a conflict with ET because JI and ET are only 2 cents off for fifths, which few people can hear. All the other notes are played JI by ear. If a piece is in a key in which the open string does not fit JI, the note is typically played by finger on another string, so that JI can be maintained, as well as vibrato. The horns likewise pitch every note by mouth and ear more or less to JI.

Only the percussion instruments have fixed pitches and are tuned ET, and these are not the dominant instruments of the orchestra. In fact, because of the ET problem, keyboards are no longer a part of the normal orchestra, and pianos are only rolled out on stage for piano concertos. Somehow on those occassions the orchestra manages to play by ear to tolerably match the piano's ET. And that is in fact what steelers are required to do when we play our fretless instruments by ear along with guitars, basses and keyboards that are tuned ET.

The difference between orchestral instruments and steel guitars is that the orchestral instruments don't tune anything fixed to JI. They don't tune any thirds fixed. They simply play them JI by ear. But a steel guitar has to make a choice to tune the thirds to JI or ET or somewhere in between.

At the same time steel guitars do not necessarily have to be tuned totally ET like pianos in order to play in all keys. Whatever chords are tuned JI at one fret in one key, will play JI at other frets in other keys. The steel has a potential problem when the root is switched to different strings as the pedal or knee combination changes, or as the chromatic strings are used. But pedal stops and compensators can maintain JI for many chords even then.

So the question is not whether to tune totally to JI or totally to ET, but rather where can we tune JI and where do we have to tune ET, and where can we split the difference. It all depends on what your copedent is, what chords you predominantly play, what kind of music you play, and what other instruments you play with.

This is why this is such a fertile field for discussion for pedal steelers. Swapping tuning methods and ideas on all this like Carl D. has so helpfully encouraged us to do can be very educational for those of us who don't have all the answers. And to those who insist on all ET all the time, or all JI all the time, and who lose patience and obstruct these discussions, I can only say relax. If you have all the answers, then you don't need threads like this and you can leave them to those who are interested in them.

So I say carry on gentlemen, I'm learning stuff. I wish more people who tune JI would post their methods over on the thread Carl started for that.

Apparently the "How do you tune ET" thread was resolved. You have to do it with a chromatic tuner. Piano tuners do it by counting beats caused by the out of tune ET intervals. But they may only tune a piano a couple of times a year, and may spend a couple of hours doing it. Obviously that doesn't work for steel guitars. I myself tune at least 3 or 4 times a year, whether my steel needs it or not.

[This message was edited by David Doggett on 18 September 2003 at 08:33 PM.]

Thanks for submitting the tuning chart, which raises no doubts in my mind about its usefulness. But realistically, if we reach a point where steel guitarists as a whole, cannot tune the instrument to an acceptable level of proper pitches, after ascertaining the 440 E note, the problem becomes more serious.
Moreover, it's the artistic touch of the man sitting behind the instrument. Steel guitars commonly detune without mechanical interference, simply by quick changes of temperature. Give me a break! I'm sure every player has experienced setting up his/her steel, tuned basically to 440, under an air conditioned system. In 10 minutes, a tuning check will reveal a variety of detuning, with each string reacting differently to the cold blast. Sunlight will quickly alter a "perfectly" tuned steel guitar. This befuddles any sort of strict adherence to charts, or methods of tuning. The solution would be to develop a quick touch-up, guided by an "in the ball park" tuning. Once the band kicks off, the player's ear should be the best guide to musical readiness.

If someone will advise me how to post an Excel spreadsheet chart, I will post this in the form of a JI E scale and in the form of a standard E9 copedent tuned JI.

There is a lot of stuff to study here, and I will mention a few things that I noticed. First, as b0b and Bill suggested, it would not be a great idea to tune exactly by these numbers. They don't incorporate cabinet drop, which will be different for each instrument. But ignoring cabinet drop, with this JI ratio copedent some things work out nicely, and others don't.

The EG#B triad is 440, 437, 440, exactly as a JI major triad should be. With the A&B pedals down, with no cabinet drop the AC#E triad is 440, 436, 440. One Hz is 0.25 cents, so this is off from JI by only 4 cents, and few people can hear less than 5 cents off. So if you tune your A&B pedals by ear to this chord with the E as the reference (as I do), this triad will be fine with the bar. But the whole triad will be flat at the nut to the extent of your cabinet drop (which flats your reference E's). If you tune the A with the pedal down to 440, and tune the E's JI to that, your E chord at the nut will be sharp to the extent of your cabinet drop. Thus, cabinet drop will only be a problem at the nut, and with the bar your ear will compensate for cabinet drop (provided it's not made out of tin). If you try to tune both triads ET 440, The E's will be off in one triad or the other, to the extent of cabinet drop. And it will be off both with the bar and at the nut.

The A pedal + F lever combination will not work at all with this JI tuning. The C#FG# triad will be 436, 443, 437 at the nut (ignoring cabinet drop). With the bar, if you adjust the root to 440 (say to match your bass player - he is tuned ET to 440 isn't he?), the triad will be about 440, 447, 441. The 3rd is 10 Hz sharp from JI, or 40 cents. Youch! However, if you forget the chart and tune the F lever stops by ear to either of the other two strings in the triad, you can get a good JI 440, 437, 441 for this triad. Your F lever will be off outside of this triad, but how often do you use the F lever for anything else? By itself it is good for an augmented chord. But a little disonance is all part of that sound.

I tune my 1st and 2nd strings with the 5th string as the root of a B chord. This triad, BD#F#, is 440, 437, 441, by b0b's JI ratio chart, which is about what you will get if you tune this JI by ear with the 5th string as the reference.

There is one mystery this chart cleared up for me. I was wondering, if you tune your open tonic chord (E) JI, what happens if you move the bar up two frets to play a II chord. Is that the same notes you would get from the JI scale (that is from playing the piano notes on a piano tuned JI to the E scale)? The answer is no. The JI E scale by the ratios says that F#A#C# (II, IV#, VI), should be 441, 438, 436. The 3rd of that chord is very close to a JI 3rd, but that 5th is off by 4 Hz or 16 cents from what we expect of a major 5th. Compared to ET, the VI of the JI scale is flatter than the III is. Playing it with the bar gives 440, 437, 440, if your tonic is tuned JI. Now I don't know which one of those chords we should be aiming for. Does JI mean you keep JI within the chord you are playing, or with the JI scale of the key you are playing in?

This tells me something very interesting. The pedal steel doesn't handle JI tuning like a JI tuned keyboard does. You can't play a sweet II chord on a JI tuned keyboard, but you can on a pedal steel. With the bar, you don't keep JI with the scale of the key, but you do keep JI with the root of the chord, which in many cases may be better. In other words, the steel can not only keep JI when modulating to another key, it can play JI chords within the same key in ways a keyboard or fretted instrument cannot. Is this a great instrument, or what?!

[This message was edited by David Doggett on 19 September 2003 at 11:55 PM.]

Your latest reply is very informative, and most interesting. It's amazing to read how well you've "covered the bases" in programming an approach to tuning methodologies. In light of the many points that you have stressed, concerning proper tuning, I've become curious about a matter that would involve 2nd, and 3rd parties.
Namely, the bass guitarist, and the rhythm/lead guitarist's tuning abilities. Have you ever experienced playing in a band, or group of musicians, and discovered the bass lines to be flat or sharp? The 3rd and 4th string "attacks", of a thunderous out of tune walking bass guitar, will compound the problems of discord, and disrupt the total harmonic values. The steel guitarist is subjected to unnecessary tuning checks, if the discord goes unchanged. Disclaimers have been known to run rampant,in similar situations, and that is where the well trained ear properly identifies the problem. Needless to say, that any improperly tuned instrument in a band will detract from the steel guitar's total sound. I list the bass guitar as the most critical of any group, whereby the steel guitar is not uniformly geared, to meld with a volume crazed band. The singlemost feature of the steel guitarist's ability to produce varying degrees of volume swells is lost completely.

Bill H.

[This message was edited by Bill Hankey on 21 September 2003 at 05:05 AM.]

Bill, your question about the bass player being in tune is really important. In a group you have JI ears of singers, fiddlers, horns and steelers trying to play in tune with tin eared, but ET tuned basses, guitars and keyboards. How does this work? I think the JI ears mostly try to keep in tune with the bass player as the music moves along. To match the other ET instruments, the bass should probably be tuned ET A=440. But if a bass player with good ears tuned JI for the key of each song (he'd have to retune between songs), or split the difference with some type of mean tuning, all the JI instruments would sound better, and the ET ones would probably sound okay. But this could be a problem if there was a modulation to another key within the song, which is the main reason they developed ET for fixed pitch instruments.