quote:

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I was taught the standard account of how Bach (1685-1750) composed "The Well-Tempered Clavier" as a demonstration for equal temperament. I have since learned that some challenge that version of the story, suggesting instead that Bach was in fact advocating an intermediate system

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It is interesting to note that NO pilot would rely on his senses to determine his altitude or airspeed, etc.

No surveyour would rely on his eyes to determine if the lines were being put on correctly on a football field.

No audiologist would rely on his senses to test our ears.

No electronic technician would rely on his senses to test for voltage, current or ohms.

No Dr in medical research would rely on his senses when doing testing for most of the things research dictates.

No official at a horserace would rely on his senses to determine who won in a close horse race.

No asrtonomer would rely on his senses to test for a given star's distance from earth.

No bacteria tester would rely on his sense to test for same.

No reputable nurse would rely on her senses to test someone's blood pressure or temperature.

No reputable pool service tech would rely on his senses to test the pool's Ph ratio

No chemist would rely on his senses to test the many things he must test.

No reputable Judge would except a Cop's senses in determining whether a defendant was or was not speeding.

No reputable technician would rely on his senses to determine how much power an amp was producing at any given moment.

NO Lab would depend on a person's senses to determine the exact time of day.

No food producer would rely on a person's senses to determine how many calories, vitamins, minerals, etc was in a candy bar.

No machinist would rely on his senses to determine if a milling machine was taking off exactly 5 ten thousands of an inch when cutting a piece of metal stock.

Ad infinitym.

YET, many musicians are detemined to use one of the most innacurate testing devices ever known; to determine if a steel is, or is not in tune.

What hath man wrought?

quote:

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What hath man wrought?

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speedometers

Altimeters

tachometers

gas guages

microscopes

stethoscopes

volt ohmeters

Oscilloscopes

electric, gas and water meters

cash registers

calculators

PC's

surveying scopes and assoc. equp.

yardsticks

tape measures

micrometers

telescopes

scales

feeler gauges

wrist watches

metronomes

thermostats

humidisatats

barometers

wind velocity meters

depth gauges

ad infinitym

But use a tuner on a steel guitar?

"God forbid!"

carl

[This message was edited by C Dixon on 17 September 2003 at 07:26 AM.]

Re the electronic technician, ..no it is the engineer and Ph.D. that would do that. Lots of electricians stick their thumb in the socket to see if it is hot.

If the ear is the sensing element, and the brain the interpreter that must be satisfied, then these are the best to use to evaluate the tuning's merit in a given situation. After that quantifying the tuning in cents/Hz etc. helps to return quickly and accurately to what was deemed satisfactory to the picker, not necessarily to the band or the audience.

Once the open strings are departed from, and only two or three strings are used at a time (let alone single notes)at "speed picking" rates, accuracy becomes very relative. To measure this, digitize a sound passage and step thru it with a frequency counter. Some pickers are better than others, ..none seem to be absolute.

Exact is not always pleasing in any subject. Lots of pickers complain about the exactness of BIAB's timing making it too mechanical sounding, ..so there is a "humanizing" function to mess it up a bit.

There is a saying about "biting one finger or the other" that could apply here; If you adjust 3rd's(or other intervals)one way in one inversion, you mess them up in another (in any tuning containing more than two tones).

Re the NO ONE WOULD list, ..You might want to add:

Those that would talk about tone should define it with a spectrum analyzer.

Those that would talk frequency should define it with a frequency counter.

Those that would talk mechanical structure should quantify it with the appropriate measurement equipment and terms.

Etc.

Now we all know that most folk/pickers do not have the equipment, the knowledge, or the inclination to do the above, ..but then all folks are not Doctors, electronic technicians, etc. as per your list. As time goes by, these "sophisticated" methods become more common place, ..electronic tuners replace tuning forks, and "give me an E" for instance.

No where in the list do you address directly what NO PSG picker would or would not do?

Is there room for more math & science re the PSG, ..I think so, but most pickers should minor in it, most builders should major in it, and the rest of us just enjoy the "bar room BS".

The Ahura-Mazda thing again.

[This message was edited by ed packard on 17 September 2003 at 07:49 AM.]

We agree to disagree (for the most part anyway)

luv ya man,

Thank you... J-D.

An other question is (and that I think may go along with Carl's brain storming): If some of you (BE incl.) realy tune your steel cold turkey ET... let's say for just all of the open string notes first... do you tune all your pulls straight to your tuner too, disregarding the altered intervals between those pulled strings and the open strings that may have wandered off a little due to cabinet drop or what ever you may call it (I know YOUR guitar doesen't have it... but let's asume your tuning some elses guitar, and these all have it, now don't they )?

And then to those that have stated some thing to the take of: ... I tune all straight 4XX and then I just tweak my G# a little... Do you then tune your B-pedal G#-to-A-raise sharp to make bakc up for that little tweaking? And isn't the ET-sharp 33rd interval between strings 5&6 with both pedals depressed (probably being the most plaid 3rd interval position in the E9th playing style) not bothering you too, and if so why do you think it doesn't?

EX:

If one string is at 330 Hz ... another is at 331 Hz .. you will hear 1 beat in 1 second.

If one string is at 330 Hz and another is at 335 Hz ... you will hear 5 beats in a second.

For the Equally Tempered scale ... the factor in between adjacent pitches is exactly the 12th root of 2.

If you take 440 Hz and sucessively multiply it (and its products) by this number 12 times you will end up with 880 Hz.

Here is an ET octave (rounded to 10 decimal places ... in Hz):

 A   440.0
 Bb  466.1637615181
 B   493.8833012561
 C   523.2511306012
 C#  554.3652619537
 D   587.3295358348
 Eb  622.2539674442
 E   659.2551138257
 F   698.456462866
 F#  739.9888454233
 G   783.9908719635
 Ab  830.6093951599
 A   880.0

As far as your other question about tuning intervals to zero beats (JI) ...

There is a set of ratios that... when applied to a reference note ... will give you the "beatless condition".

There are actually several different sets of JI ratios ... the most common is the 5 limit.

For the standard chromatic scale:

1/1   (1)
16/15 (2b)
9/8   (2) 
6/5   (3b) 
5/4   (3) 
4/3   (4) 
45/32 (5b) 
3/2   (5) 
8/5   (6b) 
5/3   (6) 
9/5   (7b)
15/8  (7) 
2/1   (octave) 

Here is the JI version of the above octave (in Hz):

A  = 440
Bb = 469.33
B  = 495
C  = 528
C# = 550
D  = 586.67
Eb = 618.75
E  = 660
F  = 704
F# = 733.33
G  = 792
Ab = 825
A  = 440

Looking at ET vs. JI in terms of beat frequency ....

If you want a beatless major third interval for a 220 Hz A string ...

220 x 5/4 = 275 Hz ... the JI C#.

Since 277.2 Hz is the ET C# (based on A440) and the JI C# is 275 Hz ... The beat frequency between them is:

277.2 - 275 = 2.2 beats/sec.

This is how I set up that chart earlier in this thread.

Since pitch is a logarithmic "thang" ... the beat frequency is a function of the octave you are in.

EX:

For an A and a C# ... here is the beat frequency in 3 different octaves

220 x 5/4 = 275    277.2  - 275  = 2.2 b/s

440 x 5/4 = 550    554.4 -  550  = 4.4 b/s

880 x 5/4 = 1100   1108.8 - 1100 = 8.8 b/s

I sure hope this is what you were asking for

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www.horseshoemagnets.com

[This message was edited by Rick Aiello on 17 September 2003 at 02:10 PM.]

Can't resist, ..if turn about is fair play, what do mean when you use the term "art"?

The landscape painter may not use meters etc. to mix his paints, but if he is using commercially prepared paints, I bet the paint/pigment producer did.

The "worth his salt" expression comes from the salt given to the slaves, .."worth his picks" might fit better with the forums theme.

It would seem that the artists artistic expression is inherently limited by the materials with which he/she works; Paint, strings, instruments, bars, picks, pickups, amps, etc., all of which can be "math & science" described/defined.

Aside from the dictionary definition of "art", I would venture that it is how one uses what they have, ..or per country idiom "what you do with what you got".

After thinking it over, maybe "HOW you do what you do with what you got" is better.

RE "worth his salt", ..nicely found in the music world in a song by Odetta = "no more auction block for me, no more pint of salt for me, many thousand gone", ..beautiful tune.

[This message was edited by ed packard on 17 September 2003 at 01:39 PM.]

quote:

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According to "Johann Sebastian Bach The Learned Musician", the new biography by Christoph Wolff, rated five stars in the Bovine review, Bach wrote WTC and most of his keyboard works for the Kirnberger tuning. Kirnberger is available on my Yamaha P-80 and I play the WTC with it. It sounds sweetest in the key of C, but unlike Pure, Just, and Pythagorean, it sounds good in all keys. Each has its own sound.

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If you haven't already, please give some thought to whether or not WTC and Bach's other keyboard works are written in a way that accentuates the postive aspects that each key would have in Kirnberger. It seems to me that could come darn close to deciding the issue once and for all, if there are obvious enough differences from key to key in Kirnberger.

Thanks for mentioning that book again. I'll definitely track it down.

[This message was edited by Jeff A. Smith on 17 September 2003 at 09:05 PM.]

quote:

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please give some thought to whether or not WTC and Bach's other keyboard works are written in a way that accentuates the postive aspects that each key would have in Kirnberger.

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Does this relate to steel guitar tuning? Yes!

Bach lived in an era when tuning systems were changing, and so do we steel players. He was aware of equal temperament, just as we steel players are in 2003, but he preferred compromise tunings just as most of us do. Just as Bach stayed in the "easy" keys most of the time, we tend to play only the "easy" chords at each fret most of the time. Just how many chords we can play at each fret depends on what tuning we choose.

If you tune to Just Intonation, you can probably play only a very few chords on each fret. For example, on E9 tuning open strings, you would have trouble playing a B major triad and a F sharp minor triad. One of them will sound bad, and most players who tune towrd JI avoid playing one or the other of those.

If you tune ET, you can play all 12 major and minor triads on open strings, and they will all sound OK (not great but OK)

If you tune in between, as I try to do with a sort of meantone approach, you can play about half of the major and minor triads. On my E9 open strings, I can use G,D,A,E,B,F#,C# major.

The mathematics and science of
sound perception/acoustics do not match the mathematics our music. Therefore looking for some sort of fundamental mathematical relationship is pointless.

Very respectfully, we will agree to disagree.

Thanks for posting,

Thanks for starting this "debacle", ..lots of fun for us folk with time on our hands and not into performing so practice is not important to us.

I would suggest some reading:

Temperament by Stuart Isacoff
The Physics of Sound by Richard E. Berg
Genesis of a Music by Harry Partch

Also the works of Heimholtz.

The problem you have discovered has been studied and written about for centuries. You can even go back to the ancient Greeks and the works of Pythagoras to find the contradictions between our current musical system and basic physics. The information you are looking for is readily available in more scientific and academic circles than the steel guitar forum.

Temperament is a very good book to get started on to get a historical perspective.

You seem to state that the beats we hear are the frequencies diference the two notes are apart. I actually believe that the beats we hear is a secondary resonance (clash) between the two main frequencies not finding a comon point of resolution... or better various at different times during a certain time (a moving spot of crossing). Your formula using "clean" fractions instead of the usual root based logarhithm seems to confirm that by resolving the issue. Am I reading this right?

As an adolescent I used to build model air planes equiped with two stroke gas engines... theses things would bring revolution of 20000rpm. We used resonance escape systems of farious lenghts that could be fine tuned in oreder to get the highest possible engine output. The way one would fine tune these things was... you guessed it... tuning the beats out (of the engine sound)!This had nothing to do with my or whom ever's ears... it's a phisical phenomenom.
Our human urge to resolve, break down and explain every thing we discover or experience by the means of "perfect mathematics" may have led us to use a formula just too beautiful (logarhythms) to be true enough to satisfy that phenomenom.

CHANGING THE SUBJECT just a little:
Only one person mentioned tuning using harmonics (chimes). I tune a guitar or bass by ear just listening to the 5th intervals, just plucking both open strings and if I'm not sure I use chimes.
I have never used it on steel because I am way to eager to her my intervals "pure" (JT) and I want them pure with the bar on and in the middle of my main playing range (frets).
But I do remember that, Tom Brumly I think it was, posted a guide on how to tune an entire E9th pedal setup by the use of harmonics (chimes). Has anybody used this system and if so, what type of tuning did this produce (JT or ET)?

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               Bobby Lee
-b0b-   quasar@b0b.com