Tempered tuning chart

Brad Sarno · Post by **Brad Sarno** » 4 Jan 2004 6:18 pm

Check out Mark Deutsch's webpage on the equal tempered tuning chart.
http://www.bazantar.com/grid.html

It's incredibly useful for understanding the relationship between equal tempered notes vs. the naturally occuring harmonically resonant notes that many steelers tune to. The real useful column is the one on the far right that shows in cents the differences between the equal tempered (what an electronic tuner calls zero or straight up) and the "real" notes. The left column shows the ratio from which our naturally occuring intervals are derived. This chart shows 66 divisions of the octave. Notice the major 3rds that fall almost 14 cents flat of "straight-up". That's most people's favorite major third although there are 2 other valid ones not counting the ugly sounding one that our tuner calls "in tune". This is pretty much a western mathematical breakdown of what the Indians learn by feel. It's the best demonstration I've seen of how out-of-tune much western music is, and by showing the fundamental ratios that derive these natural intervals you can see exactly how compromised and un-natural many of our commonly used notes are.

Also check out Mark's instrument, the Bazantar. It's a real in-tune monster.

Brad Sarno
http://www.bazantar.com/grid.html

Jim Cohen · Post by **Jim Cohen** » 4 Jan 2004 6:59 pm

This is pretty much a western mathematical breakdown of what the Indians learn by feel.

It's amazing that they can stand to listen to any western music. Everything we play must sound terribly out of tune to them!

Brad, could you walk me thru that chart a little bit? I'm having trouble finding the 14 cents flat third, for example. It looks like the chart is writte for key of D, so I'm looking at F# and not seeing any -14 there. What am I doing wrong here? Thanks.

Rick Aiello · Post by **Rick Aiello** » 4 Jan 2004 7:31 pm

Here's another with 700+ ratios ...Anatomy of an Octave.

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www.horseshoemagnets.com [This message was edited by Rick Aiello on 04 January 2004 at 07:42 PM.]

chas smith · Post by **chas smith** » 4 Jan 2004 7:36 pm

Jim, the major third is going to be the 5/4. The chart is dividing the octave into 66 parts, unlike the traditional 12, so the (traditional) just scale would be, 1/1, 16/15, 9/8 (and 10/9, sometimes there are two major seconds because the 9/8 is in tune with the 3/2 but not the 5/3), 6/5, 5/4, 4/3, 3/2, 45/32, 8/5, 5/3, 16/9, 15/8, 2/1.

So the Just 3rd is 5/4 and the tempered 3rd is the 12th root of 2 to the 4th power .[This message was edited by chas smith on 04 January 2004 at 07:44 PM.]

Jim Cohen · Post by **Jim Cohen** » 4 Jan 2004 7:38 pm

Oh, sure, I knew that. Of course I knew that. Why wouldn't I know that?

Jim Cohen · Post by **Jim Cohen** » 4 Jan 2004 7:40 pm

p.s. just one more question: does this tell me how to tune my steel, or is that just a mundane question that shouldn't be asked?

Bobby Lee · Post by **Bobby Lee** » 4 Jan 2004 7:41 pm

Here's a chart that shows the ratios that most steel guitarists prefer.
<center>

</center>

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<img align=right src="http://b0b.com/Hotb0b.gif" width="96 height="96">Bobby Lee - email: quasar@b0b.com - gigs - CDs, Open Hearts
Sierra Session 12 (E9), Williams 400X (Emaj9, D6), Sierra Olympic 12 (C6add9),
Sierra Laptop 8 (E6add9), Fender Stringmaster (E13, A6),
Roland Handsonic, Line 6 Variax

jolynyk · Post by **jolynyk** » 4 Jan 2004 8:14 pm

OUCh, YIKES, my head hurts...

Brad Sarno · Post by **Brad Sarno** » 4 Jan 2004 9:27 pm

Jim, it's actually -13.69 cents, not -14. Just rounding it off. It's the one based on the ratio of 5/4.

Brad

John Bechtel · Post by **John Bechtel** » 4 Jan 2004 11:56 pm

It may be of no value, in this particular instance, but; if you want to get dizzy, did you know that sharps and flats are not the same pitch? Examples: C# is higher in pitch than Db, D# is higher in pitch than Eb, etc, etc. . . . For some reason, it causes the Key of Eb to be the purest or most pleasing to the human ear! Don't ask me to explain. It would take me too long, not being a man of many words! I think the explaination was started above with the reference to the division of musical tones, as we recognize them!

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“Big John” Bechtel
http://community.webtv.net/KeoniNui/BigJohnBechtels

Brett Cookingham · Post by **Brett Cookingham** » 5 Jan 2004 12:22 am

You guys are nuts!

David L. Donald · Post by **David L. Donald** » 5 Jan 2004 3:04 am

No Brett they are deep.
I can be understood, but takes time like most thoery.

RON PRESTON · Post by **RON PRESTON** » 5 Jan 2004 4:32 am

I DO enjoy studying the "Arts", and all the theory that goes with it, and I understand a lot of what you are talking about, BUT, I still think the BEST tuner that I use..(And it WORKS) is My EAR......Sometimes I wish that I could NOT hear "Overtones" as well as I do. ASK JACK STRAYHORN, or Ron Lashley Jr.
TRUE Story here...When I was on my FIRST day working at Emmons, Jack was "Tweeking" a Steel to be shiped. He was picking the 4th string E and the 5 string B, and was trying to "Get it right". Joann Acoth was showing me around the Factory when we walked towards Jack, and I said.."Your 4th string E is Sharp about 3 "Cents", and he looked at me "Funny", pulled the tuner out, checked it, and Jack "Hasn't liked me since". He ask me.."How did you KNOW that?" I told him I could hear it. Sometime TOO GOOD, and it will Drive you crazy if you let it. Jim Aycoth can tell you too about the "Ear" thing that he has seen and heard when I was "Tweeking" the Steels after Jack Left. I almost got fired one day when I was tuning one and Jim walked by and said.."Ya Gonna TAKE ALL DAY TUNING THAT THING"? (Oh, God, I'm gonna get SUED here) He was SOMETHING ELSE to work for, He was fair, BUT, he wanted things......well, that's another thread. I wanted it RIGHT, even if it might get just a "Smidget" out due to shipping, which didn't happen often. My problem in life is that I'm the type of Guy that is a "Perfectionist"...No matter WHAT I do in Life. I "Throw a Weenie" if the band is "Slacking", because people look at "The Band", NOT the single player who is "Screwing it up.......OK, OK...

Bengt Erlandsen · Post by **Bengt Erlandsen** » 5 Jan 2004 5:12 am

I can agree w the best tuner is the ear. But it can cause some frustration also. I really like the sound of the C# in the open A chord when the C# is tuned -14cents flat but frustration occurs when using that note for something else than a 3rd. Because to my ears the B - C# does not at all sound like a whole tone step to my ears no matter what fret I am playing at. If you have never played a regular guitar or a piano you might not hear that interval the same way so it wont be a problem for you but somebody else might say that things are way out of tune.

Bengt Erlandsen

RON PRESTON · Post by **RON PRESTON** » 5 Jan 2004 6:12 am

True, My Friend,
But, Don't forget, a guitar is tuned 440 on all six strings...No temper tuning there. A pianio is "Temper" tuned. I have read that in the 1700's, Bach, Brahms, Beethoven, or SOMEONE in that era had "Heard", or, from my readings, The Mestro could "See" the "Color Vibrations" of each note. (and HEAR it in his head) Wow..Everything "Vibrates" to it's OWN Mz, Everything! The universe would be "Out of Kilter" if there were no harmony, if you will. The spectrum of a Rainbow has NO defining "Lines" between each color. Same with Tones, or Notes that "Vibrate" on the same Frequency. They "Blend" in PERFECT Harmony...FWIW, I have ALWAYS belived that the City of Jerico in Bible Days Fell due to the "Perfect" Blend of Powerful horn Notes all at once for a sertain period of time. You can ROCK, if you have, (Which I don't) that perfect Harmony of the Universe. VERY FEW had that ability since time began. :0

Brad Sarno · Post by **Brad Sarno** » 5 Jan 2004 6:38 am

David Doggett · Post by **David Doggett** » 5 Jan 2004 8:06 am

Even in Western music, remember it is only keyboards and fretted stringed instruments that really adhere strictly to "straight up." Fretless strings, horns and even vocals are playing or singing to their ears, and unless a keyboard is really dominant in the mix, they wiil be playing and singing to JI. Even with fretted guitars, I rarely see a guitarist that tunes straight up and leaves it there. They are constantly playing the chord for the next song, and tweaking if it doesn't sound right (meaning JI usually).

Now I have just become aware that some fretted bass players use tuners designed for bass that incorporate the compression of ET that is done by piano tuners to the lower octaves of a keyboard (On another post Paul Franklin said he tunes his E strings to 442 to match the stretching that piano tuners do to the upper octaves of a keyboard). It seems like everybody's ears cue on the bass line when playing in a group, and when laying down separate tracks in a studio. So if it's a fretted bass, it seems more likely we are all trying to match that moreso than the piano. So I think in real life, fretless strings (including steel guitar), horns and vocals are reaching some compromise between the JI their ears want and the ET of the bass and/or piano. Maybe that's why Indians can stand to listen to it. Or maybe they can't - some of it I can't stand to listen too either, but that ain't only due to intonation.

David Deratany · Post by **David Deratany** » 5 Jan 2004 8:28 am

My head is reeling from all this!

Thankfully, I am getting better at recognizing the absence of beats and am working to get my new E9/B6 offsets nailed down and programmed into a VS-II. If I can do that, I think I will try to avoid exposure to further dialog on this subject, unless I feel the need for a non-surgical lobotomy.

Bud Harger · Post by **Bud Harger** » 5 Jan 2004 8:58 am

Please forgive me, all of you super pickers that use this technical stuff...but, it makes me dizzy!

Try this one time as a test of simplicity on the E9th tuning, top to bottom:

SEE FOLLOWING POST FOR PROPER SPACING!
<pre>
Open P1 P2 P3 Eb F
442
439
439 441
442 439 440 436
442 439 439
439 441
442
442 440 436
442
442 439
</pre>
That's not all the changes, but you get the idea.

This is not original. I got this from a no-nonsense picker off the Forum...like him, I'm not so sure that the human ear can hear those minute diferences like .5 cents. This works great for me.

Goofy, right?

bUd

[This message was edited by Bud Harger on 05 January 2004 at 08:59 AM.][This message was edited by Bud Harger on 05 January 2004 at 09:13 AM.][This message was edited by b0b on 05 January 2004 at 09:42 AM.][This message was edited by Bud Harger on 05 January 2004 at 10:23 AM.]

Bud Harger · Post by **Bud Harger** » 5 Jan 2004 9:09 am

My spacing didn't work out and I don't know how to fix it.

Anyway the changes are:
P1 changes are @ 439
P2 changes are @ 441
P3 changes are @ 439
Eb changes are @ 440
F changes are @ 436

Sorry for the confusing post.

bUd

Bobby Lee · Post by **Bobby Lee** » 5 Jan 2004 9:45 am

I agree that the ear is the best tuning device. These charts and numbers simply validate what our ears tell us. No, we're not crazy. Our instruments do sound more in tune when they're not tuned to the center of the tuning meter. These charts and numbers explain why.

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<img align=right src="http://b0b.com/Hotb0b.gif" width="96 height="96">Bobby Lee - email: quasar@b0b.com - gigs - CDs, Open Hearts
Sierra Session 12 (E9), Williams 400X (Emaj9, D6), Sierra Olympic 12 (C6add9),
Sierra Laptop 8 (E6add9), Fender Stringmaster (E13, A6),
Roland Handsonic, Line 6 Variax