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Jeff,

I do not believe that I "originated", but rather "distilled" from numerous other methods I have been exposed to. First was John Travis' s up a 3rd up 3rd down a 5th. Used that for years, then Sanderson/ Coleman, then "both ways from the middle" (this probably being the catalyst for what I settled on. Though it is not foolproof (as you know), it is dead simple (I like simple), and easily diagnosed and correctable in usually short order.

The caveat is that it does not work so well on poorly scaled pianos (i.e many small ones and POJ). Since these PSO's actually CANNOT be tuned in ET anyway (no matter how hard you try) I usually tune EBVT on these and they sound far better for it.

WARNING: For any who are going to pounce on the above statement claiming that I am deviating from the accepted standard in the musical world and doing a dis-service to the client...save your steam. A fudged version of ET on these things amounts to a bad UT, so a good UT is a blessing for these pianos and clients since they sound better all the way around.

On a reasonably decent instrument this method works beautifully with very little mental effort expended. Takes a little practice but like I said, if you nail the F3-A3 3rd with the speed THAT piano wants (because it can tell you), then it is flawless.

Now as to the 5ths...I long ago decided not to "tune" with 5ths (in ET). I accept that 5ths will vary within the temperament and with the piano. I can't control everything so I choose to control the 3rds, 4ths, 6ths, and octaves and accept some variation in the 5ths. That said, if I hear a particularly noisy one I will go find out why...maybe I goofed, maybe something moved, but I can usually find the source quickly and fix it. On occasion, it can't be fixed without ruining too many other things so I let it live as it wants to.

Your thoughts?

Peter Grey Piano Doctor


Peter W. Grey, RPT
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My thoughts? At one time I really liked fifths, that is the ones made of glass and containing various spirits. wink

I have to agree that some 5ths cannot be tuned to sound good, only less bad, like those just above a break in short pianos. I believe it is because of the scaling and both the 3:3 and 6:4 partial matches can be heard. In those situation I choose to make the 5ths sound as least bad as practical and tune the other intervals to them.

But there is something else too. There are those times when I know the temperament should be able to be improved, but I just couldn't figure out how. So I look at the clock, sigh, and start expanding the temperament and patch up the mess left behind best as I can as I go along.

I am realizing now, for me, that it was due to not paying attention to the minor thirds. Everyone mentions the M3-M6 test, but within an octave temperament, there is only 4. That ain't enough information to know if both (or even either) of the SBIs are correct. But listening and really understanding the m3s can determine where problems lie.

Sure, M3s are easier to hear, but does that mean they better define ET than m3s? Nope!


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Originally Posted by UnrightTooner
For instance, given one of your M2s, assuming it is 200 cents wide, how much error will there be if a note is tuned as a 4th to one of the notes of the M2 and a 5th to the other, resulting in these two intervals having the same beatspeed?
about 1/2 cent

I tried testing this by cranking up the temperament simulator:

About 1/2 cent or a bit less is correct when the beatspeeds are equal when, for example, tuning E4 to the existing A3 and B3 or tuning D4 to the existing A4 and G4. Also importantly when making those adjustments to E4 or D4 it does not disrupt the progression of M3rds.

When actually tuning however I am not trying to make the beatspeeds exactly the same. For me there is always a little give and take with preference generally for slower 5ths. When expanding up from A4 I will tend to make the 5ths a little more pure and let the 4ths beat a little faster. The opposite when expanding down from A3 in most cases but there will normally be compromises when encountering wound strings and the break. In all cases, clean octaves are the priority and should over rule other compromises.


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Originally Posted by Chris Leslie
Originally Posted by UnrightTooner
For instance, given one of your M2s, assuming it is 200 cents wide, how much error will there be if a note is tuned as a 4th to one of the notes of the M2 and a 5th to the other, resulting in these two intervals having the same beatspeed?
about 1/2 cent

I tried testing this by cranking up the temperament simulator:

About 1/2 cent or a bit less is correct when the beatspeeds are equal when, for example, tuning E4 to the existing A3 and B3 or tuning D4 to the existing A4 and G4. Also importantly when making those adjustments to E4 or D4 it does not disrupt the progression of M3rds.

When actually tuning however I am not trying to make the beatspeeds exactly the same. For me there is always a little give and take with preference generally for slower 5ths. When expanding up from A4 I will tend to make the 5ths a little more pure and let the 4ths beat a little faster. The opposite when expanding down from A3 in most cases but there will normally be compromises when encountering wound strings and the break. In all cases, clean octaves are the priority and should over rule other compromises.

Did You misunderstand my meaning? Perhaps I misread what you wrote. The beatspeeds of a 4th and 5th should NOT be same when a common note forms them with an M2. If they are the same speed, there is about a 1/2 cent error. The same with contiguous 4ths and contiguous 5ths.

This leads to something I had to work out myself long ago. Why it is not in any tuning instruction kinda baffles me. A definition of aural ET is when ALL intervals are progressive, including 4ths and 5ths. But consider how little an error in tempering it would take to make two chromatic SBIs have the same beatrate! If F3-A#3 P4 is about 500.125 cents wide and F#3-B3 P4 is 500.000 cents wide, they will beat at the same speed. So to guarantee that these two intervals are progressive, each note could have no more of an error than something like 0.031 cents. (There is a shorthand number I use. 17/16 is in the ballpark of the 12th root of 2...)

Heck, you couldn't even hear the difference even if it was possible. The problem is if you actually attempt this, only the SBIs in the middle of the temperament will be correct. The ones towards the ends will be more and more in error. You can still make an octave temperament "work" by having everything progressive, but you can't keep it up when expanding it up and down the scale.

But for a practical purist, if there is such a thing, the beatrate of 5ths should slightly more than double each octave while the 4ths should slightly less than double each octave. So somewhere in the treble, the 4ths and 5ths should beat the same when having a common note. This makes sense when you consider that a large octave type, like 6:3, is appropriate in the bass, with 4:2 in the tenor, and 2:1 in the treble. Since the P4-P5 test indicates a 4:2 octave, you can see how this would happen.

Anyhoo, all this considering led me to what I do now, which you first mentioned, Chris. Tune the temperament within a 5th. For this to work, make all the 4ths beat as equally as possible. The M3s and m3s will tell you if for THAT 5th the 4ths are at the right speed.

SO THANKS AGAIN CHRIS!!!!


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Virgil Smith liked to give close attention to the m3rds also.

Peter Grey Piano Doctor


Peter W. Grey, RPT
New Hampshire Seacoast
www.seacoastpianodoctor.com
pianodoctor57@gmail.com
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