Although I have tried many ET sequences I still prefer the William Braid White sequence, but I keep trying variations of it. I want to mention one in particular, and hopefully others will have some to share.

I am going to assume those that are reading this are familiar with the sequence.

After tuning C4 and F3 then tune F4 and A#3. This helps to determine the best octave width by having the F3-C4 fifth, C4-F4 fourth, F3-A#3 fourth and A#3-F4 fifth. The beat speeds of these intervals and of the octave can be adjusted before any more notes are tuned. Even though this adds an extra note (A#3) in the “wrong” direction, it also allows a variation of the M3 inside M6 outside check higher in the scale and hopefully without straddling wound and unwound strings. When tuning E4, by progressing through the sequence, the beat rate of G3-A#3 can be compared to C4-E4. Just like the M3 inside M6 outside test, these intervals will theoretically beat the same speed. In practice I always notice that the M3 in each of these checks must beat slower than the other interval. It is interesting that William Braid White mentions that when tuning F#3 that the interval F#3-A3 should beat the same rate as C4-E4, even though his table of beat rates say otherwise! I have found that they really should beat at the same rate also.

So, anybody else have variations on the BW sequence to share?

Hey Jeff,

I have always found a variance with any of the math equations on pianos. In my experience, I am always adjusting the “feel and blending” of the temperament on every piano. Oh sure the 6ft. and longer ones take the math better, but no two are the same. I have even tuned two pianos of the same make and the temperament is not the very same on both. Just a subtle difference……

Sometimes with the Braid-White sequence I will set the F3 -F 4octave, and then set the Bb with both, one side is a fifth and the other a fourth. The Bb should beat equal on both sides, the bottom F should be sharp of Bb and the top F should be sharp of the Bb. BUT the F-F octave should remain a pure octave at the same time. This gives you a mental foundation to work in the middle of the circle of fifths. My father used to say “now you lose the beats in the middle.” What he meant by this was you blend out the scale to see if it comes out to the foundation you laid on the perimeter. Make sense sort of?

Had a tough one the other day, a late model Baldwin upright 6000…… unusual string pattern…had to do it this way. Yes, the beat rates in the old table there could be interpreted as a guideline maybe…

The joy of math is that 2 + 3 =5 but so does 3+2=5. Braid-White math can be added in either direction with the same result.

For concert tunings I would most likely change to the traditional way of math for that one. I have never tried your proposal though. It is fun to try and trick the math though, to see if you can make it fail in some way…good exercise for the brain…….

Dan:

Nice to see that black key below C called a Bb. That is how I think of it, and have to force myself to write A#. Yes, when the Bb beats at the same rate with both F’s, it is a pure 4:2 octave. Oddly, the Bb does not need to be tuned accurately for this test. I’ve been “pushing the envelope” lately and making the fifth beat a little slower than the fourth so that there is just a little life in the octave. And then by also listening to the fourth and fifth with the C and F’s, I know if I have gone too far and if the F's are in the right palce for that amount of stretch. A little stretch in each octave seems to make the ends of the piano agree with each other more.

I agree that the math, especially the theoretical non-inharmonicity math, is just a guideline, but a practical guideline. I can’t help but look at the tuning puzzle much like a navigational exercise. We know the earth is round, but we act as if it is flat. But it isn’t quite round, it is a bit like a potato which usually doesn’t matter, but sometimes it does. And then depending on how the earth’s features are projected on a flat sheet of paper, the projection is more useful for some things than for others.

Likewise with the various tuning schemes and checks and tests. iH is always “The Man Behind the Curtain”, but usually when tuning aurally it doesn’t matter, but sometimes it does. And there are so many different tests and checks. Some are more useful for the treble, others for the bass.

I think iH does come into play with the variation of the M3-M6 check I mentioned. I’ll call the variation an m3-M3 check. If the lowest note of the m3-M3 check is raised an octave, it becomes the M3-M6 check. But if the octave is smaller than 6:3 (as is usual), then the m3 beats faster than the M6 would and of course faster than the M3 does. I particularly like this for the G-Bb, C-E check to make sure that the E is not too sharp.

My temperament sequence originally started as a Braid White many years ago and it modified over the years. I had found that it ended up more closely resembling K Swafford's "Every-Which-Way" temperament, which to this day works the best for me when I aurally set a temperament. Although it was probably posted on the forum before, here is a link to it...

http://tiny.cc/L37YB

To practice my SBI's I used to tune up two octaves just using a cycle of fifths and fourths and see how close I could get to the double octave. Then I would check the RBI's and other interval checks to see what went wrong. My mentor could get it so close on one pass many of us thought it was some kind of voodoo tuning. This is all old school stuff with the newer sequences working almost the other way around and just giving aproximations and larger deviations for the SBI's in favour of getting the CM3rds and RBI progressions spaced more evenly early on.

The computer I use on weekends doesn’t play well with the new PianoWorld site…

Emmery:

Mr. Swafford seems to be a very straight shooter. I have read and learned from his sequence before.

Wow, two octaves of fourths and fifth, then check the double octave! Hitting it dead on would be voodoo.

Yes, newer sequences start with RBIs, and the first set of CM3s is considered to be written in stone, rather than an approximation. I just recently realized that the progression of piano pitches cannot be the twelfth (or nineteenth) root of anything because of changing iH. This means that the 4:5 beat ratio (which is based on the twelfth root of 2 to the power of 4) or any other beat ratio is not written in stone. It may not matter on some pianos, but on one with a “hockey stick bridge” or a very challenging break I think it matters a great deal.