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Martin:

Congratulations on reaching your goal of setting a temperament with 4ths and 5ths! Getting SBIs to be progressive is an accomplishment beyond simply tuning the temperament with SBIs. You must be doing better with your hammer technique.

You may not understand just what I mean by “about ½ bps” for the 5ths. I would say that all your fifths beat about ½ bps. And while we are on the subject, you mentioned that you did not get much stretch. If the temperament octave was 4:2 that really is satisfactory. If it was not, well, try making the 5ths beat a hair slower, like closer to ½ bps If the SBIs are tuned to theoretical beatrates, the octave will be narrow due to iH. The 4ths will be OK, but the fifths will be a bit too narrow.

You may think that going from 2/3 bps to ½ bps (about ½ cent) would cause a total stretch of 6 cents in an octave when going around the circle of fifths, but it does not anymore than a pure fifths tuning results in an octave that is 24 cents wide. ½ cent in a fifth is divided by 7 semitones which results in less than 1 cent for an entire octave.

Since listening to the beatrate ratios is working for you, consider trying slightly different beatrate ratios. Instead of the 3:2 and 4:3 ratios when comparing the 4ths and 5ths, try 2:1 and 3:2. This will probably only be necessary until you learn to hear the tempering of the SBIs directly instead of counting beats.

Kees:

I agree that theoretical beatrates are very useable on well scaled pianos. The combined effects of iH are largely self-correcting. And the idea that the octave size makes much of a difference just doesn’t cut the mustard in my book. If you are changing the octave width enough to make a difference, then you are beyond the point of octave sounding even close to pure. An M3 would have to be changed about 1 cent before it beat the same as the next chromatic M3. Over the course of a set of CM3s, this would be about 3 cents in an octave, almost enough for a pure fifth tuning!

But when the scaling is not good, well I won’t repeat my litany again right now.

” You say that when a break in scaling occurs, the thirds will cause the fifths to be mushed around to fit.”

Yes, if you use RBIs to set the temperament. That is why I use SBIs.

You really should use the Forum’s quote feature so what is said is kept in context.

I herded Alaskan Brown Bear with a NOAA Hydrographic Survey Launch:

According to my calculation on a poorly scaled piano the difference in F3A3 beatrate between 4:2 and 6:3 octaves is something like 0.1 bps. On a well scaled piano much less.


Again according to my calculations on a small piano the beatrate of F3A3, when based on a 4:2/6:3 compromise octave gets as low as 6.7 bps. That is only 0.2 bps less than the ideal number (6.9) and corresponds to an error of 0.4 cent. Surely on crummy pianos you can live with that. On well scaled concert grands the error is less than 0.1 cents if you go for 6.9 bps with a metronome.

Of course I could have made an error in my calculations. It would be nice to know what is the bps of F3A3 on spinets in your practical experience, if you know?

Kees

too bad there's no "like" button on here, I like the boat c/o Jeff.

Personally I just balance it out, hear it, go with it, ... every piano is different and to get the most pleasing and aesthetically perfect sound from it requires personal presence and attention.
SM

Maybe slightly off topic, but I though brown bears were land animals.

Kees

I have seen them swimming across Shelikof Straight, like 30 miles.

One of the biggest jumps in scaling I have come across was the Wurlitzer Petite Grand. I have to make F3-A3 and A3-C#4 beat at the same speed for the SBIs to sound best. On a Kimball Spinet (not a Whitney, different scaling...) F3-A3 beats the same as G3-B3. But I often wonder just what I am hearing in the 5ths. There is often much trash. And there would be a big difference between the 3:2 and 6:4 partial matches. It could very well be that I am tuning for the least obnoxious sound. I may not actually be tuning "about 1/2 bps" for the fifths.

Here is a scaling graph of a Wurlitzer Petite Grand. It isn't the same scaling as the one I encountered. That one had bichords up to G3 or so. But notice what happens around the break:

Jeff:

Yes if the break occurs in the temperament octave all bets are off. If not, I claim F3A3 stays pretty darn close to 6.9 on any instrument.

Why would you not move the temperament octave up to be above the break on that Wurlitzer Petite Grand?

Naively I would assume that the highest M3 that crosses the break will beat slower than you would expect compared to its upper neighbor, as the lowest note of this M3 will have a higher IH constant than expected, so the 5th partial will be closer to the 4th partial of the upper note. Does this conform to reality?

Kees

I agree, but there are always exceptions.



Then the RBIs beat too fast for me to be sure that they are progressive. As a compromise, I have modified Dr. White’s sequence so that the first RBI is A#3-G4, about 10.5bps. Then when E4 is tuned, I have an inside/outside check (A#3-G4, C4-E4) to make sure things are on track before there is an RBI progression that transits a break, such as F3-A3, G3-B3.



Ugh! In my haste this morning (more bears to brand…) I chose a poor example for a challenging scale. It is definitely different than the Wurly I tuned. This one shows a more typical example where the M3s straddling a break causes them to beat faster than those above the break. Tuning the SBIs and then listening to the resulting RBIs will tell the story.

Steinway S: