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Precisely! Truer words were never spoken. For many years, I thought (and still believe) that when tuning ET, one must check Slowly Beating Intervals (SBI) against Rapidly Beating Intervals (RBI). Otherwise, one may lead oneself astray by concentrating on one kind of interval alone.

The temperament from Owen Jorgensen's second publication, the Marpurg-Neidhardt Composite Quasi Equal Temperament is a perfect example of that. The Major thirds, when played, sound virtually identical to ET but the 4ths and 5ths are wildly unequal!

The Reverse Well problem that I have for long identified has the opposite problem. The 4ths & 5ths may all sound acceptable but the 3rds & 6ths sound uneven.

With the latest idea that I have been advocating, I set a chain of Contiguous Major thirds first and foremost as a framework. From there, one can tune the whole rest of the piano and get very even sounding RBI's without ever checking them!

The inherent problem in constructing a temperament by starting with a chain 4ths & 5ths and only being able to use any RBI checks after several notes have been literally guessed at as far as tempering is that some cumulative error will inevitably be the result. At that point, when RBI checks become available, it is impossible to know which previous errors have occurred, where they are and how much error is involved in each of them.

Now, it is probably true that some very fine technicians were able to cope with that problem and yield an acceptable and perhaps even a seemingly perfect ET that way, most technicians never really got it right by following a 4ths & 5ths sequence. They end up with uneven Major thirds precisely because of what John Travis identified in the middle of the last century as the "tendency to err towards the just (pure) fifth".

Well Temperaments have about half of the 5ths tuned either pure or nearly so and the rest tempered more than in ET. Reverse Well has exactly the same characteristic but in exactly the opposite manner.

John Travis advocated tuning a temperament from C# rather than C for that reason. He actually said in the tuning chapter of his first publication of A Guide to Restringing that starting from C# would yield a "more equal" temperament!

Considering that he wrote that (I have the book and can prove it) at about the same time that George Orwell wrote the novel, Animal Farm where the pigs declared, "All animals are equal but pigs are more equal", I find it ironic that Mr. Travis was actually trying to find a way to avoid Reverse Well!

While Mr. Travis clearly believed only in ET, he obviously saw that technicians quite often produced a disharmonious temperament if they started the sequence on A or C. If the sequence started on C# however, the first half of the temperament sequence could have pure or nearly pure 5ths. If the last half of the sequence ended up with "wolf" 5th, one could "back up" through the 4ths& 5ths and therefor even everything out.

Lo and behold, John Travis described a way to construct a Well Temperament rather than a true ET! When 10 years ago now, I looked at the whole idea of constructing a true ET, I latched onto John Travis' idea of "Up a third, up a third and down a 5th". This idea worked well to first set a chain of contiguous Major thirds. From there, one could take the "Up a third, up a third, down a 5th" idea and progress to the rest of the temperament.

The next note to be tuned would be F#3 from C#4. That interval could be tempered by estimate and the next note, A#3 again be tuned by estimate but then there would be two Major thirds to check for evenness. The more notes tuned, the more number of checks available would emerge.

I went with that for years until I discovered an even better approach.

One would think so . . . but actually not in my experience. When I tune 4ths/5ths, I check with the thirds and go and modify my 5ths until the 3rds are right. When I just make the thirds right, the 4ths/5ths are OK and I don't have to tweak nearly as much.

As I mentioned, I grew up tuning 4ths & 5ths. I was challenged by Let's Tune Up by John Travis to try the thirds approach. Having gone both ways, I find the 3rds approach better for me and there is some basis in objective physics for that to be true.

Now, I should be clear that there was a learning curve for me. If I had given up during that learning time, I might have concluded that it wasn't worthwhile. But it didn't take long. It's an approach that I commend to those who might like to try. If not, I know there are many good folk doing outstanding tunings using approaches that I don't.

Both are probably true, that is a priority question, the M3 can be progressive when focusing of 5th s (even if that logic is not usually learned).

I have heard enough overstretched temperaments with progressive FBI and too disparate 5ths to know that the 2 methods provide different results, harmony wise.

That is also that 5th s are really a foundation in harmony.

And it is challenging to listen to 5ths as if they where FBI...

The goals in my temp sequence (I learned from Alfredo that one, before then I tuned F3 F4 A4) is progressive M3 and M6 in A3 A4, so you imagine well I am using FBI too.
But all intervals must be in the range of acceptability, there is one for the fast beating and one for the slow beatings. The one for the slow beating is large so we think they are less precise.

I for years did not believe it was possible to tune an acceptable temp with progressive 3ds using only 5ths and 4ths, and it is somewhat in absence of checks, for sure, but you may be surprised if you do that right in a good octave, that you will be really near.

That is the pitfall some tuners fall in. Then they tune a temp that is perfect for modern music, but there is not enough consonance job done at the 5th level.
The day they discover they can tune UT in a cycle of 5th, it free their mind of that focusing, and their tuning change (hence the success of UT's)

Not to say an efficient tuner could not even tune "directly" M3, or 10th, whatever, when in doubt in the 5-6th octave I mostly have to listen to the 17 th to know if I can trust my ears or no.

I did not like so much the 5th and 4ths precedently. Find they slowed me, where not as sparkling as FBI's, etc... was a little considering 5th 4ths tuners as "old school"

Tuners may change with age and due to exchanges with other tuners

Both intervals have their characteristics and their use in music - I noticed that our best tuners in concert service where very attentive to 5ths (the M3 are very fast to evaluate).
I was not sure of the reason at that time, as I thought as you "tune the M3 and it is done".

This may be due to the iH and the voicing, but some compromising is done (again) between the progressiveness of the M3 and the good swell of the slow beating ones.

Differences in speed of slow beating intervals is not as much noticed so they do not cause real trouble, but then there is no reason the difference should not be parsed all along the scale is not it ?

It just play a little role in the global congruence, harmonically wise. those ET that lack musicality are probably due to that.

I just don't get it why anyone would confine themselves in this way. I sometimes tune in noisy environs and use every check note as it becomes available. Some notes, if the tuning is already close I will use, before they have been tuned as comparison aids from inside and outside the temperament range. All tuning intervals have the same usefulness to me.

I have a sense of tempo and rythm from time spent playing for major ballroom dancing competition orchestras. That helps but is not infallible.

I think that many potential fine tuners were ruined, both in temperament setting and developing excessive stretching habits by a steady diet of spinet pianos early in life. Large pianos are much easier and don't need all that stretch. (spinets don't either if they are reasonably voiced), but trying to lay a good temperament in the usual area is doomed to fail. I say to all tuners in that position, don't expect anywhere near perfection on a spinet but along with a steady diet of spinets comes many big old uprights. There's no excuse for a poor temperament on a big ol' uprite, nor for excessive stretching. If it sounds as though it should be stretched more, perhaps you have developed lazy listening habits. Do yourself a favour and tune them properly then you will always be ready for a better class of work. Never stretch more than half a beat in the whole of the treble and don't stretch at all in the bass. You never hear the drunken warbling 10ths and 17ths that we get fond of on good recordings. Theres a good reason for that. ....properly taught tuners.

Too many tuners are self taught or taught by self taught tuners who never really learned. It's all there in the oldest books but we need a properly taught mentor. As we are discovering, there ain't too many of them.

I challenge this statement. Any "inherent problem" of using a 4ths and 5ths sequence is you need to be able to recognize a properly tempered SBI. If you can't, then by all means use some other sequence. How rare this ability might be, I really don't know. It is worth developing if possible.

I am reading an awful lot about backtracking. I tune all unisons as I go for many reasons. One of the side effects is that it sure does discourage creating the need to backtrack. Backtracking is like a student who starts again every time they play a wrong note. It's an unnecessary habit. And it's only a beginners habit that can persist in spite of added experience.

Once the first 4 notes are right, everything else should follow, otherwise the result is a patched up effort.

Sometimes, for fun, I'll set the A, Bb, B & C on the scale electronically and do the rest by ear.

In a large piano, the beat rates become a rote procedure. On a smaller piano I used to use more minor thirds so that no M6 reflected outside the bearings would be too fast. If the M6th aren't too fast or slow the M3rds and 10ths won't be either. Make sure none of the 4ths & 5ths are too noisy and go. It was never worth any more of my time than that.

With large pianos there no need to re-invent the wheel every time. Too many spinets on the early learning stages might lead a tuner to believe so.

Ok, I am the one that used the word, "backtracking" first, I think. Allow me to clarify.

What I should have said, instead of backtracking, is one needs to refine.

Kent Swafford says it, so well, with regards to temperament tuning and the refining which is inevitable and necessary,

"The successful piano tuner will understand the difference between the first attempt at laying the bearings and the subsequent refinement of that initial temperament. The objective while tuning through a temperament sequence is not perfect results the first time through.

The tuning resulting from the first (or second or even third)
pass through the temperament sequence only needs to be good enough to allow the refinement procedures to proceed. The purpose of tuning through a temperament sequence is to provide a temperament that can be refined in the separate refinement procedures.

Get through the temperament sequence without belaboring it and move on to temperament refinement. The temperament refinement procedures are where one can achieve close to-perfection tunings. A temperament sequence is only the preparation for fine tuning; it is not fine tuning itself. Great tuning is accomplished during the refinement procedures, not during the temperament sequence."

Mark D.:

I am not so sure about the refinement idea, especially with poorly scaled pianos. What I look for is that ninth tone falling exactly where it should. If it doesn't, and I continue to the end without -backtracking-, when I then try to -refine- I come with some checks that say a note in question should be higher and other checks that say it should be lower.

I know that this is the essence of Mr. Swafford's "Every Which Way" method, but the result is an iffy-wishy temperment that when expanded results in iffy-wishy octaves, 12ths and double octaves. There is a place for it, though. It is great when doing a touch up to be able to quickly get a compromise from various checks to decide which string to tune the rest of a wavering unison to.

Jeff

I am not entirely sure where you are coming from and where you are going with regards to what you have written. Can you please explain.

What I am trying to get across, is that there is going to be some refining, and fudging when temperament tuning.

When I tune, I tune from A4 down to A3 and divide that up with the CM3's, A3/C#4, C#4/F4 and F4/A4. I will often run through the A4 to A3 sequence using the 4ths and 5ths and then correct things so that there is a smooth progression of 3rds.

I am reminded of what Don Mannino said, which is important for those of us who do not work on high end pianos all day every day to realise and accept,

"it is a little dangerous sometimes for people to get overly obsessed with perfection in tuning temperaments. No, I don't mean it's OK to be sloppy, but some tuners do spend an awful lot of time working out a beautiful temperament, only to spoil it with inconsistent octaves and unisons. I think that's what stops a lot of tuners from bothering with trying new temperaments - they are happy with getting something passable in some of the awful pianos they work with every day, and it just doesn't have relevence to their daily lives to worry too much about this level of perfection."

I use the whole tone way of tuning the temperament, using the intervals to tell me what is going on and to work things out. In general I work out an ET but not always.

Please do tell me more about the 9th tone.

Jeff, I got the ninth tone issue you are speaking about. I just did not click at the moment I was reading your last post. I thought you were possibly speaking about employing the 9th partial in some way or other.



Are you willing to explain in greater detail so as to enlighten me?

Thanks

It is interesting to note that the Steinway Voicing and Concert Prep manual still insists on an aural 4th/5ths A-A tuning.

I still tune 4ths/5ths F3-F4, and check with lots of 3rds/6ths along the way. In some ways, this topic confuses me....why does anyone try to insist that ONLY 3rds or ONLY 4ths/5ths is correct? Any competent tuner uses all intervals to tune and check their temperament, don't they?

The fact that I 'lay the bearings' with a 4ths/5ths does not mean I disregard the 3rds and 6ths. Refinement of the orignal settings means that you roll the contiguous and continuous intervals...and adjust accordingly. What's the issue?

Smiling,
No!
Really!
I am,

Thanks Jeff, I agree.

I learnt to tune aurally and and began tuning for clients in 2005. I then began using Tunelab in 2011. It was from the beginning of this year that I have returned to tuning aurally, but do use Tunelab for PR.

Mark D.:

Yeah, the ninth tone might be the place to talk about the whole thing.

I am going to use the classic sequence by Dr. White: C4, F3, G3, D4, A3, E4, B3, F#3, C#4, G#3, D#4, A#3, F4. Yes, it really does end with F4 with the final check being the F3-F4 octave. The ninth tone is C#4. Up to this point if every 4th and 5th was just a hair tempered too much, or tempered too little, it may not be noticeable. But if F4 happened to have been tuned, or if you use the m6 F3-C#4 as a substitute for the M3 C#4-F4, the incorrect tempering will become apparent compared to the m6 F#3-D4 and/or M3 C4-E4. The bps of the m6 F3-C#4 and/or M3 C#4-F4 should fall between the other two. Well, on a small piano it could be off. The test for a 8:4 octave happens to be the m6/M3test.

Another way to put the previous paragraph is that it takes 9 tones in the circle of fifths to construct a ladder of CM3s. If you have everything right, the ninth note proves it, and if you don't the ninth note proves that too!

Then the question is what to do about it? Often the problem is something slipped a little like E4, in which case the check is at fault, not the temperment. But let’s say everything is a little iffy-wishy because all along you planned on refining. So you back up a little, say to B,3 and try to make things better. You run the rest of the temperment start playing chromatic M3s and “refine” things. You know, it is not hard to get the chromatic M3s progressive within just one octave if you are willing to fudge on the rest of the intervals. And that is probably what will happen.

So now you have reasonably progressive M3s in one octave and you start to expand it. You tune F#4 and listen to the M6 A3-F#4. Hmmm, it really isn't beating quite the same speed as the M3 B3-D#4, but didn't somebody that writes posts with thousands of words say that the outside M6\inside M3 test is not to be trusted and they never use it? Ok, ok, as long as the M3s and M10s and M17s are progressive it is ET, right? And sure the resulting 4th and 5th might not sound quite the same as the others, but tuning 4ths and 5ths is "'old school" (Thank goodness!).

This is what I have experienced when “refining” instead of, well, tempering correctly. I better stop before rounding up would put me at 1,000 words.

Thanks Jeff, your posts here have been illuminating.

ANothyer illuminated, ! please take care, not auto ignition on you !!

I'd add to Jeff comment that you also can secure the first octave with those 4ths and 5ths, then you have very soon fast beating intervals (a M6 A3 F#4 in my case) to tell you where you are going -

Thanks for your post and concern Isaac

Please explain further.

+11

Hello, Joking is my concern, on a Saturday !

If you secure the initial octave with 2 4th and 2 5th it helps to have sooner fast beating intervals and it is also a strong setup, even if based on slow intervals.


But one may stop focussing on octave types and simply tune "good" octaves, with the tuning done using more 4th an 5th , it is soon easy to tune direct octaves with the same level of precision than iof yopu where making a comparative test at each of them.

A sort of side effect but that makes a difference.

Rartely I need to compare 10th and M3, if I do so they are right usually.

Impossible!

In the domain of pure and applied mathematics, Number Theory shows that the Euclidean algorithm in quadratic reciprocity in its distribution of primes(variable integers)with or without the diophantine equations found in modular arithmetic(before the 19th Century), proves that nothing higher than +10 is allowed - this is called Finite Fields.

Of course, there will always be the naysayers, mostly Europeans and Asians, the so called "Young Turks", with their new ideas.
What's next?!? +12??? +13???