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Bill Bremmer wrote, "The Octave and 5th comparison with the Double Octave method leads directly to Triple Octaves by and at F6. It is the goal of most of the high level concert techs that I know of."

And Bill also wrote,

"From what I have always understood, the Steinway does have a higher Inharmonicity Profile than a Yamaha. It is my belief that the popular "Equal Temperament with Pure 5ths" style comes mostly from Steinway concert technicians who find out quite naturally that the instrument "wants" to be stretched more than a Baldwin, Yamaha, or Mason & Hamlin. I think what the big mistake may be is to think if that style of tuning is good under those circumstances, then it must be under all.

But Virgil is also no fool. He demonstrated to a group in Chicago once that he could tune ET from a beginning octave that was actually narrow. He also tuned all the octaves much "purer" than he usually does. It created quite a different, "mellower" sound. Some people, some circumstances may require this or any neutral compromise in between. Each choice you make has an effect and just like the intended positive effects of any medicine, there are negative side effects. Drawing a line down the absolute middle will always work, yes but the point is that there are other options."

From readings only, as I did not compare the scaling, Yamaha grand and steinway grand (Hamburg) have asimilar IH.
But, Steinway is providing more partials, that may suffice to allow for a more enlarged tuning, and it also may provide an impression of higher iH.
In the end the iH is just making the pitch less pure, the spectra more "shadowed" , that is not relaly how I would define Steiwnay tone.

What would say that the iH is higher is slower fast beating intervals, possibly Yamaha will be a hair faster but not by much.

Some high tensions scales have low iH and does not accept stretched octaves without sounding harsh . Boesendorfer, Fazioli come to mind.

My theory is not absolutely prooven, as pre WWII French pianos where mounted with soft (and very robust) strings, while they accept large temperament octave (named sometime here "Pleyel temperament" .
Of course we see them with old hardened strings, What I noticed on grand Pleyels when tuned with ETD is that there was a really very low IH in the treble octaves if compared with the mediums to the point some software can be lost.
Try to enlarge the treble octaves then and the tone is out of focus.

When they are tuned as they need they are very pure possibly the wire is really tense a lot and that lower the iH even more

Anyway, the thread has developed nicely and thanks for your input Isaac. My understanding and experience is limited, though fortunately, it is slowly on the increase. The things which i have asserted and spoken of in my thread i do practice, so I speak from experience, but I do not claim to have arrived or know it all.

I hope and trust that it may be plainly evident that i have made tried and trusted claims, though maybe different from others.

I continue to disagree but will chime in anyway . Stacked 4:2 octaves will ALWAYS produce wide double octaves. The smaller the piano, the wider the double octaves. And they SHOULD be slightly wide. On large grands, between 4:2 and 6:3 is appropriate in the midrange. On studio sized pianos, 4:2 is more appropriate to avoid double octaves that beat too much. And for spinets and most consoles, octaves between 2:1 and 4:2 are best. Interestingly these stretch schemes naturally happen with pure 12ths.

This should be apparent when considering the nature and effects of inharmonicity. When there is no iH, there is no difference between octave types. As iH increases, there is more and more difference. Of course the lower partials should be used when tuning smaller pianos. The lower partials are less affected by iH.

Thanks Mark, I recall that a little insecure feeling that most concert technicians have to some degree (they rely mostly on experience to be certain that their tuning is goos)

I suppose that at some point the tuners kjust stop to bother and they consider their work is "as it is" and that will be good.

the "secret " if an eventual secret exists, is to keep coherence between 5th hence twleves and doubles, and octaves, doubles, triples. This gives a sort of scale the tuner can refer to.

I now listen to tunings by geeting the feel for the level of consonance in the 5th and 6th octave zone.

I can find tunings that sound good in mediums and alittle "pinched" in the beginning of treble.
Others that are excellent and grip the ear nicely in all broken chords venues, but sound a bit harsh if they are to be played in close harmony (always in the same "pivot" place between 5 and 6 th octave.

I would agree for more variations in the way the basses are tuned, than for the most balanced way for the diskant/begin of the treble, I'd say those 5th and 6th octaves must rely closely to the harmony in the center of the piano, then the piano have a strong fundation of 4-5 octaves with maximum congruency.

The rest can probably be tuned in diffeent ways depending of the context, in my opinion.

Then if the tuning is enterely based on slightly tempered 12th balanced with 15th, that scheme can be kept all along because of that strong consonant spot it exite.

I dug around for a post by Don Mannino which I had read quiet some time ago and managed to find it. Don was responding to Bill Bremmers thread/post on ET via Marpurg.

I really do appreciate Don's writings and like this one too and thought it may be helpful to those who may be interested,

" Bill,

That is a nice sequence, and I agree that it is often helpful to start with some verifiable pure intervals, then use them as a point of departure to tune the necessarily non-pure intervals in the temperament. I'll try to play with this sequence a little and see how it works for me.

I use the contiguous 3rds to start my temperament, and the only issue that comes up when I teach others about it is that the width of the octaves is somewhat negotiable, and is a part of the tuning process that can confuse setting smooth contiguous 3rds at the start. If one decides in advance to tune precise 4:2 octaves and you verify them it works pretty easily, but I usually tune a little narrower than that, and occasionally a little wider. So this throws another fudge factor into the initial tuning process that might keep me from being able to claim a truly "perfect" equal temperament.

Tuners who try to simply tune a "clean" octave without using a test can then get very confused trying to make the contiguous 3rds work out. The A3-A4 octave might be 4:2, but the F3-F4 might be a little narrow and the contiguous 3rds get goofed up. And of course, small pianos with not so nice string scales kind of make one have to fudge every step of the way....

Finally, it is interesting to look at a different view of tuning like this, but 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 relevance to their daily lives to worry too much about this level of perfection.

I do agree it's nice to have a really well tuned temperament in a good piano that is also in great condition. Especially if the temperament is carried out well into the treble and bass with good octaves, and the unisons sing evenly."

Another excerpt from a post from Bill Bremmer,

"If you tune a 4:2 octave in the temperament and midrange, it will sound very "pure". This may sound ideal but in fact, the best tuners actually tune something a littel wider than that. But going all the way to a 6:3 is a bit too wide. Therefore, the ideal compromise is something in between."

Though Bill's and some other folks promoted optimal octave size, a 4:2+, may be favoured by many, one needs to realise for varying reasons, many professional tuners will tune their own different "optimal temperament octave" and continue from there.

Please also take note that a 4:2 just octave is clean sounding, I would state without hesitancy that it is cleaner sounding than the 4:2+ octave.

According to Rick Baldassin, the area between F3 and E5/F5 is an area that the just 4:2, 4:2+ and 4:2- octave may be tuned, so I suppose any of these octaves would be optimal. The just 4:1, 4:1+ and 4:1- double octaves area is between E3 and C8.

This is true, if you can't hear the beating 8:4 partial. This situation occurs the higher up you go, as the 8:4 becomes fainter and approaches the limit of our hearing. Also, older tuners may have some hearing loss and that can make the beating 8:4 hard to hear.

A narrow 4:2? Maybe in the treble. I would be interested in knowing under what circumstances a 4:2- octave is acceptable according to Rick Baldassin. Rick?

Mark, did you read what Don Mannino wrote a few posts earlier? I copied and pasted an old post he wrote.

Let me know your thoughts.

Mark, just thinking and thought you may be of some assistance,

1. Can one tune a just 4:2 octave as the temperament octave and then tune the double octaves pure from say A#4 to C8?

2. Can one tune a 4:2- octave as the temperament octave and then tune pure 12ths from A#4 to F7 and 2:1 octaves from there up to C8?

3. Are you able to tell me the test/check for the 3:1 triple octave please?

That is not my experience. Let's see if we can agree on some things and work from there.

First, let's define some things to make discussion simpler.
Let's define an octave that is tuned between a 4:2 and a 6:3 as a 4:2+, meaning slightly wider than a 4:2, but narrower than a 6:3.

Do you agree that a 4:2+ octave produces:

very wide 2:1
wide 4:2
narrow 6:3
very narrow 8:4

where the term "very" is used to indicate only slightly more wide or narrow than just the term wide or narrow.

Hi Mark,

Sorry I did not reply to your earlier post asking for clarification. I will now.



The first double octave available is F3F5, so A#4 to E5 can't be checked.
The test for the pure 4:1 double octave (at F3F5) is
Db3F3 = Db3F5. (M3=M17)

You can tune with pure 4:1 octaves but you will end up with very narrow 12ths and narrow triple octaves.




The temperament can be tuned using any temperament octave size. Then the octaves above can be tuned using any size as well. The question is "what will it sound like?". Pure 3:1 12ths will result in noisy double and triple octaves. 2:1 octaves in the treble sound fine by themselves, but don't produce clean double and triple octaves below.

Pure 12ths are only available to be checked starting with C5. (F3C5) The 4:2- octaves in the F3A4 temperament will sound wonky, with much noise in the treble. Their quality can not be maintained with pure 12ths; keeping 4:2- will produce extremely narrow 12ths.



m6 below = M17
Example: Tuning F6
F3Db4 = Db4F6

But the secret is fitting F6 into the P4 "window"

Play these one after another and listen for increasing beat speeds: (Note, the difference in these speeds is extremely small.)

M3<M10<M17<M6

Db4F4 < Db4F5 < Db4F6 < Db4Bb4

then check the triple octave.

Hope that helps.

Hi Mark,

I found the post you referred to. Here are my comments.



The technique of contiguous 3rds starts with two octaves, A3A4 and F3F4. If they are not the same size, getting smoothly increasing 3rds is impossible.




That really baffles me. I will need to look into this more. I cannot bare to tune 4:2- in the temperament. They are not clean what-so-ever. Please somebody respond. What is he talking about?



Still baffled. How does the F3F4 and A3A4 octave size affect the ability to tune the temperament and get evenly increasing M3s, which is by definition, ET? And what is "perfect equal temperament"?



Right on!

Thanks for the post.

Thanks Mark for your posts

I agree with a lot of what you say, but not everything.

I would like to bring to your attention your inconsistency with regard to you saying you tune whole tone as Virgil did, but then you constantly speak about certain partials ringing here and there and everywhere.

Though I agree that there is a system of tuning partials and that partials may and do ring, here and there and everywhere, what I am saying with regards to whole tone tuning is that it is possible to produce a top quality tuning by whole tone tuning alone, without any worrying about partials ringing.

Did not Virgil do it?

The other thing is this, which you are not grasping/accepting and that is this, which I have been saying throughout this thread and say it again and I do think that this was the key to a powerful technique of and for tuning, but nothing fancy, but which Virgil said and practiced,

"Tuning checks are essential for evaluating the accuracy of the tuning, both during the tuning and when it is completed. It is important to know that each note being tuned is correct, because of the other notes being tuned to it.

Much time can be wasted in retuning notes that were incorrectly tuned to notes not correctly tuned. An octave or interval may sound acceptable, but still not be in tune.

Playing an octave or chord is not a reliable tuning check; neither is playing a piece after the tuning is finished. A skilled tuner can eliminate that "out of tune" feeling (sound) and make the tuning sound acceptable in a few minutes, but the piano will not really be in tune.

The amount of expansion and contraction of each interval necessaery to achieve a quality equal tempered tuning (I would go so far as to say all tuning, whether E.T or H.T), can only be determined by use of tuning checks. Checks are used before the note is tuned to determine if the note is sharp or flat and by how much,during the tuning, and after it is tuned to check the accuracy of the tuning."

Thanks,

Yes, it does help and I agree.

Though I may not agree with you on certain things you have said, here I agree and accept.



Mark, please will you explain what you mean here.

Thank you.

Sure, we can agree that a wide 4:2 produces a wider 2:1 (measured in cents) and a narrow 6:3 produces a narrower 8:4 (again, measured in cents). Whether the term VERY wide or VERY narrow is appropriate is really up to interpretation. On a concert grand there is much less difference between octave types than on a spinet.

If we can agree that the difference in octave types is dependent on iH (the size of the piano) then we can continue our discussion to include the effect of the octave type and iH on the double octave.

Mark:

I see no problem with ET being possible with any width octave (or any width of any other interval for that matter) even if the octave changes width, as long as it changes progressively. However, I do see a problem of defining ET as progressive M3s. (You can take a clinical ET and raise F, A and C# 50 cents or more and still have progressive M3s.) A better RBI definition would be progressive M3s and M6s.

And I too, along with Mr. Mannino, tune narrow 4:2 octaves in the mid range. I don't know if we do it for the same reason, however. I do it on small pianos. It keeps the double octaves from beating too fast.