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Thanks GPM...

I tuned my own piano today in EBVT III. I couldn't figure out for the life of me how to post it here so, I opened up a YouTube account and posted it there instead... I am not a piano player so critics regarding that, are not allowed... In the last part of my playing, if you call it that, you can hear that pipe organ effect that Bill talks about.

http://www.youtube.com/watch?v=lqsvVocZtD8&feature=youtu.be

Piano sounds great, Jer! Here's the embed:

http://www.youtube.com/watch?v=FnP1LARipgI&feature=youtu.be

Here's another one. I don't know the name of the song. I remember hearing Elvis Presley singing it. If anyone knows it, let me know.

Thanks Loren! How you do dat???

This one was recorded on my wife's cell phone. iPhone 4 (?) quality sucks....

Jer! It sounds great! I will comment on your playing. (Sorry. That's Piano World for ya!) Very expressive and lovely noodling! Thanks for posting!

--Andy

Thank you so much, GP! What a great way to start the day! I shall now merrily bounce off to work with this spritely tune in my heart! God, I love that one!

Thanks Andy! It certainly has a particuar sound, EBVT doesn't it?

Giving my bud Jerry a hand. Here's his cell phone video embedded.

Hey Jerry,

Sounds great......!! Ebvt 3 def has made my piano sound like a larger one, along with its tonal coloring, it all makes for a very enjoyable experience.

Thanks GPM!

I think one of the things that I like about it, is the versatility that it has. We can stretch things more than normal, or less than normal to create a varying differences in "color" or tone or sound or whatever we want to call it.

I do have a hard time with hearing the out of tune octaves and 3rds, things like that but, it definately, gives a whole other sound than ET does. Good or bad, it is a matter of preference from anyone of us.

On 5/11/2010 you wrote: (page 65 of this thread)



heh. You had NO idea. What a wealth of information here, by the way.

and yes, back during those blind tests I guessed 50/50. I think I like the sound of well tuned, fine instruments. :-)

Forrest

And Jerry, you're a better player than you give yourself credit for!

Andy, I did a pitch raise on a Lester spinet yesterday. Made me think of you. The belly of this piano was still solid, and it really had alot of sound. It amazes me how loud some spinets are.

GP's piano to Bill's measured tuning..it definitely had alot of stretch. When I've been tuning it aurally, it has been tighter. So, it was different than what I'm use to. I'll have to try this. I've done stretch tunings, but it's usually been when doing more of a pure 5th's tuning.

I have been tuning EBVT occasionally the past couple of years, but have been trying to stay out of the "temperament wars" here. I have had it on my home piano at times, and kind of like it. Usually if I tune it, I do so aurally. I've kind of been running my own quiet experiment. The thing is, people don't seem to notice one way or the other unless you tell them. EBVT is a mild well temperament. Most people just aren't that attuned to the difference. I can well believe that some of you tune it all the time. The pianos would sound nice.

I did have one guy, who owns a recording studio, really notice. I tune this piano regularly. One time I decided to put EBVT on it. When I was playing at the end, he came in and said: "What did you do? Did you voice it? It sounds fantastic!" All I had done was tune. He's had me use EBVT ever since.

One reaction was the opposite of what I expected. As technicians, we think of the slower M3's as being less noisy. Well, for one person, it made the M3's stand out. The beats on c4-e4 went from fast to slow. Inaudible to audible. Some people hear fast beating as clean or pure. When you slow them down, the beats become more obvious. It is especially noticable on 10ths I think. Just something to think about.

So, I've had a couple people notice. But that's been about it.

With ETD's we have all sorts of different temperaments available. For me, the value of EBVT is that it has made aural tuning of uneven temperaments accessible. I really hadn't tried before. Personally, I'm really not interested in tuning EBVT with the machine. It's fun to figure out aurally. If I'm going to use the an ETD, I just do ET.

Ha-ha-ha! Thanks for saying so, Roy! Nice to be thought of! Wooden elbows, I hope?

So, in the "Three Coins in the [*ahem*] Birdbath" post, I mentioned the French Suite that I was working on. I recorded all movements "session style," not "performance style," (in other words, a bunch of takes, one movement at a time) and I've been so busy with day job work (and so dinked by the time I get home), that I haven't even listened to all the tracks to see if I got anything usable out of all of the movements!

But I did get the Allemande done this week. So, for your listening pleasure (I hope) is the first movement of Bach's French Suite No. 1 in D min., the Allemande:

https://www.box.com/s/17644897477f5924cc8f

from Johann Sebastian Bach's Little Note Book for Anna Magdalena Bach: Complete, pref. by Arnold Schering, trans. by Kurt Oppens, (New York: Kalmus, 1949). 1940 Lester spinet in EBVT III, two Sony ECM 220s through a Yamaha Audiogram USB interface, into CuBase AI4, with DC8 noise reduction and Switch file conversion.

My intention is to string the movements together into one track, because I have an over-arching interpretive concept for the Suite. And that, my friends, is called "a teaser." I'm going to see what I got out of the Courante, now...

--Andy

Thanks Roy, for your very objective opinions. While I can see that a very few people may be so used to the evenness of ET, those professional artists that have the privilege of playing on freshly and expertly tuned pianos quite often, in all the years (20 now) of tuning the EBVT, I have never encountered a pianist that found the key colors provided by a Well Temperament to be disturbing.

Pianists simply don't have the focus on beat rates that piano technicians have, if they do, it is a rare person. Even among piano technicians, my 21 year experience as a tuning examiner has told me that it is actually a rare individual who knows all the ins and outs of all of the checks. Otherwise, every technician who presented him or herself at a tuning exam would get Temperament and Midrange scores on those exams of at least 90.

If that were actually happening, the bar would be raised and it has not been for many years. It still remains true that about 50% of those who present themselves for the first time at one of those exams miss the mark and have to try again.

That means, at least to me, that the perfection ET that so many people strive for and have written at length about in this forum is still actually an elusive goal for many. An ETD can actually do it better than most aural tuners can.

I say all of this to preface what I ran into again today, the last of 21 piano tunings I did this week. While having encountered Reverse Well at least three or four times elsewhere, the very last piano I tuned this week was a used but rebuilt-action Steinway Model S Grand, sold and delivered here from out of state. The 1930's model Steinway was the epitome of the value of the Steinway as an investment. Original strings and dampers and a flawless soundboard! Only the action had been rebuilt with all new parts and that work had been superbly done.

The seller is a dealer whom I have known for over 25 years and has occasionally posted on here. He is the world's nicest guy. He plays the piano very well and is a superb piano technician who personally services all of the new and used pianos that he sells. He always has been, as long as I have known him, a person totally dedicated to music and the piano industry. He is successful in his business because of that.

The piano had been delivered a few months ago but the seller figured it was about time for the promised tuning that would go along with the sale. The seller has experimented with the EBVT and has been quite intrigued by it. He said that he did not expect the piano to be very much out of tune but that he had tuned it in ET.

Before going to the client, I promised that I would, in this case, discuss and get permission to tune the EBVT III before proceeding. I put in my muting strips and played the M3's within the F3-F4 octave and you guessed it, what I found was not ET at all but Reverse Well!

Now, it was not a seriously bad case of Reverse Well but nevertheless, it was just that. The F3-A3 M3 was a bit fast, so was the G3-B3 M3 but that F#3-A#3 was slower than the two intervals on either side of it. Nothing drastic but still, that is what it was. The G#3-C4 M3 was too slow to be considered correct and sure enough, the C4-E4 M3 was the very fastest interval of the entire progression, surrounded by a relatively sweet sounding B3-D#4 and C#4-F4 M3. The A#3-D4 M3 was also too fast.

These were all the classic symptoms of Reverse Well. If the technician had really known how to use the Contiguous Major Thirds (CM3) checks, these errors would have not been made. I heard after checking the M3's, very pure sounding intervals among the white keys but some obvious "fudging" among the black keys. That is exactly the reverse of how to tune a Well Temperament.

In discussions with this technician, I learned that he had no concept at all of what a Well Temperament should sound like. He had not been trained that way, so he said. He had known only of ET.

So, as far as he was concerned, this piano had been tuned in ET and had been done so for fear of doing anything out of the ordinary. ET is the "safe" way to tune, as he and almost any other technician must believe. To just "throw" a Well Temperament at somebody might be a "risk".

But instead of actually tuning ET, that technician made the same mistakes as nearly everyone who has been trained to use 4ths and 5ths to tune ET nearly inevitably makes. They use a sequence that is far more conducive to tuning a Well Temperament but start out making 4ths & 5ths a little too pure and end up compromising the end of the sequence. It is so blatantly apparent to me that this is how it happens. There is no other plausible explanation for it.

All of the 4ths & 5ths sounded "kinda, sorta, pretty even", some a little more "pure" than others but then there was that one that obviously didn't fit anywhere at all. That one would have been at least a 2 point error on a tuning exam. I have to say that from my experience, I would say that the temperament, as I found it, probably would have passed a tuning exam. However, saying that, it is the exact description of some kind of Historical Temperament except in reverse practice.

Now, the temperament could have drifted, yes and that one "wow-wow" not be what was originally there but I find it very difficult to believe that nearly any temperament that I examine which had been tuned aurally would somehow morph into a Reverse Well configuration. There must be something very consistently going on here and I think I know what it is and I have known it for more than two decades.

This was a Steinway and it had been tuned by one of the best technicians. I have heard Steinways at Steinway Hall in New York City that fit the same description.

So, is any temperament that would "get by" on a tuning exam, "equal enough" to be taken and considered to be ET? Is a Well Temperament that is mild enough to also fit within exam standards and pass as ET to be condemned because it was deliberately done but a Reverse Well temperament that was intended to be ET (and was believed to be ET, offered as ET and accepted as ET) to be let go as simply a bit of imperfection?

In other words, if you know what you are doing, is that unethical but if you don't, whatever you do is OK? Let's go around reporting and exposing all of the people who don't make full disclosures of every technique they use to every client. Let's also tell everyone else who does his best with whatever limited knowledge and skill he may have that whatever the results are, it is OK because the intent to be correct was there. That does not make a lot of sense to me. Neither does people who have no idea what they are talking about telling me how I should interact with my clients.

Enough said about that. Reverse Well is a fact of life as far as I am concerned. It has been practiced and represented as ET for the entire 20th Century and certainly continues today. Surely not by everyone who has tuned pianos but quite more often than anyone I have ever met or known wishes to be comfortable with knowing or admitting.

What I know to be true (and no one on here will ever be able to convince me otherwise) makes a hoax book like Isacoff's, "Temperament" truly laughable. I know that many people have been suckered by it but I am not one of them.

Jer,

I loved your vids! I only wish I could play stride piano like you do. I also loved the sound of the EBVT III in them. It sounds like the way I would have tuned many a piano.

GP,

I got through a lot of your recent postings but still have more to enjoy. I am so glad that a professional musician like you, who has no particular ax to grind, one way or the other, has recognized the beauty that Well Temperament and octave stretch (outside the box) can provide!

On the subject of octave stretch:

I need only remind everyone that (as our colleague on here, Ed Foote was known to say, ((forgive me is I do not quote it completely accurately)),), "The piano is ultimately an untuneable instrument!" The issues of temperament and stretch can never be totally resolved. One can only arrive at a compromise that is pleasing to the ear under any given circumstance.

With regards to temperament, one can, of course, totally equalize the scale to minimize dissonance but at the expense of consonance.

With regards to stretch, one can, of course make single octaves sound pure but at the expense of double, triple octaves and beyond being out of tune, not to mention octave-fifths and double octave-fifths.

No matter which compromise is chosen for stretch, there will be beats which will be found to be objectionable under certain circumstances.

So, I will comment on the way the Bass is tuned in the data that I left GP and which he is now using. The first time I tuned his piano, I did not stretch the Bass so much. However, upon the second attempt, I had Patrick Wingren along with me. He is a professor of piano performance and was so before he ever learned anything about piano tuning.

Patrick learned piano tuning well enough to receive superior scores on his tuning exam. However, no one has ever scored a perfect 100% on any such exam, nobody at anytime, anywhere. One of his "errors" had to do with the low Bass. When I heard it, I confirmed the "error" but immediately added that if all of the Bass were consistently tuned that way, it could also be perceived as a good sound.

So, when I was at GP's house the second time, I had all of the rest of the piano tuned, unisons and all before I attempted to tune the low Bass. When I was ready, I called Patrick to collaborate with me on that. I used the damper pedal, played the note being tuned as well as the octave above, octave-fifth, double octave, double octave-fifth, triple octave, triple octave-fifth and quadruple octave. Each note of the low Bass was tuned entirely aurally by the very best match to all upper partials that could be found.

GP heard this going on and came into the room and made a positive remark about all of the wonderful sounds that he heard coming from his piano. Patrick verbally agreed with me when I found the best partial match. I recorded the results and GP has tuned his piano that way ever since. The "numbers" look absolutely wild but there they stand. They come from the piano itself, not from any calculated or theoretical calculations.

I sometimes tune a piano that way, sometimes not. When I have a small but fine piano such as the Steinway S I tuned today, I often do. I also tuned the Yamaha C3 for the UW Men's Choir concert (which I posted on here) that way. When I hear the first notes that the piano plays, it sounds to me like a 9 foot concert grand!

The stretch in the opposite direction, to the Treble and High Treble also give the ear the pitches it inevitably wants to hear rather than theoretical frequencies. Who cares if while "banging" on a single octave, a beat is heard? Banging on single octaves is not music. What is typically played in the Treble and High Treble of a piano is actually music and the piano should be tuned to serve that music rather than what a piano technician hears when banging on any particular interval.

What is also heard on that particular track is a piano that modulates from one key to another. There is a choir of men's voices that seem to have no trouble at all singing in tune with a piano tuned in an unequal temperament and with highly stretched octaves. Is this not contrary to what most piano technicians and music educators believe? Should not every pitch of the piano be tuned to Helmholtz's theoretical frequencies in order to produce the best ensemble sound? Certainly, I have listened to many music educators assert that.

I can only answer them that theoretical ET is merely a paradigm from which true music beauty can be measured. Surely, if every tone, every interval in music were perfectly pure, music would be quite uninteresting.

Here, for the convenience of anyone who may have missed it, is the link to that one track from the University of Wisconsin Men's Choir concert (December, 2011) that featured a piano. I certainly did tune the piano in the EBVT III. I did not ask anyone permission to do so, not because I believe that ET is the standard and because if I wish to do something else besides the standard, I should ask permission but because the piano was in Reverse Well before I tuned it. In my view, that cancels completely any need to ask permission to do anything. That seems to be most often the case. I also stretched the octaves to the hilt and did not ask permission to do that either. I tuned the piano the way I usually would for such an event.

[Near the end of the track, you may hear an odd, high pitched sound. It is coming from someone's cell phone that was left in a coat pocket back stage.]

Ralph Vaughn Williams: Man shall be Just

https://www.box.com/s/ea642d1482eb9cf1fb2f

Bill,

What an excellent post. I have listened to your Vaughn Williams link several times, and after this post, especially, I find it fraught with meaning. That includes the whining of the cell phone toward the end of the performance, much like the whining that we always seem to hear from other quarters whenever anyone asserts EBVT III as a beautiful and serviceable temperament. The piano in your recording sounds wonderfully resonant, and provides a totally appropriate, balanced and musical accompaniment to the voices!

--Andy

Thanks for the explanation Bill. I was interested to compare your tuning of EBVT to what I have been doing. In the temperament area, I think I've been getting it right. I haven't read this whole thread, so maybe I've missed some explanations. But I'm still trying to get my head around the concept of stretching EBVT. I think of a well temperament as being calmer, or sweeter, in the favored keys. That's the purpose, right? Put the dissonance in the far keys. Which is why I've being tuning it with tighter octaves, to create more of a "sweet" overall sound. I think of stretched tunings as being more tense, or edgy. Brighter, with more tension, in the treble, to cut through or carry over an orchestra. Deeper bass. A "bigger" overall sound. So, to some extent, they seem to be opposite concepts, applied to different aspects of the tuning.

And yet it works. I have to admit that the way you set up the tuning of GP's piano sounds great. So please don't think I'm being critical. It's just interesting. Like I say, I'll have to try it.

Roy, thanks for the feedback. the 12/15 stretch style, as it creates a harmonic set that erase some beating is allowing to have the benefit of stretch without the inconvenience you state. a viable compromising between harmonic and melodic justness. But there is possibly more in that. as partial match are raised.

anyway just with an even beating / tempering at that level, the tone of the piano is deeply modified and enhanced at the individual note level, as you noticed.
Now, this is possibly viable only with instruments that provide some iH which lessens the speed of the fast beating intervals.
On non in-harmonious tones the beating at octave and double octave level lower the consonance in the mix. Also the faster beat of FBI is not comfortable to me.Anyway I am trying to have answers on that debated point, with analysis in the "scala" software ( kind of dedicated spreadsheet with many generation models and analytic functions) .

Scala home page

Due to logarithmic scales may be the slightest difference in the ratio can provide a large enough difference to generate that harmonic convergence, but I am unsure in the end, the tone is enhanced on a piano, eventually on an harpsichord (despite the little level of iH) Some of the harmonies are warmer when using an organ tone, but the quietness sensation is not at all the same.

Then what I like to understand is if the tuning model is using "acoustically just" intervals, or a ratio between them, can the iH be left aside and the theoretical justness be used.
Those tuning frames are creating some iH and they are creating it in logarithmic way, so it may be possible. But still unproved to me.

Roy,

I developed my aural tuning stretch style which I carried over to ETD use long before I ever tuned any non-equal temperaments. Although I hit upon it on my own, I saw soon after that Steve Fairchild using the same idea. Kamin, Afredo and Berhard Stopper all seem to have similar concepts.

Ben McKlveen once said that technology starts out simple, then it becomes complex but eventually reverts to simplicity. With regard to how I stretch the octaves, I can say that I have also followed that path. So, even though I have written very detailed instructions on just how I go about it and shared them privately with some people, I found that they were too wordy to put on my website. I never quite finalized them. If I were to put something on there, it might be more like what I can knock out for you right here:

After completing the F3-F4 octave, tune down to complete the low tenor to include whichever notes are on the low Tenor bridge, reserving the Bass wound strings for last rather than first. I have more than one reason for doing that. Not to be dismissed is the concept of leaving the easiest part, the part that goes most quickly for last, thus giving the most difficult and time consuming part priority. It also provides for a "cool down" period in the stressful task of tuning. It will leave the technician more relaxed and less keyed up when the job is finished.

The other important aspect of tuning the Bass last is that a decision can be made at that time as to just how to blend the very high but audible partials of the low Bass with whatever has been established above. There is no right or wrong decision except in the case of submitting to the taste and desire of the client, should there be one. Otherwise, the way a technician perceives the low Bass tuning as best fitting the particular piano in its circumstances would be the right decision. This is something that Kamin has often pointed out.

Bear in mind that the low Bass will have audible partials well beyond the 8th partial. The difference between the 8th and 16th partial can easily be 20 cents. I know this because I have often measure it and have done so many times in front of groups as an instructor. So, no matter what decision is made in the low Bass (Octave 1), there will be beats in the octaves, one way or the other, whether they are perceived or not.

Starting on E3 and descending from the F3-F4 octave, play the single octave, E3-E4, create a reasonable sounding octave but slightly on the wide side. Compare the 4th and 5th contained within the E3-E4 octave (A3 and B3). Try to make the octave, 4th and 5th all have the same quality. When that is achieved, play all four notes simultaneously and hold them with the Sostenuto pedal if the piano has one (or use the damper pedal in the same way the Sostenuto pedal would be used if it does not). Find the place for E3 that creates the stillest, most nearly beatless sound when all four notes are sounded simultaneously.

Follow the same sequence to the bottom of the Tenor bridge or all the way to F2 on a large grand. If you are tuning ET, this will create very similar sized octaves from one to the next. It will also compensate for any small inequality there may be in the temperament and resolve any problems with irregular scaling all at the same time.

It will create a descending scale from the temperament octave that is so flawless or nearly so, that any rapidly beating interval checks in ET will be virtually unnecessary. They will largely be redundant and merely confirm that you have found the optimum placement for each note merely by creating the purest sound. When tuning a non-equal temperament such as the EBVT III, no rapidly beating interval checks will be necessary at all.

When ascending from the F3-F4 octave, do a mirror image of what was done when descending. For example, when tuning F#4, play the F#3-F#4 octave, create a reasonable but slightly wide octave, compare F#4 with B3 and C#4 below it, make all three intervals have the same quality (nearly but not completely beatless). Then, play all four notes simultaneously using the Sostenuto pedal to hold them. Adjust F#4 slightly if necessary so that the sound of all four notes played together is as nearly still and beatless as possible.

In ET, this will also create a very smooth and progressive stretch that will need very little or no correction using any Rapidly Beating Interval (RBI) checks. When tuning a non-equal temperament such as the EBVT III, it will naturally produce octaves that vary in actual width from one to the next but the amount of width variance will be nearly imperceptible when single octaves are played. Do this all the way to F5.

Therein lies the tiny difference there will be between tuning the EBVT III aurally and using an ETD calculated program. The calculated program will produce octaves that progress on a smooth curve. If one has no aural tuning ability to make the tiny adjustments that would improve the results of the calculated program, the results will still be quite satisfactory.

This would be true of any aurally verified and adjusted ETD tuning in any case. A very highly skilled aural tuner can always improve an ETD calculated program or manipulate that program to produce the ultimately desired results. A lesser skilled tuner can still do quite well with an ETD and probably get better results than might be possible with aural tuning efforts alone. It is all about one's level of skill but also a reason to aspire to a higher level of aural tuning skill if one does not have that skill.

From F5 to F6, tune first a reasonable sounding but slightly wide single octave. Then, using the Sostenuto pedal, compare the double octave and octave-fifth and give both intervals the same quality. Neither is perfectly pure but the beat in either is very nearly imperceptible. Both will sound virtually pure. Now, play all four notes together, using the Sostenuto pedal. Example: Play F3-A#3-F4-F5 simultaneously and adjust F5 slightly if necessary until the sound of all four notes played together is the stillest and most nearly beatless sound possible.

Once again, when tuning ET, this will create a beautiful expansion of the octaves that will need little or no RBI correction and thus is the most efficient way to produce an optimum sound. The clarity will be unquestionably the best the piano can produce.

When tuning a non-equal temperament such as the EBVT III, the octave widths will vary ever so slightly but as single octaves are played, that variance will be nearly imperceptible as well. It will serve to mitigate the dissonance of the wider RBI's but also serve to make the more tempered fifths sound virtually pure when actual music is played.

It will give the piano a sound that has an uncanny purity to it, even though no intervals are really perfectly or technically pure. They are just so close to being that way and the wide intervals are as exactly wide as the narrow intervals, so the very slight beats that are there tend to cancel each other from perception.

This, as far as I can gather, is what Kamin, Alfredo and Berhard Stopper have all tried to achieve. Each has a slightly different way of describing it and bear in mind that English is a second language for each of them, so what they have said may not have come across quite so clearly and simply.

They all also seem to believe as well that such an octave tuning approach would only work with the strictest of ET. I have also read from others who have that opinion. However, having done what I do now with octaves and non-equal temperaments for more than 20 years, I can surely say that the same approach works for virtually any mild Well Temperament, Mild Meantone or Mild Modified Meantone as well.

For that matter, I use something similar when I tune 1/4 Comma Meantone. If the octave to be tuned is associated with a pure M3, I simply play that chord and tune the octave so that the four note chord has the purest sound. If the octave being tuned is among the black keys and has a dissonant M3, I tune the octave using the 4th and 5th within it, the same as I would for ET or any mild non-equal temperament. If the "wolf" 5th is involved, I simply leave that note out and tune the other three for the purest sound.

These techniques are probably more like what tuners in the 17th-19th Centuries did. There is no reason that they could not work just as well today. It leaves the perfection of ET a matter that only has to be addressed within the temperament octave itself.

If you ask me, the key to the perfection of ET is to learn to use the Contiguous Major Thirds (CMT) tests. If one starts a temperament octave with an initial set of perfected CMT's, one can hardly create a significant error after that. Any errors that do occur can also easily be identified and corrected using CMT tests. If a solid foundation for ET is built that way, all of the other tests are unnecessary and redundant, including the use of RBI tests in the octaves.

There are some similar but unnecessary tests for the EBVT III as well. I have noticed them simply when aural tuning but they can be found on Jason Kanter's graphs and Doel Kees as found some as well. They aren't necessary, so I didn't put them in the instructions.

What can be done that is far more effective is that for any two intervals which are supposed to be equal beating within the EBVT III temperament octave, once they have been tuned to as equal beating as possible, play the two intervals together, the same as I recommended for octave tuning. For example, to tune D4 equal beating from G3 and A3, tune D4 until both the 4th and 5th below it have the same quality, then play all three notes together and adjust D4 slightly if necessary until the purest, most very nearly beatless sound results.

For the two intervals that are pure, use the commonly know test note for each and play all three notes together. The purest sound will emerge when the interval is perfectly pure and not slightly wide or narrow. For the F3-C4 fifth, that test note is G#3. For the G#3-C#4 fourth, the test note is E3. The test notes only need to be approximately in tune for them to work.

Playing the four notes together even works for such equal beating pairs as the A3-C#4 and A#3-D4 combination. When those two pairs are truly equal beating, there will be a suppressed beating effect that is heard. The rapid beats of each will tend to cancel each other, the same was, (I believe) that noise cancellation systems work. Whether it is the same phenomenon or not, that is what happens when two tempered intervals beat equally: there is a distinct suppression of the beats.

Now to the High Treble. If a moderately stretch High Treble is desired, one can continue comparing the double octave and octave-fifth all the way to C8. It will create a very nice sound and may be what is preferred by many technicians. However, I can tell you from experience that most pianists and musicians will prefer even more stretch from F6 to C8 than that.

Therefore, what I have long done once reaching F6 is to tune it as a beatless interval to the double octave-fifth below it. Once I reach C7, I tune that to the triple octave below it. You will probably find that the double octave-fifth and the triple octave will be the same or very nearly so, an insignificant difference between the two if there is one, ET or non-ET alike.

From F7 to C8, I tune pure quadruple octaves. The best way to do that is to play the three octaves below the note to be tuned, hold them with the Sostenuto pedal and tune the note to being tuned so that it simply rings the truest with all of the notes below it. One can also play all octave and octave-fifth combinations. For example, to tune F7, play F3-A#3-F4-A#4-F5-A#5-F6, hold them and find the sweet spot for F7. Do the same all the way to C8.

The very same aural tuning procedure can be used to customize any ETD calculated program. Al one has to do is be sure that from F5 to C8, that the ETD is reading the note to be tuned on the fundamental (Partial 1). When finding a compromise between a double octave and octave-fifth, the ETD pattern will show equally sharp and flat for the double octave and octave-fifth, respectively but both will only be a very slight amount.

When finding the exact compromise, enter that value into the program and tune to it. For F6 to C8, altering the program is a simple matter. Stop the pattern when the note which is a double octave-fifth, triple octave or quadruple octave is played, enter that value and tune to it.

For the Bass, F1 to F2, (with the entire rest of the piano being already tuned), tune a reasonable but slightly wide single octave first, then using the Sostenuto pedal, play the octave, octave-fifth and double octave above it (include also the double octave-fifth is you like). With all notes sounding, adjust the note being tuned until the purest, stillest, most nearly beatless sound is heard, the very same as when tuning the higher octaves.

For a moderately stretched low Bass, (A0 to F1), the same technique as was employed for F1 to F2 can be used. However, it will generally be at or about F1 that you will begin to hear what may be perceived as a "jingle" or resonance in the single octave on all but the very largest 9 foot concert grands. Even those will exhibit some of this in the very lowest few notes.

The "jingle" or resonance that is heard is actually the difference between the 16th partial of the lower note and the 8th partial of the upper note when an octave in the low Bass is played. There may also be other such very high partials involved. These are actually rapid beats but they may not be perceived that way because they are relatively faint and they do not sound unpleasant.

If they are heard, they can actually be matched to one or the other RBI's above them. For example, if a resonance is heard between F1 and F2, play the corresponding M10, F2-A3. Match that resonance with the rapid beat of the F2-A3 M10. You can't go wrong with that.

If however, there is the desire for a deeper sound from the low Bass, the technique I used for GP's piano, Andy's piano and the Yamaha C3 in the recent recording I posted is what I would suggest. With all of the rest of the piano tuned, unisons and all, starting on F1, first tune that octave until it is obviously too wide. Now play all of the octaves and octave-fifths above it using the damper pedal this time so that everything in the whole piano rings. Sharpen the note that was tuned obviously too flat just until everything seems to ring true.

When doing this, you will find by ear another kind of "sweet spot" where more of the higher partials of the lowest strings actually blend better. Not everyone will like it, of course and I actually only do that occasionally, not all the time. However, when you do choose to do it, you will enjoy the sounds the piano is making and so may the customer. In fact, when I was doing it, GP heard those sounds and came into the room and made a positive remark about what he could hear from another part of the house.

When using the extra low Bass option, you'll be surprised at how truly low you can go (no pun intended). If you read those figures on an ETD that your ear told you were the best partial matches, you'll see some remarkably negative figures: -20,-30, -40 cents sometimes. No calculated program ever dares to go that low! (At least my ETD would not). I suppose a device like Tunelab or Verituner might do anything you told it, I don't know. I wouldn't know what to say about it either, such as splitting the differences among several partial matches. I just do it by ear.

Anyway, that is what I have to say about tuning the octaves. I could say it all in a single sentence: All octaves, 4ths & 5ths are tuned equal beating. A couple of years ago, I published an article about octaves in the PTG Journal but I don't think it included the parts about sounding notes together and finding the most beatless sound. Perhaps I will use what I wrote today as the basis for something to put on my website.

Bill,
Great post!
Once again you have taken the time to really explain clearly your way of approaching tuning, in a way that is really accessible. I look forward to trying your multiple note sounding method.

How timely...

About a month ago I started a short thread about "cross training/ear training". It was about tuning/listening experiments I was playing with. The results of this messing around have now completely changed how I hear, listen and tune...Thrilled I am...and Bill's quote above, by coincedence, describes exactly what I've started doing in my tunings, giving me the most musical tunings I've pulled off.

Just messing around I started trying to tune a grand in the shop that I had already removed the dampers from. Through the initially confusing jangle of undamped sounds I started to be able to hear and tune the unisons in this open belly, then the octaves, then the fifths, again all through the undamped belly. The interesting thing for me was/is, that these unisons and octave were the most musical unisons I had ever tuned. I mean musical here as intervals and unsions where the strings of each note were not only in tune but their their octave and multi-octave groups, but were coupled in a way that I have, for sure, not heard previously in my tunings, but I frankly only very occasionally hear it in the tunings of others.

I hear now a quality of sound. That quality has of course a beating component, but the beats are only part of the coupled sound. I won't try to explain that sound, because its an experienced thing. But the cross training forced my ear to abandon the beats in themselves as a crutch, and listen to the whole sound of the whole belly.

So, I took this on the road, and in running my stretches, simply tried to set up the conditions in a real tuning, that allowed that multi-octave coupling to happen, without the jangle of the whole belly sounding. Running the stretches but opening up multi octaves/fifths with the sostenuto, tuning till the sound coupled and "filled' out, very much like Bill described in the quote above.

By far my nicest, most musical, low stress tunings ever...pardon my celebrations but this really turns me on!

Interestingly, on a couple of recalcitrant unisons, the ones that will not come clean, I raised all the dampers and tuned the unison again. The open belly, forced me to hear the whole gestaht, or whatever, and when I lowered the dampers I had an ex-naughty, now clean unison...very interesting.

Also I really like tuning each unison with the sostenuto pedal holding that note's damper up so I can hear the attack as well as the tail as a whole sound. It also seems to be easier on the ears as well.

Jim Ialeggio

Disclaimer..the temperament in an undamped belly is much more difficult, but my comments here are about hearing a quality of coupled sounds rather than tuning an an entire instrument with dampers up.