Bill:

I agree with you that more tempered means further from just intonation.

I’m trying to wrap my mind around all the effects of your tempered octaves. The most important effect, of course, is how it sounds. Who is to say that an UT doesn’t need to be more unequal as the octaves are stretched to have the same key colors?

If a fifth is tuned narrower than in equal temperament, another fifth is tuned wider. There is no getting around that. But I was looking for a point of reference, and I think I have it.

I am getting more and more confused by the 4:2/6:3 stuff. Could you give a concrete example. If you start with A-440, what would be the frequency of the A below it if it is a 4:2 octave, and what would it be if it is a 6:3 octave?

If it depends on the specific piano, and you cannot give a formula, use something common, like a Steinway M. Explain how it is figured out.

If you keep the octave fixed, then you would be right. A fixed octave means there is a certain amount of tempering that must be distributed to all the 5ths. More tempering to some 5ths means less tempering to others. But if you allow the octave itself to be expanded or contracted, then the total amount of tempering of the 5ths changes. So it is possible to have all the fifths tuned a little closer to pure, for example. But to make a .2 cent difference in all the 5ths would require making a 2.4 cent difference in the octave.

A-440 means the fundamental of A4 is 440 Hz. That does not say anything explicit about any of the other partials of A4. That would be determined by inharmonicity.

Then you ask what the frequency of A3 would be. I assume you mean the fundamental of A3, which is somewhere around 220 Hz. But it is not exactly 220 Hz. Here is where the 6:3 vs 4:2 octave stuff comes in. When you tune the A3/A4 octave, you are listening for beats at the coincident partials, which would be 2:1, 4:2, 6:3, 8:4, etc. For example, the 4:2 partials mean the 4th partial of A3 beating against the 2nd partial of A4. If there were no inharmonicity, then all these partials would cease beating at the same tuning, and that would be where the fundamental of A3 is exactly 220 Hz. But because of inharmonicity, the 2:1, 4:2, 6:3, and 8:4 partials do not all fall into line at the same tuning. So you listen to the most prominent of these partials and tune for a zero beat, perhaps unaware that other partials are still beating slightly. In some cases you can distinctly hear several of these coincident partials and selectively tune for a specific one.

So a 4:2 octave is one where you have made the 4th partial of the lower note beatless against the 2nd partial of the upper note. That can give you a slightly different octave from one where you make the 6th partial of the lower note beatless against the 3rd partial of the upper note. That is how we get different octaves that are contracted or expanded, and still they are called octaves. And that is also why tuning a specific kind of octave can affect the overall tempering of other intervals, like 5ths.

Robert:

You may want to rethink this. If the fifths are tuned as you say, starting at the bottom of the keyboard and not tuning any fourths, each octave would be tuned about 0.3 wide.

Regards,

My question is, where do they fall?

Here is an example using the inharmonicity data from a Mason & Hamlin A:

The 4:2 octave A3/A4 has the fundamental of A3 at 219.818 Hz so that the 4th partial of A3 and the 2nd partial of A4 are both 881.089 Hz.

On the other hand, the 2:1 octave A3/A4 has the fundamental of A3 at 219.887 Hz so that the 2nd partial of A3 and the fundamental of A4 are both 440.000.

The difference between 219.818 Hz and 219.887 hz is only .54 cents. This is because there is very little inharmonicity in this portion of the scale.

However, if we shift our attention to the octave C7/C8, we have a much different situation. If we fix C7 and then consider tuning C8 for a 2:1 octave or a 4:2 octave with C7, then difference is about 4 cents. That is, the 4:2 octave is 4 cents wider than the 2:1 octave.

Is that what you are looking for?

Robert, thanks a lot for chiming in. I hope you will attend my class on Sat June 21 at 1:30 PM in the Garden 2 room. The tuning will be entirely aural but I want people to hear what I'm doing the best possible. I especially would like you to confirm (or deny) the "pipe organ" effect.

If you can figure out a way to get it with a calculated tuning, you'll be the first! Aurally, it is a very simple matter but electronically, the only way I know to get it is manually, note by note. Still, it involves the natural inharmonicity that each piano has rather than being "pulled out of thin air" as some people surmise.

I've had several more of my customers confirm with delight since I last reported. I have yet to find a single person who denies or scoffs at the notion that the C Major arpeggio having been tuned in the EBVT with tempered octaves played across the entire piano with the damper pedal held down, produces an effect that sounds uncannily like that of a pipe organ. "YES! it REALLY does!" (with a broad smile indicating delight) is the usual confirmation when it is done again a time or two.

The theme of the Convention is "The Intentional Technician". If you can eventually find a way for your programs to do exactly what I intend aurally, I'll bite the bullet and sell my SAT, learn to operate a device with your programs on it and be your foremost advocate!

Ah, yes. I see. I was mistakenly thinking about the 12-step circle of 5ths and 4ths. That's where I came up with the 2.4 cent difference in the octave. But I think you are right now. The degree of octave expansion would be about 1.5 times the degree of 5th expansion.

Sort of. If I may, what method are you using to get these pitch numbers? Are they measured, or are they computed?

There is some more math that I need to do, but one of the first things that I notice is that the difference between 219.818 Hz and 219.887 Hz is only .089 Hz. That is one beat every 11 seconds. Frankly, that is not going to make a lot of difference. It might barely be audible. It is not going to make much of a difference in setting a temperament octave.

The difference between octave types can be much greater on challenging pianos. The tests for the different octave types can be used to get an idea of the difference in iH across the wound/ unwound break. Knowing this can help in making decisions on the best way make compromises. This is just another way of making all the intervals sound equally bad.

I got those numbers using TuneLab and some actual inharmonicity measurements of a Mason and Hamlin A. The measurements were not for the notes used in the example, but TuneLab estimates the inharmonicity for those notes based on the measurements that were taken.

BDB,

The 219.818 and 219.887 frequencies are at the fundamental level, that is at the first partial.

So we are not talking about one beat every 11 seconds.

In a 4:2 octave, what you hear is the fourth partial of the lower note and thus the difference of .089 Hz must be multiplied by a factor of 4, that is .356 Hz. One beat every 2.8 seconds.

Now if you hear at the 6:3 octave the .089 Hz difference must be multiplied by 6, that is 0.53 Hz, and you hear a beat every 1.8 seconds.

I think that makes indeed a lot of difference!

Gadzar:

You seem to be refering to the beats that might be heard when playing the octave. If there are no additional test notes being used, an aural tuner would simply tune the octave where it sounded best. By using test notes, the beat difference can be more obvious. And these test notes are also parts of intervals that may be played. A half cent difference on each of the four notes of two intervals that can be compared, can add up to two intervals being two[/b] cents different from each other. But this sort of error can also be noticed with chromatic RBI checks.

Regards,

No, by a factor of 2. If you apply a factor of 4 to a 2:1 ratio, that is the 8:4 ratio. The actual result if you compare this way is one beat every 5.6 seconds, and at a strength far below that of the 2:1.

What I mean is that if you tune a 4:2 octave you hear at the 4th partial of the lower note of the octave, so a difference of .089 Hz in the fundamental of that note is 4 times greater when testing the 4th partial with the 3rd-10th test.

And if you test the 6:3 octave, with the m3-M6 test, what you hear is the beatings between the 6th partial of the lower note of the octave against the 3rd partial of the upper note of the octave, thus the difference of 0.089 Hz. is multiplied by 6.

It's that simple!

This has been a great thread for an amature DIYer tuner like me. I've used Bill's EBVT temper many times on my S&S B and it sounded great. That piano is gone and now I have a D and I'll try out the EBVT on that soon. Bill has always been very patient and enthusiastic toward me even though I'm not a RPT. The same goes to Ron who has helped me many times on the VTer forum. Thought I'd just say hi and thanks.

As another amateur, I'll second that. I've been tuning EBVT for 4 years on my concert grand. Whatever we call it "sustain" or "decay", it sure sounds like a big pipe organ to me when I play arpeggios with that temperament. I think of it as "breathing", not unlike those pipes. It's why I've stuck with EBVT and won't budge. Equal sounds truly dead by comparison. After reading these four pages, I went and played keyboard spanning arpeggios on that piano tuned just last week. Pipe organ. Actually, I play those arpeggios all throughout the tuning process, aside from all my interval checks. When I've got absolute clarity and maximum sustain and that pipe organ effect, I know I've done my job.

WOW!

I've just tuned my Petrof in EBVT with my Verituner, with the figures that appears in Bill Bremmer's site. It's unbelievable! I am really amazed! I didn´t know my piano could sound this good!

I've played the Prelude N° 1 in C major of Bach's Well Tempered Clavier and it sounds incredible. The notes seem to last for ever.

The harmonies sound totally different from those in ET. The more I play the more I feel I play better and better. It seems the EBVT does help playing better, there are resonances I've never heard in ET, as the prelude progresses down the scale different colors in the harmonies make a richer performance, but I do not do it my self, it is the temperament.

All the pieces of Bach I know sound richer, full of colors I had never heard before.

ET by comparison sounds out of tune. The thirds sound harsh. The music sounds monotone.

I realy like the sustain increase of the notes when played in a chord or in a sustained arpegio.

Now I know what you call pipe organ effect!

I am really interested in learn to tune EBVT aurally but I don't know how to spread out the temperament.

Bill, how do you tune notes E3 down to C3 and F#4 up to B4?

You have already explained how you tune the treble. But how do you tune the bass?

Must A3-A4 be tuned as a 6:3 octave, as it appears in your article? Isn't it incompatible with tuning F3-F4 as a 4:2 octave?

Gadzar:

Yes ET sounds lifeless and cold in comparison to EBVT.

Did you try VT's pre-programmed EBVT with the Average style? How does it compare to what you did with the parameters from Bill's web site?

I was using VT's EBVT+Average on my Kawai K-8 and I hear the pipe organ effect, even though ETD-tuned EBVT is not as good as aurally tuned the way Bill does it. Could be that the effect is more pronounced when EBVT is executed properly a la Bill Bremmer?

All:

I hope this is not taken the wrong way. If someone experiences a “Pipe Organ Effect”, it is a valid experience. Someone else may not. Bill says that he only experiences it in certain keys of EBVT when the octaves are tuned a certain way. This way of tuning the octaves is not an automatic option in ETD’s.

This reminds me of a challenging piano I tuned the other day. I made the intervals in the tenor and bass all sound equally bad. When I was done, I cringed while playing Fur Eloise. The owner said they got goose bumps, it sounded so beautiful! "Beauty lies in the eye (or ear) of the beholder."

UprightTooner:

Yes, one man's meat, another man's poison, etc. And I guess the customer's always right, even if he is tone deaf.

I tried those keys that Bill mentioned. I heard a what I believe to be that effect, but it was not strong. Perhaps it wasn't it. What I do know is that tuning first to ET, and then to EBVT was a revelation to my ears, pipe organ effect or no.

Digitus,

Yes, I have tuned EBVT preprogrammed in the VT, but with another style because "Average" gives me baddly beating octaves in the pianos I have tried to use it.

I have tuned EBVT in my Melodygrand console, which is horrible! And I have not heard the pipe organ effect. I liked the tuning, that's all. Not a big deal, I have tought.

But in the Petrof, EBVT did a huge difference from ET. And now I want to try it tuned aurally, to hear the difference.

Upright,

I want to learn to tune the octaves the way Bill Bremmer says, to see if I can get this pipe organ effect. Yes you are right, maybe I have not achieved it. But anyway the Petrof sounds really great!

I've tryed to tune EBVT aurally in the Melodygrand, but it was more difficult to do than to understand. When comparing against Verituner I've found differences of 4 to 5 cents in some notes! I am not sure if A3-A4 must be tuned as a 6:3 octave, that gives me a strong beating and I suspect that it is the culprit of most of the big differences I've got against Verituner. In this piano there is a big difference between a 6:3 an a 4:2 A3-A4 octave.

I have the same experience, not only with EBVT but with other tempers as well. The best style for my piano is "clean" which gives me very pure octave. I have a S&S D. When I had my B the expanded style with a few aural offsets in the 5th octave gave me the best results. "Average" never seemed to work too well.

* Stupid question deleted *

Yes,

With every piano I have used the Average style I had bad results, from small spinets to concert grands.

Have you tried the styles of Ron Koval?

They seem to work fine in all pianos I have tuned. He has designed three main styles named Normal, Small, and Baldwin Studios. And of course the fourth style: Koval One For All, which is posted in this thread.

No not yet. I was going to and then I sold the K-8. My new piano (a Sauter Omega 220) should be arriving in a couple of weeks.

This is the piano that I had in mind when I asked the question that started this thread. The responses that followed were, and continue to be, simply wonderful. I am very grateful to everyone (particularly Bill) who took the time and effort to post.

Thanks to all for the comments. I especially hope that Digitus will find the EBVT to compliment his fine new instrument.

The day after I returned from the PTG Convention, my computer over heated and was ruined. Fortunately, I had many important documents backed up on CDs but one of them, the detailed instructions for tuning the EBVT which I was still working on was lost, so I will have to start that over. I still have the rough draft for tuning the octaves.

Gadzar, the short answer for what you do in the Bass is a "mirror image of what is done in the treble. The double octave is still compared with the octave and 5th. Going down from the Temperament octave, tune an octave first, then compare the 4th and 5th, favoring the 5th slightly over the 4th. Once F2 is reached. tune an octave first, then compare the double octave and octave and 5th, making each interval equal beating (having the same amount of tempering). Each will sound very nearly beatless.

As for the EBVT vs. ET, it has been noted by any number of practitioners and pianists that when they try virtually any mild (Victorian style) well temperament, they immediately find it appealing. The EBVT was designed to be easily tuned and most importantly, replicated by any aural tuner. However, the fact that it contains so many equal beating intervals, it apparently has some extra "magic" to it. It simply sounds more "clear" and incredibly "in tune" compared to some others.

Thanks, Ralph for chiming in on this. I had remembered someone saying that they had noticed the "pipe organ" effect quite some time ago but I had forgotten who it was, so thanks much for confirming that. I continue to ask my clients on a daily basis what they hear when I play that long, C Major arpeggio. Often, it does not require any hints, the first word out of their mouths is "organ". It is always said with an expression of delight and amazement. It was indeed confirmed at the PTG Convention as well.

To adapt a calculated ETD tuning so that it reflects what I do aurally and/or manually with my ETD, use an extra amount of stretch, particularly in the high treble. From the top of the Temperament octave (F4), play up 5ths. If you hear any which beat more than 1 beat per second, set the ETD sharper (try 1 cent), try the interval again to see if it sounds better. Usually 1 cent is enough. I usually only have to correct D5.

When you reach F5, set the ETD so that it is reading on Octave 5. Now, play the note 2 octaves below and then an octave and 5th below. Some notes will register exactly the same for both. Others will show slightly sharp for the double octave and slightly flat for the octave and 5th. Find the point where the pattern is equalized for both and enter that into the program. Continue that way to E6.

At F6, reading on F6, play the note two octaves and a 5th (starting with A#3 in the temperament octave). Stop the pattern and enter that value in your ETD. Continue that same way, all the way to C8. Tune to those values.

For the Bass, check 5ths from the bottom of the Temperament octave (F3), down to F2. If any 5ths beat more than 1 beat per second, flatten the bottom note (trying 1 cent first) until the 5th sounds more acceptable. Check to determine if the octave and/or 4th is not too exaggerated and adjust accordingly, however, favor the 5th above all.

When F2 is reached, the ETD will probably be reading on the 6th partial (2 octaves and a 5th above the note being tuned). Starting with F2, play C4 and stop the pattern. Enter that value in the ETD. Continue the same way, all the way down to A0 and tune to those values. Check afterwards to insure that no octaves or double octaves are excessive wide and beating and adjust accordingly.

Most often, no adjustments need to be made but some pianos have some irregularities which require a compromise. That is the way I have tuned using an ETD since 1991. It provides for using the piano's own unique inharmonicity to tune the octaves both very low and very high. It causes all octaves to have an optimum alignment and thus creates the "pipe organ" effect where octaves and 5ths seem to reinforce each other as the sound from low to high sustains.

Thanks Bill. We are glad to have you back from the PTG Convention.

Bill:

Sorry about your data loss!