Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum EBVT F3-A3 beat rate

I am curious as to how the EBVT temperament will change if I choose to make the F3-A3 beat rate slower than 6 bps. I remember reading that it will become more of a well temperament, but I would like to know whether all of the keys will change equally (the additional tempering is spread equally across the remaining keys) or whether some keys will change more than others. If the latter, does anyone know which ones are affected most and how?

I appreciate any information that somebody is willing to provide.

P.S. I realize that eventually this thread will devolve into an argument about whether EBVT is a good temperament. I am hoping that I can get some useful information before that happens.

The EBVT is a Well Temperament. There are actually an infinite number of possibilities for a Well Temperament. If the initial F3-A3 M3 is set slower than 6 beats per second, it will affect all other intervals tuned thereafter. It will change the character of the temperament but if everything is done properly, the result will be what is known as a "stronger" Well Temperament.

You can, for example, create an early 19th Century style Well Temperament by starting with 5 beats per second and an 18th Century style Well Temperament by starting with 4 beats per second.

I recall analyzing this in the past. As Bill said when you set FA to 5bps you get a nice but much stronger well temperament. Looking just at the numbers it seems to be quite optimal, with the narrowest fifth 1/4 comma narrow just like in Werckmeister 3. However if you set it to 4 bps, GD is more than 1/4 comma narrow, which is usually considered to be too much off, and M3s on on G# and C# are pythagorean (worst still acceptable in normal baroque WT's). So I think the limit is 5bsps to use without modifications.

Here is the data as transcribed by Owen Jorgensen for the 18th century Well Temperament (using the same sequence as the EBVT but beginning with 4 beats per second):

18th Cent EB WT Data from Owen Jorgensen
(Transcribed and rounded off)

M3's in cents
CE: 5.262
FA: 7.887
A#D: 11.397
D#G: 16.647
G#C: 21.506
C#F: 21.506
F#A#: 21.506
BD#: 17.379
EG#: 14.290
AC#: 11.665
DF#: 8.156
GB: 7.032

Beat Rates of 5ths
CG: 2.2
GD: 1.8
DA: 1.8
AE: 1.0
EB: 1.8
BF#: 1.8
F#C#: 0.0
C#G#: 0.0
G#D#: 0.0
D#A#: 0.0
A#F: 0.0
FC: 0.0

This is very informative and helpful- thank you both

The general "theory" behind the well temperament is to concentrate as much consonance into the simple keys as possible and dump the dissonance left over into the more remote keys. Pythagorean does the same, but to an extreme degree making too much unplayable.

A good "well" temperament creates a pattern that gradually distributes the dissonance as sharps or flats are added to the key signature. Some are better at it than others, favoring several keys over others. Thomas Young gave us an "adjustable" (to personal taste) temperament that follows the progressive pattern extremely well.

EBVT seems to do similarly and can be tweaked or adjusted by varying the speed of the starting major 3rd F-A (Young does it by varying the C-E major 3rd). I think you get "results" quicker with EBVT. You must follow the pattern though, and your tuning ear may rebel at first with some of the 4ths and 5ths, but you need to test it out musically to determine where you think it works best for you.

BTW, if you speed up that F-A 3rd a tad, the end result is nearly indistinguishable from ET, especially according to Bill's latest published pattern. His original pattern kept C-E same as F-A. This method puts more consonance in C major (standard well practice). Current pattern changes that slightly. Both are very good, and I consider it a matter of personal taste and circumstantial application.

By all means experiment with it. Just stick to the pattern. That's the key. (Forgive the pun).

Pwg

It seems that the most potentially objectionable 5th would be CG. If that is indeed a problem, is it better to adjust the C or the G? It seems that changes in the C would sacrifice the equal-beating aspect of the temperament. Any opinion on this?

My experience has been that this "objectionable" quality of 4ths or 5ths pretty much disappears when MUSIC is being played on it, that is, music that is composed with these idiosyncrasies in mind. Or, music of one's own composition that exploits the consonance or dissonance, and resolutions now available in this tuning style that are not really available in ET.

It is the tuner's ears that are accustomed to ET that generally object to these things in well temp. I include myself in that. But when the music starts...that all goes out the window.

So my advice is ... Don't worry about it. Just make sure you are following the tuning pattern accurately. If make a sizeable error somewhere that can scew the effectiveness of it (just like in ET).

Pwg

Sorry if this question is ignorant but what is the preferred method for measuring beat rates accurately? I just tuned EBVT by ear and I am happy with the result with noticeable key coloring and nothing objectionable but I would like to know with some accuracy what my starting F3-A3 beat rate was.

There is virtually no music where an open C4-G4 5th is played. If you find something that actually has that, you can still play it on a piano tuned in the EBVT. That is the danger of the technician "banging" on an interval, saying it is unacceptable and thus dismissing the idea entirely. You can also similarly "bang" on some intervals in ET and get the same results. There was once a service call I had to make when the young man complained about the tuning that had been done by another fine RPT technician. He was playing Chopin and "banged" on a M10 interval that had been tuned very well and properly in ET. He said it sounded out of tune to him.

The 1/4 Comma Meantone Temperament has 5ths that are 5.3 cents narrow but with pure M3's. Again, there is no music written for 1/4 Comma Meantone that has open 5ths in the midrange. It is all harmony. A triad quite effectively "swallows" the sound of the highly tempered 5th, leaving what sounds like perfectly pure harmony.

If you play a C Major triad on a piano tuned in the EBVT, it actually sounds as if it is a much stronger temperament. That is because the equally beating M3's and M6's tend to cancel each other. The tempered 4th or 5th is "swallowed" in that sound. Therefore, I am satisfied with the EBVT as I presently have it defined. That was accomplished 11 years ago.

By the way, the EBVT can be tuned from a C fork and starting with the note, C4. You just change the order of the sequence. F3-F4 was chosen as a temperament octave because that is what most contemporary technicians use. The A as a starting pitch is of course, because A-440 is the standard, not C-523.3. Tuning from an A fork within an F-F octave rather than a C fork within a C-C octave is merely a transposition. The EBVT does not place F Major as the tonal center. The tonal center is still C Major and therefore the EBVT adheres to all of the rules of Well Temperament with the exception of what Owen Jorgensen identified as an "insignificant micro-imbalance" which is necessary to maintain all of the pairs of equally beating intervals.

One of the nice things about equal beating intervals is that they tend to reinforce each other, especially in the lower, slower 3rds and 6ths. I believe this is responsible (largely) for why this temperament performs so well. It changes the sorority of the instrument. In ET nothing is the same except random intervals. Little re-inforcement available.

Pwg

From my document of detailed instructions:



It is actually fairly easy to do. Lots of technicians gravitate closer to 6 BPS when trying to tune the same interval in ET. It has a natural sound to it. No one can accurately tune any interval to a rate that electronic equipment will verify as being exact to a single decimal place, let alone more.

For most pianos, you can find that rate electronically without using a calculated program. In the Tune mode of the device or software, set it to read Octave 3 on the 4th partial (actually listening to Octave 3 on Octave 5). Tune A3 to 0.0 and F3 to 1.0. Once you get that sound in your ear (much like most technicians do for the 7 BPS of ET), you should be able to do it sufficiently accurately to get a proper representation of the EBVT.

If you are an aural only technician, I recommend the metronome or even the second hand on a watch and listen to get a triplet pattern for each tick of the metronome or each second of the watch.

6 bps is far easier to deal with than 7 bps.

One of the first lessons (for me) in aural tuning was to replicate the speed of one second. Being a percussionist for many years, this was not particularly difficult for me. It may be for others though, but it really is pretty important. In ET, 4tgs beat at essentially 1 bps, G-B 3rd beats at 8 bps, F-A 3rd 7 bps. If you KNOW what a second is it is relatively easy to figure these things out. Then, of course there is comparative beat rates. I actually find comparative beat rates easier to accomplish than equal-beating beat rates on un-related intervals.

6 bps is a simple triplet figure. If you don't know how to replicate it, ask any drummer, anywhere. They ALL know how to play triplets, and will gladly play them for you. Memorize it, play it with your fingers, your teeth, your saliva, your feet...get the picture?

Compared to 5 or 7, 6 bps is a piece of cake. And EBVT has a lot of it. How much simpler can it get?

Pwg

I assumed that finding 6bps would not be difficult for the seasoned tuner. However, before attempting EBVT I only tuned electronically so beat rates were somewhat meaningless to me. Having said that, I am moving away from machine-dependent tuning (likely,in part, due to the ease of setting an EBVT temperament as well as the general desire to go that direction anyway) so now I am becoming more aware of beat rates. From what you wrote it sounds like 6bps is the more "natural" rate so that should help.

Speaking of beats, I am having difficulty -at times- while expanding out the temperament when making the octave, the fifth, and the fourth all sound similar. Obviously, octaves should not have significant beats so in that case (as Bill previously wrote) one should favor the octaves at the expense of the 5th and 4th.

What I am unsure about is whether the goal is to keep things equal beating as much as possible or are the 5th and the 4th simply used to check whether the octave that has been tuned is correct in order to facilitate further expansion outward? Put another way, should I be striving for the best sounding octaves possible or it is better to be satisfied with a reasonable sounding octave that attempts to equalize the beating of the 4th and 5th?

Many thanks, as always, for the assistance. I want to make sure I get this right.

6bps...just listen to a ticking clock and click your teeth in double triplets to the tick. That is 6bps. If you find that hard, start with 4 bps. Get that solid. Then go to 8 bps which twice as fast. 6bps SWINGS right in between. Has a totally different feel. 1/3 of EBVT is made up of 6 bps.

(I cannot sleep with a ticking clock in the room as I will endlessly beat out rhythms to it.)

Now to your question:

In this context (of EBVT) yes, you would strive to equalize the beating of the 4ths and 5ths, trying to make the octave sound similar. If you end up with a "busy" group, then slightly favor the 5th, which will in turn slightly favor the octave.

Just like with equal temperament, you will not get the same results on every piano. A "less than optimal" spinet or console is not going to behave quite the same as the nicer grand or large upright. But as you know this is equally true with ET. The advantage with EBVT is that you are providing the player with more pleasurable harmony in the parts of the keyboard that they are most likely to be playing in. Therefore their experience at the keyboard will be noticeably better. They are not going to venture out into the more complicated keys for the most part. As you become more familiar with EBVT as well as your clientele and their musical wants and needs, you can adjust accordingly. A truly classical pianist WILL in fact venture out into the more remote keys, and they will begin hearing things that they didn't hear before...things they like.

Of course, you should still strive to be aurally proficient at tuning ET as you may be called upon to do it at any time.

It is interesting to me that you say that until recently, beat rates were somewhat meaningless to you. That tells me that you really had no way of aurally verifying what you had done using the machine. This is at the heart of most controversy over machine tuning vs aural tuning. I am glad to learn that you want to become more proficient at aural-only. Although difficult, you will benefit.


Pwg

Thank you Peter. You did all of my work for me. I can only add that as Staveoff works to learn to tune the EBVT aurally, beat perception and control will be more easily learned than it would be trying to learn it in ET first. Owen Jorgensen started his students with Equally Beating Temperaments and then taught them ET last. All of his former students are excellent tuners and technicians.

Staveoff, since the EBVT is what is known as an Irregular Well Temperament (not a negative label, just a descriptive one) meaning that all 5ths are of varying sizes, you will find it easier to make a good compromise among some octaves-4ths-5ths but others, more challenging. In the case of a more difficult compromise, do what Peter said: Favor the octave and 5th a little more than the 4th. At or about the lower part of Octave 5, 4ths become virtually indiscernible anyway, so they are no longer a factor.

The G4-D5 5th is always a little challenging. It is OK to put a slight beat in the octave to accommodate it. It will not be any wider in any case than what you would get with some of the more maximum stretch ET versions that are out there.

6 bps is triplets at MM=120, 7 bps is triplets at MM=140.

This is precisely what I have noticed. Pieces that I have played dozens of times are taking unexpected turns that I often find myself stopping to find out what the special sound is. I was not getting this result by tuning EBVT by machine so I opted to learn aurally. It's an added benefit that setting the temperament in EBVT is easier than ET (based on what others have said as I always used a machine). Heck, I may even go for a tuning fork just to be old school.

As for beat rates, I had never known what they were; I just knew that something was too fast or too slow to my liking based on what I was accustomed to hearing. Just like you folks who have tuned ET so many times you already know what 7bps sounds like when setting the temperament. With ET, however, you can find out whether you are wrong if the contiguous 3rds beat rates don't increase as you go up; EBVT doesn't have that check built in. Once you make an error from the F3-A3, the error is propagated unknowingly. However, as was written before, it will still produce an okay temperament; it will just be different. I wanted to make sure that I was on the right starting point. Experimentation can go from there, if desired.

And, as I pointed out in a previous post, the ability to RESOLVE to a milder key is strongly enhanced in well temperament, which EBVT is in this category.

You will be glad you made this jump into aural tuning. There will be some frustration in the process, but anything truly worthwhile takes work and effort. Keep it up!

👍

Pwg