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Originally Posted by Bernhard Stopper
Patrick,

I suppose that you can agree that musical intonation preference for melodic perception is proven to be more pythagorean like, especially for the major thirds. I think this is status quo of teaching at music universities, as a lecturer for composition you have probably knowledge about this.

What is the reason for this? In believe that our brain´s neural network has been highly optimized over evolution to reduce redundancy. If we assume that this neural network ignores the fifth partial for musical processing, we can have an explanation why we prefer melodically a more pythagorean third over a harmonically pure third in the musical perception


Bernhard,

about the aim for pythagorean major thirds, could you elaborate a little on where you see that preference? Is it in melodic solo lines? This is the only I can think of, where the lead player/singer often want to stay as sharp and separated from the rest of the music, bringing tension to the interaction between him/her and them.

As for harmonic content, though, in my experience, the intonation is gravitating towards just. This goes for the ensembles I've worked with; strings, brass, woodwinds, choirs.

Ed Foote, in a post in another thread, described ET as a hyper-active intonation, robbing the listener of the chance to interact with the musical output through their autonomic systems. I agree fully, and I sincerely believe that non-conformed tension/release is a vital part of a chord progression.

I also subscribe to Ed's impression of stretched ET - the more stretched it is, the more restless I become. Again, this is just me. Many seem to like your sound.

In ET there is no single calm, peaceful M3rd. They are all just as 'spicey', uneasy, or whatever we may call them. It is a compromise in a dangerous way, because it little by little robs the receiver of the ability to hear pure intervals - be it 5ths, 4ths, 3rds or whatever. Actually, it's even worse: It replaces just intonation with compromised intervals, and trains the listener to accept them as 'the best in tune they can be' (just look at Alfredo Capurso's reasoning here. )

That said, EBVT III is not exactly giving all listeners just intonation revelations, either. But slight as its deviation from ET is, it still encourages the listener to listen in a different way. That I like!




Last edited by pppat; 07/15/10 08:26 PM.

Patrick Wingren, RPT
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Question I've been wondering about EBVT for a while. Is it my imagination or is F major, not C major, the "quietest" of the keys? Why is C busier than F? In Bremmer's description of it, C should be the most still. This confuses me about EBVT. Help?

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If tuned according to Bill's original instructions for EBVT (This is what I do when I tune it...or at least try), the beat speed for the C4-E4 3rd is the same as F3-A3. If this is followed, this should ultimately make the key of C slightly "mellower" than either F or G, providing a progression from C to F to G (though they all pretty much sound much nicer than in ET.

However, if I am not mistaken, the published instructions for "EBVT-3" speed up this C4-E4 3rd. Personally I don't like this unless I am attempting to come "closer" to ET for some reason. Some evidently feel that the tonality differences in EBVT are still too great, therefore they modify it to be less so.

However again, if one is using an ETD to try to produce this temperament and tuning scheme, I personally do not think it will work accurately AS INTENDED. The reason is that the ETD simply uses cent "offsets" from ET to achieve "EBVT". On a nice well scaled piano this may work fine, but on lesser instruments with weird scaling compromises this can result in unintended consequences that do not accurately represent how EBVT works.

To do it "as intended" and to achieve its effectiveness, one must UNDERSTAND Well Temperament and how it is constructed. Then one must apply this understanding to the production of EBVT on a "less than ideal" instrument. I believe this can only be done accurately by ear/analog rather than digitally. So, if you are experiencing odd things in it AND you are using an ETD to do it, this may very well be your problem. I use EBVT (original version) very regularly and am very pleased with it, as are those who receive it on their pianos.

You must understand that the difference between ET and UT (or WT) is that UT "favors" some keys over others (tonally), whereas ET does not favor any one over another and in fact true very hard to make all keys sound THE SAME (atonal). But you may already know this.

Peter Grey Piano Doctor

Last edited by P W Grey; 10/21/21 09:47 PM.

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Thanks for these thoughts. I'm an aural tuner and I don't own an EDT and I also own a pretty nice grand. I've been following EBVT III.

Two questions, one about the original EBVT and second about why C would be mellower in either version.

First, how can I get a copy of the original instructions? I can email Bill I guess. But basically, sounds like you're saying, I don't need the original instructions because the difference is not speeding up the E? If I've understood right, I'll gladly give that a try. Thanks for the tip!

Second, my comment still stands about EBVT III though, that the C doesn't seem historically accurate. No matter what the beat rate between C-E, wouldn't F be more still because the fifth is pure? Not sure I get why C would be more mellow.

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Tonality (or the perception of feeling) comes primarily from the 3rds and 6ths in the music, not the slow beating intervals. The difference between v1 and v3 does comprise a few other intervals other than CE. If you go to Bill's website the instructions are there.

In a nutshell, the FA, GB, and CE 3rds all beat the same in the temperament region at about 6pbs. This makes the CE significantly less dissonant than in ET. You will need to tune this a few times and play it. Then I believe you will hear the difference. (Thonas Youngs temperament of 1799 puts the CE 3rd at about 4 bps...really nice to my ear. You must understand the concept behind good WT, not just the analytical part.

HTH

Peter Grey Piano Doctor


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Thank you for your interest. All Well Temperaments are also Cycle of 5ths based Temperaments and so is the EBVT. The CE third is always the slowest as it is in the EBVT. The difference is that the sequence for construction has been transposed from C3 to C4 to F3 to F4. That places the CE 3rd an octave higher. The C4-E4 3rd beats twice as fast as the C3-E3 3rd, as it would in any Temperament, ET, WT or otherwise. Therefore, in the EBVT, the CE 3rd is the slowest as it should be for a Well Temperament (WT) and as it is shown in Jason Kanter's graph.


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You can read all of the current information about the EBVT. icluding Jason Kantor's graph on my website here: www.billbremmer.com/EBVT

Here are the basic instructions:

Summary Sequence for tuning the EBVT
1. Tune A3 to the tuning fork or from A4 at A-440 as a 6:3 type octave.
2. Tune F3 from A3 at 6 beats per second.
3. Tune C4 from F3 as a pure 5th.
4. Tune F4 from F3 as a 4:2 type octave.
5. Copy the F3-A3 beat rate (6 beats per second) at C4-E4.
6. Tune G3 from E4 (a M6) at that same rate, (6 beats per second).
7. Tune B3 from G3 again at that same rate, (6 beats per second).
8. Check and correct each of the previous 6 beat per second beat rates for similarity.
9. Adjust E4 (slightly sharpen) to beat equally between A3 and B3.
10. Tune D4 equally beating between G3 and A3.
11. Tune A#3 from F3 so that the F3-A#3 4th beats the same as the G3-C4 4th
.
12. Tune C#4 from A3 so that the A3-C#4 M3 beats the same as the A#3-D4 M3.
13. Tune G#3 from C#4 as a pure 4th
.
14. Tune D#4 to beat equally between G#3 and A#3.
15. Tune F#3 to beat equally between B3 and C#4


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Bill,

I see only two variations in this sequence from your original instructions, specifically (9) and (15). They are both very slight and "relatively" insignificant (except possibly (9) in the overall tonality picture. They both would tend to mitigate (what some might term as) excess dissonance in certain keys. I will play around with this. Thx

Peter Grey Piano Doctor


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What were the original instructions for step 15? I'd love to try both.

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Tune F#3 as a pure 5th from C#4

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Again, thank you for your interest. The EBVT was originally conceived in 1992, now 30 years ago. At first, it was just an intuitive/empirical (by the seat of the pants) idea that I knew I could get by "fudging this and that" (from the point of view of ET). The results were good, however, from the very first attempt but I wanted something I could replicate and for that matter, something I could pass on to another technician and have the results be as identical as possible.

So, it was the writing of just how to do it that was the real challenge. I chose the idea of "Equal Beating Temperaments" from Professor Owen Jorgensen. With that plan, every interval tuned is either pure or made to beat exactly the same as another. It is common to "temporarily tune" a 4th or 5th pure first and then compare it to a previously tuned interval and then cause it to beat identically with that comparison interval. Some 3rds are also tuned identically, one to the other, in the same way.

This turns out to be a highly accurate way of reproducing the same plan and results every time over any other method that has lists of theoretical beat rates for example or simply instructions that say, "a little faster or slower than...". The challenge, therefore was to make the EBVT conform to this method. Yes, it took a lot of trial and error to get there but the plan was finalized by 2007. Since then, I have only changed the order slightly so that the sequence more closely follows the actual Cycle of 5ths.

I no longer use or speak of "EBVT II" and "EBVT III". Those were simply refinements that utilized the Equally Beating principles but which I had not yet realized were available. I'll explain: The C4-E4 M3 is initially tuned at 6 BPS, identically with the initial F3-A3 M3. When G3 and B3 are tuned, it creates a pure 4th between B3 and E4. This is fine but the more pure 4ths & 5ths there are, the more harshness there will be at the bottom of the Cycle of 5ths. It can also cause some intervals at the top of the Cycle of 5ths to be a little too tempered to sound acceptable.

This was the case with the A3-E4 5th. Then, I realized that I could mitigate this problem by equalizing the A3-E4 5th and the B3-E4 4th. That happens by raising the E4 just slightly so that the 4th and 5th below it beat equally. It does very little damage the the CE M3. That 3rd is still the slowest of all, as it should be. This step was initially put at the end of the sequence and the idea was labeled the "EBVT II".

Initially, the F#3-C#4 5th had been pure but this caused the F#3-A#3 M3 to be a bit too harsh. The F#3-B3 4th was also a bit too wide. I realized that I could mitigate both the 3rd and the 4th at the expense of the pure 5th by raising F#3 until the 4th and 5th above it beat equally. That was called at the time, the "EBVT III". This leaves only two pure intervals: the F3-C4 5th and the A#3-C#4 4th. The result however is a very nice balance and an abundance of equally beating intervals. Those help to give the EBVT the very harmonious sound that it has.

I moved the raising of E4 from the end of the sequence (EBVT II) to step 9. Raising F#3 (EBVT III) always was and still is the last step. These two steps can be eliminated if one wants to do that but it will change slightly the character of the temperament, making it more akin to an early 19th Century WT than late 19th Century.

There is no other temperament exactly like the EBVT but according to Professor Jorgensen, the 18th Century Temperament Theorist, Johann Georg Neidhardt had sketched an idea that in its proportions, closely parallels the EBVT. There was no known use of that idea, however and there were never any written instructions for it. It was simply an idea that in the future, there would be a need for a temperament that was very nearly Equal Temperament (ET) but would still retain the distinct character of the cycle of 5ths.

As it is, the EBVT does exactly that: The deviations from ET are quite small. They are small enough that if a piano tuned at A-440 in the EBVT and one tuned in ET are compared chromatically with each other, they both seem to be alike on most notes but with only a slow wave that can be heard on a few notes (particularly C and G). It is not enough, however for a musician to consider the difference to be "out of tune".

That being said, the EBVT provides for 24 distinctly different Major and minor key tonalities in the proper alignment with the Cycle of 5ths that satisfies and adheres to the rules for Well Temperament. Therefore, a piano tuned at A-440 in the EBVT can be used successfully with any other fixed pitch instrument, (electronic keyboard, harp, tuned percussion, guitar, organ), including another piano tuned in ET. This has actually been done at one concert that I know of.


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Bill,

Interestingly, I have sometimes intuitively tempered that f#3-c#4 5th on some pianos for precisely the reason you mentioned. Thanks for the historical review. Very helpful.

Peter Grey Piano Doctor


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Peter,
I routinely "fudged" both C4 and F#3 for the same reasons until I realized that there waa an Equally Beating opportunity there all along. It's something like playing a game of chess and not seeing an opportunity until later in the game.


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Edit: E4 in previous quote. I would often raise E4 to slightly to improve the A3-E4 5th.


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So true 👍

Peter Grey Piano Doctor


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Very interesting, thank you!

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I couldn't understand a thing about the graphs, My Piano In EBVT III" thread for the sake of continuity. Your first post there was a good place for it

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