This, too, is a subject carried over from an earlier thread. I could PM Kees (aka DoelKees) about this, but I thought others might be interested to follow the discussion and chime in.

Kees: You mentioned a TuneLab plug-in that you wrote, possibly solving the initial stretch choices in extending the temperament into the rest of the mid-range? As has been discussed here earlier, I think none of us has been able to get the same ETD results as we can get aurally.

As I've followed your posts carefully since you joined here, I know that if you're on to something regarding the maths behind it, it's worth checking out. I don't have TuneLab myself, but I could run it in trial mode on my Pocket PC. Would you like me to measure the tuning result of your plug-in against what I get aurally?

I would really be interested in this too.

Pat:

I PM'd you long time ago about getting me a recording of your aural EBVT3 tuning, and am still interested. Strip mute the piano and record each note separated by a silence, and I can take it from there.

I remember trying to reconcile the computed tuning, following Bill's verbal recipe to the letter, with the offsets he provides, using inharmonicity data of the piano brand he tuned, though not the specific piano, and found there was quite a bit of discrepancy. I tried to tweak the math to account for vagueness in Bill's recipe to improve the match. For example what is a "pure 5th". For me it's an equal beating 3:2 6:4 compromise. That seemed to improve things. On high inharmonicity piano's there seems to be no way to tune D5 in a way consistent with Bill's requirements though.

Quite a few people have emailed me their tunelab inharmonicity measurements and I sent them my computed EBVT3 offsets. Responses were very positive.

Kees

Kees,

I have completely missed (or forgotten about) that earlier request of yours, sorry about that.

So what you'd like to have is single strings, recorded on a digital media, right? I'll record an EBVT III tuning on a grand, and send it over.

If you're interested, I can compile a list of ambiguities in your aural EBVT3 recipe which you can perhaps clarify. They are ambiguous from a mathematical point of view, as you sometimes refer to intervals being "improved", "acceptable" etc. Not so easy to program on a stupid computer

Let me know.

Kees

Kees, Bill,

I tuned a Yamaha C5 in EBVT III for a performance tomorrow, and recorded all the pitches (x 3) with the muting strips still in.

I also did some 10ths, 12ths and other runs. Too late to put it up on the web tonight, but I might find some time tomorrow.

I did my best to be faithful to the temperament and to be fair in the stretch, and I have to say that the end result was much better than the slightly "watered out" version I've been using lately. I really really like that F-C pure 5th, will go back to the original.

Bill, you truly have a phenomenal temperament! EBVT III, to me, is sheer beauty. If somebody might be able to implement this on an ETD, I bet it's Kees

Kees, why don't you take that list into this thread? I'm sure some of us tuning the temperament could contribute to the task of bridging the gap between numbers and adjectives!

Ok Pat, Bill, let's start with step 1 of EBVT. The instructions I have state to tune F3A3 at 6bps instead of the usual 7bps.

Now on all piano's that I have data on the F3A3 third, when tuned in ET, beat from 6.3 bps (on the lowest inharmonicity concert grands) to 6 bps on large uprights to even slower.

So the first adjustment I made is to first compute a standard ET F3A3 for the particular paino, then scale its beat rate for EBVT by a factor 6/7. Usually this comes to be about 5 to 5.3 bps instead of the 6.

This improves dramatically the agreement with my computed tuning chart and the one Bill provided me with for a Steinway D, for which I have two measured instruments.

Needless to say when I check my calculations on a hypothetical piano with no inharmoniciy Bill's number are right on.

I'll post comments on the instruction on how to extend the temperament in a bit. They are crystal clear for aural tuning but computers do not know what a "reasonable" octave is

Cheers,
Kees

Hmmm, I don't know. Duh.

I think "tune F3A3 1 bps slower than resulting from contiguous thirds in ET" is what the aural instruction should be and a factor 6/7 slower for computers. Have you or Pat ever timed the beat rates?

Kees

I have been using tunelab for years now. When I first got it, different temperements were built-in. I had fun, but was not so aware. Unisons were my thing back then.

So I took measurements of inharmonicity on many pianos, and kept tuning ET.

EBVT only goes a few cents sharp or flat here and there. It's just a nice temperment.

I took the offsets that were posted on this forum, and created a new temperment in tunelab.

Now, if I load a former tuning for a customer, I can change the temperment. And it works well.

I really do not see the problem about temperments.

The top and bottom ends are always better by ear, but tunelab works really well.

Well, thank you for that vote of confidence.

As far as I know all ETDs use the method of having 12 UT offsets to be added to the offsets related to stretching and inharmonicity, irrespective of the octave. A paradigm shift is needed here as EBVT needs 88 unique offsets, which depend on the inharmonicity.

Currently the only way to implement EBVT with an ETD is in tunelab and it involves emailing the IH data to me, and I compute the custom tuning.

Kees

Kees,

Do you feel that tunelab, when given the different temperment offsets, and the ih measurements for a certain piano, does a good job? Of stretching it?

It does a perfect job. But EBVT required a stretching that is different from normal UT's, which tunelab does not do.

For all other UT's the temperament is transposed unaltered over the keyboard. As it should be.

Kees

Yes, Kees... I think that both Bill and I are doing two things:

1) relying on the 6 bps framework symmetry -the anchor points - of EBVT III.
2) slowing them down a bit on shorter instruments.

I learned this from Bill in a kind of upside down way: my first EBVT III:s were on grands 6ft+, and 6bps worked fine. 6bps works on shorter instruments, too, but then some of the fifths are heavily compromised (Bill, I don't know if you remember me asking about exactly this in the beginning when I hit a brick wall with a spinet kind of piano). Anyways, I can confirm first hand that Bill subconsciously drops his 6 bps down in speed when he deals with shorter instruments.

The reason I know is because it was the first instrument I ever played that Bill had tuned... At the PTG convention this summer, I played a short Petrov, if my memory doesn't fail me? Anyways, the "balanced frame-work" (F3-A3, C4-E4+, G3-E4+, G3-B3) was there, only slightly slower than 6bps - I heard it as "between 5 and 6 bps, which corresponds well with you math.

This is fascinating, because of course Bill does this without thinking twice about it. Hence the need of an interpreter

Kees, I have on paper, the 2 EBVT III tunings Bill did for me...This later one has much more of a stretch than the first one. These are exact figures for all 88 notes. Of course this was designed for my piano. Would these figures help you in any way?

See, I have this feeling that once we sort all of these adjectives vs. math issues out, your unique calculation could easily be implemented into any of the leading ETD:s out there, if anybody dared. My first hunch was that TuneLab might show the greatest interest (you and many other PW members endorsing it), but that was not the feeling I got from my initial feeler.

Ok all, bed time here now. It's 7 AM, and I start teaching in the afternoon. We're on to something good - let's keep this thread active

I agree Patrick, this is something good. I'd really like to see something come of this.

Unlike with ET where the contiguous thirds "find" the exact speed of F3-A3, I always set it at 6 beats per second (or at least I perceive it that way when tuning either version of the EBVT. After all, who could tell if it is exactly 6.000 beats per second or not.

The point is that on short scaled pianos, when I use the contiguous thirds, I can hear that the result is a slower beat than the usually perceived 7 beats per second. It is a mistake to impose that beat speed on such a piano. It will skew everything else if that is done. I know that people often do it but that is why they can't get other intervals to work out as they expect afterward. The reason, of course is that on such pianos, the F3 string will often have very high inharmonicity unless it happens to be a wound string.

This may be the reason that some have said that contiguous thirds "don't work" in ET. The key to having them "work" is not to impose an arbitrary value for the F3-A3 M3 but to allow the set of the four contiguous thirds from A3-A4 to discover the right value. When that is done, everything else will fit into place normally and as expected.

Now, with well temperaments, the rules of the game are somewhat different. A well temperament can still be a well temperament and have all of the described and defined properties even if the results vary from one piano to another.
When I do the EBVT (any version) aurally, I usually do not go to the extent of measuring the initial 6 beats per second against a metronome although I sometimes do. I just estimate it; it sounds like what I want to hear and go with it. So, there definitely can be some slight variation in it.

However, when I use the programmed tuning/direct interval approach, I always set A3 at 0.0 read on the 4th partial. When I set F3 at 1.0, the F3-A3 M3 inevitably sounds like 6 beats per second to me. The Steinway tuning was measured with a metronome and so was Grandpianoman's. The only time I can recall that 1.0 did not work for F3 was recently when I tuned Andy's Lester spinet.

In that case, there is a long bass bridge with six tri-chord wound strings extending up to F#3. It is a very short scaled piano. The lowest plain wire tenor strings were presumed to have very high inharmonicity while the highest wound string obviously had much lower inharmonicity. In that case, F3 at 1.0 sounded like 7 beats per second to me.

I used a metronome and settled on F3 at 0.0. Normally, one would expect both F3 and A3 as read on the 4th partial and set at 0.0 to beat at approximately 7 beats per second. In this case, the low inharmonicity string had to be tuned sharper than usual to produce 6 beats per second with the high inharmonicity string.

Now, I don't know the higher math and couldn't at this time begin to dabble in it. If I were to set F3-A3 as slow as 5 beats per second, I could still use the EBVT sequence but it would alter the rest of the temperament enough to be more like an early 19th Century temperament. Indeed, I use the very same sequence to tune an representative 18th Century style temperament but start with the initial four RBI's at 4 beats per second.

When I do that, I can leave the F3-A#3 4th beatless. The rest follows exactly the same as the original EBVT. Changing the initial F3-A3 M3 by just 2 beats per second creates an entirely different WT which Owen Jorgensen said was a Young-Werkmeister composite. I can see what he meant by that because it has 6 beatless 5ths like Werkmeister but the initial M3's and M6 are slightly faster like Young's.

I would tune this 18th Century style temperament's octaves the same way I would the EBVT's. That is by equalizing octave and 5th combinations. Therefore, a calculated ETD program would not work well. Some octaves would be too wide and others too narrow. However, a meantone temperament will work well because all of the tempered 5ths are tempered equally.

Accordeur,

It is fine to use the ETD program for tuning the EBVT III. However, you will want to aurally verify the span for F4 to F5. After tuning according to the program, play the 5ths beginning at A#3-F4 to A#4-F5. If there are any that sound too intolerably narrow, you will want to widen the 5th. This may mean simply sharpening the upper note but if the 4th below the note being tuned also sounds quite fast, you may want to flatten that note rather than sharpening the note being tuned. Sometimes you may want to do both. Often, it all sounds acceptable except for the G4-D5 5th. Inevitably, you will want to sharpen D5 by 1 cent.

Using the calculated ETD program for tuning the EBVT III can produce acceptable/satisfactory results but the they are never quite as perfect as with aural tuning or tuning the octaves by direct interval. I am working on a long article that explains all of this in exact detail. It will be presented as a handout to the attendees at my classes in Michigan and at the upcoming convention. The article will also appear on my website when it is finished and will be submitted to the Journal for publication.

Bill, I think the key is that you feel them sounding like 6 bps, but I suspect they might be a tiny bit narrower. Let's settle on 5.5 and be happy all, shall we? Just joking

Anyways, when I tune small pianos in EBVT III, my "beat rate framework" is indeed maybe 1/2 bps slower - somewhere between 5 and 6 bps. Otherwise I get a really strange place for G3, which leads me to having a hard time placing D4, and getting a twangy G3-C4 fourth.

I have to admit that I haven't ever done the math on this one, this is just empirical research.

I will start making the sound files from yesterday's recording in an hour or so.

Thanks GPM, you send them to me long time ago and they are helpful.

Kees

Bill, if the contiguous third method for tuning ET produces F3A3 at 6 bps on a small piano, surely the F3A3 in EBVT must be beating slower, agreed? I programmed it in as a factor 6/7 slower, to agree with your idealized numbers.

Does that sound about right?

Kees

Correction: I meant from 6.9 bps (on the lowest inharmonicity concert grands) to 6 bps on small uprights.

I'd better get my numbers right...

Kees

Kees, thanks for the correction. Your ET F3-A3 window (6.0-6.9 bps) should equal an (5.2-6.0 bps) EBVT III window for F3-A3.

(6.0/6.9 = 0,8696 | 6 x 0,8696 = 5,22 }

Does this sound reasonable? Aurally these numbers are close to what I end up with, although I have to admit it has to be a ridiculously short and quite severely "musically challenged" piano before I go below 5.5 bps. As of today's date, I've done that exactly once... It salvaged my temperament, though, so it was def worth it.

If you do it then it's reasonable. I have the strange task of recovering a mathematical specification of a temperament from aural tuning instructions, which is the inverse of the usual problem.

Kees

I guess you're right, Kees. I do it by the seat of my pants, you are the math whiz.

Let us see if I can help with bringing maths and ears together. Here are the single string recordings of a Yamaha C5 tuned in EBVT III. Tenor break at A#2/B2, treble break at D#5 (I think?).

As I mentioned earlier, I tried to stay as true to the temperament as I could. Same thing about the stretch - I did it as faithful to the temperament as I was able to.

Every note is struck three times, to ensure good samples. The files are in 16-bit wave format.

2011-03-22 EBVT III single strings A0-C4 (wav-16/236 MB)

2011-03-22 EBVT III single strings C4-C8 (wav-16/171 MB)

[EDIT 2011-03-24 04:00 CET+2]
I had extremely slow downloads on my dropbox as I checked it for speed a sec ago... I'll try to find alternative servers. [/EDIT]

Here my questions about the aural tuning instructions for EBVT3,
attempting to get everything precise and independent of taste and common
sense. The goal is to make the instructions precise enough to implement
in an ETD. The quoted material are Bill Bremmer's instructions.

I'll post questions about the bass later on.



Here I take the F3A3 beatrate to be 6/7 of the beatrate resulting from
an ET. On concert grands it is close to 6, but on tiny little spinites
it may become 5.

In the instructions for the temperament scheme we should state what kind
of "pure fifths". I assume they are to be 3:2.

The above is all crystal clear.

How should the 4th and 5th be tuned to have "exactly the same tempered
sound"? Equal beating?
Two issues:
(1) What do you want ideally? Have the 5th and 4th beat proportionally
according to the rations of ET, or beat exactly equal?

(2) What is a "reasonable octave" precisely? I checked in my software
that the 1:2 or 4:2 octave does not beat faster than either the 4th or
5th. In practice the octave beat rate is always much slower, so this
check is superfluous (for a computer which makes no errors).

So D#3 and D3 are tuned with the same method as E3.

This is unclear. Should the 4th and 5th above C#3 have the same relation
as for D3? If so, how does tuning C#3 differ from tuning D3? In practice
the octave is never a problem here, but I need to know if the 4th above
C#3 should be purer than the 5th above it, or the same, or in the usual
ET beat proportion.

I understand whatever method is used for C#3 should be u8seed for C3.

So what is the desired relation between the beat speed of C#4-F#4 and
B3-F#4? Equal? 4th slower? 5th slower?

So what is the desired relation between the beat speeds of the 5th and
4th below G4? Not the same as we have to "favor slightly the sound of the
5th over both the 4th and the octave". The octave here is always beating much slower at the 2:1
and 4:2 level and seems to play no role. In my implementation I made the
5th beat 2/3 as fast as the 4th.

So whatever the precise method for G4 is is what we use for A4.

What beat ratio you want here for the D#3-A#4 5th and the F4-A#4 4th?

So whatever the precise method for G4 is is what we use for A4.

Clear.

The way I understand it, we should tune and equal beating D4-D5 4:2 octave and
G4-D5 3:2 fifth here.

The way I understand it, we should D#5 and E5 with the same method as
D5.

Thanks Pat, that's a lot of data. I appreciate your effort.
It will take me a little while to analyze.

Kees