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Hi Jeff,

You wrote:

..."Here are some questions.

If we use a practical definition of ET on an actual piano as "All discernable chromatic major 3rds and major 6ths have progressive beatrates." what tolerance in cents is required for each note?"...

The "tolerance" would not be "required", perhaps "allowed"? In my experience, none;

..."What is the repeatable tolerance of typical ETDs in cents?"...

I do not know about ETD's; in any case, any tolerance will mess up the (final) beat-rate progression;

..."What is the tolerance of an experienced tuner's ability to place a note at the pitch he desires in cents?"...

I cannot answer for others, but myself: perhaps zero.zero;

..."What percentage of modern piano scales are capable of being tuned with progressively beating major 3rds and major 6ths across the break while keeping the same octave/12th stretch scheme above, below and across the break?"...

The "scheme" must consider also 4ths, 5ths, 10ths, 15ths and 17ths, and you can think of a very, very, very high percentage. In other words, scaling is not the problem at all. Sometime you get a false string across the break, but that's a different question.

Regards, a.c.

I get about 0.2 cent, in the sense that if 4 notes are off by this much in just the wrong direction, a previously perfectly progressive chromatic M3 pair becomes equal beating. I haven't checked M6, but assume it's about the same.

According to the manuals, Verituner = 0.01 cent, SAT-IV 0.005 cent, Cybertuner 0.01 cent. Didn't find it in the tunelab manual.

Another question is how accurate can one aurally compare beatrates to determine if they are progressive or not.

Kees

Kees, you wrote: ..."I get about 0.2 cent, in the sense that if 4 notes are off by this much in just the wrong direction, a previously perfectly progressive chromatic M3 pair becomes equal beating. I haven't checked M6, but assume it's about the same."...

Ok, and then... what happens one octave above (or below) (edit: with the same tolerance)? My guess, some M3 will reverse;

..."According to the manuals, Verituner = 0.01 cent, SAT-IV 0.005 cent, Cybertuner 0.01 cent. Didn't find it in the tunelab manual."...

On top of that, there is still hammer/pin/string_stable_pitch individual skill, not in the manual;

..."Another question is how accurate can one aurally compare beatrates to determine if they are progressive or not."

Very very accurate, I would say, as it is only a question of rhythm, when you are strict and honest.
.

U

Exactly, Alfredo.
In my own first experiments, all those years ago, I worked out the metronome speeds for four beats per click in RBI's. 8 beats per second being semi quavers (sixteenth notes) at mm=120. Working out the same rhythm for 7.3 beats per second, etc. at a slightly slower mm setting and so forth. While taking exact numbers like this as gospel is not entirely correct, this method gave me a better start, I think.

Somebody years ago on this forum said that a sense of rhythm is more important than a sense of pitch in tempered tuning.

I was thinking much the same in response to UT's questions; that perhaps it's more appropriate to think in terms of beat rates than cents.

As I said a very long time ago, beats are the divergence from just intonation, while cents are the divergence from equal temperament. Beats are natural and can be heard, while cents have to be computed.

UnrightTooner:

First, I think all technicians here, taking the time out of their day to post, have practical experience with implementing ET on the piano. The difference may be in the quantitative understanding of what they are doing.

Second, aural tuners never think in cents, because they change in relation to frequency across the spectrum (A2 - 16c/Hz, A4 - 4c/Hz, A6 - 1c/Hz). Cents resolution decreases as frequency increases.

#1 - Just concerning M3rds/M6ths in the temperament region (again this changes as frequency increases), about +/-0.75c at the maximum. If any one note varies more, it will exceed the window of 'progressive'.

#2 - As Kees said, about 0.01c for machines internally. This does not mean a tuner can transfer that precision to a pin, or that the +/-0.01 machine point is the right point.

#3 - An experienced tuner with a good piano should be able to make stable changes on the order of 0.1c. Finer variations necessary for uncompromising tuning are on the order of 0.01c.

#4 - This is a very small number of pianos, in the 7'+ range. Some variation and compromise is always necessary across the break, even in the finest pianos, due to the reduced inharmonicity of all wound bass strings.

As a test I tuned F3-A4 using tunelab. A recording of the M3, M6 and m3's is here.

Do they sound progressive to the expert tuners?

Kees

Hi Kees,

My tuning approach is to find intervals that don't fit and fix them. The quality of my tunings are dependent on how good my ear is in telling me if something doesn't fit, not telling if it is perfect. I teach my students that instead of looking for perfection, simply try to improve on what you hear could be improved. As your hearing gets better, you are able to hear more and more precisely. As you fix more and more subtle inaccuracies, your tunings begin to "appear" more perfect. But as my swimming coach says "There's always someone faster than you.", i.e. there's always someone who hears more that could be improved.

So, for temperament, I would look for any RBI that slow down instead of speeding up, (because trying to decide if a RBI increases more than it should is just too darn difficult for my weak ear) and then confirm with other tests to find which note could be improved, and do just that, make it better, not trying to be perfect, that illusion comes later as you are refining more and more subtle inaccuracies.

FA -
F#A# -
GB -
AbC -
AC# - slows down
BbD -
BD# -
CE - slows down
C#E# -
DF# - slows down
EbG -
EG# -
FA -

FD -
F#D# -
GE - slows down
AbF -
AF# - slows down
BbG -
BG# - slows down
CA -

FAb -
F#A -
GBb -
AbCb -
AC - slows down
BbDb -
BD - slows down
CEb -
C#E - slows down
DF -
EbGb - slows down
EG -
FAb - slows down
F#A -

Now, I know you already know what the speeds are by using your software, so you may be able to make me look like a fool here, but, understand that this is a snap shot in time, a "guess" if you will. If I was at the piano, I would be using multiple tests to confirm my "guesses" and also confirm if my corrections didn't knock something else out. If half of these are right, I would be impressed.

The m3's were tricky. They actually sounded right on, but the "slows down" were like figments of my imagination. I don't use m3's much, especially up there.

(Addendum - Tunelab?! I didn't realize that until just now. Very interesting. How sure are you that the pitches match Tunelab? How did you create the stretch? Six notes within F3 - A4 would've been best.)

Thanks Mark, it is nice to put your money where your mouth is as the saying apparently is in English. I do hope you will not be the only one to do so. I haven't analyzed the beatrates yet, but will do so when I find time.

Regarding tunelab: I just used the default sampling for ih provided with tunelab. This is intended as a test of the ETD, so I didn't want to do anything unusual.

Kees

Doel,

I'm not an expert tuner yet, so take my opinion for what it's worth.

No, those series of chromatic intervals you played do not sound progressive to me.

What kind of piano is this? It sounds like a short upright. Where is the break between wound and unwound strings? And where is the break between bass and tenor section?

I'd be interested to hear the inside out M3 / M6 tests. Can you post a recording of that?

Many thanks for the recording and the invitation to comment. You're brave!

We do not have to agree, this is more about how we think.

1. Ok, instead of asking "how many cents", we could say "how many beats" but only as a ratio of the beats of the intervals above and below the interval in question. (1 bps means 4 times as much in the F2-A2 M3 than the F4-A4 M3.) The ratio of any two intervals a semi-tone apart is about 15:16. The problem is that the further that an interval is tuned from just intonation, the further you may change the pitch of a note and still have the interval be progressive. M3s are a little more just than M6s, but P5s are way more just. In the above definition of ET, which no one has disputed, we can consider just the M3's for tolerance, because they are closer to just than the M6s. As has been correctly pointed out, the permissible error of one note in a pair of chromatic intervals must be divided by 4 for the allowable tolerance of all four notes. So when adjusting the beating of one interval by changing one note, it cannot be adjusted more than 1:16 of the beatrate before the intervals are no longer progressive. And when we consider all 4 notes, none can be adjusted more than 1/48th of the beatrate. It ain't much. When you work this out as cents, I get the same answer as Kees, of course: +/- 0.2 cents.

2. Repeatable tolerance is different than advertised accuracy. I have never used an ETD, but from reading many posts about their use, when measuring a note over and over, the repeatable accuracy is +/- 0.3 cents.

3. Again from reading many posts, it seems that the ability of a typical experienced tuner on a typical piano to set a note where they want it to be is +/- 0.3 cents. I have to kind of wonder about this, as it is the same repeatable accuracy for ETDs. So how would anyone know? But when I take a sober look at my own abilities and considering the extremely small change in beat rates that this would equate to, I think I believe it.

4. Once in a while I will come across a piano that has a break that does not cause some sort of "wrinkle" in the tuning. They have all been modern studio uprights or modern baby grands. I am not saying that a seamless break is best (I have my doubts), just that they are very rare in my experience.

So some believe that they can always achieve progressive M3s and M6s on any piano across any break without much compromising. Well, I will consider this to be an "Indulgent Mystery".

Kees brought up a very good point: "Another question is how accurate can one aurally compare beatrates to determine if they are progressive or not." I would think at least the difference between 15:16 and 16:16 or we wouldn't talk about using chromatic beatrates as checks.

Myself, I think I can distinguish about 4 times finer. This all fits in with what I consider my ability is to put a note where I want it. I often can hear that some M6/M3 tests have the M6s a little faster and some the M3 a little faster but cannot do much about it. But since the ETD vs Aural opinions are starting to rear up their ugly heads, let me also bring up the RBI vs SBI argument discussion. The chromatic beatrate ratio change for a given change in pitch with SBIs is 7 times greater (more precise) than with RBIs.

This all does mean something to me. A practical definition of ET on an actual piano as "All discernible chromatic major 3rds and major 6ths have progressive beatrates." is a good one. It is just barely achievable, but still objective without resorting to scientific instruments. So ET, being definable in the real world on real pianos, CAN be a standard. But if someone wants to use it more as a reference for something else that they prefer, well, it doesn’t cause me physical pain.

Not so much, some intervals are Ok other do not progress enough, or too much.

Could the software show that the beat rates are not even/straight and they change in time?, there is some sort of "bloom" due to the beat rate speed varying very slightly.

Folks, I am not here to argue.

I am just going to reply to Jeff.

Jeff, I have not done extensive checking but have checked my aural temperament and octave tuning with tunelab, not so recently.

From what I recall, depending on the pianos and myself (i suppose), in my temperament, I could get absolutely spot on to a cent or more off. With my octave tuning, I seemed to be about a 1 cent off of the 4:1 double octave stretch in general.

FWIW

Don't ask me anything to in depth, you'll confuse me!

The break does cause a minor problem, if one can say that.

I always tune 4ths, 5ths across the break, I listen to the octave and 3rds and move on.

No in depth questions, just an intriguingly simple one. When you compared your temperment to tunelab, were the M3s and M6s progressive?

Nice test - I assume you will post the analysis later?

The first three thirds sound the same speed to me, G3-B3 sounds perhaps a fraction slower than the preceeding two.
The next progress fine.
C-E and C#-F are slower than the preceeding thirds. D-F# resumes the progression. Difficult to hear above that, but E4-G#4 sounds fast compared to F4A4

F3-D4 is too slow, F#3-F#4 too fast. The next progress until A#3-F#4 which is slower, and the C4-A4 is too slow as well.

The m3rds I find a bit difficult to hear in this context.

I would listen, but I can't seem to get at the file.

Jeff, I do not recall, unfortunately!?

I too, am not able to get at the file.