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Thank you Bill Bremmer for the additional info and the example.
I also noticed and glad to see that, in comparison to your 2007 article, 4:2 octaves instead of a compromise between 4:2 and 6:3 octaves will make things simpler for the tech that I am planning to propose your method. And now A#3 is tuned as a fourth up to F3 instead of the 5th down from the F4 as was in the article. Also the contiguous fourths-fifths within these A3-A4 and F3-F4 octaves are now equal beating. Am I right?
If I may ask a few more questions:
As I understand from the mail exchanges with this tech he is uncomfortable with 5ths and 4ths. So would it be okay to add a M3-M6 check for the F3-A#4 4th using C#3? (I am aware that he will already be comparing F#3-A#3 third, but still)
Any other checks that would make it easier for him to tune fourths-fifths in this temperament?
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Well Bill, that was quite a RW post for deciding not to post on the subject anymore here. Jeff, I meant that I was not going to post any more RW videos. By now, you should know that I believe the use of 4ths & 5ths sequences is responsible for RW. Your topic is about comparing the two kinds of sequences. It is on topic and pertinent to bring up the subject of RW. You already know that I say that a 4ths & 5th sequence tends to cause cumulative and compounded errors. You asked in your first post, "Let's see where this topic goes!" You start with a theoretical supposition that I find rather implausible. It appears to me that you and many of our colleagues on here find what I say to be implausible too. How could any tuner get that far off!? My answer to that question is, "Very easily". If you can find any evidence that the use of CM3's tends to create a trend towards a particular kind of error, then you should point that out. Make your own video or sound recording that demonstrates it if you will. Find a You Tube video that supports your argument. Find somebody else who says something akin to "Nearly every aural tuner who begins an Equal Temperament Sequence with CM3's ends up with cumulative and compounded errors. The results can hardly be considered to be ET but instead are (fill in the blank with the name for it and ask why no other technicians are noticing it). As to your question about why aren't other technicians noticing how commonplace the RW error is, that question has been asked and answered many times over. Perhaps I should be the one who is asking you that question? I know the answer. I wrote it again in this thread but you still ask me why so I am asking you the same question: Why don't they notice it?
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Hi Hakki and Bill, Hakki, thanks for noticing that the F#3-A3 minor 3rd should beat faster than the A3-C#4 Major 3rd, and slower than the C#4-F4 Major 3rd. And thanks Bill for confirming that and your detailed post above. The reason I like this, is that it fits in nicely with 'comparing' beats rather than 'counting' beats. Bill, it goes hand-in-hand with the Jack Stebbins "Let the Piano Tell You" method for setting the initial 5 contiguous Major 3rds. For those of you who haven't tried this method, basically it boils down to estimating an initial Major 3rd (A3-C#4), then tuning an octave from the note you just tuned (tune C#3), then you place the desired note (F3) in the middle. In other words, you have a fast-beating M3rd, a slow-beating M3rd, and your job is to just place the note so that it ends up beating somewhere in between. Very easy to do, IMO. The great thing is that you could be way off on the initial guessed Major 3rd (A3-C#4), but by the time you find the 'middle'-beating 3rd (F3-A3), the middle note (F3) is dead-accurate, for that size piano. Then the method has similar self-correcting steps after that, to get the initial 3rd (A3-C#4) dead-accurate as well, if it wasn't a good guess before. Hakki's observation as well as Bill's confirmation makes a nice test for F#3 once it has been tuned as a 5th below C#4. The window from A3-C#4 to C#4-F4 is pretty tight, if you got the initial 3rds accurate to begin with. There's your test that you asked for, Mark. As long as F#3-A3 minor 3rd fits in this window, you can be assured that you are at least in the ballpark - better yet, you're in the box-seats!
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OK, then I was correct, Bill. You are turning this into a RW blog. To me, ET is ET and everthing else is UT.
Read my original post and consider this. I am saying that both sequences can compound errors that are not noticeable until the same point in each sequence. Given the same error in the 4ths and 5ths for each sequence, the total accumulated error in the U3U3D5 sequence is smaller, perhaps small enough to make it difficult to know what or where it is. It may even be glossed over without dealing with it. But the same error with a 4ths and 5ths sequence will compound larger and can be more easily noticed and more directly dealt with.
But really, an experienced tuner should know what properly tempered 4ths and 5ths sound like and it shouldn't be a problem. There have been Topics about this.
If you are saying that the U3U3D5 sequence is better for novices, I guess I won't disagree. I was the only novice I have had dealings with so my very positive experience with learning a 4ths and 5ths sequence means very little statistically.
But I am not interested in the subject of learning to tune. I am interested in the objective differences between the sequences. That is what this Topic is about.
Jeff Deutschle Part-Time Tuner Who taught the first chicken how to peck?
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Hi Hakki and Bill, Hakki, thanks for noticing that the F#3-A3 minor 3rd should beat faster than the A3-C#4 Major 3rd, and slower than the C#4-F4 Major 3rd. And thanks Bill for confirming that and your detailed post above. The reason I like this, is that it fits in nicely with 'comparing' beats rather than 'counting' beats. Bill, it goes hand-in-hand with the Jack Stebbins "Let the Piano Tell You" method for setting the initial 5 contiguous Major 3rds. For those of you who haven't tried this method, basically it boils down to estimating an initial Major 3rd (A3-C#4), then tuning an octave from the note you just tuned (tune C#3), then you place the desired note (F3) in the middle. In other words, you have a fast-beating M3rd, a slow-beating M3rd, and your job is to just place the note so that it ends up beating somewhere in between. Very easy to do, IMO. The great thing is that you could be way off on the initial guessed Major 3rd (A3-C#4), but by the time you find the 'middle'-beating 3rd (F3-A3), the middle note (F3) is dead-accurate, for that size piano. Then the method has similar self-correcting steps after that, to get the initial 3rd (A3-C#4) dead-accurate as well, if it wasn't a good guess before. Hakki's observation as well as Bill's confirmation makes a nice test for F#3 once it has been tuned as a 5th below C#4. The window from A3-C#4 to C#4-F4 is pretty tight, if you got the initial 3rds accurate to begin with. There's your test that you asked for, Mark. As long as F#3-A3 minor 3rd fits in this window, you can be assured that you are at least in the ballpark - better yet, you're in the box-seats! I am thinking, why not tune a few 4ths and 5ths in order to produce an M6. Then tune the first M3 that should be at the same beatrate. If when constructing the ladder of CM3s it proves correct, well and good. If not, make some adjustments. I think I came up with a sequence like this a few years ago and posted it, but never got around to giving it a good try. Well, Christmas is coming!
Jeff Deutschle Part-Time Tuner Who taught the first chicken how to peck?
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I am thinking, why not tune a few 4ths and 5ths in order to produce an M6. Then tune the first M3 that should be at the same beatrate. If when constructing the ladder of CM3s it proves correct, well and good. If not, make some adjustments.
Why not tune each 4th & 5th slightly too little tempered and end up with both the M3 and M6 slightly too fast or slightly too tempered and end up with the M3 and M6 slightly too slow? Why not temper one 4th or 5th too little and the other too much and end up with a M3 that sounds right but an M6 that doesn't and then "correct" the problem by adjusting the wrong note?
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I am thinking, why not tune a few 4ths and 5ths in order to produce an M6. Then tune the first M3 that should be at the same beatrate. If when constructing the ladder of CM3s it proves correct, well and good. If not, make some adjustments.
Why not tune each 4th & 5th slightly too little tempered and end up with both the M3 and M6 slightly too fast or slightly too tempered and end up with the M3 and M6 slightly too slow? Why not temper one 4th or 5th too little and the other too much and end up with a M3 that sounds right but an M6 that doesn't and then "correct" the problem by adjusting the wrong note? The ladder would show the error. It would not be progressive.
Jeff Deutschle Part-Time Tuner Who taught the first chicken how to peck?
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My first impulse on hearing Bill's Bösendorfer example was to figure how to convert that tuning to a reasonable ET by moving the fewest notes. Variations of the game are how few notes need to be changed to finish up slightly sharp or slightly flat to match the rest of the piano more closely or put it back between pitch parameters. Often this works with a good temperament that time and atmosphere hav warped but this one cannot be salvaged.
Since all my tunings are used sooner or later in instrumental ensembles they have to be reasonably accurate and within pitch limits, fifths and M3s are my friends and allies in this.
I have used various variants of up a third up a third down a fifth since the '70's. Of course, all the beatrates for pianos over 6' are similar in most pianos and become extremely accurately memorised whether we want to or not. I bet I still can remember the slightly slower beatrates for the hundreds of Wurlitzer spinets I must have tuned at one time of I had to tune one now.
I really would like to know what is so inaccurate about this system. Bearing in mind all systems take practice and experience, I just find this one far more convenient and because I always tune complete unisons as I go and use every useful check as it becomes available, there is no backtracking.
Amanda Reckonwith Concert & Recording tuner-tech, London, England. "in theory, practice and theory are the same thing. In practice, they're not." - Lawrence P. 'Yogi' Berra.
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.....
I really would like to know what is so inaccurate about this system. Bearing in mind all systems take practice and experience, I just find this one far more convenient and because I always tune complete unisons as I go and use every useful check as it becomes available, there is no backtracking.
Did someone say it was inaccurate? I am saying it has similar problems in the same places as a 4ths and 5ths sequence: How far do you have to go before you really know the 4ths and 5ths are right? If you have time, could you try your sequence with 4ths and 5ths that are a bit too pure an tell us where it becomes a problem?
Jeff Deutschle Part-Time Tuner Who taught the first chicken how to peck?
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Hi Bill,
I am following your posts with interest. I want to expand what I already know, and also challenge you with my knowledge to test my own understanding of it, and my teaching skills, at the same time.
Ok, so, from the point of view that we are trying to help tuners who are trying to pass the RPT exam, and students who are just starting to learn this skill, isn't this approach, up 3rd, up 3rd, down 5th, too difficult to learn? I mean, hearing m3's in the temperament is hard enough, now we are asking them to fit it in between two M3's?
(By the way, I did use that today and it helped me refine a bit more early on. Thanks.)
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Jeff, My first fifth is down to F# so there's a minor third right there with the established pitch note. I can use that test interval all through the system as I progress. My experience won't let me leave this interval too slow because of the RBIs going out of the bearings downwards would be too fast. Nor can I allow this interval to be too fast either because that will make RBI's too fast going up from the temperament. Consequently the chance of my fifths being too pure is pretty slim.
Either way, I know my fifth is not errant by the tone quality of the complex interaction between the high harmonics at the "noise" level. That can't be taught reliably but can be learned reliably. Of course there's always the A below (not yet tuned) as a purely comparative 6th-10th test if it's reasonably close. Sometimes I might tune the F# first of all then a fifth and check the A-C#. Why not?. I'm constantly considering how an interval will affect the rest of the piano.
Mark, what you said reminded me of the many people I have met who simply can't hear RBI's. I have even been told that I must be imagining them. I was once told I must be imagining them. I had a tuning student who never heard RBI's all the time I knew her but she was an extremely reliable tone regulator from the start and went on to be a technician for a large dealership.
This may be related to the other thread about colour or something to do with the more emotional appreciation of unequal temperaments. Perhaps it might be something like a hundredth monkey syndrome (I know, I know) why so many of us can hear them now and the excruciating sound of a too fast thIrd, (particularly in alt) didn't bother most people and still doesn't, apparently. Even in ET, the RBI's in alt must be set with great care.
Maybe even the reason for experienced tuners who's thirds have never made sense. They simply can't hear them. Probably can't hear SBI's too good either.
The common concept of any kind of tuning is fourths and fifths. Even people who know little of music kinda know this, culturally. There may even be a subliminal communal guilt that if we don't use fourths and fifths we cannot be doing it right.
Amanda Reckonwith Concert & Recording tuner-tech, London, England. "in theory, practice and theory are the same thing. In practice, they're not." - Lawrence P. 'Yogi' Berra.
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Jeff, My first fifth is down to F# so there's a minor third right there with the established pitch note. I can use that test interval all through the system as I progress. My experience won't let me leave this interval too slow because of the RBIs going out of the bearings downwards would be too fast. Nor can I allow this interval to be too fast either because that will make RBI's too fast going up from the temperament. Consequently the chance of my fifths being too pure is pretty slim.
Either way, I know my fifth is not errant by the tone quality of the complex interaction between the high harmonics at the "noise" level. That can't be taught reliably but can be learned reliably. Of course there's always the A below (not yet tuned) as a purely comparative 6th-10th test if it's reasonably close. Sometimes I might tune the F# first of all then a fifth and check the A-C#. Why not?. I'm constantly considering how an interval will affect the rest of the piano.
Mark, what you said reminded me of the many people I have met who simply can't hear RBI's. I have even been told that I must be imagining them. I was once told I must be imagining them. I had a tuning student who never heard RBI's all the time I knew her but she was an extremely reliable tone regulator from the start and went on to be a technician for a large dealership.
This may be related to the other thread about colour or something to do with the more emotional appreciation of unequal temperaments. Perhaps it might be something like a hundredth monkey syndrome (I know, I know) why so many of us can hear them now and the excruciating sound of a too fast thIrd, (particularly in alt) didn't bother most people and still doesn't, apparently. Even in ET, the RBI's in alt must be set with great care.
Maybe even the reason for experienced tuners who's thirds have never made sense. They simply can't hear them. Probably can't hear SBI's too good either.
The common concept of any kind of tuning is fourths and fifths. Even people who know little of music kinda know this, culturally. There may even be a subliminal communal guilt that if we don't use fourths and fifths we cannot be doing it right. "My experience won't let me leave this interval too slow...""Either way, I know my fifth is not errant by the tone quality of the complex interaction between the high harmonics at the "noise" level. That can't be taught reliably but can be learned reliably."Yes, I agree. Many of the possible errors in any sequence are just not a problem when you know what you are doing. (Who knows how much of what we do is really done at the subconscious level and we only think it was done consciously...) But I am playing "what if" to take an objective look at the differences between these sequences. And I should thank you and others for their input. I am taking a different look at things, especially the idea of combining the two sequences by playing "why not?" I tried what I mentioned in an earlier post on an old upright yesterday: construct a M6 with SBIs, tune the first M3 in a CM3 ladder to that beatrate, and then prove the SBIs that created the M6 by trying to fit the next M3 in the ladder in place. I knew "by experience" that the M6 was a little fast but decided to continue anyway to see what would happen. Sure enough the second M3 wouldn't fit. When the SBIs were adjusted, the inside outside test working, and the CM3s set; then I had a sound structure to continue after only the sixth named note. I am going to work with this sequence some more. There are some variations and I am not sure what might happen when crossing a break with it. I don't know if starting a new Topic would be best or not if I get it worked out.
Jeff Deutschle Part-Time Tuner Who taught the first chicken how to peck?
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Bill, You had asked for a graph of the Bosendorfer tuning that Kees had analysed. Here it is in cents from just arranged in the standard circle of fifths from C. It clearly shows a trend toward RW. Regards (Edit: More accurate data)
Last edited by Mwm; 12/19/13 10:00 AM.
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Mwm,
I appreciate your support and find your graph intriguing. Let's give the benefit of the doubt, however. Just when was that piano last tuned? How hard was it played? Surely no scientific mind would accept that as evidence!
But let's turn the tables. When, if ever when, somebody produces a video of a technician aurally tuning ET and it actually turns out to be ET, will that be "evidence" (not just an anecdote) that ET has always been, is now and forever shall be? Will that one video (if it ever happens) prove that every piano we hear all the time anywhere and every piano that was ever tuned since Bach invented ET has always been in ET?
I have often read those who grasp at any straw cite some obscure evidence that somebody tried ET at any given point in the past, a century ago, two, three, four or even back to 5,000 years B.C. that somebody, somewhere, thought about ET! Therefore, it has always been the standard! Embrace it! (Or face it!).
Yes, I am getting off topic here, so sorry. I will take Jeff's usual tactic. No matter what evidence or logic there is which says that tuning a temperament in a cycle of 5ths will usually lead to either a Well Temperament or the opposite of it, I still don't believe it!
Show me just one video of somebody doing it and all I will have to say is that it just anecdotal evidence. Just because somebody did that somewhere, some how doesn't mean anything at all. Show me another one. Show me a dozen You Tube videos of somebody doing it and it will all still be anecdotal evidence. The scientific community would call it, "Humbug!"
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Bill:
That is a bizarre post.
Jeff Deutschle Part-Time Tuner Who taught the first chicken how to peck?
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Well, Jeff, I am waiting to actually see and hear somebody tune ET using a 4ths & 5ths sequence. Nobody has done it yet.
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Because the last 70-80 years has brought small pianos into the picture as increasingly the staple diet of the average tuner. They are confusing, if not impossible to tune. Before the 1930's the vast majority of pianos conformed to the rules of tuning. Thankfully there are fewer small pianos being made and those that are, are more tuneable by design. This has brought with it some confusion about tuning but has also instigated research.
Tuning by fifths and octaves and its' more compact derivative, fifths and fourths is only a hangover (with the headaches) from the days of WT when a wolf was expected so there was no backtracking and it was easy for even a beginning harpsichord player to do roughly but good enough. With WT there has to be an essential sense of order of things that doesn't exist with ET.
Many, if not most musicians don't hear the beating of thirds clearly, it seems. Even experienced tuners have to listen more closely to intervals on undersized pianos and some, as I mentioned before, some probably don't hear them at all or never listen closely to them.
ET readily lends itself to tuning predominantly by thirds for those who can hear them.
We are currently carefully taught not to trust our own perceptions. Rightly or wrongly, I trust mine implicitly.
How can anybody tune decent size pianos for a few years and not have al least some beat rates emblazoned on their memories? All decent pianos have extremely similar beat rates.
On any decent piano, I Sometimes tune fully more than half of the temperament octave to the one starting note by this sort of unerring beat rate memory no matter what my metabolism at the time.
That process begins with A, then C#,F,F#, E,D then C. Seven notes, not necessarily in that order. all these notes have enough cross checks between them to ensure accuracy before I continue. The rest of it then just slots in.
Whether the next note I tune is G or Bb, I have four checks for each of them just from within the octave. I can go outside the temperament octave at any time in the proceedure when the piano is reasonably well in tune already and find some checks for comparative use only. why reinvent the wheel every time? Of course it takes experience. Bad enough denying our perceptions. Why deny our experience?
Any alert tuner can start doing this with very little experience.
I always set the A electronically. I sometimes set the Bb from the same machine.
When I'm faced with an undersize runt of a piano, I might use contiguous thirds or simply rethink a little but it's all based on tuning bigger pianos. Big ol' uprights fall within that category.
Amanda Reckonwith Concert & Recording tuner-tech, London, England. "in theory, practice and theory are the same thing. In practice, they're not." - Lawrence P. 'Yogi' Berra.
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Well, Jeff, I am waiting to actually see and hear somebody tune ET using a 4ths & 5ths sequence. Nobody has done it yet. Well, Bill, if you define ET as progressive M3s and M6s, nobody has posted one here that was analyzed and was ET regardless of the sequence.
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As one who started with 4th/5th sequence as a student, later to add multiple interval checks over a 2.5 octave range, I was never happy with the result or the amount of time it took. There is, IMO, far too much wiggle room in the system for improperly placed 3rds, among other things. With very little movement of the 5th interval one can get a wide range of beat speeds within thirds. There is always a temptation to get SBI's too pure or beating in the wrong direction. Checks and corrections, usually multiple corrections, seem absolutely necessary. Backing up doesn't always reveal the cumulative errors either. For those going for speed and accuracy in aural tuning, the 4th/5th temperment is the wrong way to go.
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Well, Jeff, I am waiting to actually see and hear somebody tune ET using a 4ths & 5ths sequence. Nobody has done it yet. Well, Bill, if you define ET as progressive M3s and M6s, nobody has posted one here that was analyzed and was ET regardless of the sequence. Hi Jeff, Other thread posters have yet to converge on an adequate definition of ET. I would be willing to analyse, without comment and independent of Kees's phenomenal contributions, some temperaments posted, in terms of cents deviation from just (keeping in mind ET has M3s 13.7 cents wide from just). It would be useful to have at least two octaves C3-C5 or F3-F5 for analysis as it would show the evenness of the temperament over a slightly wider range. Regards
Last edited by Mwm; 12/19/13 03:19 PM.
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