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What surprises me is that this is not taught more! What you say about the 6ths makes total sense. Once you can wrap your brain around this concept you can predict what may happen with beat speeds in these pianos. It makes it much more fun! I use to go nuts going around in circles trying to make those 3rds beat the "right" speed. Since beginners are mostly tuning these types of pianos, this concept will hopefully become more common knowledge.

Jeff, if the piano is detuned for an exam or a substantial pitch raise, the test notes are NOT in a convenient place, (as I have said over and over), therefore, if you want to use them, you have to adjust them too and it is simply not necessary and furthermore is counter productive. No audible beat in a 4th or 5th puts it within a narrow enough range to be workable. The system clearly works just as written. You always want to re-invent it to something "better" before you even try it and then fail and go on to say it doesn't work.

Ryan, a perfect ET can still be constructed across the kind of break you describe and it doesn't compromise any interval all that much. If F3 is a wound string and all strings are above it are plain wire, you can still construct the series of CM3s within that F3-F4 octave, construct the rest of the temperament within that octave and proceed below F3 without any compromise that would cause the temperament to be something other than ET. The M3-M6 tests will work too. All one has to do is follow the steps and not second guess them or re-invent the whole thing on the fly. But if you try to impose theoretical beat rates on everything (which is in any case, humanly impossible), it will fail every time.

I started learning how to tune on an acrosonic spinet. Lowest plain wires are on G3. I always tried to get close to 7bps on the F3-A3 third and set my CM3's. I took the Randy Potter course and CM3's were one technique that was advocated and it said that short scales may require a slower F3-A3 third due to "inharmonicity"- but didn't go into a lot of detail beyond that.

Anyway, the E3-G#3 M3 slowed way down no matter what! Every time! As if TIGHT tuning pins and a student hammer didn't make it hard enough!
It wasn't until I slowed the F3-A3 M3 to near 6bps that everything started to fall in line.

It was reading Bill's articles on his website that helped it click a little better for me, even though I was familiar with CM3's. It was still tricky at first but now has become virtually indespensible for me.

I haven't tried the Marpurg variations yet, so I can't speak to that but CM3's are a good tool. When the chain is "off" you can really hear it and it usually is fairly easy to hear the culprit.

I usually try to get 6 CM3's from A2-A4 as per the Baldessin-Sanderson method Gadzar mentioned. This goes part of the way towards dealing with scaling issues over breaks early on. It takes me a little longer but is usually worth it. Then I go onto a Potter F-A temperament which is basically up a 6th, down a 3rd, down a 3rd three times plus a few more steps to make a 10th(F3-A4) which is kind of backwards from Bill's up a 3rd, up a 3rd, down a 5th. And it can be tuned as a 3rds/6ths sequence or a 4ths/5ths sequence or a little of both and you don't have to change the order of the sequence.

There's another variation I've been experimenting with involving establishing the width of a 12th early on and balancing that with CM3's.

I have to say that learning the CM3's gets you REAL CLOSE. If anything, it's trying to get the first 2 octaves to match that may get tricky when that F3 is a wound string. But, once you get the "feel" or the "ear" as to the roughly 4:5 progression of CM3's the temperament usually falls right into place.

When I have a lot of trouble with a difficult (to tune) piano, because it's not well scaled, or it has dead strings, false beats or any other problem, I take out my Verituner and I tune the temperament with it. Technologie is a good thing!

But the point here is to find a sequence which guarants enough accuracy in a reasonable short amount of time. If I have to make 29 tests to see if an interval is correct that’s fine with my search of perfection but it’s not good for business.

If I can get a good set of CM3rds without tests and then an acceptable temperament with only a few tests: That is proficiency! If after that I have enough time to refine my tuning, then there are tones of tests which can be used to do that.

The important is to be able to produce aurally a good temperament in a short amount of time in a reliable way.

Thank you very much, CJ. Once the F3-F4 octave has been tuned, if one wants to establish another octave below that, tuning F2 to F3, then filling in the A2 and C#3 notes really works the same as it does with the octave above it, even on such pianos as an Acrosonic. Tuning octaves from A2 to A3 and from C#3 to C#4 gets those notes close, then it is a matter of listening to whether there is that small, slower/faster relationship and making slight adjustments if necessary but still maintaining "pure" sounding octaves in all of them.

Then, filling in the notes in between in similar fashion, octaves first, then checking 4ths & 5ths, then as more final and finer checks, the CM3s and minor thirds, the scale can be perfectly equal and still maintain all proportions. The method for doing it really does have an effect on the outcome. The method will work on all pianos.

That method begins with the F3-F4 octave CM3s and using the F3-F4 octave as a unit, then placing C#4. If it is determined that the chain of CM3s does not quite work out, no matter to how small of a degree, the initial F3-A3 M3 is adjusted but because F3 has moved, so must F4 by the same amount. The F3-F4 octave must serve as a unit in itself and therefore does not involve any estimate whatsoever. Then C#4 may or may not need to be moved as well.

I'm afraid that none of the CM3 schemes I have seen written up explain the technique in quite the same way. It is more like, "Play around with these notes until everything seems balanced". That may work but then again, it may not. That is the critical flaw I have seen with all other CM3 schemes.

Both in a roughing in procedure and in the finest review and correction, the series of 4 CM3s from F3-F4 MUST be used (not just 3). In the finest review and correction, it must be determined that both the F3-F4 and A3-A4 octaves are of the same type, size or width (all three of these terms are synonymous).
When you have smoothly ascending and descending CM3s spread over a chain of 4 intervals (again, very importantly, 4 not just 3) AND you have determined that both the F3-F4 and A3-A4 octaves are of the same type, those five notes are as close to ultimate accuracy as is humanly possible.

The same can be replicated from F2 to F3 on any piano that exists, regardless of scaling. If this seems to contradict what any other description or method involving CM3s says, if only slightly, then it is a reason to validate the subject of this thread, a "New Look at Tuning CM3s".

There really is something new about it (sorry BDB). Yes, the basic principal was known in the early 20th Century, I read that again in Owen Jorgensen's "Tuning" book yesterday and noted I had put a paper clip on that chapter but had forgotten about it. It is still true to say however, that it was not brought to light until the early 1980's by Dr. Sanderson. I recall hearing Rick Baldassin talk about it and the "move the notes around" business back then too.

Every so often, I review older material I have known for many years to see if there is anything more I can pull from it. First, I found something with the CM3s I could apply a specific technique to. Then, I took a look at the "Marpurg" temperament and asked myself, "What if I applied the same equal beating technique that is used to tune the G3, B3 and D#4 of that temperament to the notes which were tuned as pure 4ths & 5ths? Would they then be moved to the correct position for a true ET? The preliminary results I got aurally were that it worked.

A theoretical analysis by Owen Jorgensen revealed that it was still slightly imperfect but within a very small margin. He told me that he had never heard of such an idea before but that it was very clever indeed. Slightly imperfect not withstanding, that was still good enough for me to put forth as a valid technique.

Trials with many, many people who otherwise did not have the skill to tune an acceptable temperament revealed that what they could produce on their own with no coaching, yielded results that are acceptable by PTG's standards, often within the superior range and yesterday for the first time with no error at all according to PTG's standards and by using PTG's methods for scoring.

Show me or tell me who, where and when ever did that using the Braide White sequence! Who ever tuned a temperament octave where and when, using no checks whatsoever, that yielded results that close to absolute perfection?

Thanks again, Rafael, you wrote your post as I was writing mine but you seem to very well understand my point and purpose.

Bill:

If a piano is so far off that the test notes for fourths and fifths are unusable (You do not mention how far off this is, so neither will I) then the test notes for octave types will be too far off, also. But, I don’t remember reading in any of your instructions about tuning these test notes so that the correct octaves can be tuned.

And I suppose that anyone that has a tuning sequence that works well for themselves can say to someone that it does not work well for: “The system clearly works just as written. You always want to re-invent it to something "better" before you even try it and then fail and go on to say it doesn't work.” Your statement is outrageous.

Jeff, for the UMPTEENTH time, the ET via Marpurg is a ROUGH tuning sequence that includes tuning the CM3s as the first few steps. This thread is about tuning those CM3s and any test notes for the two pairs of octaves will be too far off to be useful.

If the piano is detuned for a PTG tuning exam, the test notes you would want to use when FINE tuning are ROUGHLY 4 cents off, either sharp or flat at random. If you are using the sequence for a pitch raise, the test notes you would be using during FINE tuning are however far off the whole piano is, like maybe a 1/2 step. You wouldn't use such test notes when you change the pitch of a piano even 10 cents. I wouldn't use them if I were changing the pitch even 2 cents.

An octave is an octave until you get to the point where you decide to define the octave as a certain type or a compromise of certain types. For those who are struggling to learn aural tuning, the difference between those types may be far too much to try to manage. Therefore, I VERY CLEARLY SPELL OUT (if you ever bothered to actually read what I wrote, you would not have written what you did) that the octave is to be tuned beatless as it is approached from the wide side. You make the octave obviously wide, then you narrow it just to the point where it stops beating.

Most novices can understand that and do it. Throwing all kinds of fancy checks and extremely small distinctions between 2:1, 4:2 and 6:3 octaves at an aural tuning novice loses them and is also completely USELESS when performing a pitch raise or when moving notes into a workable position on a PTG exam detuned piano. If you tune the octave the WAY I DESCRIBE, the most likely result will be a nicely workable 4:2 octave. The difference there may be between the F3-F4 and A3-A4 octave is also likely to be insignificant when using the technique the WAY I DESCRIBED IT, for the purposes I described it, as a positive and very nearly perfect step in the right direction, not the way you want to do it in your ultimate quest for the holy grail of perfect ET.

Now to address your second paragraph. I very clearly remember you writing, more than once but I am not going to bother to look up either post, that you said you had figured out a way, nearly instantly, of taking the ET via Marpurg sequence, AS I DESCRIBED IT, (the results being EXPECTED to be slightly imperfect as they most often are)and created your OWN version of it that was perfect.

But since the ET via Marpurg sequence begins with and DEPENDS upon the CM3s which you CONSISTENTLY claim can NOT EVER be accurate (as much as 2 cents off per note by your own mathematical wizardry), then that must mean that your "perfected" version of what I wrote and which I teach and will continue to teach, CAN NOT EVER work either.

You never posted your "perfected" version of the ET via Marpurg. You only claimed that it would yield perfect results where as what I labored long and hard at does not.

Therefore, what I want to see is YOUR version of the ET via Marpurg which I suppose does not use CM3s since they can never be accurate and which does not use any checks whatsoever of any intervals and no estimates of any kind. The miracle system. Anyone can do it. You thought it up right then and there, so let us all be the beneficiaries of your wisdom. We all want to see the way you would tune a detuned piano or a piano needing a pitch raise by tuning each note exactly and precisely right the first time with no corrections of anything at all being necessary.

I want to see those octave types and 4th & 5th checks all factored in too. Remember, I say they aren't necessary and can't even be used during a pitch raise or for roughing in a detuned piano. So, you must have figured out a way to do everything with no checks and no estimates whatsoever. So, let's have it. What is this marvelous method?

Bill:

I am interested in discussing, not arguing. Your gauntlet will not be picked up.

In http://www.pianoworld.com/forum/ubbthreads.php/topics/623061/1.html I posted:

”But first, I noticed that the ET via Marpurg sequence has the ability to refine the first CM3 other than by using intervals with beat rates halfway between. When the just 4ths and 5ths are created on one note, they also create chromatic m3s or M6s with the other 2 notes. The other two notes can then be adjusted so that the chromatic m3s or M6s beat at the correct 15:16 ratio, the same as any other chromatic intervals. After retuning the just 4ths and 5ths, and checking the octave type with the other notes, the same refining can be made to each M3 in the CM3. Of course, if the CM3 is very accurate, these are just checks and not refinements.”

The basic idea is that listening to chromatic RBIs can create a more accurate temperament than listening to RBIs 4 semitones apart. Your ET via Marpurg sequence creates chromatic additional RBIs when the SBIs are tuned, so why not listen to them to check the original set of CM3s? Even though these chromatic RBIs are not properly tempered, they will all be the same width (if the M3s are all the same width) and the beat speed progression will prove this.

For triumpteenth time, Tooner, you do all the checks after all the notes are filled in. Each of those notes will be very close if not within tolerance and they will not be subject to cumulative error as you suggestion definitely will. An aural tuning novice attempting the tuning exam may have used up all available time at that point. If he/she has been struggling with a myriad of checks the whole way through, the sequence may not even be complete by that time. If it is a pitch raise, is the precision you insist upon with each step really necessary? Won't the results be skewed even as you progress through the sequence?

I asked Owen Jorgensen about your "15:16 ratio". He said it was only approximate, not really all that accurate. So, if someone who is not really accustomed to all of the RBI checks that you insist upon fumbles with them, 15:16 being a significantly smaller difference than 4:5, how much more accurate would those results really be?

It boils down to this: why not do it the easy way, the way which anyone can hear, control and get to within an amazing degree of accuracy first, then use any known way of refinement rather than doing it the hard way and lousing the whole thing up?

We seem to be talking about two different things. I am talking about the accuracy of CM3s. You are talking about passing an exam. But if the 15:16 ratio is only approximate, then the 4:5 ratio is only a guess.



I know you assume that I must not have tried this, or I would be a convert. This shows you have a conceited opinion of your methods.

I have tried many, many things, including your methods, and feel that I have wasted a great deal of time. Here is the problem I encounter by starting with a set of CM3s, roughing a temperament in and then polishing it up. Sooner or later the question comes up whether the F and/or the C# (assuming that A is used as a pitch source) are really where they should be.

For the way my mind works, I need a direct path back to the pitch source, not two possible paths, just one. I have found situations where one could be high, the other could be low, or both, and no way to know for sure.

It is like drawing a twelve pointed star by making a rough triangle and then later, after sketching in the other nine points, trying to make it more accurate but not knowing if the first triangle really is a equilateral triangle or not.

It is too bad that you do not see how highly I value your ET via Marpurg idea. It makes it possible to tune a very accurate set of CM3s. If I dealt with mostly well scaled pianos, I would use a variation of the sequence.

Tooner,

Excuse my irruption in your discusion with Bill, but I think I have something important to say in what you are talking about.

I remember once you have said me to tune fifths using m3-M3 test looking for a 8/7 ratio. The m3 should beat 8 times in the same time the M3 beats 7 times.

My question is: If you are able to accurately adjust such a small difference in the beating of m3s and M3s, why can't you adjust an accurate 5/4 ratio between two contiguous M3s? At first one can conclude that's easier than the more thin ratio 8/7!

Gadzar:

I am glad you jumped in for a number of reasons.

I do not take note of how long it takes an interval to beat a certain number of times, and then compare it to how many beats another interval produces in the same amount of time. What I do is notice how close the beat rates are to each other, and compare that to what I know the “closeness” should be. The smaller the closeness, the more accurate I can hear the difference. As an analogy, I could draw a freehand mark on a piece of paper one inch from the edge more accurately than one 5 inches from the edge.

But even if a set of CM3 were tuned to an exact beat ratio of 4:5 (which I think Bill says not to do), this would cause an error. The beat rates would not quite double in an octave, and the octave would be narrow.

But the main idea is that the beat rates of chromatic intervals will show errors that intervals many semi-tones apart will not. And in the chromatic m3 and M6 tests that are available in Bill’s ET via Marpurg, although the ratio should be 15:16, this does not need to be listened for. If one chromatic set of m3s or M6s beats, say 7:8, another will beat closer to 1:1. When all three sets have a small, audible, and equal progression, the set of CM3s is very accurate.

Another reason I am glad you jumped in is that it gives me an opportunity to correct something I said a while ago about the m3-M3 test for a 6:4 fifth. There hasn’t been much interest in this test, so I did not see any reason to mention it before. I had erroneously thought that regardless of the position of the test note, that the ratio would be 8:7. Actually, like all other tests, the difference in beat rate of the test intervals is the beat rate of the 6:4 fifth. The m3 could be 2 bps and the M3 1 bps, with a ratio of 2:1, but if the correct beat speed of the 6:4 fifth is 1 bps, then the fifth is correct. However, once when the beat rate of the fifth is correct (by whatever method), then the test note can be correctly placed with a beat rate ratio of 8:7. If someone knows what the progression of RBIs that are two semitones apart sounds like, this can be useful. This is all very useful to me, especially when tuning challenging pianos.

Don't waste your time any more, Tooner, it is obvious you have your own opinion which you have had before this thread ever started. That opinion is that the CM3s aren't accurate but the Braide White sequence is. You won't read the material and do what it says, you make up your own version of it which you did again in your last post and then proclaim it doesn't work. You have done this over and over again.

There are other popular sequences which use the CM3s. One has been written up recently in the PTG Journal. Both mine and that one have similarities. Both will be videotaped at the upcoming PTG Convention which you are not attending. The classes for people wishing to take the PTG tuning exam also teach the CM3s. What will not be taught and not be taped and has not been written about in the PTG Journal is your favorite obsolete idea that is 100 years old. CM3s are taught in PTG's study material for passing the tuning exam as they are at the North Bennett Street school, Chicago School, Randy Potter and other schools.

So, now that you have chosen to insult me by calling my work and endeavors "conceited", I will not respond to you on this subject any further. I have already tried to do that but you protested saying I was cutting off the discussion right in the middle of it. There was no middle, there was no beginning. But this is the end. You still don't believe the CM3s can be accurate no matter how many times and ways anyone tries to explain it to you.

So, just keep tuning the way you do. Start your own thread about that. I surely won't argue any point you make. I know you have done it before but it went nowhere, so try again. See if you get anyone to agree with you. Write your own article. Submit it to the PTG Journal (they do take articles from non-members if they consider them to have merit).

You always insist on having the last word, so go ahead and have it but as you do, consider than nothing whatsoever you have said about either the CM3s or the ET via Marpurg sequence has convinced me or persuaded me to change anything about what I teach. If any of my students brings up the Braide White sequence, I will say what I have said here about it and not consider any of your arguments. In my mind, none of them have ever had any merit whatsoever.

I know that, excuse my english, it is difficult to me to express my ideas clearly.



When tuning CM3s you first tune A3-A4 and F3-F4 octaves the width you exactly want them to be, then you divide these two octaves into CM3s, so the ratio is not exactly 5:4 but very close. And the octaves are the width you have decided, they won't be narrow. There are no cumulative errors (as in Braid-White sequence).



Obviously, it is the same with all test notes, the test note can be way off tune and the test still works, in fact you can have 2:1, 3:2, 4:3 which are really easy to hear and check accurately, with a little sense of rythm. And you can have 5:4, 6:5, 7:6, 8:7... ...16:15, which are more difficult to estimate accurately.

But I have one question: Why the difference must be 1 BPS? Can't it be 1.1 BPS, or 0.9 BPS, or whatever value near 1 BPS is demanded by the iH of that specific piano a that specific point in the scale?

As I said before, the nice thing about CM3s sequence is that first you set your octave width, acordingly to the specific iH present in that piano at that point and then you divide the octave into M3s! Well, not exactly that, in fact you divide a M10th into 4 M3s: F3-A4,A4-C#4, C#4-F4, F4-A4. Thus the ratio 4:5 is an approximate value which must be refined accordingly to iH, by adjusting your initial estimate of F3 up or down to achieve a smooth progression of beat rates of M3s up to A4.

This is far more accurate than assuming 1 BPS for a 4th, which is an arbitrary value pulled out from thin air! (Where have I listened that phrase?).



Challenging pianos: it is all about them!

If you are tuning a well scaled piano you seldom hear a difference between a 6:3 octave and a 4:2 octave in the temperament area, so the temperament is easy to tune. And all of the tuning falls into place without much troubles. I am convinced the CM3s sequence is best suited to tune bad scaled pianos with a lot of iH, i.e. spinets and baby grands, where you find jumps in iH from one note to the next in the temperament area.

I will stop posting to this Topic out of respect to the Original Poster.

"Obviously, it is the same with all test notes, the test note can be way off tune and the test still works"

This is only true to a certain point. Indeed, in my article, "Midrange Piano Tuning", I suggest more than once that the tuner adjust the test note until the interval beats very rapidly, at or near the limit of discernibility. The idea is that the more rapidly the two intervals beat, the better one can hear any slight difference. If the intervals beat slowly such as one or two beats per second, one may not be able to detect any difference there may be.

Having said that, some of my students have said that if they tune the test note so that it beats as rapidly as I suggest, they become distracted by the "sour" sound. So, they prefer to have the test note to be very approximately where it should be in a fine tuning. Certainly, any tests which involve minor thirds cannot be very far off.

In my fine tuning sequence, I suggest an octave size that is a compromise between a 4:2 and a 6:3 octave. For the A3-A4 octave, that involves the minor third A3-C4. If C4 is already where it should be, the A3-C4 m3 will beat at or nearly the limit of discernibilty, so I suggest temporarily sharpening C4 very slightly so that the A3-C4 m3 can be better heard.

If one is performing a pitch raise of just 10 cents, all test notes will be unusable unless they are also adjusted with each step. During pitch raises, the pitch is expected to drift as the tuning is accomplished. This makes the use of test notes which in fine tuning, are used mostly to confirm that an interval is correct more than to form it, unnecessary and counterproductive during a pitch raise. The greater the change of pitch, the more useless and counterproductive they become. Indeed, a finely tuned interval during a large pitch raise creates more error than an interval that is purposefully mistuned to anticipate a drop or rise in pitch as the case may be.

Regarding an a tuning exam detuned piano, each pitch is detuned alternately flat and sharp by approximately 4 cents. The examiner makes no effort to precisely detune the piano. So, some pitches may be a little more than 4 cents flat or sharp. Therefore, any test notes are likely to be too far off to be useful as they are. Any test interval will either beat far too rapidly or far too slowly to be useful unless it is also adjusted as the sequence progresses.

A test note must also be tempered in the right direction. A M3, M10 or M17 which is narrow, for example is not valid. Although this is not likely on an exam detuned piano, it could be the case but if the task is to lower the pitch of a piano, it may likely be what is encountered.

This would make tuning a 4ths and 5ths sequence extremely cumbersome, especially for an aural tuning novice. I suspect that those examinees I have observed whose results had errors so large as to fall far below a passing score, even to the point of a negative score (that is marked as a zero) had this problem.

Imagine trying to tune a series of 4ths and 5ths and trying to use a test note for each that is so far off that it too had to be adjusted by a fairly large amount with each step! If the person is barely familiar with the test note process, this would be extremely cumbersome, confusing and defeating. If there were a way of simply tuning each pitch to a very nearly precise point first until all 13 notes of the temperament octave is completed, then with all pitches very nearly correct, the test notes would then be far more useful.

However, as I demonstrated to myself last week, using a 4ths and 5ths sequence alone with no checks can produce disastrous results. An aural tuning novice could end up fighting with the entire arrangement the entire time and lose the battle in a very sorry way. When I would work with such individuals after the fact, it became clear to me that the problem was never once that the tuner could not perceive the errors, they just could not control them. As I say in my article, the essence of aural tuning is the perception and control of beats. Aural tuning novices can always perceive beats but they often do not know what to do to control them.

I have also determined that aural tuning novices cannot manage such fine distinctions as a compromise between a 4:2 and a 6:3 octave. Since a 4:2 octave will work just as well for tuning exam purposes, I teach novices to tune octaves as beatless, approached from the wide side. Using that technique, a test interval will generally confirm that the octave is the 4:2 type.

Therefore, when roughing in the temperament octave on a detuned piano, a test interval is not helpful but if the tuner progresses to the point where a fine tuning of the temperament octave can be done, the test for the 4:2 octave is easy enough to learn and execute. Even an aural tuning novice can confirm that both the F3-F4 and A3-A4 octaves are of the same size and therefore be quite certain the the CM3s from F3-A4 are as precisely tuned as is humanly possible.

At that point, the rest of the temperament octave can be checked and refined. I never once had a student who could not at that point, distinguish the very smallest of errors and also correct them. They really feel a sense of accomplishment when for the first time in their career, they have produced a temperament octave that is perfect to within PTG's tolerances and have done so entirely by ear.

I never use any such tests for 4ths or 5ths. Those tests were originally meant to confirm that a 4th or 5th is beatless when tuning Historical Temperaments which require beatless intervals. When both test intervals beat equally, the 4th or 5th is confirmed as beatless. Their use in tuning ET is most effective when trying to prove an error rather than to confirm an interval is correct. If a 5th is slightly wide or a 4th slightly narrow, for example, it may sound acceptable when played alone but the test note will reveal that it is tempered in the wrong direction. Other interval tests will confirm a very obvious error in such a case.

In testing for equally tempered intervals up and down the temperament octave in the fine tuning process, it is not necessary to use 3:2 or 6:4 tests for every 5th. If any 5th is not tempered enough or too much, unevenness will be quite apparent in other intervals. Such a test can be useful in correcting an isolated error but really not necessary. Causing the 5th in question to conform to all other related intervals is sufficient. The test for the 5th would merely be redundant.

Trying to construct a temperament by using test intervals for 4ths and 5ths each step of the way would not only be extremely cumbersome but would not guarantee accuracy. Since the test must prove two slightly different beat rates rather than equality, it becomes a judgment call in each case. A ratio of 8:7 for example (if that is really what it is) is very difficult to judge as correct. Even if it is judged as correct, there is no other control over that judgment.

The series of 4:5 CM3s on the other hand, has 4 controlling intervals, each being the judge of its partner and all 4 being the final judge. Using a test for 4ths and 5ths in each step only makes each interval sound correct with itself and not necessarily correct with any related intervals or in the perspective of the entire temperament octave. Therefore, in my opinion, tests for 4ths and 5ths in temperament construction have very little value at all. They serve at best to confirm a large error rather than a small one.

I shudder to think of the struggle I would impose on a student and myself if I were to try to persuade them to do this using a classic 4ths and 5ths sequence! Most of them would just get lost in the whole maze and give up trying to learn to tune aurally. Using a method that produces consistently superior results however, encourages them to go ahead and take that test. They are permitted to use their ETD in Part 2 of the exam to tune the outer octaves and to ensure that the midrange is stable enough to pass the stability test.

I do not feel in any of these cases that I have taught merely the techniques required to pass the exam and that really, the technician has not truly learned aural tuning concepts. What I have done instead is to link very likely for the first time for these people the perception (which they already have) and the ability to control beats. They have then found the confidence needed to judge whether their ETD tunings are the best they can be. They often go on to do custom programming of the ETD which they were not confident in doing up to that point. Many of them go on to serve on Master Tuning Committees and attempt a qualifying exam to train as examiners which must be done entirely by ear.

I used to think that dropping the aural tuning requirement for RPT would be acceptable as many PTG Associates have desired and even demanded. I no longer think that would be acceptable because I have seen many times over what benefits learning aural tuning skills has provided for people who previously did not possess them. This can also be true for those who for whatever reason, choose not to join PTG or take the tuning exam. Any ETD user can and should learn the basic aural tuning skills it takes to tune the midrange accurately. Once that is accomplished, outer octave tuning can be mindlessly simple and easy.

They can also make sense out of the value there may be in tuning non-equal temperaments in the future. They can use 4th and 5th test intervals effectively to confirm beatless intervals when they are required. They will be able to understand the difference between ET and the non-ET and the purpose for using a non-ET. Using correction figures with an ETD becomes more than just inserting some irrational looking figures and producing crazy sounding results. Those results will have a meaning and a purpose behind them when the tuner possesses aural tuning judgment.

Aural tuning judgment is the goal of aural tuning instruction and education. With judgment, a technician can understand why some tunings sound better than others and not just wonder why.

Come on UnrightTooner, do you leave the discusion when things become difficult to you?

You are right Bill, the test note can and thus should be adjusted where it produces the optimum beat rate audible to the tuner. What I was trying to explain is that the test note can be moved and the test still works. Sorry about my extrapolations.

And for the sake of that "respect" you have now launched another thread called "Errors" where you intend to highlight the supposed erros in what Bill states?

I think the best I can do is ignore all of your posts from now on. Sorry.