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Tuning the 4ths and 5ths Temperament
#2108267 06/26/13 07:44 AM
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Much has been said against the 4ths and 5ths Temperament/Sequence of tuning, but is it really that problematic and antiquated?

I learnt to tune by using the 4ths and 5ths sequence. I was also taught to back track if one got "The Wolf" howling at the end of it. Obviously there are checks to help as one progresses through the temperament, but back tracking was and is inevitable.

But the question that needs to be asked is, is this so terrible and backward and unnecessary and is there a better way that will cut all of this backtracking and to and frowing out completely?

My answer is, there is no such system, and I am not going to go into great detail about that except to say that, it is inevitable whatever sysytem you use, there will be some backtracking and refinement needed and that the more you tune a particular system the better you will get at tuning it and the result of that is "Less Backtracking".

Yes, there are good temperament systems and poor ones too, but whether we like it or not there is going to be some sweat, blood and tears in learning to tune it, and the rest of the piano too.

The sitting down and seeking to understand what one is doing and to actually implement what one is doing is difficult and those that persevere, conquer. Those that conquer, are those that have worked hard at it, deserve the congrats, and usually go on to higher ground, learning the never ending intricacies that are involved in tuning, and the other areas of piano technology.

Anway, to get back onto the 4th and 5th temperament. I looked at Mario Igrec's book website, and found what he said on the 4ths and 5ths temperament interesting and helpful to understanding and tuning the temperament using the 4ths and 5ths sequence. Yes, there are other systems, etc...but the question we got to ask again is, which one is the best and why? When that is answered, we can go onto asking another, how much backtracking and fiddling around is involved to get things right?

I would submit, that there is always going to be fiddling around with the temperament sequence, and that for a number of reasons.

Thinking of Bill Bremmers continual seeking to refute the 4ths and 5ths method, and the main reason being is, as he says, there is an accumulation of errors, is valid. On the other hand, we need to ask ourselves, Has Bill himself found that one system that has no fiddling about and backtracking and accumulation of error?

I would submit that, If he had, he would not be changing his tune (temperament sequence, though admittedly he has held to the CM3 sequence), every couple of years of how to go about tuning the temperament, and he has. It is understandable too. This is piano tuning folks and living in an imperfect world.

So has the CM3 sequence got one up on the 4ths and 5ths sequence?

What Mario has said,

" The sequence starts by tuning the middle A to the fork, and establishing a P5 and P4 in the octave. The octave should be just slightly wide but without perceptible beats, and the P4
should beat just slightly faster than the P5, both under 1 bps.

You can spend a little more time on these two notes because they will serve as aural templates for the beat rates of the other P5s and P4s you will tune.

Tune the next five notes to D#4 by tuning P4s up P5s down. Make the beat rates the same as the P5 and P4 you tuned initially. Next, start at the middle A again and tune the five
notes in the opposite direction of the temperament circle. Compare the last note, G#4 with D#4. If this P4 is wider than beatless but beats under 1 bps, congratulations!

If it beats at more than 1 bps, it is too wide—increase the beat rate of the P4s and P5s a touch in both directions. This will narrow the P5s and widen the P4s, and raise the notes tuned during the first half cycle, including the D#4, while lowering the notes in the second half cycle. If the P4 D#4-G#4 beats at less than 1 beat in 2 seconds, doesn’t beat at all, or is narrower than beatless, decrease the beat rates of the P4s and P5s. Make corrections until all the P4s beat at approximately the same rate, slightly faster than the P5s.


Last edited by Mark Davis; 06/26/13 08:08 AM. Reason: minor correction

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Re: Tuning the 4ths and 5ths Temperament
Numbered #2108276 06/26/13 08:05 AM
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Mario does speak of checks that accompany this system but you will need to purchase his book. So, what I have posted is lacking the checks along the way, that will help one to tune this sequence successfully.


Last edited by Mark Davis; 06/26/13 08:06 AM.

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Re: Tuning the 4ths and 5ths Temperament
Numbered #2108284 06/26/13 08:26 AM
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There are other questions that one can ask too.

If the emphasis today and the "consensis" is that well temperaments are the must and ET is out, then we need to ask ourselves, How far away is a RW from any WT really? I have not received a satisfactory answer yet.

Though I understand the intricacies involved in fine tuning, and am ever learning, I do wonder why such an attack is made against the RW. For an experienced, seasoned and accomplished piano tuner, who for whatever reason did not successfully execute an ET on the piano he was tuning for a concert pianist, how perceptible would it be, without an unnecessary over fussing nit picking, and that would accomplish what?

Why would someone who promotes WT be so vehemently against an RW when an RW could so easliy pass as one of the multitude of WT's that exist and would also pass as a very acceptible tuning?

Anyway, I diverge, from the main topic, but nevertheless it has it's place.





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Re: Tuning the 4ths and 5ths Temperament
Numbered #2108291 06/26/13 08:58 AM
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Originally Posted by Mark Davis

....If the emphasis today and the "consensis" is that well temperaments are the must and ET is out...


Although there are a few piano tuners out there who would want to believe this or are trying to actively promote it, the truth and reality is that there are only a very small handful (less than a dozen) amongst the thousands of tuners worldwide who do.

Besides, modern piano's since the turn of the last century are designed and built with a string scaling formula/program which assumes the ideal tuning for that piano is ET and the calculations are formed on this parameter. The speaking lengths/diameters/windings and related individual tensions are all calculated to fine precision based on equal temperament. Tuning to anything outside this parameter will always result in a compromise on the instruments intended design and its intended use. Some people think its not enough to matter, others think it does.

Reverse Well is a non issue in the real world and any tech who tunes by ear which ends up with RW in place of ET should really be reaching for an ETD. An ETD set for ET will not produce RW....period. The majority of techs here in N.A. use an ETD either as stand alone or in some form of hybrid ear/machine collaboration.

When I learned to tune temperaments by ear, one of the very first things taught to us was how to recognize and avoid RW during the process. I know many people who tune using 4ths and 5ths method who produce fine ET tunings in spite of some pitfalls than can accompany it.


Last edited by Emmery; 06/26/13 09:04 AM.

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Re: Tuning the 4ths and 5ths Temperament
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I simply understand RW as a lack of tempering on the first 5th of the sequence.
If that is, this is a beginner defect, and easy to correct.

Something we can think about too is that we will be enlarging the octaves, if not a lot, at last enough to have the sounding just.
I see no reason why 4ths and 5ths could not as have some progressivement then. It just installs a preparation for stretch within the temperament.

Backtracking is reduced when using ladder of 3ds, hence it's success. But the appreciation of the slow beating Intervals is left aside. They are just used as a tool to obtain the FBI progression. This only can lend to uncontrolled quality of those important intervals.

Also, th 3ds will have variable speed depending of the scaling, it is not always guaranteed that a perfect speed progression of consecutive M3 allows the nicest 5ths.

Whatever sequence is used, I believe it will be more musical to focus on 5 the and 4ths and not judge them by the winning progression of FBI.

It also gives the tuner an excellent ear training to apprehend those intervals directly. Without controlling them by FBI checks.
Open the door to very fast tuning corrections when necessary.



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Re: Tuning the 4ths and 5ths Temperament
Numbered #2108305 06/26/13 09:46 AM
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All:

Now here is a subject I can sink my teeth into!

First, is it possible to tune a temperment WITHOUT using 4ths and 5ths? I doubt it. You could say that ALL temperment sequences are 4th and 5th sequences.

Next, where is the dividing line between ET and, well, everything else? Is it just progressive M3s? No, because you could take any set of CM3s and raise them all the same number of cents (well, up to 99 cents theoretically) and still have progressive M3s. How about progressive M3s AND M6s? I would say that is definitely ET, but what accuracy are we talking about? Would you believe to guarantee that all M3s and M6s are progressive each note would have to be +/- 0.25 cents? But in reality with some fudging some notes can be off by 0.5 cents. Still, that is a very high degree of accuracy.

How about the infamous PTG exam standards? Interestingly, the accuracy for tuning progressive CM3s is about the same accuracy required by the exam. It should be no surprise that tuning by CM3 is popular. It is “teaching to the test”!

Anyhoo, of course every sequence requires going back and forth. I wish I understood number theory enough to prove how many steps is required. It seems that every sequence requires 8 or 9 notes to be tuned before the temperment is locked in.

So what intervals do you want to mostly tune until you have the temperment locked in? Well, for me the answer is to use the ones that are affected the least by iH. Those are the ones with the lowest partials. Of the traditional temperment intervals, M3s have the highest (5-4) followed by M6s (5-3), P4s (4-3) and P-5s (3-2).

But what about other, non-traditional temperment intervals? (Yes, those that have read my posts know what is coming next…) How about the P12 (3-1) and the P8 (2-1, 4-2)? A temperment can be tuned with just one P12 and completed with P5s and P8s. The first 8 notes ( in order) to lock in the temperment are: A4, D3, D4, A3, E4, G3, E3 and G4. And not a single M3!

OK, the Topic is about 4th and 5ths sequence. But we all know everyone is going to post what their favorite is. My argument for 4ths and 5ths over M3s and M6s is the amount the partials are changed by iH and it matters little what sequence is chosen. You are going to have to tune 8 or 9 notes before you have it locked in. Besides, you are going to have to tune some 4ths and/or 5ths sooner or later anyway. Why not learn to use them for the entire sequence?


Jeff Deutschle
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Re: Tuning the 4ths and 5ths Temperament
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I learned the 4ths and 5ths temperament as articulated by William Braide White from my father. It's what I grew up with. I moved to a 3rds and 4ths temperament after trying it and finding that I was able to do a better job. At the time I couldn't say exactly why, but my opinion now is this:

1) There are multiple coincident partials with 5ths which can confuse exactly what you are listening for. Although in some instances more has been made of identifying which partial (if any) you are tuning to than is necessary or relevant, in the case of the temperament, it is quite important which set of coincident partials is the the one you are working with.

2) Increased granularity with 3rds vs 5ths. Its simply easier to discriminate between 6 beats per second and 5bps or 7bps tuning thirds than it is to discriminate between .6 bps and .5 or .7 bps. tuning 5ths. WIth 3rds, your precision requirement is reduced by a factor of 10--not insignificant.

3) 3rds are the "check" for the 4ths & 5ths temperament and the definition of the equal temperament. The single best illustration of the equal temperament is evenly beating and slightly increasing speed with contiguous ascending thirds. So, logically, instead of hoping that this phenomenon occurs with tuning the 4th/5th system, why not simply make it happen? If you get the 3rds right, then the 4ths and 5ths will be OK. Put another way, a 1bps difference in a third is something that is audible and matters. But who cares if a 4th of 5th is a hair faster or slower than what we target?

4) With 3rd/4th tuning, you are able to establish solid anchors within the temperament octave (or slightly beyond if you expand your temperament area). If you tune 3 thirds, you are at the next octave. It is a fairly easy matter to tune three 13-cent-wide thirds within one octave compared to tuning a circle of 4ths or 5ths and arrive back at an octave up at the end of the piano -- or beyond.

In conclusion, whatever works for you is fine with me. And, certainly, there are folk that do very fine work using fourth/fifth temperament. However, I'd suggest that if you give third/fourth temperament a try you may find that, like me, you won't go back.


Keith Akins, RPT
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Re: Tuning the 4ths and 5ths Temperament
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It does not matter whether you use 4th and 5ths or if you use 7th and 29ths. The important thing is understanding and recognizing the characteristics of the temperament you are using and from that, being able to correct any mistakes that are in it. If you need to get from New York to Philadelphia, it does not matter whether you use a plane, a train, a bus, or a transporter as long as you end up in Philadelphia. What you do not want to do is insist on using one method and because of that, end up in Boston.


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Re: Tuning the 4ths and 5ths Temperament
Emmery #2108322 06/26/13 10:27 AM
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I learnt to tune by using the 4ths and 5ths sequence. I was also taught to back track if one got "The Wolf" howling at the end of it. Obviously there are checks to help as one progresses through the temperament, but back tracking was and is inevitable.


As I see it, this is a recipe for Reverse Well. What is described here is exactly how and why temperaments intended to be ET end up being in fact, Reverse Well. If you don't know what Reverse Well is or sounds like, how would you know if that is what you actually tuned or not?

It seems to me that some people want to believe that what they wish to be the truth actually is. If you had heard the number of times I have heard Reverse Well on pianos, you wouldn't dispute what I am saying at all.

Just wanting to believe that there are only about a dozen tuners world wide who tune pianos in Well Temperaments does not make it true. There are more than that in the city in which I live! It is being taught at the PTG convention in a couple of weeks and not by me but by a PhD who teaches it in numerous venues and has been teaching it for more than two decades. He is not the only one. The number of times I have seen figures pulled out of thin air and published as fact on here has been astounding!

The work I have been doing for 10 years now to find a better way to construct ET is not for my benefit. I became an RPT with a score of 100 in temperament 30 years ago and yes, I used a 4ths & 5ths temperament to do it. And yes, I back tracked and used a myriad of checks to sort out the errors in the 60 minutes I had to tune C3-C5 single strings only. If I had to do that to make a living, I would have been out of business decades ago!

Yes, there is, in fact, a way to construct a temperament one time with no back tracking necessary because each step of the process confirms that the temperament is correct. It is there for anyone who wants to avail themselves of it and the results in how it makes the piano sound are nothing less than stunning! It literally makes the music "float" out of the piano.

Any technician has the right to use whichever method they please or feel comfortable with. One can chose to repeat the first year's experience for a lifetime and never progress beyond that or one may choose to always seek a better and more refined way of practicing one's art and profession. I choose the latter, so if in your mind that qualifies me to be in the "arrogant piano technician" thread for doing so, then please re-post any of my comments there. It would only encourage me.

Reverse Well is indeed possible when using an ETD. It is another example of believing what one wishes were the truth to actually be factual. I am not going to bother to explain how it can happen for your benefit, however. I am only going to say that the use of an ETD does not necessarily lead to the perfection that some people wish it would.

Piano scale design is based upon theoretical ET for the same reason that ETD's use theoretical ET as a paradigm. If you believe that the piano scale is designed only to be tuned in theoretical ET, then you should tune the pianos you service that way and find out for yourself that what you are saying is not true.

Your ignorance is your strength. What you don't know about your own profession would fill an entire book case yet you choose to broadcast what you don't know on a daily basis.


Bill Bremmer RPT
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Re: Tuning the 4ths and 5ths Temperament
Bill Bremmer RPT #2108329 06/26/13 10:37 AM
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Originally Posted by Bill Bremmer RPT
Quote
I learnt to tune by using the 4ths and 5ths sequence. I was also taught to back track if one got "The Wolf" howling at the end of it. Obviously there are checks to help as one progresses through the temperament, but back tracking was and is inevitable.


.....

Your ignorance is your strength. What you don't know about your own profession would fill an entire book case yet you choose to broadcast what you don't know on a daily basis.


And what does this last comment say about YOU, Mr. Bremmer?


Jeff Deutschle
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Re: Tuning the 4ths and 5ths Temperament
kpembrook #2108337 06/26/13 10:52 AM
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Originally Posted by kpembrook
.....

2) Increased granularity with 3rds vs 5ths. Its simply easier to discriminate between 6 beats per second and 5bps or 7bps tuning thirds than it is to discriminate between .6 bps and .5 or .7 bps. tuning 5ths. WIth 3rds, your precision requirement is reduced by a factor of 10--not insignificant.

.....


Please forgive me for zeroing in on this one point. I am singling this out to explain something, not to take it out of context.

The more an interval is tempered from just intonation, the further it can be from ideal and still be progressive. A M3 that is about 7/8 cent too wide will beat the same as the M3 one semitone higher. A P5 that is 1/8 cent too narrow will beat the same as the P5 one semitone higher. This could drive you nuts. However, comparing contiguous P4s or P5s or comparing P4s with P5s that share a common upper or lower note gives an accuracy of about 1/2 cent. It is very useful, IF you can easily compare SBIs. Everyone has different skills and preferences and priorities. Whatever sequence works best is the one to use.


Jeff Deutschle
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Who taught the first chicken how to peck?
Re: Tuning the 4ths and 5ths Temperament
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Originally Posted by Bill Bremmer RPT

It seems to me that some people want to believe that what they wish to be the truth actually is.

This entire posting is the perfect example of that.
Originally Posted by Bill Bremmer RPT

Any technician has the right to use whichever method they please or feel comfortable with.

Apparently technicians are not permitted to do this in your world without being insulted.
Originally Posted by Bill Bremmer RPT

Your ignorance is your strength.

And yours is the PTG’s weakness.

Re: Tuning the 4ths and 5ths Temperament
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Bill, your post is shameful and venomous! Pull yourself together man!




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Re: Tuning the 4ths and 5ths Temperament
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Yes, I learnt to tune using the 4ths and 5ths sequence but I have learned to use the CM3 sequence too.

My journey learning to tune, from 2002, and prior to that, I had been working in a piano restoration workshop for about 9 years, has brought me to learn from many well known piano tuners. I learnt of Bill in about 2006, and began applying the CM3 sequence he was advocating in about 2008.

I have learned from Rick Baldassin, Dan Levitan, Kent Swafford, Rick Butler, Virgil Smith, the PACE series, the PTG resource file, and many others that I forget of at this moment. Each of these people adding new and different perspectives and pertinent information that the other had left out due to lack of space and time in writing what they have.

Anyway, the main reason I started this thread is because I think that what Mario has written on the 4ths and 5ths sequence is valid, interesting and of benefit to those who are interested.

I think that Mario probably may write about "Advanced Temperament/tuning" in his book too.

So, some questions to be asked,

1. will someone who is learning to tune ET from an expert tuner, who is teaching them the 4ths and 5ths temperament, learn how to tune faster or slower than someone who is learning to tune from an expert tuner who is teaching them the CM3 sequence?

2. Will, the person who learned to tune via the 4ths and 5ths sequence, be able to execute an ET as efficiently and accurately as someone who learned the CM3 sequence?








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Re: Tuning the 4ths and 5ths Temperament
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I was trained using the Braid-White method as many were in the early seventies. Still tune using 4ths and 5ths, but have had numerous discussions about temperament sequences and have tried many of them.

Using 4ths and 5ths are difficult for some to hear so best for them to use 3rds and 6ths.

I think it is the difference between using millimetres and centimetres rather than inches and feet.

Both achieve the same result.

Re: Tuning the 4ths and 5ths Temperament
UnrightTooner #2108431 06/26/13 01:06 PM
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Originally Posted by UnrightTooner

The more an interval is tempered from just intonation, the further it can be from ideal and still be progressive. A M3 that is about 7/8 cent too wide will beat the same as the M3 one semitone higher. A P5 that is 1/8 cent too narrow will beat the same as the P5 one semitone higher. This could drive you nuts. However, comparing contiguous P4s or P5s or comparing P4s with P5s that share a common upper or lower note gives an accuracy of about 1/2 cent. It is very useful, IF you can easily compare SBIs. Everyone has different skills and preferences and priorities. Whatever sequence works best is the one to use.


Jeff, thanks for this!


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Re: Tuning the 4ths and 5ths Temperament
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What I find interesting is that all of those who originally learned the Braide-White sequence had to supplement that knowledge with other information from somewhere else in order to actually be able to tune a true ET.


Bill Bremmer RPT
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Re: Tuning the 4ths and 5ths Temperament
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Have you not supplemented your knowledge since you first began learning to tune?

What I find interesting is the changes you have made over the years in your approach to how to tune ET via the CM3 sequence and the employment of the 4th and 5th within that sequence. Anyone who knows your work, knows that you have made changes over the years.

Why is that Bill? Is it not bullet proof? Is it not without accumulation of error? Why the changes?


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Re: Tuning the 4ths and 5ths Temperament
Bill Bremmer RPT #2108441 06/26/13 01:17 PM
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Originally Posted by Bill Bremmer RPT
What I find interesting is that all of those who originally learned the Braide-White sequence had to supplement that knowledge with other information from somewhere else in order to actually be able to tune a true ET.


What I find interesting is the fact that more aspiring technicians are driven away from membership in your favorite club by the continued bloviating you do here.


Re: Tuning the 4ths and 5ths Temperament
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Mark,
Just ignore the postings so that your thread is not destroyed by one person with an agenda.

Let’s just move on with the topic at hand.

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