Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum Tuning a temperament using CM3's and P4/P5. Video.

Hi Everyone,

I recently finished giving my basic piano tuning course to two students from Australia and New Mexico, and I've edited one of the classes down to just show how I tune the temperament.

With all the discussion about CM3's and P4/P5 sequences, I thought this would be interesting, as I use both.

The entire class has been uploaded to my classes youtube channel (see link below) but this video has been edited to be more educational.

Feel free to post any questions.

Here's the link: http://youtu.be/tOv_CoPP-lQ

Mark:

My internet connection often has stops and starts. Could you briefly explain how the sequence works? I am guessing you start with a ladder of CM3s, and then use pure, perfect 4ths and 5ths somehow. Is this like Bill's ET via Marpurg?

I don't know Bill's sequence. I would post the document but you really need to see the video. Find a service that allows you to download Youtube videos to your hard drive and then watch it later.

Try this one: http://www.clipconverter.cc

I think you will really like it. I spent a lot of time editing it so it was easy to understand.

Thanks for the interest.

The point of using contiguous major thirds is that, you can see how far off you are after tuning only four fourths and fifths, rather than twelve. After tuning the first series of fourths and fifths, you can compare the next series with the major thirds, so you are not likely to stray as far. You have more guideposts.

That method really helps. Nothing builds tension in the gentle tuner's soul like the suspense of waiting 'till you have completed the octave to see where you are, and the crushing disappointment of finding an error when you get there.

There is no there then.

There is there, but it often must be moved to a different "there".

Thanks - Then I can understand there when there is then.

Didn't Einstein say something about it all being relative?

No, but Gertrude Stein said something about there being no there there. Except there is here.

Now this has to be the best answer yet to how the initial CM3's can be checked! So, I thank you for that, BDB. I was really tempted to post something negative on the 20,000 post topic, like I would prefer more quality than quantity.

When I set up an initial set of CM3's, I am depending upon them to be accurate. The best I can say is that the check for them is self contained. One must have 2 pairs of octaves, F3-F4 and A3-A4 which are identical (regardless of chosen width) and the 4 CM3's must progress evenly and by a small amount (a 4:5 ratio).

One must set this sequence up and review it perhaps several times. If it is the pitch correction phase of tuning (where each note is being raised substantially for example), it can be expected that any of these five foundational pitches may drift slightly. If all that is being attempted is a rough tuning, such drifts are to be expected and are therefore inconsequential.

Upon a final and truly fine tuning, however, this foundation needs the utmost scrutiny. Therefore, after setting each of these 5 pitches, they need to be reviewed with the utmost scrutiny to insure that the above definition (underlined) is met.

It will always , in the end, still be a judgment call. I have previously pegged the error tolerance at 0.5 cents and I hold to that. In other words, even upon the utmost scrutiny, any of these 5 initial pitches can be off by as much as a 1/2 cent and go unnoticed.

That is where what BDB has said above in the quote comes into play. Upon development of the rest of the sequence, any error in the initial set of CM3's may be identified and therefore corrected. BDB's phrase, "You have more guideposts" is the essential key. If the second guidepost does not agree with the first, then look for a small error in the first guidepost. In the end, there will be three such guideposts and all must agree.

When that happens, all of the other possible checks such as M3-M6, Chromatic 6ths, "inside 3rd outside 6th", evenness of chromatic 4ths and 5ths, contiguous 4ths & 5ths, etc., will only be redundant. The CM3's are the single most powerful diagnostic tool there is for error in ET!

My explanation was not how major thirds are checked, but rather, why they are used.

That the major thirds get faster as you go up the scale is certainly the case, but to say that it happens "evenly" is ambiguous. If you tune C-E-G#-C-E from a C-fork, or C#-F-A-C#-F from an A-fork, the rate that the beat rates change doubles between the first third and the last third, an octave above, and everything happens geometrically in between. The rates go roughly 5, 6, 8, 10 beats per second (and even that is a bit off), rather than 5, 6, 7, 8.

Having that many thirds to tune right off the bat makes it fairly simple to check them. There is a bit of a "how" for you!

Sorry to say this, but after some point, I felt that you lost your way and control and the temperament just slipped out of your hands.

I think it is you who lost my way.

There, there now.

Huh?

He was responding to my post not you.

Just joining in on the silliness from a few posts back.

BDB, I recall that you once said something about an M3 an octave higher than an M3 below will beat at twice the speed (which is perfectly true) but I remarked that there is no possible way to discern whether one interval is beating twice as fast as another.

I had wanted to get into this for Doel Kees on another thread about the difficulty of discerning the beat speed of F4-A4 but I will do it here. I am sure he will see it.

One does not normally listen to chromatic M3's for evenness in that range, to be sure. The approximately 14 beats per second of F4-A4 in ET is at or near the limit of discernibility, that is true. In that range, one would normally use 10ths to check for evenness since 10ths will be clearly discernible (being approximately half the speed of M3's in the upper 4th octave. They are more like the M3's in the upper 3rd octave below).

That being said, (and I know I have covered this in my article on Midrange Piano Tuning but I will reiterate it here), The F4-A4 M3 serves as a final judge for the three CM3's below it in this way: If the F4-A4 has a gentle and easily discernible beat, it is too slow! That means, as a consequence, that the F3-A3 an octave below it is too slow! If the F4-A4 M3 beats so rapidly as to be indiscernible (and has a kind of "sour" sound), then it is too fast and that means that the F3-A3 M3 an octave below it is too fast!

In either case, as I pointed out 10 years ago (and Jim Coleman, Sr. pointed out in some writing or another in the 1980's ((thanks to Mark R. from South Africa for pointing that out)),), both F3 and F4 must be moved accordingly! C#4 may (probably will) have to be also moved. All would usually be slight adjustments, to be sure.

This all means that when the F4-A4 is correct, it is at, or near the very limit of discernibility. Not anything more, nor less. If one needs to use the "ghosting" technique to hear it, then fine, use it.

I'll say it once again to make it perfectly clear and understandable: Three CM3's alone are not enough! Almost anything could be deemed to be "progressive". The fourth M3 must fall in line too or else it means the lower three are all invalid!

Having said that, your point, BDB, to which I thank you again, that when a second and third set of just two CM3's does not quite work, then it will identify a small error in the initial set of 4 CM3's. It is a way of making all of the pieces fit rather precisely and accurately, leaving no gaps or any interval favored over another. That is true ET!

[I don't mind at all listening to a piano tuned in true ET but I do not want to hear any piano tuned in Reverse Well and have it claimed to be ET! If I do hear such an example, I will point it out immediately and ask for Doel Kees (and anyone else who can hear it) assistance in confirming my observation.

Beginning January, 2014, I will post a running blog on Reverse Well, citing all the examples I have collected and soliciting any others that technicians may observe. At some point, such a collection will have to cease to be anecdotal and demonstrate a definite trend.

Whether those observations are from very recently tuned pianos or not, any "fast-slow" progression of M3's will not be able to be attributed to progression of time or environmental factors. If a temperament sounds fairly even, then it was constructed that way. If a temperament exhibits Reverse Well characteristics, then it must have been constructed that way, plain and simple.

I want to rid this world of Reverse Well! If anyone perceives that goal as me promoting my own business, then they should complain to the moderators of this forum and see what that response will be. Good luck!]

I am not interested in "silliness" but I am interested in eradicating Reverse well from Humanity.