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Hi Bill,

I would also love to hear the tone-cluster process in action. The video about ET via Marpurg that you posted a while back really helped me, even though someone was just using their cell phone to record you. That's all we need though. Could you have someone at a convention just hit record on their cell phone and maybe you could demonstrate setting the temperament and the notes immediately surrounding the temperament, but not too high or low on the piano, for time's sake (and video memory sake on the person's cell phone).

That would be awesome, because it would allow some of us who can't meet you in person to still learn from you.

Thanks!
-Erich

The videos on my website were taken by and put up by PTG and they were not done with a cellphone. I can ask (and plan to do it) PTG to record the demonstration. I used the ET via Marpurg for the Jazz event and will at the convention. The tone cluster idea is simply to play the intervals used in constructing the temperament all together after they have been played separately.

It is a very simple but revealing idea. For example: When temporarily tuning the F3-C4 5th as pure, you tune the 5th so it sounds apparently beatless but you don't know yet if it could still be slightly wide or narrow. So, you play the "test note" G#3 and compare the F3-G#3 m3 and the G#3-C4 M3 and determine if they seem to beat equally or not. While that may be a fairly exacting test, it is still a judgment call. However, when you play the entire minor triad, F3-G#3-C4 and the F3-C4 5th is truly pure, the chord will seem to just "hang there" with an uncanny stillness to it.

If the F3-C4 5th is not quite pure, you will hear the slow beat much more clearly than if you play the F3-C4 5th alone. Furthermore, play the two test intervals and listen to how loud they sound. When the 5th is truly pure and you play the entire triad, you will hear that it sounds immediately much softer. That is the beat canceling effect!

When you go on to complete the temperament and make any two intervals beat the same, do likewise. After you are satisfied that a 4th and 5th beat alike, play them together as a cluster. It will be a mildly dissonant chord but once again, if they beat exactly alike, that cluster will have that uncanny stillness to it and will sound softer than either interval played alone. If one intervals beats slightly faster than the other, you will effectively hear the difference emerge as a slow beat.

So, the process of tuning the rest of the piano goes likewise. If you are tuning the octave, G3-G4 for example, you would naturally first make a reasonable sounding octave that is slightly on the wide side of pure. Then you would compare the 4th & 5th below G4. Do what you would always do but then play all notes together. If all intervals are perfectly equal, you will hear that the tone cluster just "hangs" there, very still and perfectly beatless because whatever beats there are between the intervals are canceling each other. You will again hear that the tone cluster sounds quieter than any interval played alone.

It even works for setting the initial pitch and the first two octaves, A3-A4 and F3-F4 in the temperament. For the pitch, match A4 to the Fork, then play the test note B1 (better than F2 because B1-A4 will beat very rapidly). If there is any difference between A4 and the fork, you will hear that very slow beat much more clearly than if you play A4 and the fork alone.

For the initial octaves, use the test note that verifies a 4:2 octave. For A3_A4, it is F3. For F3-F4, it is C#3. When the octaves are a perfect 4:2 type, you will hear the stillness as with all other intervals. If it is not perfect, it will be clearly revealed.

Of course, this idea will tune the piano very well for any kind of music. If you believe only in using ET, you really can't tune a piano to sound better than using this method. I use other temperaments most of the time, yes but I still use the tone cluster technique to construct them too. In the case of the Jazz event, the ET via Marpurg was a good choice because the pianist often plays sharply dissonant chords that lie within an octave or extend slightly beyond an octave. Even though the chords are sharply dissonant, there is a very "clean" sound to them.

Hi again Bill,
Thanks for your reply. That seems to clear up some confusion for me anyway. I would love to hear this in action. Sorry, my bad about guessing someone recorded you with a cell phone. It just had that kind of visual/audio quality that reminds me of cell phone recorders. But at any rate, today's cell phones like the latest Samsungs and iPhones are more than adequate to capture your demonstration, if you can't get the PTG to do a more formal video for you (I'm just suggesting).

I am already using your ET via Marpurg (and mindless octaves for expansion) every time I tune a piano, but I will have to try and incorporate this beat-cancelling method into the mix as well. I like the idea of simplicity and not having to rewind and correct RBIs that don't quite make the cut when checking right after the temperament has been set.

Thanks again Bill. I hope you can get the PTG to set up a video session for you. Take care,
-Erich

Erich,

Grandpianoman is supposed to have me at his home at the end of the month. Perhaps we can make the video there. He has the equipment.

The whole idea of the tone cluster is to prove right then and there that the note which has just been tuned is correct and will not need any further checks. Sure, other checks can be performed but they will prove to be merely redundant.

The ET via Marpurg actually started out as a flawed idea because technically, 4ths & 5ths in ET do not beat quite equally. However, the distinction is an extremely small one. Knowing this, I at first thought of the ET via Marpurg as merely a rough tuning idea, only useful for getting the piano close.

Then, our friend Raphael from Mexico city produced a document from the UK which actually advocated the idea of equal beating 4ths & 5ths. I wish I could see that document again because the author claimed it made for a better sounding variant of ET.

With that in mind, I thought of a way to better construct the temperament. Surely, using a test note for each of the temporarily tuned 4ths & 5ths would help avoid getting any of them slightly wide or narrow and therefore spoiling the results.

I really don't know how or why it occurred to me to play the note being tuned, the note from which it is tuned and the test note(s) all together but once I discovered that it was very revealing, I went with it ever since.

So, the whole idea is not some new kind of tuning never before done, it is really an idea that simplifies the process and is very exacting. Because each note tuned is absolutely correct before moving on, it is also more efficient.

Any and all other temperament sequences for ET require an estimate for each note being tuned, then multiple checks to prove that it is correct. Some sequences require two or more estimates before there is any proof available. That can easily lead to a compounding of errors and it can be difficult to ever know just where those errors are and how much error there is at any point.

This method does away with all of that! I hope it catches on. It can make many aural tunings far better than they have been.

I tried both of these examples and it works remarkably well.

I can hear the interference of the two different rapid beats, if they are slightly different, as a "meta beat", a slow beat between the rapid beats. By making the meta-beat go away I can make the two rapid beat rates the same much more accurately than when just listening to them one after another.

A good name for this technique is I think "interferometry" (see wikipedia for example).

Kees

Thanks for the new vocabulary term, Kees. I looked up the article. Wow! Way over my head. I am not sure of even how to pronounce that word but I am glad you saw something in what I was saying.

The most pleasant surprise I had was when I first set the pitch and got a 0.0 reading out of it! I had never been able to do that before! I could get close, yes, within a cent but never right smack dab on the bull's eye. It wasn't just a fluke either. I have been able to do it ever since.

As I mentioned, I also now use the same technique when tuning the EBVT III. With its many equal beating intervals, it works quite nicely. My favorite is A3-C#4 beating the same as A#3-D4. Played all together, it makes a for a dense and very dissonant tone cluster. I experimented with that and deliberately made one M3 beat a little slower than the other just to see what would happen. The difference reveals itself very obviously.

I also hope you saw from an earlier post that I would treat the octaves of any temperament similarly. It does not mean that the EBVT III morphs itself into or closer to ET in the upper octaves as some people seem to think. The relationship between notes changes somewhat in ET too.

The first WT I learned to tune was the Vallotti. That was 25 years ago. It was my instinct even back then to equalize octaves and 5ths, double octaves and octave-5ths, etc. It was what made for an in-tune sounding piano.

I only wish you could hear the recording I have of the Beethoven Emperor piano concerto that I did in February, 1990 using the Vallotti with octaves as I described. Unfortunately, that was done on cassette tape and I have no way of transferring that for use on my computer. In the third movement in particular, the piano has this razor sharp, in tune sound that takes my breath away every time I hear it!

I even found a way to use the tone cluster technique when tuning 1/4 Meantone. If I were tuning an octave where the M3 is pure, I would simply play the Major triad and tune the octave note until I heard the purest sound. It is amazing how that seems to literally swallow up the highly tempered 5th. When the chord C4-E4-G4-C5 is played, for example, the equal beating C4-G4 and G4-C5 4th & 5th cancel each other and the chord sounds perfectly still and pure!

If the note was associated with a wolf diminished 4th (extremely wide and dissonant M3), I used the 4th & 5th as with ET or an WT. If the octave involved the wolf 5th, I simply left that note out.

I can also tune 1/7 or 1/9 Comma Meantone the same way and get really beautiful octaves.

http://www.hardwaresecrets.com

Mr.Bremmer:

The above link shows how to do a transfer the old way.
If you want to get a new cassette player that converts via USB they go from $20 to $100.
Just Google cassette to mp3 converter for more info.

Check out the ION Tape 2 PC USB Cassette-to-MP3 converter/$108


-H.W.

Thanks for the tip, Herr Weiss. I knew there must be some equipment to do that, so I will look into it sometime soon. I have some real gems of piano concertos for which I tuned the piano in a Well Temperament or Modified Meantone Temperament but all are on dusty old cassettes that I would have to dig around in boxes that are stored away to find.

They all disprove the notion that many technicians still have that only ET would work in such a case. Quite to the contrary, another local technician who has been hard core anti-ET for at least 30 years persuaded me at the time (which is now 20 years ago or more) that if there is "only one item on the menu", the piano should be tuned in a way that expressed that one item the best, not a "one size fits all" arrangement.

The idea I had of equal beating octaves and fifths (and multiples thereof) dates back at least 30 years for me. I used it to take my tuning exam 30 years ago.

The idea of making double octaves and octave-fifths beat equally (regardless of temperament choice) has always been what I have done for at least 30 years. It is something I discovered on my own and again, I don't know how or why I discovered it, I just did.

I was afraid to even talk about it for a long time because if I did, other technicians would shoot down the idea. I would be asked, "Would that work on the tuning exam?" (expecting of course, that it would not). I used the Sostenuto pedal too which was unheard of. The idea became known as "mindless octaves" because you didn't have to think about it. An obvious error would slap you in the face and wake you up! Weird, wacky ideas that no one else ever talked about and could not be found in any book, so they were dismissed as pure folly.

That never deterred me, however because I did use them to pass my tuning exam and I qualified easily to be an examiner trainee having used them. I never even started training as an examiner for 8 more years but when I showed other examiners what I did, their eyes opened widely and jaws dropped in amazement at how precise the technique really was and how well it worked.

I tuned a piano in an early version of the now solidified EBVT III at the PTG Convention when it was held in Milwaukee (1992 or 1993, somewhere around then). Jim Coleman, Sr. and Virgil Smith were in the audience. Mr. Coleman approached me quite enthusiastically at the end of the recital saying, "You have done something with the octaves. I don't know what it is but I like it!"

Mr. Coleman later had me talk to Dr. Al Sanderson (the developer of the first really useful Electronic Tuning Device (ETD)) and said to Dr. Sanderson on my behalf, "Listen to what this man has to say! He really knows what he is talking about."

This newer idea does not change the older, it only serves to make it even more precise. To me, comparing two intervals separately and determining whether or not they sound alike is a little like the way orchestras tune. The oboist sounds the pitch, then stops. The other orchestra members tune to what they think they heard! Professional musicians seem to make that work but we cannot tune a piano that way!

So, comparing a double octave and an octave-fifth separately can be fairly exacting. I have found that even novices can distinguish very small differences in beat rates. However, it is still always a judgment call. It is still possible by just comparing separately, to favor one interval over the other. The tone cluster technique eliminates that error.

I will be giving two classes at the upcoming PTG Institute next month. At the first, on Wednesday, (a single period class) I will tune the piano myself, demonstrating the technique, including pitch and temperament. Hopefully, I will finish in time for the audience to hear music examples played by audience member who are pianists.

The second class will be on Thursday for two periods. I will ask audience members to tune the piano under my direction. All who are interested and able to attend will be welcome to either session but if you want to get your hands on it, come to both, see and hear what is done, then come to the second session and bring your tuning hammer!

I will record numerically the results, hopefully of both sessions. Again at the end of the second session, I hope to be finished in time for the audience to hear music from a piano that they, themselves have tuned!

The PTG Institute will provide a camera at both sessions. It will be there, focused on the keyboard and projected on a screen so that people can see easily which keys are being played. There would be no reason why whatever the camera captures cannot also be recorded. Only the PTG Institute has to agree to provide the recording cards.

Thaat is the kind of 5th quality 6:4 used by the Cordier "pure 5th tunings"

Hello, You did not wrote about it until a few years back of today, may be 8 years , but it is certainly not the subject, you have been doing so much searching and teaching about temperaments that you could be granted for it without problem, in my case.

That balance is used as some sort of standard test for basses since long, the "even beating" aspect was not really taken in account before 2000 in what I could read on the subject.

Then did you understand how the temperament could agree with it (in ET) ?

if not it is only a stretching method.

What I find funny is that piano tone is too complicated to be made really in equations. in theory it could, but practically remains a slight difference betwenn the acoustical output and what can be assessed with beat equivalences, partial pitch measures.

I guess that the tuner, at some point, begins to deal with the level of power ouptut the piano may provide, and shape it so it goes more toward the fundamental or more toward the top of the spectra.

I have used a lot the M3>10th 17th tests, to the point I can just listen to one of those intervals and know I am in the ballpark of justness.

But then I also could only listen to an octave quality and the amount of resonance it contains, and now if that particular octave is "in the mood" What would have take me tests and compromise is just "engraved" today in my ear.

This is extremely noticeable with the 15-12 relation as that "consonant" node is so easy to excite, it remains apparent in the octave (and I would say in the unison, but this sound too much esoteric probably)

Best regards

Isaac, I have never tuned the ET with pure 5ths whether that be attributed to Cordier, Lucas Mason or anyone else. I don't think it sounds good at all. In order to do that, you must have an overly wide and beating octave and the 4ths beat at least 2 beats per second. All Major thirds sound tart and mildly dissonant since they too would be about 16 cents wide.

It is an example of favoring one interval, the 5th over all others and at the expense of all others. It may sound appealing to some people if used on a large concert grand in front of a symphony orchestra playing a flashy piano concerto such as Grieg, Rachmaninoff or Liszt but hardly for anything else.

Furthermore, I can well recall the many times when someone attempted that on a small, home piano but was afraid to stretch the octave sufficiently to accommodate it and ended up tuning Reverse Well and a rather blatant example of it. It did not sound good to the customer!

What I was talking about was yes, the 6:4 test for a pure 5th, which is simply to find the note that would make a 5th a minor triad. In the process of tuning the ET via Marpurg, there are six temporarily tuned 4ths and 5ths. They are each subsequently retuned by comparing the temporarily tuned pure interval with another that is temporarily tempered twice the amount they would be in ET.

The process works well because by temporarily tuning exactly pure 4ths and 5ths, the temporarily tuned pitches are exactly and precisely 2 cents away from the goal. When equalizing a 5th that is exactly 2 cents too wide with a 4th that is exactly 2 cents too wide, the result becomes a perfectly balanced equalization of both intervals.

Rather than starting with a temperament octave that has a noticeable beat in it (as even I used to do), I am now advocating a rather conservative 4:2 type central octave. This permits the 4ths and 5ths within that octave to beat equally much more easily than if the central octave were any wider.

The result is that the 5ths are actually a tiny amount more tempered (narrow) than in theoretical ET, not less. If I were to make the central octave wider than a 4:2, it would actually cause the 5ths to beat faster, not slower!

I am confused by that statement. Without IH the fifths in ET via Marpurg range from -2.7 (narrower (faster beating) than ET) to -1.3 (less narrow (slower beating) than ET).

Kees

Kees,

I was wondering about this as well.

Surely, if the octave is widened, then the 12 fifths that are (implicitly) contained in it, must also be widened? [Edit: and since they are narrow in ET, this would mean that their beat rate is slowed as they are widened.]

I did not read all, I confess !

Of course if one want those equal beating 5ths the octave and double octaves are really enlarged a lot.

Most tuners that use it modify it for their taste, not relying on the beat rates of the instructions.

Those days I tend to believe that the partial mtatches are not the best tool to describe an octave.
I do not even use anymore the M3 10th test, but sure enough I have very conservative octaves, simply not sounding dull. I hear all thru resonance May be if I used tests I will discover that the octave size varies with the piano. Most probably.

Regards

The answer is in the fact that the 5ths must beat equally with the 4ths. If you widen the octave, in theoretical ET, the 5ths will beat slower but the 4ths beat faster. Therefore, if the goal is to have 4ths & 5ths beat equally, the wider the octave, the more tempered (narrow) the 5ths must be.

Not really "enlarged" very much at all!

That seems a paradoxical conclusion: the circle of fifths must close and if it gets bigger the total size of all fifths must increase.

I think we can't just state "4ths and 5ths are equal beating" as only some specific 4ths are equal beating with some specific 5ths.

For example it is not hard to see that F-C will widen if you stretch the octave by thinking through the ET via Marpurg steps for the 4th and 5ths spanning the M3 F3A3 and seeing what happens if you slightly raise A3. G3 will then raise about half that amount in the first step, and in the second step C4 will raise about half of that, resulting in a less narrow F3C4. Lowering F3 is of course the same thing.

Kees

Kees,

I know what the theoretical graph looks like. When I wrote an article about the ET via Marpurg for the PTG Journal, I said that it looks far more irregular than it sounds. When I tune the temperament either aurally or using a calculated program, the 4ths & 5ths all sound alike to me which is the goal.

That means that you have to narrow the 5ths just a little more so that the 4ths also become a little less wide. The 4:2 central octave makes that work out nicely. If I tuned a wider octave than that, I would have to narrow the 5ths even more to make them beat equally with the 4ths. At least, that is the way I see it.

This PTG thread has calculated beat rates for 4ths and 5ths for different octave sizes, I found it useful in helping understand this discussion:
http://mail.ptg.org/pipermail/pianotech/2009-February/003758.html

Well, you are wrong. Did you read what I wrote at all? Why don't you try it and you will see.

For example, CF beats twice as fast as CG in ET via Marpurg, not equal.

PS you still have two wrong numbers in your offsets on your webpage, so I hope nobody is using those (wrong) offsets.

Kees