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Hi everyone,

Since there has been some recent discussion on the Pure 12th tuning (Jeff, Rafael, B.Stopper, Bill, me and others), I thought I would give a clear demonstration of this method by recording my home piano, just tuned with the Pure 12th expansion method.

Since the recording is long, I divided it up into 2 parts. Part One is where you can hear all my checks and test intervals starting with the initial A3-A4 octave, through the F3-F4 temperament, and on to the pure 12th expansion for the entire range of the piano.

If listening to the proofs of the temperament and progressive intervals does not interest you, please click on the second link below which is Part Two. Here you will be able to listen to 'yours truly' play pieces in most 12 keys, demonstrating the overall effect of this method.


These examples are played on my Yamaha U1 upright piano:

Part One - Proofs and Test Intervals:
http://www.mediafire.com/?6kjy46ppzinwmvn

Part Two - Overall Sound with Musical Examples:
http://www.mediafire.com/?dp1zxg10eu0ww7o


As I mention in the clips - comments, suggestions, and comparisons with other temperament expansion methods are welcome. I hope you enjoy listening to the examples as much as I enjoyed playing my freshly tuned home piano!

-Erich

Erich:

Thanks for posting!

It sounds very, very nice.

Sounds great!

So I tune a standard equally tempered scale, extend it, then tune down and up in pure 12ths?

Thanks Jeff and Dan.

Dan:
Yes, tune the ET F3-F4 using your method of choice. I highly recommend Bill Bremmer's ET via Marpurg (videos on his website). It is hard to go wrong with this sequence. For additional help before I start the temperament, I use Stebbin's "Let the Piano Tell You" method of getting the F3-A3 and A3-C#4 and C#4-F4 right where they need to be for that particular size piano. Then after you tune the temperament octave, fill in the gaps - F#4,G4,G#4 using some standard check intervals. Then fill in E3 and D#3 right below the temperament.

When you reach D3, you have your first 12th to tune using A4 above. Then just descend all the way down (maybe stop short of the low bass for stability reasons). Then start with A#4 and you have 12ths below to tune it to. Go all the way up using 12ths, then 19ths (double octave plus 5th) when it's too high to hear the possible beating vs. pureness. All 12th/19th intervals outside the temperament gate should have a still, motionless, pure sound to them.

Let me know if this method works for you on the particular piano you try it out on. I know that Rafael and Jeff now have run into slight problems right outside the temperament area on certain pianos. We might have to re-think a way around these issues. So far I have been lucky with the 5 pianos I have tried.

-Erich

I am receiving very positive responses for the two months that I have been using this method and Bill Bremmer's sequence for the F3-F4 temperament is proving to be very accurate and very stable. I have been tuning A3-A4 temperament for about 12 yrs, so this is a huge change of perspective for me. I'm thinking it may be because I have been tuning 3rds and 6ths above A4 for so long, that I am extending the temperament above F4 to C5 (using standard check intervals), before extending 12ths to the treble and bass. The F3-C5 seems to be a sold 12th to extend the temperament from and I haven't been noticing any new issues with the notes right outside the temperament. Tomorrow I'm going to see how the D3-A4 12th feels.

Erich, thanks for the posts and examples.

Thanks for the nice comments, Erich and Dave. I am listening to the music files now. It is a very nice and smooth sound! I submitted a class proposal for the PTG convention next year where I will present the ET via Marpurg as a "Master Class", that means the audience will actually tune the whole piano under my guidance. The whole piano, including the unisons!

It will take a double period of course but at the end, those who tuned the piano will get to revel in the sound afterwards. I will show how to use tone clusters to find not only the notes within the temperament but the outer octaves as well. Rapidly Beating Interval (RBI) checks will not be necessary but we may try a few of them here or there just to prove that they are not needed.

What is interesting about this approach is that it goes back to skills that 17th-19th Century tuners had. It uses none of the very complex, back and forth checking and comparing of intervals that has become commonplace today. It is also what I have seen used by some of the most advanced tuning technicians today. It seems that tuning technique have come full circle. A back to basics approach makes the whole thing simpler, easier and the results speak for themselves.

The Institute Committee has not yet released its decisions yet on which classes have been selected, so if you personally would like to attend the session I have planned, a note to Ryan Sowers may help encourage the decision to put it on the schedule.

I think I'll give it a go, Erich.

I can set a fairly spot-on ET with a traditional 4ths & 5ths based sequence. But thanks for the suggestions.

Will post my thoughts when I've had a chance to try it out.

Thanks for listening Dave B and Bill.

Bill,
I really hope they let you do that proposed Marpurg masterclass - that would be great! A lot of people on this forum have tried and liked your method (and I spread the word as much as I can), but I think the whole tuning world needs to know about it! At least others could give it a listen and try it once for themselves. Also the Stebbins "Let the Piano Tell You" method is awesome. Thanks again for your wonderful insight and helpful contributions.

Jeff and Rafael have had some issues on smaller pianos right when they reach D3. We are trying to figure out a work-around to this problem. Do you have any thoughts as to why this is happening, or any possible solutions?


Dave B,
I have directed Jeff to your post above because he is thinking along the same lines as you, meaning get the F3-C5 pure 12th first. I could also try this out on a smaller piano (I have access to a bunch of spinets where I teach) and report back my findings. Although, with my demonstrated 'hybrid' method of Stebbins, Marpurg, then 12ths, I have had success so far out of the temperament gate. I might blindly put this hybrid method on a small spinet or baby grand with breaks at inopportune sections, and just see if it flies. If it doesn't work, I might have to re-think the temperament/12th area.

-Erich

All:

When tuning 12ths, the best check for the chosen ET sequence is the octave. If none stick out as the temperament is expanded with 12ths, you made a good choice.

Erich,

The first recording was problematic for me. I think that my PC is somehow distorting the audio files, or perhaps I'm hearing an MP3 compression artefact or something. I get a permanent wow-wow of the notes, about 2 beats per second, at the fundamentals. For example, when you play the A3-C4 m3, I hear the normal beat at E6, as expected, but I also hear A3 itself wow-wow-ing about twice per second, as though the unison is out of tune. This made it very difficult to evaluate the tuning, especially slow-beating intervals. Did anyone else pick this up? I'm wondering whether it's in the recording, or some problem on my side...

But I really enjoyed the second recording - not only the resulting stretch of the bass and treble, but also your choice of pieces, smooth renditions and talented playing! What a pleasure listening, thank you very much!

Erich,

I'd actually like to incorporate Jack's idea into the mix. What I know how to do today is the sum of what I have learned from many others along the way, including Jack. I talk and sometimes work with Jack on exams at every convention. We exchange thoughts and ideas.

One anecdote I remember well was the time I showed him how one could find a double octave just as precisely by ear as one could with an ETD. I used as an example, tuning F5. I set the ETD at F5, read on the fundamental. I played F3 and stopped the pattern. Then, I played A#3. The pattern then rolled sharp. I adjusted the ETD until the pattern rolled equally sharp for F3 and flat for A#3 but both were very small amounts.

Then, I turned the ETD display away from me so that I could not see it. Then, I tuned a double octave, F3-F5 aurally until there was no beat. I then showed him that the A#3-F5 octave-fifth sounded narrow and beating too much for comfort. I then sharpened F5 slightly so that the F3-F5 double octave and the A#3-F5 octave-fifth both sounded apparently beatless. If you really listened, you could hear that neither interval was perfectly beatless but they both sounded pure at first take (and would be perceived that way by a musician). The most important thing was that they both sounded alike.

Then, I turned the ETD around and played F5. The pattern stopped dead on! Jack's eyes opened wide and he smiled. "I really think you're on to something there!", he exclaimed. Two years ago, I showed the same thing to Randy Potter with pretty much the same reaction.

The thing is, that I had been doing that since the early 1980's, long before I had ever started experimenting with different temperaments or alternative ways of tuning ET. I somehow got the idea of using the sostenuto pedal to do this. I qualified to train as an examiner on a tuning exam in 1983 using that method.

I hardly dared talk about it. When I did, other technicians viewed it with much skepticism. The first question they asked was if someone could pass the tuning exam that way. My answer was, "I did it that way for my tuning exam". Any time I have conducted or participated in a tuning exam master tuning, I used that technique and it proved to be the technique that could then be cross checked and proven with M10 and M17 checks. It has amazed every examiner who has seen me do it. I am still today one of the very few people who uses the sostenuto pedal to tune.

If I get the class that I proposed, I will get the attendees to learn how to use it too.

Hi Mark,

Thanks for the comments/compliments. About the recording, I used the nice Zoom H4n handheld stereo recorder. I just sat on my piano bench, put the recorder on a night-stand beside me and talked into it. Then when it was time to play, I just turned my waist to the piano and started. Easy for me to record that way, but maybe choice of mic location could have been more optimal. Sorry you are getting the false beats on your end.

When I played those A's and C's at the beginning, I hadn't tuned any unisons yet. That is the pure sound of the muted string (temperament strip) with the middle of the tri-chord doing the speaking. I know for a fact that at this middle area of my piano, there are no false string beats to be heard anywhere. It is a small upright, but a quality Yamaha nonetheless. However, as I get down into the bass, there are weird beat patterns due to inharmonicity all over the place and I apologized for it on the recording. I wish I had a big grand piano to record with.

It also could be the compression to mp3. If I had set the recording to high-quality .wav however, the file size would be huge and people wouldn't be willing to sit there while it downloaded, waiting to hear something. So I chose a more internet-friendly mp3 conversion. Lastly, it could just be your computer's sound card or mp3 playing software causing distortion.

Unfortunately, I only know the basics about all this recording/converting tech. This allows me to do a simple recording like this, but I can't really expound beyond that. I hope you are able to rectify the situation. One more suggestion: updating your software drivers (.dll's on Windows?) could maybe help.

Thanks and good luck,
-Erich

Erich,

I'm very backward when it comes to software drivers and the likes. I take your word for the beat-free strings, absolutely! Really, I was just wondering whether anybody else listening to the first recording had picked up similar problems.

I'll try to listen to the file on my PC at home. Perhaps it's better on that one...

Mark:

I went back and turned up the volume all the way and listened very carefully to A3 on the first recording. I think I can hear what you are describing, it is like an LFO (Low Frequency Oscillator in the synthesizer world) or very slow tremolo effect like 1 bps. I quickly went to my piano and played the same note alone and with the C4 (minor 3rd) and I can't hear it! That is weird.

Since I ruled out a false beat, I now can assume it is a resonance due to the recording (microphone placement, recording a muted string, etc.) I'm not sure if this is what you are referring to, but if you skip ahead a little in my recording when I say that I have filled in the temperament-area gaps and tuned the unisons, the LFO is not there anymore.

Maybe I should just call it a UFO - Unidentified Frequency Oscillation - ha ha.

So, in conclusion, there might not be anything wrong with your software or soundcard. Just so you know what I was doing at the beginning, I tuned very close to a 4:2 octave on my smaller piano. The F3-A3 M3rd beats about the same as F3-A4 M10th, but the A3-C4 m3rd beats a little faster than C4-A4 M6th, so it is not quite a 6:3 octave - more close to a 4:2 or right at it. The wider 6:3 would beat too noticeably on my upright.

Hope this all helps.

-Erich

Indeed, Erich, that does help. The question of octave width wasn't clear to me, because the UFO (ha-ha) was interfering with my listening. In fact, from what little I could make out, the m3-M6 test (6:3) sounded more equal-beating than the M3-M10 test (4:2).

And yes, the LFO seemed to have lessened or even disappeared later...

I'll give the file a listen on my home PC tonight. I have half-decent earphones and free-standing speakers there, while I only have cruddy monitor speakers here.

Same here, Mark. I thought the octave was much closer to 6:3 than to 4:2.

My bad guys - yes it was between a 4:2 and 6:3, leaning towards the 6:3 side I guess. According to Bill's octave tuning instructions on his website, the optimal octave slightly 'fails' both 6:3 and 4:2 tests. In other words, the A3-C4 minor 3rd needs to beat just a little faster than the C4-A4 Major 6th (both would beat equally for a true 6:3). And, the F3-A3 Major 3rd needs to beat just a little slower than the F3-A4 Major 10th (both would beat equally for a true 4:2).

Thanks for your corrections. I hope I am on the right track with this optimal octave business.

Not sure what y'all are talking about, but it sounds nice to me!

Thanks PianistOne!

We were just talking Piano Tuning 'shop'. Basically there are different widths of octaves that a tuner can tune where, to the average listener/pianist, the octaves still sound perfect. On smaller upright pianos and baby grands, a smaller octave width will probably sound cleaner. And on a concert grand for public performance or recordings, a wider octave gives more clarity/brightness/power and eventually cutting power when you tune those same octaves in the bass and especially the treble. But the difference between 6:3, 4:2, 2:1 (partial number ratios) octave sizes is very small - fractions of a cent, and there are 100 cents inside each half-step on the keyboard!).

So, if one just walks up to a piano and plays an octave, I don't think there are any aural tuners out there who can hear that small of a difference. Therefore, there are tests that an aural piano tuner can use to see which octave he/she has just tuned. Also, I believe an electronic/software tuning device will probably be able to 'hear' the difference.

That's what we were talking about. Hope this clarifies. Thanks again for the compliment!

-Erich

No sweat about the octave size, Erich. Mine was just a comment from a beginner who may have a reasonable ear, but whose hammer technique is in its infancy - I still battle to set things like octave sizes reliably and repeatably... Kudos to anyone who can.

By the way, the "LFO" was just as bad on my home PC, so I just left it at that. Not to worry!