Hello
Can anyone of you tuners give me some tutorial of how to tune Berhard Stoppers temperament aurally? Is there a recording of the thmperament avaliable, e.g. How sounds the octave, how the fifth and the duodecime? What are the checks, to know if I am on the right way or not? And how sounds this "beat masking effect"?
Many questions!! Thanks for all the tips and help

Toni

Toni:

You will probably need to contact Mr. Stopper directly. It is a bit of a mystery... tuning pure twelfths is a different matter.

Already tried!! Need more help thank you!

I found a PTG article at http://www.piano-stopper.de/dl/PTG2008_StopperTemperament.pdf and am reading it now. I will let you know what I think after.
Pure 12ths is not a "temperament" technique per se, it is a technique for tuning the treble (and can be used for bass as well) that produces consistent octaves. That I can help you with. I've tuned pure 12ths (pure duodecimes?) for many years, but now prefer tempered 12ths as a compromise for pure triple octaves and better sounding double octaves.

This might help, at least as far as hearing what it sounds like...a few years ago, I recorded my grand piano using Mr. Stoppers software, I posted these and a few more files in a posting comparing ETD's. Here are a couple of the recordings. The piano is a 1927 M&H 7ft Grand with the LX playback system. I tuned it using Mr. Stoppers software.

The Age of Innocence played on the LX by B.Pezzone https://www.box.com/shared/s4huo9y1pm

Oh Danny Boy (jazz version) played by E.Reed on the LX. https://www.box.com/s/degdfasivzvwkh3q5xza



I found a classical recording I made that I never posted here before, using the Stopper tuning.

Earl Wild playing Brahms on the LX. https://www.box.com/s/mikdttqniq8051wp48fa

So far, the article seems to be selling some software, and a tool to play 12ths with one hand.

The first step in the temperament seems to be to tune a pure 12th with the software. Not needed. To tune a pure 12th, say F3C5, use the check note a M6 below F3 (Ab2). Ab2 does not need to be in tune, just creating audible beats with F3 and C5.
Make Ab2F3 = Ab2C5 (M6 = M17). This is by definition, a pure 3:1 12th. (Beats will be heard at C5, partial 3 of F3, and partial 1 of C5)

Also, if you play Ab2F3C5 together, all at once, the beats will produce a beat like this:
wah-Wah-WAh-WAH-WAh-Wah-wah-Wah-WAh-WAH-WAh-Wah-wah...
where the capitals indicate loudness.
So a non pure 12th will produce a beating or phasing of the beat. When you hear a solid beat (at C5, no phasing or slow pulsation of the beat) while playing Ab2F3C5, then you have a pure 12th.

Also note, if all your M6s from F3 to B4 are steady and evenly increasing, and you use this technique to tune the 12ths above, then all your M17s will be smooth and increasing. Pretty cool, huh?

It's a shame Mr Stopper is so protective over his tuning sequence. It would be nice to know what the 'cancelling effects' are that he refers to in the brief section on aural temperament tuning. The implication is there is some alignment of beats within the temperament so that they cancel. I'd like to know what is actually involved.

Brahms?

Well, the only "cancelling" I can think of may be in the octave itself. When an octave is tuned just right, IMHO, (beatless, as the old-timers say), it is possible to imagine the beats at the different co-incidental partials cancelling each other out. The accepted size (PTG RPT) for the mid-range is between a 4:2 and a 6:3. This means the octave will beat as a:

very wide 2:1
wide 4:2
narrow 6:3, and a
very narrow 8:4

and the "beatless" size is, as one can imagine, the size where the 2:1 beat cancels the 8:4, and the 4:2 beat cancels the 6:3.

When I teach octave sizes in my course, I go through all the theory with check notes, etc, then I say, "just tune the octave beatless, listen to the treble, and try to get rid of all that noise.". Nine times out of ten, when we check, the students have tuned a clean octave (beatless?) that is between a 4:2 and a 6:3.

The pure 12th technique produces octave sizes that are not only between a 4:2 and a 6:3, but at the same spot within that window for all the octaves.

I learned this from Dave Renaud, who learned it from Jack Stebbins, and I was told that this is the standard that the PTG is using to tune the treble on the master tuning of exam pianos.

Using this technique, I was able to get 98% on the treble for my first RPT attempt. The graph actually followed the changes in the string diameters.

As for cancelling the beats of the thirds or sixths in the temperament, I don't believe that is possible. (Unless maybe the inside/outside M3/M6 could produce beat cancellation if played at the same time. i.e. F3G3B3D4.)

Right you are! I was looking at some E. Wild Chopin I had also recorded. Thanks for the correction.

Hear, hear! I second these thoughts exactly.

I am by far no expert on the Stopper tuning, but I have heard his tuning at a presentation he gave. The cancelling effect that struck me was the following:
the octave (eg: A3 - A4) sounded clean and pure, both the fifth and fourth (A3 - E4 and E4 - A4) sounded proper, with the slow roll. But when all three notes were play together, the beats were cancelled out and the sustain had a smooth, clean sound, almost reminiscent of a pipe organ. It was really something. I think this effect has to be experienced, otherwise all talk is speculation.

A lot has been written on his tuning on this forum, Stopper himself made many posts a few years ago. It's all in the archives....

Thank you all for your information and help. I have already tried to tune the Stopper temperament aurally. I asked Bernhard how to do, he told me to do the doudecime aurally pure and then go on as usual.... But no further help and tests. I askes another german tuner, but... no answer.

Grandpianoman: thanks for the recordings, sound very nice, I have found them already on my way through the archives. Do you also have a recording of the temperament tuned with Bernhards software? Would be nice to clearly hear only the temperament, and all the intervals.
Mark: thanks for your detailed infromation and the test for the doudecime. I read the file again you added ( I knew it before) and unfortunately there is no description of the way through the temperament.

I can't imagine that there is no instructional sheet out there of that tuning. The software is too expensive to buy without really knowing that it is worth it. But I am really interrested in this tuning!

Can't you send me a Christmas present, Bernhard? and to all the others who are interested in your tuning?

Toni

All:

I think Mr. Stopper hears things in a way others do not. He has been adamant that his tuning is NOT pure 3:1 twelfths.

As far as beat cancelation in general, any time three notes are played and the beating of two intervals equal each other, there will be beat cancelation. In the case of 3:1 twelfths (NOT as Mr. Stopper's says he tunes) this would include a stacked fifth and octave. The same thing happens with a stacked 4th and 5th with a 4:2 octave.

Toni:

I have tried many times to use a sequence that uses multiple 12ths along with octaves, 4ths and 5ths within them. I always end up with 5ths that are too pure and a M3 that is too slow compared to its neighbors when tuning the 9th note of the scale.

What I have come up with is a sequence that fits within one pure 3:1 twelfth:

A4 to fork
D3 to A4
D4 to D3, check D4-A4
A3 to A4, check D3-A3, check A3-D4
E4 to A3, check E4-A4
G3 to D4, check D3-G3, check G3-E4 (first RBI check)
E3 to E4, check E3-A3
G4 to G3, check D4-G4

You now have an octave tuned for each of the 4 ladders for tuning sets of contiguous major thirds, if you are so inclined. Since I do not believe that CM3s are appropriate across or near a break I do not use them. Instead, from E3 I tune up by fifths and down by octaves always staying within the first pure twelfth that was tuned: D3-A4. The checks are similar to the checks in Dr. White's sequence only with more of them.

That is NOT correct. Yes, whenever three notes are played, there are two beat rates created, but they will never cancel out unless the two waves are exactly the same frequency and OUT OF PHASE! I.e. With identical frequencies, you can have constructive interference (waves are in phase and beat is louder), or destructive interference. (Waves are out of phase and beat is cancelled.)

Mark:

You have a point. Cancellation is not the best term to use. I think you know what is being talked about. Do you have a better term? In other words do you have something constructive to say?

Another way to put it would be the difference frequency of the beats is zero.

Hi all,

To me the Stopper tuning masks Major 10ths (1 octave + Major 3rd) and Major 17ths (2 octaves + Major 3rd). Normally when I hear a classical recording of a piano tuned in 'conventional' ET, I can spot the 10ths/17ths right away inside the large Major harmonies being played (C-E in a C Major chord). These beats will sometimes fight against the slightly fainter, but still noticeable Major 6ths inside the same Major chord (G-E). Once you have tuned a fair amount of pianos, you cannot 'un-hear' this 10th and 17th beating in listening to piano music (which can be a good or bad thing - ha). That's how I can immediately tell if the piano is in tune, other than the obvious unisons of course. And usually on a classical recording, so much care has been placed in the tuning, that you can hear the precisely placed beat-rates all over the place.

Not so with the Stopper tuning. Take another listen to the Earl Wild recording (thanks Grandpianoman). Whenever there is a Major harmony, the 10th's/17th's should stick out like sore thumbs (at least they do to me), but here, even though the same amount of tuning care and precision is applied, I cannot hear the 10ths/17ths and 6ths so well. They are hidden in the mix, or muffled, or masked.

This is what gives the tuning a 'still' or pure quality. This in contrast to conventional ET where there is a lot more activity going on in the beat-rate department.

No pun intended, right?

I thought I was being constructive by helping to clarify the terminology.



If the difference is zero, you can still have constructive or destructive interference.

To be fair and honest, your post was clear and everyone should have inferred that you meant out-of-phase destructive interference. However, the situation can occur where the beats add up, so I thought I should mention it.

Toni, you're welcome.

Unfortunately, I don't have a recording of just his temperament.

Going back through my box.net archives, I found these...since I tuned and recorded all of these back in 2009/10, my tuning has improved, so please forgive some of the unisons.


Stopper Tuning-1927 M&H 7ft RBB Grand played on the LX system.

Earl Wild playing the Liszt Ballade No 2 in B minor on the LX, Stopper Tunic OnlyPure Tuning--Corrected in Audacity.mp3 https://www.box.com/shared/qo5nskakfs ( caveat: I remember Mr. Stopper was ok with this recording, except for some of the unisons. Also, that is a pretty bombastic piece...when it was done, my tuning was not where I left it. Stability has improved since then.)

E. Reed Jazz 2 Stopper tuning https://www.box.com/s/3mtx82cdnnmk3zoe4f2q (first time posting)

E. Reed Jazz 1 Stopper tuning https://www.box.com/s/ev1m6cw9234l2vcgtxcj (first time posting)

Mark, as much as I understand a wide 4:2 octave is not a beatless octave, but the pure 4:2 octave is a beatless octave?

... "where the beats add up" ...

They can "add up" in two different ways. When they have the same frequency and are in phase, they can "add up" in amplitude, be louder. Also when they have the same frequency the additive frequency "adds up" to double the beat, exactly double, while the subtractive frequency "adds up" to zero. This is the basis of the "masking effect" (a better term than "cancellation") that is observed when intervals have the same beat rate. This can even happen when only two notes are played, but different sets of partials line up. It can be very obvious with bass strings where the beating of different octave types can be heard at the same time. It sounds smoother (the beating is masked) when the two most prominent beats, beat at the same rate. This may also be why a compromise between 4:2 and 6:3 octaves are popular.

An interesting thing happens when an octave is tuned where the 6:3 partial match beats narrow at the same speed as the 4:2 octave beats wide. The 2:1 partial match, being at half the frequency of the 4:2 partial match but twice as wide in cents, also beats at the same speed. So then there are three different partial matches all beating at the same speed. This is true even in the presence of inharmonicity. So this could be the smoothest place to tune a particular octave.

Rick Baldassin, in his book on pitch, basically shows that a double octave in the F5 - F7 area made up of two 2:1+ octaves will result in a slightly narrow to pure double octave and or a wide double octave.

So my guess is that a double octave made up of a wide 4:2 octave and wide 2:1 octave would produce a wide 4:1 double octave which is obviously not beatless.

When I tune M3<M17 (4:1+) my double octave is wide and beating. If I tune my M3=M17 (4:1) my double octave is beatless.

A 4:2 octave may be beatless at the 4:2 partial, and the 2:1 may then cancel out the 6:3, but the 8:4 beating will be heard.

It needs to be repeated that, if one was to tune an octave to sound as clean and clear as possible, concentrating on eliminating the higher partial noise, and then analyse its size, one would find the octave to be a wide 4:2 and a narrow 6:3. Try it. It "sounds" beatless but we know that there are beats at all the partials. Why and how does it "sound" beatless? Cancelling is the only explanation I can come up with. But an explanation is not really needed, only the experience of hearing it and analysing it and coming to that conclusion, re:size and quality.

I will post a video if anyone is interested.

Hi Mark,

Yes, that is right. The M3=M17 test is that for a pure 4:1 double octave.

Maybe your M3<M17 difference is too big.

Try this:
Tune M3<M10<M17<M6
So that the M10 and the M17 fit into the M3M6 window. Note the M3<M6 window is just the test for a wide P4.

Note also that this produces a tempered 12th. You can also tune
M3<M10<M17=M6
which produces a pure 12th

Cheers,

The following is by Bill Bremmer,

Please see new thread Clean Sounding/Beatless Octaves

If you focus your hearing on the 4:2 partial only, or the 6:3 partial only, of course you will hear a beat. Read the part about the "whole octave sound" by Virgil Smith. Only when you are listening to the whole octave sound, as musicians do, that you can sense the "beatless" quality of a well tuned octave. You are on the right track. Keep searching, keep reaching.

Hi all,

I would call the masking effect of OnlyPure tuning a beat suppression. The beats are there, but at a noticeably lower level than in other tunings I've heard.

Bernhard does not really tune pure 3:1's. During the seminar (PTG K.C., 2011) he only used the spanner tool in setting the very first 12th, and then for a few troublesome intervals later on.

He finishes all unisons of a string first, then moves on to place one string of the next note in an optimal spot in relationship to the previously tuned open unison, and - very interesting - he often throws in a third note (previously tuned, open unison) for kind of a "second opinion".

Sounds like another flavor of the approach practiced by Virgil Smith . .. .

Hi Pat,

I'm glad you chimed in. I was at the Stopper seminar where he taught the aural sequence as well.

I must admit at that time my brain was a bit overwhelmed and the actual protocol of setting of the temperament somewhat, but not totally escapes me. I use the software to set it. Over the last couple of days, I've been looking at the chart he provided, trying to remember what he was doing. I'm still at a loss to remember clearly what he was doing.

A4-D3 forms the first defining P12,set with his 12th spanning gizmo(just a piece of wood shaped to hit the 12th simultaneously). Then as he moved through the sequence he broke it down into 2 parts:

part 1 moves from the original P12 by fifths and octaves when available till you reach G#3.

part 2 starts with D4 ( I assume??? taken as the 3rd note of the D3,D4.A4 3 note combination) and again moves through a 5th/octave sequence till it ends on D#.

Closing the temperament circle was not presented as as important as other temperament sequences..but I'm could be remembering this fuzzily.

My recollection, and this is the interesting part to me, and the part that I took to heart, is he used 3 note simultaneously sounded combinations to set a single string of each new note at its "quietest" spot in relation to the other 2 open unison notes of the 3 note combination. He definitely used this 3 note combination outside the temperament,but I think inside the temperament he used it as well to set each new note.

That technique was to set each new tone in the progression, notice the word set not check, but set each new note in relation to a 3 note simultaneously played combination. For example the 1st note in the sequence after the initial A4-D3 P12 as tuned open unisons was a single string of A3. This was set by playing the 3 notes A4,D3,A3 together, setting A3 in the place where the beat masking became apparent.

My recollection was that this 3 note tuning was the essence of the entire procedure...I think both inside and outside of the temperament. But!!!! I'd like to hear if that was your recollection, or what your recollection was...to see if I totally missed it.

Jim Ialeggio

As long as close major harmony is good any method pushing the consonance at the 12 15 level is good.

"pure" does not mean the 3d partial line with the fundamental, but the mix of all partials are not producing noticeable beats.

as long as the 5ths are not beating audibly we are in the "pure" concept.

My brother (violonist, solist) temper his 5ths (less than piano tuners probably) for tone and justness reasons...

Hi Jim,

I think you're absolutely right on the money! Everything you write is the way I recollect it. Thank you for this, it also confirmed that I remember it right.

Bernhard told me in an e-mail this Fall that he's working on a book about the tuning and its theoretical background, and also that he would most likely include RBI checks, too, to help newcomers to the system get on the track more easily.

Thank you very much, I thought it must be somehow like you dircribed. To tune the contiguous thirds is not the problem, more to know, how this beat masking effect sounds and where it happens. sometimes I tune down in fifths and then check with the octave and the doudecime.

Where does the beat masking effect happen? Why between your ears, of course!

I am not trying to be "smart". Bear with me a moment. The human mind looks for simularities and differences. When one thing is the same, or nearly the same, as something else the mind finds them to be more acceptable. That is why ET is percieved as being in-tune even though it can be argued that it is the most out-of-tune temperment.

I cannot speak for Mr. Stopper's tuning. I can only speak for a pure 12th tuning. When you tune pure 12ths, listen to the resulting 4ths and 5ths and octaves, and then compare them to others; any departure from a VERY strict ET becomes apparent and can be corrected. Consider the span of a twelfth and the most critical RBI test: the outside M6/inside M3 test. Of the twelve possible tests, a 12th spans eleven of them. There is no excuse for any variation from ET before expanding the temperment. (This is not to say that the outside/inside test must always produce equal beating intervals. Due to scaling breaks, I do not believe this is always possible. When tuning pure twelfths, the 5ths and octaves must take priority since they form an equal beating test for pure 12ths.)

Hey Jim,

Thanks for the best post on the Stopper temperament I've seen. It's really helpful and interesting to hear from people who were at his class.

It seems from what you wrote, that Bernhard's tuning is less about the 12th as an alignment point, but more as an additional external reference point to use 3-note combinations early on in the tuning?

Seems logical to me that this is the key to his tuning, as well as what I've found in any other great aural tuning.

Has anyone else tried this? I have and I always end up with a beatless D3-A3 fifth. Much too wide to tune ET with. Or consider the "beat masking effect" if what we are looking for is the beat in the D3-A3 fifth to equal a beat in the A3-A4 octave. Well, regardless of where A3 is tuned, the 3:2 beating of the fifth will be at the same speed as the 2:1 beating of the octave when the 3:1 D3-A4 12th is pure.

But if what sounds "best" is actually tempered 5ths, 8ths and or 12ths then that's another story.

Yeah...at least I'm approaching this from that standpoint as well.

Bill Bremmer has also been approaching this from a similar perspective. In an expanded version of his PTG Journal octave setting article he's been expanding the octaves with something he calls "tone clusters".

I believe he will be presenting a class at the nationals this year on these "tone clusters". He's written about them somewhere on this forum relatively recently, but I can't put my fingers on them right now (I think it was a "unison" tuning thread).

Both Bernard and Bill seemed to feel that once you get the idea down, checking the RBI's becomes relatively superflous, as they will be spot on.

Jim Ialeggio

From what I recall, Kent Swafford was a great proponent of Bernhard Stoppers tuning sequence, maybe he can shed some light on the matter, if you asked him nicely!?