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Uh, Gary? Stoppers "temperament" IS equal temperament, just with a particular approach to stretch. (I just want to let you know that this really isn't the right thread to continue your crusade...)

The software has a unique display and response time that allows for wicked-precision tuning. It might be the only software that allows for tuning unisons one string at a time to the machine and ending up with better unisons than by ear on troublesome strings. (I know there are techs who will dispute that, but probably never tried the software...)

Ron Koval

Thanks for sharing Grandpianoman. Sounds great! As another Tunic user I agree that it is amazing software. I even use it on spinets all the time with great results.

Ron - Yes! Wicked-precision is right on.

GP,

Hi there...Ron's point regarding stretch is one you might consider. Many really good pianists relate primarily to the way the octaves and octave fifths,etc are stretched, and to the singing quality of the unisons, rather that to what temperament was used. To some degree they are inseparable, but in a another sense they may be separable.

As I see it, temperament, and I think this is what folks mostly refer to in temperament discussions here, is the interval relationships set up in the central octave or two. These relationships are stretched out over the octaves, and how this stretch is achieved can vastly alter the way one experiences the tuning as a whole. So, with any temperament the octave stretch is a defining part of the aural experience.

What Stopper's got here, similar to what Bill does with his beat cancelling effect, is a way to stretch the octaves which creates that beat cancelling effect. I mention this, because you may have a preference for the beat cancelling effect with the temperament coming in as secondary to the stretch experience...just a hunch but I figured I'd offer it as food for thought.

Jim Ialeggio

Can someone direct me to a link where I can listen to a recording of Kent Swafford's tuning the Stopper temperament/tuning on a spinet and grand, please?

This is what interests me.

Lucas Mason wrote a book called 'The New Tuning' analyzing the beat cancelling effects in common chords. This tuning was equal temperament based on the perfect 5th, or the 7th root of (3/2). He showed many combinations of beat cancelling that occurred through this alignment.

Stopper claims to have a beat cancelling effect and I'm sure there is one.. but only because there is some kind of beat cancelling to be found in all tunings!

There are so many interference patterns in tuning, even assuming that all strings have a smooth inharmonic transition, that I want to know exactly what intervals have a beat cancelling effect in Stopper's tuning. I think that he has found and focused on a common important interval that shows beat cancelling in this mode of stretch.

It's the importance of this interval then, in its occurrence in music by statistical majority, that would give value to this tuning.

Does anyone have papers or notes on the Kansas City presentation that they can scan in and post?

Much appreciated..

Not interval(2 notes) but triad. The beat cancelling, as in Bill's beat cancelling happens with 3 notes sounding. Not triad in root-3rd-5th sense, but three note grouping root-5th-octave, or root-4th-octave.

No papers to share other than the temperament sequence that could be used based on P12. He did talk about and show some sound files showing the phenomenon, but frankly, not possessing "math brain", merely being a "math brain" voyere, the explanation went over my head in the one class.

Jim Ialeggio

Hey, well that is something. Thanks, Jim, for sharing that.

I'd be really interested in getting those tuning instructions - or anything else related that you gained from the presentation - because I could infer some of the math from there.

I'd be glad to post explanations from looking at the 'source code'.

I actually meant triads as well - but the expanded triad makes sense in terms of the tuning. So he must be using slow beating intervals to counter one another in open voicing chords to make them sound pure, as they would be more so in a Pythagorean tuning.

You're welcome Scott. I always like to share on PW when I find something that sounds good.

This beat-cancelling idea...that's probably why I like Bill's EBVT III, along with the large stretch on the M&H.

Ron, Jim, ...would you say the Stopper software has a moderate stretch? What is the general consensus for stretch regarding a small piano like this, 4ft8...should it have less or more stretch due to the inharmoniciy of the shorter stings? I am just going by what sounds good to my ear. The Stopper software sounds really good on this piano. I have had others that sound good, but this one hits me right.

Ron, you are right on the money regarding the Stopper unisons. Since I have learned how to tune unisons by ear, that is what I normally do, except around octave 7...the bass I can pretty much do easily now as well. That being said, this time with the video above, I let the Stopper do ALL the unisons! Except for a FEW notes where false beats were getting in the way, the unisons were great! It certainly works as advertised. Stoppers software is very easy to use, the yellow and green triangles work quickly and are quite steady when tuning. On just about every note, I can get a perfect, steady square box. There are some occasional notes that jump around a bit, very few. What I do then is to find one of the 3 strings or 2, that are steady, and tune the others by ear.

Going by what sounds good to your musicians ear is, in my opinion what this is all about, and it trumps all the numbers at least for me. If I were to try and figure out what my musician's ear wanted to hear numerically I'd be cooked...I'd over think the question and target the wrong choice every time. One of the things I really like about this approach from an aural standpoint is that it is about listening to the open unison tones as whole musical entities, rather than dissecting the tones for single partial matches. It makes the whole tuning exercise a meditation on the sensual experience of sound.

Having said that, through the treble, I have the machine on as I find the spot I'm looking for aurally. I use the machine both to check, teach and challenge my hearing. Wrapped strings are always all aural for me.

Sorry can't help with the numbers here. Some have said Stopper's stretch is moderate, but I've had the impression it was well stretched, especially on bright or tired instruments, as the stretch can seem a bit harsh. On a nice instrument, in good voice, the stretch is quite nice. I do, though, often prefer my own slightly reduced, "still" multi-octave, multi-octave/fifth stretch aka Bill. It seems just a tad warmer...maybe because my aural stretch is less perfect the Stoppers.

Jim Ialeggio

Ok Tunewerk...PM me your email address, and I'll send a JPG of a chart he handed out. I'd post it here, but posting images is a pain in the geshputz on forums.

No text, just a graphic...that's all he handed out.

Jim Ialeggio

Hey, Mark--I was curious (because I like to listen to spinets so much...) so I did some searches and probably found what you did--nothing. Still, in searching, I ran into this:

http://www.piano-stopper.de/html/sound_examples.html

There is a Kent Swafford StopperStimmung Tuning (say *that* five times fast!) that is the Ravel selection of the list. (The other selections are good listening, as well!) (Sadly, no spinets. )

--Andy

Thank you very much for your help and time Andy!

Regards,

Hello !

I agree with you with the "coldness impression"

http://www.instantencore.com/work/recordings.aspx?work=5011986

The beats are possibly cancelled for the 12ths but not at the octave and double , with that method.

The result is a "straightening" of the harmony and resonance that may sound calm and quiet but put high treble way too high and basses not warm.

I was even hearing the triple octave "making the split" - too large gap, in a recording from Scott Kern I listened to.

To me the stretch begin to be noticeable above a 3 octave span, and I do not find it very musical.

The 12/15 is more unsuspected.

There is also a theory that state that the acoustic equilibrium will tend to 12/15 naturally so a pure 12 cannot stay tuned for long ,and break in.

I listened to the ravel, and despite being typically the kind of music that would accept a tuning with enhanced partial matching, it sound hardened, to me, with high treble out of consonance.

The interest of those stretch method is to reinforce the soprano region making it more audible in the sound mass.

For basses can be forgotten, as for high treble.

Same opinion from some colleagues after listening.
We may not confuse please our ears during tuning, with the final musicality of the piano. What we may hear as enghanced and enjoyable may straighten the harmony too much and lower the possibilities for the pianist.

In the end what I suspect is that the too much matched partials create an immediateness of the tone stabilization that use some energy - I appreciate a lot the "answer" from the other notes when one is played (and this signs good consonance) but the immediateness easily create harshness and reduce dynamics.

5ths sound better when rounded , pianos tend yet naturally to enlarged 5th , our leeway there is not that large.

I also do not like those octaves.

The treble is not tuned as much on an even line that the theory would say, so for instance the c#3 6-7 sound better , less stretched probably - F# sound a little too high
E3-4 beating slowly

Thats all folks

I would encourage anyone who is seriously interested in the actual "mechanics" behind Bernhard Stopper's one-page handout to contact Mr Stopper. That's what I did, and I'm still discovering things as I try to put his responses to my questions into practice.

Inexperienced though I am, I really like the results I get with his method(ology).

" temperament, and I think this is what folks mostly refer to in temperament discussions here, is the interval relationships set up in the central octave or two. These relationships are stretched out over the octaves, and how this stretch is achieved can vastly alter the way one experiences the tuning as a whole. So, with any temperament the octave stretch is a defining part of the aural experience."

Jim I see it more as harmony spread, even if octaves are used for practical purpose and for stretch control, I would tend to focus on 5ths as an interval that is representative of the consonance, and a base for harmony.

Practically I refined my octave tuning to the point it is really precise, so the 3-10-17 are correct, and I use them for rough checking, but I will be sure to be good if the 5th are pleasing. (for high treble they have some leeway but too large is noticed)

It is "easy" to have nicely sounding arpeggios, but that does not mean the musicality is good.

Thanks for the examples.
In the first Bach by Mr Sokolov, our attention is drawn in the text to the last chord in which we are confidently assured that beat cancelling is taking place.
My question is, then why isn't it? Which of the other notes in that last chord is supposed to be performing the cancelling function?

The notion that we can stretch excessively because any excessive beat rate will be cancelled is extremely misleading, especially to electronic tuners. That particular beat rate is too fast for its location on that piano anyway because it is over stretched.

What bit of disguising there might be on that last chord is thanks to Mr. Sokolov.
A pianist can disguise beat rates by their voicing. That is, to a pianist, the relative dynamic of each constituent note in a chord.
In this case, even an amateur could do it, simply de-emphasise or even leave out the upper note in the left hand. This will cut the beat rate in half on a well tuned piano.

Please, somebody who is conversant with this temperament tell me which note of that last chord was supposed to have been performing the function of beat cancelling because for me, the elephant in this room ain't got no clothes.

I sound uncomforteable generally speaking, (and the spread is not that large in Bach)

It is surprising that as experienced pianist as Mr Sokolov do accept that.

On the Thomas Quasthoff record the guitar have trouble to play in tune with the piano, and some chords that are supposed to be quiet and calm sound pinched.

But I understand trying new things , from pianists point of view as for tuners.

I was asked to tune differently yet, after laying a (nice !) Chas on a Yamaha U1. The tone enhancement was recognized, but the musicality was lowered on that particular piano (played by a pianist and a flutist) too fast beating was noticed.

That said, being aware of those balance (and not particularly for any beat canceling reason IMO) is a good tool and to me a sort of stretch upper limit.

It is worth comparing
Gregory Sokolov playing the same first mvt :

http://youtu.be/8gbdV3t_nk4

STopper tuning :

http://www.youtube.com/watch?v=5BrcWplvGJY

First, I'd like to thank Jim Ialeggio for sending me his original information from Kansas City. It's here now to openly enjoy and interpret, with my explanation below.

Second, Mark, it would be great if you would share what you have learned from Mr. Stopper himself and we can add to this discussion even further.



I started looking at Stopper's work 5 years ago or so. I was working on tuning alignments in the 3:1 region and was doing some simulations when I ran across his website and all the work he has done since 1988.

At one point in time, he had a summary of the mathematics behind the exact alignment of his tuning. Now, all he has posted is this:

http://www.stopper-scale.com/1.html



I thought this was interesting to post, because he literally says here that his stretch point bisects the difference between the 5th and the 8ve.

There are 1901.955c in a 12th: the same amount of extra width that's in a 5th (+1.955c). This means that in a pure duodecimal 8ve, there would be (+1.955c * 12/19) = +1.235c, and in its 5th, there would be (+1.955c * 7/19) = +0.720c. The width of a pure 5th is +1.955c, so (+1.955c - 0.720c) = 1.235c narrow. (Not quite 1.25, but not a big deal.)

So, according to his website:

Stopper's 8ve: 1.235c wide
Stopper's 5th: 1.235c narrow

We all know from translating cents to beats that they have funny, sometimes inverted relationships.

So, translating here (no iH):

Fifth from bottom note:
700.720c = 1200 log[2] (f2 / 1)
f2 (unit beat ratio) = 1.498930335
Example (A4): 1.498930335 * 440Hz = 659.529Hz

Beat rate: 660 - 659.529 = 0.471 BPS

Fourth from fifth:
500.514c = 1200 log[2] (f2 / 1)
f2 (unit beat ratio) = 1.335236224
Example (E5): 1.335236224 * 440Hz*3^(7/19) = 880.628Hz

Beat rate: 880.628 - 440Hz*3^(7/19)*(4/3) = 1.255 BPS

Fifth from fourth:
f2 (unit beat ratio) = 1.498930335
Example (A5): 1.498930335 * 440Hz*3^(12/19) = 1320Hz

Beat rate: 440Hz*3^(12/19)*(3/2) - 1320 = 0.942 BPS

Octave from bottom note:
1201.235c = 1200 log[2] (f2 / 1)
f2 (unit beat ratio) = 2.001427237
Example (A4): 2.001427237 * 440Hz = 880.628Hz

Beat rate: 880.628 - 880 = 0.628 BPS

Ratios of beat rates for 3 note combinations:

8ve : top 5th = 0.628/0.942 = 0.666 (2/3 or 3/2)
8ve : inner 5th = 0.628/0.471 = 1.333 (3/4 or 4/3)
8ve : inner 4th = 0.628/1.255 = 0.500 (1/2 or 2/1)
inner 5th : 4th = 0.471/1.255 = 0.375 (3/8 or 8/3)

Regular ET beat rates:

5th off A4 = 0.745 BPS
4th off 5th = 0.993 BPS
5th off 4th = 1.490 BPS
Perfect 12th = 1.490 BPS

5th : 4th = 0.745/0.993 = 0.750 (3/4 or 4/3)
5th : 12th = 0.745/1.490 = 0.500 (1/2 or 2/1)

Initially, it seems these ratios working out in the Stopper temperament are special, but you will find them everywhere in standard ET as well.

I think the key is not in the numbers of the ratios themselves, but in complementary equalizing (reducing one beat rate while raising another until a null effect is found). Perhaps the most appropriate beat rates to look at are those of the 5th and 8ve.

Stopper claims to be tuning to the 'sweet spot' of the 12th, in doing so, equalizing, or nullifying the beat rates of the 8ve and 5th. This seems to be a factor in the stretch, as well as the alignment of the 12th.

Edit: Earlier in this thread, Supply talks about hearing Stopper specifically play the tonic, 5th and 8ve together to elicit a beat cancelling effect. Without phase shift, I don't see how this is possible, but maybe some illusion of the 2:3:4:8 ratio that these beats occur at is responsible. Here are the functions that represent that interference with no phase shift.



My guess is that there is no 'perfect' beat rate cancellation point. I think that most likely, there is a range of effects dependent on the spectra of pianos involved, and I believe this is the difficult part of the equation that Stopper hasn't figured out how to codify or explain yet.

There may be empirical code in his OnlyPure system that knows how to achieve this effect in most pianos, based on information given, or maybe he input the balance mathematically and this allows it to come out how it will on various instruments.

Regardless, if Stopper is tuning to the 'sweet spot' of the 12th, rather than the theoretical 12th (above), then what he is doing is tuning a stretched 12th to the whole tone best point (in between a 3:1, 6:2, or 9:3), similar to how Virgil Smith would do. The result would be a slightly stretched version of the numbers above, but he claims to try and maintain the theoretical ratios.



To recapitulate, also from this same thread:



To me, this confirms a whole tone tuning technique. Few technicians do it for a reason: it is intensive and time consuming. Especially so, in working with 3 notes at a time.

This I appreciated - and shows Bernhard knows that to program a great tuning machine, each note must be individually considered. The Sanderson and RCT machines, which use sample notes and put 'blanket' tunings on pianos, don't consider this:



It may be that the only thing necessary to make OnlyPure a noticeably good tuning machine is a technique which employs this understanding, duodecimal stretch or not.

Here is the lone, mysterious handout from the Kansas City convention (Jim Ialeggio):



It's best to print out a version and turn it 90 deg. counterclockwise. This way, the notes are at the bottom: D to A. The bottom row is just a block representation of the black and white keys. Numbers 1-20 indicate the position in the tuning sequence.

He starts from A4 as the first note, then tunes the 12th down to D3 as the second note. In the 3rd block, if you look across, note A3 is tuned with respect to both A4 and the D3. The blocks remain black as he is indicating those notes be used as active reference notes. The black turns to grey as those notes are then tuned, but not immediately used as reference notes in the step indicated.

The 'Two-Sided Symmetric Form' title is kind of an artsy misnomer and only means he uses similar numbers of reference notes for each note tuned; then reverses the form to tune in the opposite direction midway (Step 12), to check the tuning as he finishes it. This is the aural sequence he chose out of all the possible sequences you could use to tune a 20 note section. Mystery solved.

Anyway, here's the whole translated tuning sequence:

1: A4 to 440Hz
2: D3 to A4 as a pure, whole tone 12th
3: A3 to D3 and A4, as reference notes
4: E4 to A3 and A4, as reference notes
5: E3 to A3 and E4, as reference notes
6: B3 to E3 and E4, as reference notes
7: F#4 to B3 and E3, as reference notes
8: F#3 to F#4 and B3, as reference notes
9: C#4 to F#3 and F#4, as reference notes
10: G#4 to F#3 and C#4, as reference notes
11: G#3 to G#4 and C#4, as reference notes

The second section he begins by starting at D4 (up a tritone from G#3), referencing A4 again and the already tuned 12th, D3, from the beginning:

12: D4 to A4 and D3, as reference notes
13: G3 to D3 and D4, as reference notes
14: G4 to G3 and D4, as reference notes
15: C4 to G3 and G4, as reference notes
16: F3 to C4 and G4, as reference notes
17: F4 to F3 and C4, as reference notes
18: A#3 to F3 and F4, as reference notes
19: D#3 to A#3 and F4, as reference notes
20: D#4 to D#3 and A#3, as reference notes

G#3 and G#4 then are check notes against D#3 and D#4 to see how the temperament turned out.

This is essentially a William Braide White sequence, using 3 note combinations and stopping midway at Step 11 - a tritone up from G#3 to D4 - to complete the sequence without enlarging comma errors. In the first section, he tunes 5ths up and 8ves down. In the second section, he tunes the circle the other way, 5ths down and 8ves up.

Al Sanderson had a more sophisticated way of limiting comma errors in a standard temperament with the stack of thirds being used in the Sanderson-Coleman temperament.

Finally, a link to the only other informational paper I have found on Bernhard's tuning method:

http://www.piano-stopper.de/dl/PTG2008_StopperTemperament.pdf

This sounds very much like what Bill B has described with his tone cluster approach.


I suspect its mathematical, as the program does not seem to "measure" before thinking. Although. on the other hand, I do find, when using the program, that it will seem to "change its mind" sometimes. As I bring a note in aurally, sometimes if I look at the display it will be well off of target. Then as I bring note to the display's target, I hear it disagreeing aurally. Then I mess around with the note and find it both on target and agreeing aurally. Somewhat mystifying.

Meaning what? like the sweet spot of a unison where there is no beat...stillness...and the tone also blooms?

Jim Ialeggio