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There is no set threshold. Some people are more sensitive than others. If you have grown up used equal temperament, you may very well find an interval in another temperament that sounds wolfish. It is also likely many unequal temperaments exceed the same threshold, deliberately or not, and are accepted as equal temperament. What are called well temperaments might not be distinguished from equal temperament if they were done correctly and if it was not proclaimed that they are not.

Bill, I am completely shocked by your question and the arrogance it implies. Are you really implying that you think it is you, as a tuner, who provides the color, and not the musician? I have spent my whole life enjoying the colors that individual pianists impart to their interpretations of the masters, and you are revealing blatant insensitivity to musical interpretive nuances by this stupid and musically immature question.

Greetings,
As we say in Nashville, "There is a more tone in a guitarist's fingers than there is in the guitar". The pianist is remarkably in control of "color", by voicing, phrasing, contrasts, etc.

However, ( um, let me say that again), HOWEVER, there is nothing the pianist can do to produce a pure fifth, a near consonant third, or the texture that comes from juxtaposing tempered harmony with pure melodic lines, (Chopin). The pianist can fake increasing intensity in modulations, but they cannot cause the tension to rise with increased dissonance. Many of us consider those musical qualities to be components of what we call "color". The tuner is in charge of the presence or absence of those physical qualities, not the pianist, so, I submit that the technician has a hand in the musical result in terms of "color". The performer has the major part, but we are in there.

HOWEVER, I know from working with pianists that there is a way to play a highly tempered interval expressively, and there is a way to play the same harshly. The musician is in control of the music, but they must do it with the material we give them. The pianist that understands the effects of temperament will play a piece differently than one that does not, even if on the same instrument and same tuning. Some pianists have an epiphany on hearing and learning this, others don't notice the difference.
Regards,

Greetings,

At most,two octaves, but usually one and a half, above and below. When you pass the fifth octave, the speed of all thirds and sixths exceeds our perception of beating, and the differences that are profound in the third and fourth octave are virtually indistinguishable. The character of the temperament will be obvious when notes from that range are played against much lower ones. Then temperament makes some strange differences.

Above the fifth octave, the the 10ths and 17ths will display temperament differences, as they can reduce highly tempered keys to beating rates that mimic a good vocal vibrato, or a pure tonic.

The M3 will become dissonant at some point as it is played lower and lower on the keyboard. Usually below G2. This is because of the intrusion of its other partials into our critical band. The more highly tempered thirds can be played lower than their more consonant brethren, because their partials are farther apart in the beginning. Some some keys of a UT will be more useful if one wanted to compose with the low thirds but not particularly have a clash. That is one effect that we don't see in ET, i.e. once you go past the point of dissonance, all of them are like that.
Regards,

Thanks Ed,

That is one problem we have when a player system is used to play examples. It often plows right through what any pianist would adjust to naturally. I'll never forget the comment of a German pianist who said when asked to comment, "[upon reaching a certain passage in the music], when I went to make the expression, I found that it was already there".

The primary reason for using a cycle of 5th based temperament is to augment the total amount of expression and color that is meant to be in the music. ET actually negates what is there to be explored.

Thanks BDB, Bill and ED for your thoughts.

BDB - I agree that some people are more sensitive to the sound of an M3, though I would argue, as you mentioned, that it is possibly a matter of exposure only to presumed ET. Enough time spent listening to other temperaments would increase their sensitivity and appreciation of the differences.

Ed - Thanks for the information. I measure the degradation of the temperament as it expands as well on my piano tuned in Young. It looks wild when graphed, but sounds reasonable. Our brains do wonderful things.

Bill - You and Ed are so right about the pianist wanting and being able to control the colour of the intervals. I find that I am intensely aware of the harshness or calmness of the intervals, and adjust the voicing of a chord to make use of the colour to enhance the emotional/musical impact of the work.

>Bill wrote:... A German pianist who said when asked to comment, "[upon reaching a certain passage in the music], when I went to make the expression, I found that it was already there"...

I had the same experience after tuning a WT, the pianist said that she didn't have to try so hard to put expression into the music because it was already written in (which ET had removed).

What really strikes me is how softly and slowly many pianists will play when they have a fairly strong temperament such as the 1/7 Comma Meantone at their disposal. In the flat keys, the piano has so much energy that they just let it "boil" out of the piano.

It's funny you should say that. I also find that I want to almost stop on every chord and listen to the wonderful sonorities, whether boiling or still, to the extant that my playing occasionally slows down to point of being unmusical. It is especially so in a piece like Debussy's 'Clair de lune', which is in D flat major. D flat major has a fairly wild M3 in the tonic and a very wild M3 in the subdominant, yet it sounds so wonderful - shimmering. I know this is subjective observation by me and my musician friends, and therefore subject to discount, but I can't help but think there is something in differently sized intervals in a UT that adds interest, life and energy to most works. But again, to each , his own.

Hi Ed,

Here we go again, after the many lines we wrote on the Modern ET’s thread. I still remember your key words... intellectual, emotional, reasonable, musical, color and equally bad sounding thirds.

What is different today (with unchanged respect on my part), it is your fairly recent statement that beyond a certain level of accuracy, issues related to tuning become “academic”. Now, on the one hand it helps me understand where your expertize might end, on the other hand it does not help me understand why you splash considerations of any kind, perhaps in the idea that words can fill a gap in deep knowledge?

..."“However, ( um, let me say that again), HOWEVER, there is nothing the pianist can do to produce a pure fifth, a near consonant third, or the texture that comes from juxtaposing tempered harmony with pure melodic lines, (Chopin). The pianist can fake increasing intensity in modulations, but they cannot cause the tension to rise with increased dissonance. Many of us consider those musical qualities to be components of what we call "color". The tuner is in charge of the presence or absence of those physical qualities, not the pianist, so, I submit that the technician has a hand in the musical result in terms of "color". The performer has the major part, but we are in there.”...

Yes, in a way I understand what you are saying, but it might be meaningful only if and when the performer can rely on a tuning that she/he already “knows”. I am sure you know about the tremendous amount of hours pro pianists need to spend, in order to control and refine their interpretation, do you think they would appreciate any fancy level of intensity, dissonances that rise here and there, depending on the piano tuner’s estrus? Would they be happy to acclimate? Please note, we are not even considering the whole tuning: in fact, there is no UT that gives you indications on how to manage octaves and expand above and below the temperament octave.

Perhaps this too is academic, do you expand by copying octaves?

Regards, a.c.

If I may answer Alfredo, I believe at least that Bill Bremmer's method of mindless octaves will effectively "smooth" out the temperament towards the extremities, and resulting in some minor octave compromises. This would temper the comical "bleating" 10ths that would otherwise occur at certain points in the lower range, and similarly progressively smooth out progression the treble.

I wonder though how ETDs handle this? Ed Foote, do you know if the Accu-Tuner replicates temperament, when using a programmed temperament, across the range of octaves?

Hi Alfredo.

As a pianist who has played in ET (or what passes for ET) on pianos for decades, and only now learning how to play in UTs, I find that I really can anticipate what kind of tension or energy the next chord or phrase will have and adjust my playing accordingly. On an organ or harpsichord tuned in a UT, one can also adjust, just using different techniques.

With regard to stretching octaves in a UT, I only have experience in Young on my piano. When I do a good job of tuning it, which is about one out of three tries, the sound of the temperament seems to be preserved from about C6 down to C2. This is, I can hear the relative, not absolute, rates of the M3s, progressing in the correct order. I am working on a project to precisely quantify the degradation of the temperament, but it will be another few months yet before I have full results. (Too much practicing and flying required right now.)

And here I thought it was such a simple question...

It is, and I gave a simple answer to it at the outset.

Hi Chris,

Yes, by words I quite agree, Bill's method might smoouth out the temperament towards the extremities. What is in Bill's mild-Well, it is a temperament that deviates from (the wrong) ET less (hopefully) than the average (how do we call them?) ET_attempts he hears around his area.

What is still missing there, it is conceiving a scale geometry where every semitone, say every note takes_meaning_from and gives shape to a whole.

On the practical side (leave the irregularities aside) there is one more (perhaps academic?) detail, namely "hysteresis"... already mentioned. This is not to say that I do not like Bill's tunings, at the opposite, I think they are very enjoyable.

All reasonable UT's, either historical or modern follow, to varying degrees, the circle of fifths, with C being most consonant, and progressing to less consonant keys further from C. Even though in one UT, C# might be less consonant than F#, in another, more, the performer still knows and anticipates the changes in tension.

A simple question with a complex answer, and, from my perspective, a thoroughly enjoyable and reasonably courteous discussion. Thanks for ' priming the pump' .

Greetings,
Yes, I wrote, " beyond a certain level of accuracy, issues related to tuning become “academic”. Are you disagreeing with that? That there is no limit? that there is no limit to how refined a tuning can be? Help yourself, I don't know any musicians that can discern tuning qualities I work with every day. My expertise ends just beyond the most demanding customers I can find.

As to your theoretical, (at least, it seems), question inre pianists and why they appreciate, my experience is that pianists either don't hear the difference or that they are strongly attracted to it. I have seen veteran teachers, traveling the country giving master classes that didn't even realize the piano was tuned in a Young, but they did comment on how resonant the instrument was. Seems like the variety of color was so correlated with the music that it didn't seem unnatural.

For many, the temperament debate is simply abstract jousting. I am selling these tunings to professional people with wide experience that are willing to pay well above the average rate. I have a hard time understanding those that think the music suffers unless everything is the same. To each his own.
Regards,

My pleasure!

All:

As a thought experiment, imagine if a piano was voiced so that all the sharps had a harsher tone and all the naturals had a calmer tone. Wouldn't this be similar to tuning a UT if the idea is to impart "key color"? Do you think many pianists would prefer this?

Lets remember that when voicing the hammers, the goal is to have mellower tones when played soft and brighter tones when played loudly. It is not just the volume that changes, it's the timbre. That is where much of the expression comes from. The ability of the pianist to change the timbre of any or all notes at will.