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Dear tuners

What is your opinion about these ultra mild, modified meantone temperaments?
Do you have any experiences with customers?

I tuned my own piano in an ultra mild meantone temperament and I enjoy the warmth of the different keys. It is very close to ET, but also different to an ultra mild WT. Everyone who plays on this piano tuned like that is full of compliments.

I also like th ET, tuned it very often, but there are times for deeper musical experiences.

As one who tunes in unequal temperaments, there's no such thing as a mild Meantone. There are a few different shades of Meantone (1/4, 1/5, 1/6 comma), the formulai for which are rather specific, and the wolf is located at a specific interval. Once one gets passed 1/5 it is really a well temperament. Richer forms of WT (Werckmeister, Young) can be quite successful on pianos, especially if one is doing music prior to the romantic period.

SMHaley, what you say is not at all true. By definition, a meantone temperament is one where all 5ths are tempered alike, including one that is the equivalent of ET, where all 5ths are 2 cents narrow. It is possible to tune virtually any gradation of meantone. It does not have to be a simple fraction of the Syntonic Comma such as 1/4, 1/5, 1/6, etc. It is also very easy to program any ETD that accepts custom temperaments.

While it may be true that the sound from some of the milder meantones is more or less indistinguishable from some of the Well Temperaments when music is played, the two classes of temperaments are mutually exclusive.

While I prefer my own well temperament, I sometimes tune pianos in 1/9 comma which has all 5ths 2.4 cents narrow. I have also programed temperaments with -2.5 and -2.6 cent 5ths. One contributor on here seemed to like the 1/10 comma meantone with -2.2 cent 5ths.

The "wolf" or untuned 5th can be placed anywhere but is usually left between G# and D# (E-flat).

To program an ETD for any gradation of meantone desired, select a 5th size. For example, 1/7 comma meantone which has a surprisingly profound effect on all music but is very easy to program. Simply round off the fraction to -3.0 (the tiny amount beyond the decimal is insignificant).

You will want the value for A to remain at 0.0, so starting on A at 0.0, subtract -2.0 which is already between all 5ths on any ETD and that leaves you with a value of -1.0 that you will add as you go around the cycle of 5ths.

A:0.0
E: -1.0
B: -2.0
F#: -3.0
C#: -4.0
G#: -5.0
Stop! Wolf roadblock! Go to plus side!
D: +1.0
G: +2.0
C: +3.0
F: +4.0
A# (B-flat): +5.0
D# (E-flat): +6.0

Arranged chromatically, starting from C, it looks like this:

C: +3.0
C#: -4.0
D: +1.0
D#: +6.0
E: -1.0
F: +4.0
F#: -3.0
G: +2.0
G#: -5.0
A: 0.0
A#: +5.0
B: -2.0

Anyone can do the same with any value imaginable. For 1/9 comma meantone, for example which I like for a piano bar or cocktail piano music, simply multiply the number 0.4 around the cycle of 5ths as I did the number 1.0 above. It can get even milder but when it gets down to 0.3, 0.2 and 0.1, the difference from ET in the music is hardly heard.

On the other hand, 0.5 creates a nice, "Victorian" type sound and 0.6 is also interesting. The 1/8 comma meantone is closest to 0.7 but is not very interesting.

Jean Baptiste Romieu was the 18th Century theorist who first thought of all these possibilities. None of those small gradations however can be defined with aural tuning specifications. They are only possible with an ETD although I have approximated the 1/7 comma meantone by ear. If people can tune ET by tuning -2 cents 5ths, then I can tune 1/7 comma meantone by tuning -3 cent 5ths. The "proof" is in the uneven 3rds and the resultant "wolf".

Bill, I think we're speaking from opposite sides of the same coin. Perhaps I was attempting to oversimplify because the last thing I want to get involved in is a convoluted temperament war, which happens way too much in this place. I was only attempting to suggest that once one gets passed a 1/5 comma Meantone, other more commonly named and used temperaments might be more apropos.

I've never encountered a situation where one has used something like a Kirnberg temperament only to call it a mild Meantone. In my opinion, Meantone (the most common of which being 1/4 and 1/5 commas) means some very specific intervals, which usually results in the wolf being particularly placed. Yes one can fudge it a little but I would consider that the exception rather than the norm. If one is not using a specific shade of Meantone I feel the other commonly applied names to be more accurate then the rather unspecific phrase of "ultra mild, modified meantone" as written by the OP. In either case an ETD is the best means at tuning any of the many choices of well tempered systems.

I don't get it. The rare time I had to tune a "mesotonique" the goal was to obtain non tempered M3.

THE 5ths where the result, if I remind correctly. Then I don't see how it can be tuned "mild".

But I am ready to agree it is possible if one goes by the etymology.
Just to ne it was a family of temperament aiming to purer M3 than usually. Keene a limited choice of tonalities

This is timely. I will be tuning by request a 1/8 comma meantone tomorrow. It will be for Beethoven on a Graf.

Thanks Bill, I have extrapolated your 1/7 comma offsets to calculate 1/8 comma offsets, and I will need to crank up an ETD to do the temperament tuning.

Isaac, the mildness, or evenness, of the tuning is determined by the fraction of the comma all the way to equal temperament which could also be considered a specific meantone temperament.

The reason why I love these mild versions of the temperaments is, that they give the piano player different possibilities for expressing his musical thoughts.

While the well temperament is useful for Bach, Mozart ( this "mild" WT is for all styles because the M3 range is from about 11,9-15,2), the "ultra mild" meantone is loved by pianists who like to play more popular music. (Also here a M3 range from about 12,7 - 15,3). But the progression of the M3 is a little different from ET.
I found this "ultra mild" meantone offsets somewhere in the forum, and if I remember correctly, Bill wrote them.

C 0.80
C# -0.80
D 0.20
D# 1.2
E -0.2
F 0.8
F# -0.6
G 0.4
G# -0.7
A 0.0
A# 0.8
B -0.4

Do not carry about the words "mild or ultra mild" that means only, that thez are close to ET, but with different key colors, nothing too complicated.
The customer love it!

This temperament indeed has meantone characteristics. To me, it's simple. WT = no wolf fifth, meantone = wolf fifth. It's not necessarily obvious on a graph as it's quite mild as is (using my custom Excel app below).



Also, since the fifths are not all equally divided, at the same time we can indeed qualify it as "modified meantone". Everything becomes clearer when the numbers are multiplied (x 7), where we can see an obvious wolf fifth (Ab major):

1/4, 1/5, and 1/6 comma meantone temperaments were very common in and before the Baroque. The 1/6 comma variant (Silbermann tuning) was supposedly disliked by Bach.

They are all characterized by having 11 P5's equally narrow by a certain amount of comma (1/4,1/5.1/6, etc), and the remaining fifth whatever it lands on (usually very wide). Only in modern days have people gone beyond that. Up to about 1/8 you will have unusable M3's and P5's, beyond that it becomes more like a circular (or "well") temperament, all the way up to 1/12 comma which is equal temperament.

Meantone temperaments are characterized by having two kinds of M3's: good and ugly. All the good M3's are the same, so there is no key color. Well temperaments on the other hand have a range from good to bad to ugly, so there is key color.

Kees

PS Comma = Pythagorean comma, i.e., the difference between C and B# if you tuned pure fifths around the circle from C to B#

This is the aural tuning sequence for meantone tuning. The "strength" of the temperament is determined by the initial beat speed given to the initial F3/A3 M3rd. A speed of 5bps will be approx for a 1/8 comma meantone.

Tune A4 to whatever.
Tune A3 from A4 as pure as possible.
Tune F3 from A3 for the appropriate beat speed. 5bps for 1/8 meantone.
Tune a sequence of tempered perfect intervals - existing F to C to G to D to existing A - with similar tempering.
Tune Bb from F with similar tempering to above.
Tune a sequence of pure perfect intervals - existing Bb to Eb to Ab to Gb
Tune a sequence of perfect intervals - existing A to E to B to F# (existing Gb) - with equal tempering.

This sequence is not very precise with regards to what the tempered intervals are, but lets say that the intervals in each sequence, be they 4th or 5ths, should have similar tension.

This is the M3rd progression for my first attempt. I think the F3A4 beat speed has ended up a little slower than 5 bps so it may be not precisely 1/8 comma:

Whatever it is, it is not meantone if it has pure P5/4's.

Edit: This is actually a 1/8 comma variant of Vallotti. Normal Vallotti has all 6 P5 from F to B 1/6 narrow all other P5's pure. This one has all 8 P5's from A# to F# 1/8 comma narrow and the rest pure.

Kees

Yep, preaching to the choir here... Its critical to remember that music from the Classical period and before had a particular "arsis and thesis." In temperament terms and those of this discussion "consonance and dissonance" were everything in the harmonic language of the period. The goal was not to be able to play in every key but to provide suitable consonance. True consonance in a cadence was often considered a pure and perfect fifth. Hierarchically a pure major third was next. With the inherent flaws of fixed pitch keyboard instruments temperaments were designed get as much consonance and purity as physics would allow... Hence Meantone... and we know about the evolution that followed. The clavichord is probably the only that allowed some degree of pitch manipulation as one played.

Even in other temperament systems beyond common Meantones, there are wolfs and other unusable keys.

A clavichord can manipulate the pitch somewhat, but not in a manner that affects the temperament. The pitch is fixed, and pressing harder raises the initial pitch, so one cannot make the tone start at anything other than the pitch the note is tuned to.

Kees, be that as is may, this is from the horses mouth:
1/8 meantone from Carey Beebe

Right, that's what I said. The word "meantone" does not occur on that webpage.

Kees

Kees, you are correct. Just erase the word "meantone" from my post.

What temperaments do you refer to? There are no unplayable keys even in the strongest (1/4') well temperaments (e.g., Werkmeister 3 and Kirnberger 3).

BTW the scala tuning software comes with over 100 (!) variations of meantone. Even crazy stuff like 1/2pi comma variants, golden ratio based, etc.

Kees

True, but if you hit a key hard the pitch-rise part of the tone is so quick that the only pitch you hear is the one you want. The characteristic "twang" sound of the clavichord is actually this fast pitch rise after hitting the string with the tangent till the tangent comes to its highest position, depending on how hard you hit the key, and you get the sustained pitch. I know because I have done it. The rule is roughly to play the root of any major chord louder than the other notes, and you can play with just M3's. Not easy, but possible.

Kees

I don't consider the keys of F# and B major in Werkmeister to be very pleasant to listen to. Perhaps your ears care less than mine do. The thirds are wildly fast and those beating 5ths, yikes.

I don't know about your ears but in WM3 BD# is only a tiny bit worse than in ET (1/12 comma wider, to be precise) and F#C# is a pure fifth.

Kees

I thought the same also up to a couple of months ago. The pianist wanted the piano tuned to Werckmeister 3 and played Chopin Barcarole which is in F#major. The result was surprisingly beautiful. Most people think that this kind of strong temperament is not appropriate, but it seemed to work well in this case.

This is also my experience. Other than Chopin, those highly tempered keys are rarely used as a M3 right in the middle of everything, but, rather, more opened intervals like 10ths and 17ths are employed. The pure fifths in the remote keys are also often used against the tempered harmony in the third for effect, as the keys with the most expressive thirds have the quietest fifths.

Somewhere, tuners get the idea that any third tempered more than 13.7 cents indicates problem. If you are aiming for ET, yes, a wider third indicates a problem. However, the musical qualities of having an orderly variety in the tempering will show itself not on the tuner's examination,but rather, in the added complexity and texture in music written during times of its use.

It's all a matter of taste. I had my piano in WM3, then didn't like some of the remote keys in Bach's WTC, changed it to Young 2, sounded different, still didn't like the exposed F#A# M3's in the G# minor fugue from book 1, changed it to ET, didn't like that, changed it to something else.... To me it's like food. I like rice and I like potatoes, but not everyday the same so I enjoy changing temperaments often. Still major artists like Ton Koopman play everything, including the remote keys of WTC in WM3. He recorded all the Bach cantatas in WM3!

More factual: The term "wolf" refers to unplayable intervals by any standard. Such as the enharmonic M3's in 1/4' meantone (say DbF if your Db is tuned as pure C# on A). Consensus from what I've read seems that any M3 wider than Pythogorean or P5 narrower (or wider) than 1/4' falls in that category. Such intervals appear in meantone up to 1/8' comma strength, and are absent in all commonly used well-temperaments. Kirnberger 1,2 is universally rejected because its P5's are worse than -1/4 comma. Still, if you personally like it, go for it!

Kees

Here are the offsets for 1/8 meantone to the nearest 1/100. (Rounding off to the nearest 10th will not make a significant difference in sound).

C: +2.07
C#: -2.76
D: +0.69
D#: +4.14
E: -0.69
F: +2.76
F#: -2.07
G: +1.38
G#: -3.45
A: 0.0
A#: +3.45
B: -1.38

If you write to Jason Kanter at: jkanter@rollingball.com and provide the above data, he will make you one of his graphs of the temperament.

Jean Baptiste Romieu was credited in the 18th Century with the 1/7 Comma Meantone which Professor Owen Jorgensen documented in his first publication, Tuning the Historical Temperaments by Ear. Mr. Kanter has a graph of that on his website. However, Romieu went on to theorize the 1/8, 1/9 and 1/10 Comma Meantones but instructions for tuning them by ear are nearly impossible to follow with any accuracy. Programming them into an ETD is comparatively easy.

Perhaps I meant the G#-D# interval. I shouldn't try to recollect facts when the blood sugar needs bolstering. In any case, I couldn't care less about the mathematical differences. I only care if the result is musical and serves the music at hand. I'm rarely a one temperament fits all sort of person, but somethings don't work well if they get away from very well tempered or "ET." Conversely, some things are as boring and bland in ET/WT that really should be unequal.

G#-D# is a just P5 in WM3.

Kees

My choice of these unequal temperaments depends a little on the piano player. When I know, a pianist likes to play Mozart, Bach or so, I make a suggestion of a temperament. I tune a section of the piano and let the customer play some bars. Mostly my decision is appreciated. Then I tune the rest of the piano.

The discussion here is very interesting!
But what is also interesting me, are your experiences with customers and the use of unequal temperaments on their instruments. (Not theory).
For a beginner, I use these weakened froms of meantone. That brings life into the keys around C. A more resonant piano sound.

Maybe you can also tell me about your personal experiences with customers, too? Or, do you also dare, like me, tune nearly all the pianos in an unequal temperament? ( mostly without asking permission!)
The goal is to tune a piano that sounds best for the player.

Not in 1/4 comma MT!

I'm a bit confused. Usually I tune 1/4 comma meantone for the harpsichord for pre-Bach music. The advantage is the growl of the near perfect thirds, and the thin sound of the near perfect fifths. As long as you don't go more than three sharps or flats, you can usually avoid the wolf. Scarlatti seems to exploit the wolf from time-to-time. Once you try dividing the comma more finely, the thirds lose their perfection, which is the point on the harpsichord. Silbermann's temperament was built for the organ, which is additionally complicated by the perfect tuning of the mixtures. Tuning finer than 1/6th comma sounds more like well tempered.

Nah, the mixtures don't complicate temperament. Mixtures and mutations appreciate things further away from ET since the consonance of pure(er) intervals coincides with the harmonic function of mutations, etc.

The way I use these forms of temperament is only to add some color to the tuning ( different keys).
And WT and MT are in my opinion quite different, even when you use the weakest from of them. Just another way of saying it. My own piano is tuned in 1/7 comma and is amazing harmonious. E flat Major is really amazing! On a customers piano it's to much in the keys far from C.
But the weakness of the "my" MT contains quite the feeling I have from the 1/7 comma on my piano.
The WT is progressive and structured around C, but only in a weak from - but very different from the MT.
My goal is to get different characters on pianos because I use different temperaments. The piano has to be playable in all keys without becoming too harsh in the keys far from C.

According to artists that I tune WT for, harshness is more a function of how the music is played than the temperament. Those highly tempered thirds can be "expressive" rather than harsh if played as part of the overall piece.
Regards,

A local colleague of mine frequently hosts salon concerts where the piano is almost always tuned in 1/7 Comma Meantone. I have heard any number of artists play Romantic era pieces in the keys which are supposedly unusable or at least, "too harsh". Those keys only sound too harsh when a technician BANGS on them and declares them to be too harsh.

In the hands of a skilled pianos, those keys become powerfully expressive. In the words o a Czech pianist who is a frequent performer there and who plays almost entirely Romantic era music in the remote keys, "I never before dared to play the piano so softly". Of course, the piano also had to be very precisely regulated and voiced.

"Harsh ": probably more a language problem!
Of course, I love my piano tuned in 1/7 comma!! And all the keys!
When I introduce a customer to UT, I start with something mild. If it pleases him, I try next time something more "strong "( sorry I can't find the right word in English). The 1/7 comma is really fun to play, but needs a little trained ears and how to use it in the pieces played on the piano.
My daughter plays the violin, but since the piano is tuned in 1/7 comma, she plays more the piano! (For heaven 's sake, what have I done 😅)

Harsh is as good of a word as any.Many Americans may call it "sour".

I'm thinking that the mutations add an extra bite to the harmony, so the underlying temperament is less of an issue.

Has anybody noticed how great the Bb-seventh chord sounds in quarter-comma mean tone? (I'm assuming the usual placement of the wolf fifth between Eb and G#.)

That extra-wide second (G# to Bb) sounds wonderful because G# is close to the seventh harmonic of Bb. And of course the rest of the chord (Bb-D-F) is just normal.

The chord inversion with G#-Bb-D-F (in the vicinity of middle C) is especially nice. Try playing the Big Ben chimes in Eb, with an Eb chord alternating with the Bb seventh chord. Beautiful. You haven't lived until you have heard a mean tone Bb-seventh chord with a G# replacing the Ab.

Another nice tune is He's Got the Whole World in His Hands in Eb. That tune never uses the Ab note except as the 7th in the Bb seventh chord. Try it, you'll like it!

Bill Smythe