Interesting discussion. Since I have been tuning the EBVT for more than 20 years for most of my clients, including several voice teachers, I can't take the "don't do it" warning seriously. Also, the dealer I work for has voice teachers in the studios and they always use 1/7 Comma Meantone.
The transposition issue comes up fairly often. Those who advocate ET only always jump on it. It is always about what you couldn't do if you tuned in a non-equal temperament. So, let me make it clear that all of that is nonsense. Otherwise, I have made my living for the past 24 years doing what "wouldn't work, couldn't work and shouldn't be tried".
Also, if a piece of vocal material is at or near the limit of one's range (either low or high), transposing up or down a half step does not help much. It would also be more difficult for the pianist. Vocal pieces are rarely written in the remote keys. Just take a look at any vocal book which is offered in several voice ranges. They simply do not transpose anything up or down an augmented 4th! Nor do they by only a half step.
If someone is working on material written in the 17th or early 18th Century, that material would have been originally heard in 1/4 Meantone. To put it in ET moves the temperament to the complete opposite end of the spectrum where everything vibrates analogously all the time. It would never
be written in a remote key! To transpose something written in D Major to G-flat Major simply does not make sense. In fact, that was one of the jokes in the English language, stage play version of La Cage aux Folles
. It was funny because it was absurd.
There is something to be gained and something to be lost in any and every decision made with regards to both temperament and octave stretch. I saw once again the suggestion about pure 5ths. Piano tuners sure do seem to like pure 5ths. But the consequence of them is to have 21 cent wide Major thirds.
If you stretch the octave wide enough that the 5ths become pure, the Major thirds will all become wider and more dissonant. The 4ths will also beat noticeably. It is certainly not going to help with voice study. Not long ago, I was called to a recording studio where someone had done that. The strings and winds complained that they could not play in tune with the piano.
So, if all things considered, your choice is still ET, I suggest you go with the kinder and gentler version of ET, the ET via Marpurg
that I will be presenting at the convention this Summer. It is what I did for that recording studio. It just so happens that I will be using it to tune the piano for the local opera company rehearsals tomorrow. The company is getting a new facility in June with two pianos in it. The music director wants both pianos tuned that way as the usual choice (but with other choices in mind for certain repertoire).
What is interesting about the ET via Marpurg is that it causes the 4ths and 5ths to beat equally. If you also choose a rather conservative amount of stretch for the temperament octave, a 4:2 type, you will find that you can tune the octaves up and down from the temperament octave and have the octave, 4th and 5th all sound alike. None are perfectly pure but all are tempered only very slightly.
When played together as a tone cluster, example: G3-C4-D4-G4, the tone cluster seems to just "hang" there, perfectly beatlessly. This is because the slight beats which are there all center around the same coincident partials either slightly sharp or slightly flat of them. The opposing beats effectively cancel each other and the result is a perfectly still sound.
In other words, it ends up sounding perfectly in tune, something which has always eluded the art and science of piano tuning. The Rapidly Beating Intervals also are not pushed into beating any faster. They are all as even sounding as can be which the intent and purpose of ET.
I have long been aware of the beat canceling effect of equally beating intervals. It is the reason why the simple keys sound purer than they really are in the EBVT and EBVT III. The economy in the simple keys keeps the remote keys from being too harsh and therefore permits virtually any style of music from any era to work and work very well.
That being said, there is no other temperament and octave stretching arrangement which can take more complete and total advantage of the beat canceling effect among 4ths, 5ths, octaves and their multiples than the ET via Marpurg.
You need to keep the two central octaves (C3-C5) as 4:2 types to get this effect. I am not sure what happens to the outer octaves because I always do this either aurally or by direct interval (but I do offer a suggestion as to what probably works below). I can get my SAT IV to reduce the amount of stretch in the central octaves by setting the DOB to -0.2. I have seen that Tunelab has a 4:2 octave setting. I don't know about other devices or software but maybe Ron Koval can help with this.
As I tune up from the F3-F4 temperament octave, I simply place the note to be tuned in that "sweet spot" that has often been mentioned in the past. It is the spot where the octave, 4th and 5th all sound virtually the same.
A couple of years ago, I was doing some strictly aural tuning for a while and discovered that if I played all four notes together, there was this uncanny stillness to the tone cluster. If I heard a slight beat, I could sharpen or flatten the note being tuned so that the beat would seemingly disappear entirely.
I wrote about it back then and Herr Stopper immediately jumped on it saying that it was the idea he had "invented". Perhaps he did discover something along those lines and it suggested the name he has given to his process, "Only Pure".
However, what Herr Stopper does (as I understand it) is to create an ET within a beatless interval of a 12th (octave-fifth). This necessarily creates a wider than 4:2 octave. In theoretical ET, 4ths beat 1/3 faster than 5ths. It is still only a very slight distinction. However, any purposeful widening of the temperament octave will cause 5ths to be stiller but 4ths to beat more noticeably. Major thirds and sixths will also beat faster and therefore be more dissonant, even if they are all more dissonant by the same amount.
When you apply the extremely small and slight changes to theoretical ET that causes the 4ths and 5ths to beat equally and
you keep your two central octaves in the 4:2 type, something really nice happens.
Once you get to the point where you are tuning double octaves, for example F3-F5. You do what has long been called the "mindless octaves". You make the double octave, F3-F5 be the same amount wide as the octave-fifth (A#3-F5) is narrow. Both are only very slightly tempered and sound virtually pure.
Now, that being accomplished, if you play F3-A#3-F4-F5 all together and hold them (perhaps using the Sostenuto pedal), you will again hear that uncanny stillness. If you hear any slight beat at all, F5 can be adjusted so that the beat disappears entirely.
You will also hear that the single octave, F4-F5 sounds very nice, virtually pure but slightly on the wide side (as it should be). When all notes are played together, they all share a common coincident partial (which is the 1st partial of F5). Whatever slight beat there is among them is canceled.
If you proceed this way until F6, you can make the first partial of F6 match exactly the eighth partial of F3. All related notes in between which all share a coincident partial with F6 will be nicely in tune with each other. Again, no interval (except the triple octave) will be perfectly pure but when the entire cluster (F3-A#3-F4-A#4-F5-F6) is played and held, it will sound perfectly still!
You can therefore tune pure triple octaves from F6-C8 and have as a result, the most beautiful sounding treble and high treble that is possible on the piano. It is so easy to do on the SAT as to be "mindless". Forget the calculated program from F6 to C8! At F6, I simply play F3, stop the pattern and enter whatever figure there is and tune to that. I continue that all the way to C8, taking the reading from C5.
It takes only a couple of minutes to enter a custom program for the outer octaves but the result is a piano that is perfectly in tune with itself, not with some calculation that may be flawed. I can, of course, store that program for use over and over on the same piano.
Tuning the Bass is a mirror image of tuning the treble. Tuning down from the temperament octave, example: E3. Tune the octave E3-E4 on the wide side but very nearly pure. Compare the 4th, E3-A3 and 5th, E3-B3. Make all three intervals sound as alike as possible. Then play the cluster, E3-A3-B3-E4. It will just hang there beatlessly!
Continue that way down to F2. Then beginning on F2 (going downward), eliminate the 4th and compare the 5th, octave, octave-fifth and double octave: F2-C3-F3-C4-F4. You will get that same, still effect when all intervals are balanced correctly.
At C2 and continuing downward, eliminate the 5th and compare the octave, octave-fifth, double octave, double octave-fifth and triple octave. C2-C3-G4-C4-G4-C5. As with the high treble, you could simply tune the 8th partial of C2 to the first partial of C5 and do that all the way to A0.
The result will be that all related intervals will be optimally tuned. You will essentially be canceling a large part of the "noise" out of the piano. Large chords spanning four octaves will sound as in tune as they possibly could. No one interval is favored over another. Piano tuning must be one kind of compromise or another. If you ask me, this is the ultimate compromise if the desire is for ET.
Below is the Jason Kanter graph of it. It actually looks more irregular on the graph than it sounds. Note that all deviations from ET are less than one cent. They simply adjust the 4ths so that they beat equally with the 5ths. Otherwise the Rapidly Beating Intervals sound virtually identical to ET (even though they don't look that way on the graph). It is "below the radar" of the PTG tuning exam and would therefore score a perfect 100 on it if used. Indeed, I know of many people who have used it successfully on the exam.
One benefit the sequence has if performed aurally is that it strictly avoids the Reverse Well error. As I see it, the danger in trying to make 5ths be too pure is exactly that. While Reverse Well is never the intent, it often does end up being the result. It certainly would not be what you would want to do for a voice teacher.
The offsets are right on the graph. If you use an SAT, simply round them to the nearest tenth and put the DOB at -0.2. Then, at C5 and above and at B2 and below, cancel the DOB.
I am not sure about what outer octave settings would replicate the precise amount of stretch needed but I am inclined to guess that 4:2 for octaves 3 & 4 but default for the rest of the piano would do it. Maybe something a little more for octaves 1 & 7. Perhaps Ron Koval may have some insight.
In any case, to use this idea with an ETD would not be difficult. Just apply the temperament offsets and a smaller than usual amount of stretch for the central octaves and the usual amount for the outer octaves. Once you have tuned using the ETD, you can play those tone clusters and you will hear the purity I have described.
If you do hear a slight beat anywhere, adjusting the beat out of it by ear would be very easy to do. After all, you are not trying to fiddle with fine tuning very rapid beats but trying to find that sweet spot where there is no beat at all! All of the Rapidly Beating Intervals will take care of themselves very nicely. I never even listen to them when using this process. It simply isn't necessary.