Question for Mr. Bremmer

[Billbrpt@AOL.COM]

In a message dated 4/9/99 9:10:17 AM Central Daylight Time, 
jformsma@dixie-net.com writes:

<< Mr. Bremmer,
 
 Yesterday I tuned a 20-year-old Cable spinet, 3/4 step flat. I used the SAT
 II, but was not really satisfied with the tuning after the pitch raise and
 two subsequent tunings. It seemed that the tenths formed by the the upper
 bass and midrange notes were beating too fast. It sounded better than when I
 had gotten there, and since it went through such a pitch raise, I wanted to
 wait a few weeks before I return to try to make it sound better.
 
 The reason I write you is because you seem to be the resident expert on
 historical temperaments, which apparently are better for these small pianos.
 Do you recommend any particular temperament for this piano? I am scheduled
 to return in 3 months. In the meantime, I have ordered Jorgensen's book on
 tuning. I hope to read about historical temperaments there, and practice on
 one that will be suitable for the Cable. If you have any thoughts, and the
 time to express them, they would be appreciated.
 
 John Formsma
 
 P.S. The owner of the piano is not all that musically adept, so I am wanting
 to experiment on this piano. I think all she will notice is the unisons and
 octaves, but I am not even sure about that. One who gets her piano tuned
 once in 10 years is not likely to have much pitch discernment, and probably
 plays within a three octave span. Anyway...I would enjoy experimenting with
 a historical temp.
  >>
Thank you for your question and your confidence but I do not consider myself 
an "expert" on HT's.  I only know what I have learned from others in PTG, 
from reading and personal experience.

Many of my HT tuning colleagues have made the remark that Well-Tempered 
Tunings can "eat" the so-called "poor" scale.  One very well-known, even 
famous RPT, Steve Fairchild discovered this and published his findings in the 
October, 1982 edition of the PTG Journal.  He called the temperament that he 
discovered and invented, "Altered Equal"  (to me, this is a contradiction of 
terms, but that's beside the point).  

It just so happens that what he came up with was the very same idea that 
Francesco Antonio Vallotti did in the early 18th Century.  You'll find one 
way to tune it on page 68 of Owen's book, "Tuning".  Read the introductory 
pages and also read sections 72 & 73, beginning on page 266 about "The 
Representative 18th Century Temperament Tuned by Personal Taste.  In these 
sections, you will literally find the license to do just about anything you 
want.  (The ET-only-or-you're-"unethical"-bunch hasn't read this yet).

There is another way to tune the Vallotti/Fairchild temperament.  Owen 
usually gives the classical, theoretical and Equal-Beating methods of 
effecting a temperament but he sometimes gives other alternatives.  The way I 
prefer to do it is not written up in this book, however. You can probably 
figure out what to do if I explain this temperament in a very simple way 
which you can keep in your head and not have to have a big, heavy book with 
you while you are "experimenting" on the good lady's piano.

Just remember that the Vallotti/Fairchild Temperament has 6 pure 5ths and 6 
tempered ones.  The pure 5ths are between the black keys and those which 
occur between a black and white key:  Bb-F, Eb-Bb, Ab-Eb, Db-Ab, F#-C# and 
B-F#.  All of the rest of the 5ths occur between white keys only and they are 
tempered *exactly* twice as much as they are in ET.  (4 cents narrow, 
theoretically or 1/6 of the Ditonic Comma).

If you start on A4 and tune a proper octave to A3, then tune up a 5th to E4, 
putting a good beat per second in it, then up a 4th to D4, putting a good 2 
beats per second in it, then down a 5th from D4 to G3 (with similar beating), 
up a 4th from G3  to C4, then down a 5th from C4 to F3.  Backtrack to E4 and 
tune down a 4th to B3.  Now you have all of the tempered 5ths.  You will 
notice that the 3rds formed between F3-A3, G3-B3 and C4-E4 all beat much more 
slowly than in ET and will beat about the same or even exactly the same as 
the 4ths that you created.  If this is not so, work this much of it over 
until they do before proceeding.

Now comes the easy part.  All the rest of the 4ths & 5ths are pure, an easy 
interval to hear and test for accuracy.  Start on F3 and tune the octave to 
F4, then up a 4th to Bb3 from F3 (and compare with the 5th, Bb3-F4 that is 
formed as a result). Then up a 4th from Bb3 to Eb4, down a 5th from Eb4 to 
Ab3, up a 4th from Ab3 to Db4 and finally, down a 5th from C#4 to F#3.

Now here is where you can practice "tempered octaves".  As you ascend from 
the F3-F4 temperament octave, try to "reconcile" the octave you are tuning 
and the 5th below it.  When you tune F#4, this will be easy.  You make a 
"pure sounding" F#3-F#4 octave and a pure B3-F#4 5th (the 4th, C#4-F#4 will 
also still be pure).  But the next one will be a little more difficult.  When 
you tune the G3-G4 octave, you will want to stretch that octave to have a 
barely audible beat to it and somewhat mitigate or "pull the tempering out" 
(as I think of it) of the C4-G4 5th.  Listen to the D4-G4 4th.  Compare all 
and leave the best compromise you can.

When you reach F5, you can start comparing double octaves and the octave and 
a 5th (a 12th).  You will have the same ease as you did when starting out 
when you tune a double octave from F3-F5 and compare the 12th Bb3-F5.  Both 
should sound "pure".  When you tune the double octave G3-G5 however, you will 
want to stretch that double octave and make it beat exactly the same as 
(Equal Beating) the 12th C4-G5, a very slow beat (4ths will no longer 
matter).  Also listen to the single octave you have created, G4-G5.  Expect 
slight tempering but don't let anything get too "wild".  Continue all the way 
like this up to C8.

When going the other way from the F3-F4 octave, you will do similarly but in 
reverse fashion.  If the piano has some plain wire below F3 on a "hockey 
stick" bridge (what many would scoff at as "poor scaling"), you can carefully 
manipulate the harmony created in that part of the scale by making any kind 
of compromise you want.  You will effectively, "eat" the "poor scale" and the 
customer and the music played on the piano will love you for it.  You will 
have a distinct advantage over all others who struggle to "get their 3rds 
right" along with the 4ths, 5ths and octaves that you need to have for a true 
ET.  Kiss them and ET goodbye and wish them well.

You can also tune a "Victorianized" version of this which comes from PTG's 
own Micheal Kimbell RPT that he calls the "Rough & Ready" Temperament.  The 
white key 5ths are tempered 1 1/2 times what they are in ET and the 5ths that 
are pure in the Vallotti/Fairchild are tempered 1/2 of what they are in ET 
(almost, but not quite pure).

I wish you good luck and success with these ideas.

Bill Bremmer RPT
Madison, Wisconsin