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Hi Bill,
Thank you for your most enlightening post.
Being a self taught tuner who is not a piano player (my theory on the =
subject of tuning is lousy because I don't understand what a 6:3 octave =
type is. I think its the 6th partial compared to the 3rd partial of the =
higher note but am not sure)
Anyway on the 1/21/2001 I answered a post from Richard Brekne which is =
below.
My comments
"With me, this results (on a good piano) being maybe all fifth's are a =
1/4 beat per sec on the flat side and the fourth's are about 3/4 beat =
per sec."
And
"I would like to see a template written for a ETD that takes into =
consideration the tuning of octaves based on the octave and the =
octave and a fifth with the tuned note set at that point equally between =
the two beats. Does that make sense ?."
I generally wind up by smoothing the lowest octave by 3 octaves and a =
third for evenness.
When you described your method you also confirmed to me that I am =
correct in my method of tuning. I have never been able to understand =
how there can be several different stretches available on a ETD when in =
reality, on any given piano, there is the natural sterch that we should =
be tuning for.
As now at the age of 62, with hearing going, I am interested in a ETD =
that is going to tune to what I want without having to set each note =
individually. Thus my question,=20
"I would like to see a template written for a ETD that takes into =
consideration the tuning of octaves based on the octave and the =
octave and a fifth with the tuned note set at that point equally between =
the two beats. Does that make sense ?."
Tony Caught ICPTG
Australia
caute@optusnet.com.au
Origonal sent 1/21/2001
snippety snip.
> That being said.. I found it interesting to read his declaration that
matching
> partials such that one has either a 2:1 or a 6:3 octave type, results =
in
an
> octave with a "slight natural beat on the flat side" and that tuning
octaves
> in which the natural beat is eliminated when the unisons are tuned =
will be
> "wider then the first seven of Reyburn's so called octave stretches".
These
> followed by the statement that "Jim Coleman's Pure 5ths temperament =
will
result
> in a natural octave bead on the sharp side."
My 'learning' of tuning pianos is a little different from many other =
more
fortunate persons and I truely lack the ability to express exactly what =
I
mean cos I am dumb but, this natural beat is the (to me) the sound or
feeling you get when two notes blend in the best. I think I am trying =
to
say 'when all audible harmonics are at their smoothest'.
With me, this results (on a good piano) being maybe all fifth's are a =
1/4
beat per sec on the flat side and the fourth's are about 3/4 beat per =
sec.
>
> Notice that these statements seem to apply equally to all ranges of =
the
> piano... with no real difference...ie a 6:3 octave in the high treble =
is
still
> going to yeild a "narrow" natural beat octave. Aside from that kind =
of
> thing...these statements open a door that might allow us to look =
closer at
the
> possiblity that there is some phenomena going on that has been =
overlooked
so
> far by those from the ETD world.
>
> If its a hearable beat like thing we are looking for... and in the =
range
Virgil
> states... it should be measurable in some sense also.
>
You will have noticed also that when tuning the bass in same piano and =
you
play a fifth, say C2, G2 whilst tuning C1 that you are tuning to a =
beatless
sound on octave and on octave fifth at the same time.
Next one is that after you tune a piano, check it and touch up (one =
string
at a time, others in note muted) the tuning with the sustain pedal on. =
For
some reason, possibley the interaction of all harmonics being induced, a
beat is audable which is the composite of all harmonic beats for that =
note.
I would like to see a template written for a ETD that takes into
consideration the tuning of octaves based on the octave and the octave =
and a
fifth with the tuned note set at that point equally between the two =
beats.
Does that make sense ?.
> --
> Richard Brekne
> RPT, N.P.T.F.
> Bergen, Norway
> mailto:Richard.Brekne@grieg.uib.no
>
>
Regards
Tony Caught ICPTG
Australia
caute@optusnet.com
----- Original Message -----=20
From: Billbrpt@AOL.COM=20
To: pianotech@ptg.org=20
Sent: Monday, April 09, 2001 3:42 AM
Subject: Re: Tempered Octaves (was Beat Cancelers)=20
In a message dated 4/7/01 9:34:40 PM Central Daylight Time,=20
ramsey@extremezone.com (Kevin E. Ramsey) writes:=20
OK, Bill. You'll have to give a dummy like me a clue. Temperaments =
are one=20
thing. Octave stretch is another. Jim Sr. said that you had done=20
"something" to your octaves, and that he liked it. What did you do? =
I have=20
found that the amount of stretch is a matter of taste; what sounds =
pleasing=20
to one tuner sounds noisy to another. So in the interest of =
continuing=20
education ( that holiest of grails which we are always on a crusade =
for)=20
clue me in. Please?
I came up with my octave tuning method back in the mid 1980's when I =
was=20
still tuning Equal Temperament (ET) but continued to use it when I =
started=20
working with HT's. I was strictly an aural tuner until after the time =
I=20
designed the Equal Beating Victorian Temperament (EBVT). The tuning =
Jim=20
Coleman, Sr. RPT heard at the PTG Annual Convention in 1993 was done =
entirely=20
by ear. Incidentally, he was sitting with Virgil Smith RPT at the =
time who=20
also came forward. I remember Jim turning to him noting that I had =
done the=20
job aurally.=20
It is really very simple but cuts right through to the very reason =
tempering=20
is done in the first place. That is, the Pythagorean Comma, the "gap" =
between what 7 pure octaves and 12 pure 5ths would create: about 24 =
cents. =20
It uses the piano's natural inharmonicity to fill that gap and goes =
beyond=20
that to satisfy the ear's enigmatic desire to hear the upper registers =
sharper than they should be theoretically.=20
Starting with a temperament octave constructed with an appropriate =
amount of=20
stretch (a compromise between a 4:2 and a 6:3 octave or just a plain =
6:3=20
octave for any of the milder Well-Temperaments) ((the earlier HT's are =
more=20
appropriately done with a minimum amount of stretch)), begin =
stretching the=20
octaves by comparing the octave itself, moving closer to a pure 5th =
but being=20
careful not to make the resultant 4th sound too "busy".=20
Once you get into the 5th octave, you will notice that the beating in =
the 4th=20
ceases to be of concern. That is because the coincident partials are =
high=20
enough that they become so weak as to be inaudible. As the 4ths =
become less=20
significant, you can concentrate more on the compromise between the =
octave=20
and the 5th, trying to equalize the beating between them the best =
possible.=20
Now, once you have 2 full octaves, F3-F5, it becomes very easy to =
determine=20
the very best compromise for the octaves possible. Here is the method =
I use=20
which I have never heard of anyone else proposing at any time: Using =
the=20
Sostenuto pedal, play the double octave, then the octave and a 5th. =
Example,=20
F3-F5, then A#3(Bb3)-F5. Find the point when the double octave sounds =
just=20
barely pure, then listen to the octave and 5th. You should notice a=20
pronounced beat (which does not sound satisfying to the ear at all). =
Now=20
sharpen the upper note, F5 until the double octave starts to beat and=20
continue sharpening until the double ocatve beats *exactly the same* =
as the=20
octave and 5th.=20
Both intervals will end up beating very slowly. In ET, they may well =
sound=20
both to be *apparently* in tune, very nearly beatless. But, you can =
only=20
find this "sweet spot" by comparing both intervals. In a typical=20
Well-Temperament, you will have some pure 5ths and some tempered ones. =
When=20
the 5th is pure, the reconciliation of the double octave and the =
octave and=20
5th will be easy: you can make both sound pure very easily. When the =
5ths=20
is tempered, you have to accept a little more beating in the double =
octave=20
than you would in ET.=20
So, you can see that when the tuning concerns an Historical =
Temperament (HT)=20
or any kind of Well-Temperament (WT), using this method of determining =
octaves will create octaves of *uneven* sizes just as the 3rds & 6ths =
(and=20
other Rapidly Beating Intervals) (RBI) are uneven in the temperament =
octave. =20
No smooth curve calculation used by any Electronic Tuning Device (ETD) =
that I=20
know of can duplicate this although when tuning ET, they may closely=20
approximate it.=20
The problem I see with using these smooth curve calculations when =
tuning an=20
HT is that they leave too much dissatisfying tempering in the =
extensions of=20
the 5ths, the octave and 5ths and the double octave and 5ths. This =
makes the=20
resultant tuning have less clarity than it could have otherwise. For =
this=20
reason, I never use the FAC program with my Sanderson Accu-Tuner =
(SAT).=20
Back to the method: If the piano has no Sostenuto pedal, you can use =
the=20
damper pedal but use it the same way you would use the Sostenuto =
pedal. That=20
is, play the notes in question first, then press the pedal to hold =
them while=20
you make your fine adjustment. There will be a little more background =
"noise" but you will still be able to clearly hear your objective. In =
a=20
vertical piano using muting strips (as I do and as I originally =
learned from=20
Jim Coleman, Sr. RPT), the strip will be under the dampers in the =
treble=20
section. You can just use the damper pedal in the same manner as =
described=20
above. =20
Continue with this method all the way to the top. The piano's own=20
inharmonicity will determine where you tune each note. When you have=20
completed the entire middle and treble sections, you can play double =
octaves=20
and octaves & 5ths up and down the scale. Believe me, any octave and =
5ths=20
which are too narrow will "jump out" at you. I realized, after a time =
that I=20
could tune entirely by ear and have rock solid consistency whether it =
was my=20
first tuning of the day or the 6th or 7th for that matter, whether I =
was=20
tired, no matter what mood I was in or even feeling somewhat ill =
because any=20
notes that were too flat would be glaringly apparent. Notes which are =
too=20
sharp will also produce noticeable beating in the double octaves.=20
This method can be duplicated exactly using the SAT (unfortunately, I =
don't=20
know about the other ETD's). Having the SAT set on the note to be =
tuned,=20
Example, F5: play the note F3 and stop the lights. Now play the note =
A#3(Bb3). The lights will rotate clockwise. Now press the Cents =
button in=20
the sharp direction until the lights slow down for A#3 and begin to =
move=20
counterclockwise for F3. Find the point at which the clockwise and=20
counterclockwise movement is *equalized*.=20
At first, this balance may be very close, especially if the piano has =
low=20
inharmonicity but it will be more pronounced as you move higher in the =
scale.=20
In ET, the difference between the two will probably be marginal. In =
HT's,=20
the pure 5th and Double Octave combination will show stopped lights =
for both=20
the double octave and the octave and 5th while the tempered 5th and =
double=20
octave will show significant movement clockwise and counterclockwise =
for both.=20
Once you have made your compromise for the note in question, tune the =
note to=20
whatever setting the SAT is showing. If you wish to store the tuning, =
do so=20
before you move on to the next note. There is no reason why you =
couldn't use=20
an FAC program that would get you close to this compromise but which =
you=20
could *customise* by making this fine adjustment.=20
When tuning below the temperament octave and on to the wound strings, =
you=20
simply do a mirror image of what you did in the treble. Most people =
seem to=20
want to tune the wound strings first. (I personally think using the =
FAC=20
program starting at A0 is *perverse*!). I, however, have good reasons =
for=20
finishing the top part of the piano first. It is by nature, the most=20
difficult, tedious and time consuming. If you get the hard part done =
first,=20
doing the easy part last helps you relax and wind down as you complete =
the=20
job. Also, if time is running out, you can move more quickly through =
the=20
lowest part of the piano than you can through the highest.=20
I usually will complete the F3-F4 temperament octave, then tune down =
any=20
notes in the low tenor that may be below that first, then start moving =
upwards, leaving the bass section for last. For tuning the low tenor, =
compare the 4th, 5th and octave. Make the octave sound just barely =
pure=20
first, then listen to the 4th and 5th. In ET, the 5th will probably =
beat=20
noticeably and the 4th will be nearly pure. Flatten the note to be =
tuned=20
until there is just a slight beat in the octave (around 1/2 beat per =
second)=20
and the 5th becomes cleaner and the 4th has a slow beat. This should =
also=20
produce a smooth progression of 3rds.=20
When tuning an HT, you will have the same occurence with tempered 5ths =
and=20
pure 5ths. The pure 5th compromise will be easy, the tempered a =
little more=20
difficult. When tuning the so-called "poor scale design" piano (of =
which it=20
seems that most pianos are, in fact) you simply need to compare all =
intervals=20
and reach the best compromise. The result will probably be that your =
3rds=20
will beat more slowly than you anticipate and your 5th may end up more =
tempered but the end effect on the music to be played will be more =
pleasing. =20
When tuning an HT with such a piano, you really can end up with the =
sweet=20
sounds prevailing over the harsh ones. In my view, the practice of =
*forcing*=20
a more pure 5th in this area at the expense of the octave, 4th and 3rd =
is a=20
mistake. It does not make the piano sound better or cleaner. It =
makes all=20
of the harmony sound more harshly than it has to.=20
When tuning the wound strings in the bass section, do a mirror image =
of what=20
you did in the treble. Example: play the double octave F2-F4 and use =
the=20
Sostenuto (or alternatively, the Damper) pedal to hold the notes open. =
=20
Adjust the double octave until it sounds pure then listen to the =
octave and=20
5th, F2-C4. Flatten F2 until the beat between the double octave and =
the=20
octave and 5th is *equalized*.=20
When using the SAT, set it to the note to be tuned, Example: F2. Play =
the=20
note F4 and stop the lights. Now play the note C4 and the lights will =
rotate=20
clockwise. Press the Cents button in the Flat direction until the =
clockwise=20
and counterclockwise movement of the lights between C4 and F4 is =
*exactly*=20
the same. Tune the note F2 to whatever setting is acheived. If you =
wish to=20
store the tuning, do so before moving on to the next note.=20
Playing double octaves and octave and 5ths up and down the bass will =
reveal=20
any unevenness, allowing you to acheive *maximum* clarity and =
consistency. =20
If you have stored the tuning in the SAT, you can check your work =
easily to=20
make sure it has held as precisely as you wish.=20
This method of equalizing beats between intervals is known as none =
other than=20
the Equal Beating (EB) method although I did not realize this until I =
started=20
to study the HT's. It is also known as "Meantone" tuning. So, don't =
let that=20
word scare you away. It does not necessarily involve the notorious =
"Wolf". =20
It simply means making an equal compromise.=20
The important discovery in using the EB principle in octaves as well =
as=20
temperament is the Cancelling Out Effect (COE) that has been brought =
to=20
light. It is well known that tuning the piano with its 12 tone scale =
and=20
Inharmonicity is a difficult puzzle to solve which requires inevitable =
compromises. You just can't really get rid of some objectionable =
sounds, it=20
seems. But, if you will take the hints I have given you here, you =
will see=20
and hear that you really can hide some of them and thus produce the =
sweetest,=20
clearest sounding, most melodic harmony possible from the piano, =
*regardless*=20
of choice of temperament.=20
Finally, to address the issue of *taste* in octave stretching: Yes, =
you will=20
hear beating in single octaves, particularly in the 6th and 7th =
octaves. =20
Some technicians get caught up in this sound when played out of =
context. But=20
dwelling on an octave played in the high treble by itself outside of a =
musical context is simply not music, just as playing 3rds & 6ths up =
and down=20
is not either.=20
The decay in that part of the piano is quick. The ear can tolerate or =
even=20
desire much more dissonance in an octave in that part of the piano =
than it=20
can in the middle. Imagine a large, concert grand in a large hall. =
That=20
dissonance in the upper octaves will actually help the piano carry and =
project much better and thus provide a much more satisfying sound than =
2:1=20
octaves will.=20
Of course, there are different circumstances. Some customers, in the =
privacy=20
and intimacy of their homes will find that kind of stretch to be=20
inappropriate. This may also be the case for chamber music or in a =
recording=20
circumstance where the piano is miked closely. Any technician should =
be able=20
to modify his or her usual approach to suit the demands of the =
particular=20
circumstances. Indeed, tuning the way I have suggested in the 7th =
octave=20
will produce "errors" when tuning for the PTG RPT Tuning Exam although =
it=20
would probably not result in a failing score. When tuning for the =
Exam, the=20
7th octave must be tuned in strict 2:1 octaves in order to get a high =
or=20
perfect score.=20
I hope this essay enlightens many of you on the List.=20
Regards,=20
Bill Bremmer RPT=20
Madison, Wisconsin=20
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