Tempered Octaves (was Beat Cancelers)

Tony Caught caute@optusnet.com.au
Mon, 9 Apr 2001 10:46:20 +0930


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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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