<HTML>In a message dated 4/7/01 9:34:40 PM Central Daylight Time, ramsey@extremezone.com (Kevin E. Ramsey) writes: <BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">OK, Bill. You'll have to give a dummy like me a clue. Temperaments are one thing. Octave stretch is another. Jim Sr. said that you had done "something" to your octaves, and that he liked it. What did you do? I have found that the amount of stretch is a matter of taste; what sounds pleasing to one tuner sounds noisy to another. So in the interest of continuing education ( that holiest of grails which we are always on a crusade for) clue me in. Please?</BLOCKQUOTE> I came up with my octave tuning method back in the mid 1980's when I was still tuning Equal Temperament (ET) but continued to use it when I started working with HT's.  I was strictly an aural tuner until after the time I designed the Equal Beating Victorian Temperament (EBVT).  The tuning Jim Coleman, Sr. RPT heard at the PTG Annual Convention in 1993 was done entirely by ear.  Incidentally, he was sitting with Virgil Smith RPT at the time who also came forward.  I remember Jim turning to him noting that I had done the job aurally. It is really very simple but cuts right through to the very reason tempering 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.   It uses the piano's natural inharmonicity to fill that gap and goes beyond that to satisfy the ear's enigmatic desire to hear the upper registers sharper than they should be theoretically. Starting with a temperament octave constructed with an appropriate amount of stretch (a compromise between a 4:2 and a 6:3 octave or just a plain 6:3 octave for any of the milder Well-Temperaments) ((the earlier HT's are more appropriately done with a minimum amount of stretch)), begin stretching the octaves by comparing the octave itself, moving closer to a pure 5th but being careful not to make the resultant 4th sound too "busy". Once you get into the 5th octave, you will notice that the beating in the 4th ceases to be of concern.  That is because the coincident partials are high enough that they become so weak as to be inaudible.  As the 4ths become less significant, you can concentrate more on the compromise between the octave and the 5th, trying to equalize the beating between them the best possible. Now, once you have 2 full octaves, F3-F5, it becomes very easy to determine the very best compromise for the octaves possible.  Here is the method I use which I have never heard of anyone else proposing at any time:  Using the Sostenuto pedal, play the double octave, then the octave and a 5th.  Example, F3-F5, then A#3(Bb3)-F5.  Find the point when the double octave sounds just barely pure, then listen to the octave and 5th.  You should notice a pronounced beat (which does not sound satisfying to the ear at all).  Now sharpen the upper note, F5 until the double octave starts to beat and continue sharpening until the double ocatve beats *exactly the same* as the octave and 5th. Both intervals will end up beating very slowly.  In ET, they may well sound both to be *apparently* in tune, very nearly beatless.  But, you can only find this "sweet spot" by comparing both intervals.  In a typical Well-Temperament, you will have some pure 5ths and some tempered ones.  When the 5th is pure, the reconciliation of the double octave and the octave and 5th will be easy:  you can make both sound pure very easily.  When the 5ths is tempered, you have to accept a little more beating in the double octave than you would in ET. So, you can see that when the tuning concerns an Historical Temperament (HT) 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 other Rapidly Beating Intervals) (RBI) are uneven in the temperament octave.   No smooth curve calculation used by any Electronic Tuning Device (ETD) that I know of can duplicate this although when tuning ET, they may closely approximate it. The problem I see with using these smooth curve calculations when tuning an HT is that they leave too much dissatisfying tempering in the extensions of the 5ths, the octave and 5ths and the double octave and 5ths.  This makes the resultant tuning have less clarity than it could have otherwise.  For this reason, I never use the FAC program with my Sanderson Accu-Tuner (SAT). Back to the method:  If the piano has no Sostenuto pedal, you can use the damper pedal but use it the same way you would use the Sostenuto pedal.  That is, play the notes in question first, then press the pedal to hold them while 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 vertical piano using muting strips (as I do and as I originally learned from Jim Coleman, Sr. RPT), the strip will be under the dampers in the treble section.  You can just use the damper pedal in the same manner as described above.   Continue with this method all the way to the top.  The piano's own inharmonicity will determine where you tune each note.  When you have completed the entire middle and treble sections, you can play double octaves and octaves & 5ths up and down the scale.  Believe me, any octave and 5ths which are too narrow will "jump out" at you.  I realized, after a time that I could tune entirely by ear and have rock solid consistency whether it was my first tuning of the day or the 6th or 7th for that matter, whether I was tired, no matter what mood I was in or even feeling somewhat ill because any notes that were too flat would be glaringly apparent.  Notes which are too sharp will also produce noticeable beating in the double octaves. This method can be duplicated exactly using the SAT (unfortunately, I don't know about the other ETD's).  Having the SAT set on the note to be tuned, 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 the sharp direction until the lights slow down for A#3 and begin to move counterclockwise for F3.  Find the point at which the clockwise and counterclockwise movement is *equalized*. At first, this balance may be very close, especially if the piano has low inharmonicity but it will be more pronounced as you move higher in the scale.  In ET, the difference between the two will probably be marginal.  In HT's, the pure 5th and Double Octave combination will show stopped lights for both the double octave and the octave and 5th while the tempered 5th and double octave will show significant movement clockwise and counterclockwise for both. Once you have made your compromise for the note in question, tune the note to whatever setting the SAT is showing.  If you wish to store the tuning, do so before you move on to the next note.  There is no reason why you couldn't use an FAC program that would get you close to this compromise but which you could *customise* by making this fine adjustment. When tuning below the temperament octave and on to the wound strings, you simply do a mirror image of what you did in the treble.  Most people seem to want to tune the wound strings first.  (I personally think using the FAC program starting at A0 is *perverse*!).  I, however, have good reasons for finishing the top part of the piano first.  It is by nature, the most difficult, tedious and time consuming.  If you get the hard part done first, doing the easy part last helps you relax and wind down as you complete the job.  Also, if time is running out, you can move more quickly through the lowest part of the piano than you can through the highest. I usually will complete the F3-F4 temperament octave, then tune down any 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 first, then listen to the 4th and 5th.  In ET, the 5th will probably beat noticeably and the 4th will be nearly pure.  Flatten the note to be tuned until there is just a slight beat in the octave (around 1/2 beat per second) and the 5th becomes cleaner and the 4th has a slow beat.  This should also produce a smooth progression of 3rds. When tuning an HT, you will have the same occurence with tempered 5ths and pure 5ths.  The pure 5th compromise will be easy, the tempered a little more difficult.  When tuning the so-called "poor scale design" piano (of which it seems that most pianos are, in fact) you simply need to compare all intervals and reach the best compromise.  The result will probably be that your 3rds 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.   When tuning an HT with such a piano, you really can end up with the sweet sounds prevailing over the harsh ones.  In my view, the practice of *forcing* a more pure 5th in this area at the expense of the octave, 4th and 3rd is a mistake.  It does not make the piano sound better or cleaner.  It makes all of the harmony sound more harshly than it has to. When tuning the wound strings in the bass section, do a mirror image of what you did in the treble.  Example:  play the double octave F2-F4 and use the Sostenuto (or alternatively, the Damper) pedal to hold the notes open.   Adjust the double octave until it sounds pure then listen to the octave and 5th, F2-C4.  Flatten F2 until the beat between the double octave and the octave and 5th is *equalized*. When using the SAT, set it to the note to be tuned, Example: F2.  Play the note F4 and stop the lights.  Now play the note C4 and the lights will rotate clockwise.  Press the Cents button in the Flat direction until the clockwise and counterclockwise movement of the lights between C4 and F4 is *exactly* the same.  Tune the note F2 to whatever setting is acheived.  If you wish to store the tuning, do so before moving on to the next note. Playing double octaves and octave and 5ths up and down the bass will reveal any unevenness, allowing you to acheive *maximum* clarity and consistency.   If you have stored the tuning in the SAT, you can check your work easily to make sure it has held as precisely as you wish. This method of equalizing beats between intervals is known as none other than the Equal Beating (EB) method although I did not realize this until I started to study the HT's.  It is also known as "Meantone" tuning. So, don't let that word scare you away.  It does not necessarily involve the notorious "Wolf".   It simply means making an equal compromise. The important discovery in using the EB principle in octaves as well as temperament is the Cancelling Out Effect (COE) that has been brought to light.  It is well known that tuning the piano with its 12 tone scale and Inharmonicity is a difficult puzzle to solve which requires inevitable compromises.  You just can't really get rid of some objectionable sounds, it seems.  But, if you will take the hints I have given you here, you will see and hear that you really can hide some of them and thus produce the sweetest, clearest sounding, most melodic harmony possible from the piano, *regardless* of choice of temperament. Finally, to address the issue of *taste* in octave stretching:  Yes, you will hear beating in single octaves, particularly in the 6th and 7th octaves.   Some technicians get caught up in this sound when played out of context.  But 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 is not either. The decay in that part of the piano is quick.  The ear can tolerate or even desire much more dissonance in an octave in that part of the piano than it can in the middle.  Imagine a large, concert grand in a large hall.  That 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 octaves will. Of course, there are different circumstances.  Some customers, in the privacy and intimacy of their homes will find that kind of stretch to be inappropriate.  This may also be the case for chamber music or in a recording circumstance where the piano is miked closely.  Any technician should be able to modify his or her usual approach to suit the demands of the particular circumstances.  Indeed, tuning the way I have suggested in the 7th octave will produce "errors" when tuning for the PTG RPT Tuning Exam although it would probably not result in a failing score.  When tuning for the Exam, the 7th octave must be tuned in strict 2:1 octaves in order to get a high or perfect score. I hope this essay enlightens many of you on the List. Regards, Bill Bremmer RPT Madison, Wisconsin</HTML>