This is a multi-part message in MIME format. ---------------------- multipart/alternative attachment 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 ---------------------- multipart/alternative attachment An HTML attachment was scrubbed... URL: https://www.moypiano.com/ptg/pianotech.php/attachments/f9/4c/77/a6/attachment.htm ---------------------- multipart/alternative attachment--
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