<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD> <META http-equiv=Content-Type content="text/html; = charset=iso-8859-1"> <META content="MSHTML 6.00.2719.2200" name=GENERATOR> <STYLE></STYLE> </HEAD> <BODY bgColor=#ffffff> <DIV>Add the B( and you have a C7 = chord</DIV> <DIV>Joe Goss <A href="mailto:imatunr@srvinet.com">imatunr@srvinet.com</A> <A href="http://www.mothergoosetools.com">www.mothergoosetools.com</A></DI= V> <BLOCKQUOTE style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; = BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"> <DIV style="FONT: 10pt arial">----- Original Message ----- </DIV> <DIV style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: = black">From: <A title=mathstar@salemnet.com = href="mailto:mathstar@salemnet.com">Alan R. Barnard</A> </DIV> <DIV style="FONT: 10pt arial">To: <A = title=pianotech@ptg.org href="mailto:pianotech@ptg.org">pianotech@ptg.org</A> </DIV> <DIV style="FONT: 10pt arial">Sent: Saturday, September 21, = 2002 7:53 PM</DIV> <DIV style="FONT: 10pt arial">Subject: Ghost Tones by = Request</DIV> <DIV> </DIV> <DIV>I mentioned ghost tone testing in an = earlier post and a few people emailed me to ask huh? What? How? So, post the following. I am also attaching this as a Word document, if anyone = cares to print out a cleaner copy with better layout.</DIV> <DIV> </DIV> <DIV> GHOST TONES IN PIANO TUNING Based on Information and Ideas Stolen from Various = Reliable Sources By Alan R. Barnard   Introduction I'll try to outline the science of strings, briefly, and their = ability to generate "ghost tones" at specific partials for accurate tuning = checks. Most readers will already know some or all of this information, but it = really helps me to understand the theory behind our practices so I assume others = will appreciate having it presented. If you are pretty new to all of this = or limited in knowing the physics of strings and/or music theory, = please sit at a piano as you read this. Experiment with the relationships I = describe; I think you’ll "get it." I’m writing this all out of my head. If I get anything wrong, = email me pronto, please, and I will post a corrected version of the whole = thing. Intervals for "ghost tuning" are ones that occur naturally in one = string so this is not a discussion on temperament or evenness-of-scale testing = (running 3rds or 10ths, for example) for which ghosts are = not appropriate. The reason for this is an "energy" problem (more on this below). Also, my presentation of theory is based on "perfect string" = science. No string, and especially not a heavy steel string, can begin vibrating = precisely at its termination points due to the stiffness of the material. This generates, of course, the "inharmonicity" that provides job security = for professional tuners and is never quite grasped by amateur "tooners." Inharmonicity, its relation to tuning, string length, size of piano, = unwanted noise in single bass strings (longitudinal inharmonicity), and other = topics, are all very interesting but beyond the scope of the present = discussion. So we will assume perfect string harmonicity in this discussion = although, ironically, it is inharmonicity that makes "ghost tuning" useful and = interval testing necessary in the first place! The Science Behind It: Every string vibrates in a complex way including ... <UL> <LI>End to end, at its fundamental pitch (1st partial). <LI>In halves, with a node (dead spot) in the center of the string, = one octave above the fundamental. This is the 2nd partial = (or, to make it confusing, some call it the 1st overtone) <LI>In thirds, with two nodes, for the 3rd partial (2nd overtone). This interval is a 12th and is = an octave + fifth above the fundamental. = <LI>In fourths, with three nodes, for the 4th partial = (3rd overtone). This is the double octave. = <LI>In fifths to produce the 5th partial. This interval is the 17th, or two octaves + fifth.</LI></UL> For a brilliant and impressive demonstration of this, ask a = brilliant and impressive guitarist to play "harmonics" for you. Especially at the 2nd partial, you can actually see the string vibrate = in two halves with a node at the twelfth fret (1/2 the string length). While = it is thus vibrating, you can lightly rest your finger on the string at this = node without dampening the sound in the least. The 7th fret = hamonic is the 3rd partial, the 5th fret is the = 4th partial, etc. Do you see the implications of this for hammer shaping? = Damper placement and length? Hammer strike line? Scaling, in general? A cellist or bassist could also demonstrate this very well. Violins = you could hear, but not see, what is happening. Did I mention that I am a guitarist (classical)? The jury is still out on "impressive," and = definitely found me not guilty of that "brilliant" thing. Here is a chart of these intervals and their musical tone = equivalents for the note C28. The key numbers listed under "Note" refer to the key = that plays, at its fundamental, the same pitch as the partial of C28. <TABLE cellSpacing=1 cellPadding=7 width=638 border=1> <TBODY> <TR> <TD vAlign=top width="33%"> Note (Key)</TD> <TD vAlign=top width="33%"> Partial</TD> <TD vAlign=top width="33%"> Interval</TD></TR> <TR> <TD vAlign=top width="33%"> C28</TD> <TD vAlign=top width="33%"> 1st </TD> <TD vAlign=top width="33%"> Fundamental</TD></TR> <TR> <TD vAlign=top width="33%"> C40</TD> <TD vAlign=top width="33%"> 2nd </TD> <TD vAlign=top width="33%"> Octave</TD></TR> <TR> <TD vAlign=top width="33%"> G47</TD> <TD vAlign=top width="33%"> 3rd</TD> <TD vAlign=top width="33%"> Octave + Fifth (12th)</TD></TR> <TR> <TD vAlign=top width="33%"> C52</TD> <TD vAlign=top width="33%"> 4th</TD> <TD vAlign=top width="33%"> Double Octave (15th)</TD></TR> <TR> <TD vAlign=top width="33%"> E56</TD> <TD vAlign=top width="33%"> 5th</TD> <TD vAlign=top width="33%"> Double Octave + Third (17th)</TD></TR> <TR> <TD vAlign=top width="33%"> G59</TD> <TD vAlign=top width="33%"> 6th</TD> <TD vAlign=top width="33%"> Double Octave + Fifth (19th)</TD></TR> <TR> <TD vAlign=top width="33%"> A#62 (B()</TD> <TD vAlign=top width="33%"> 7th</TD> <TD vAlign=top width="33%"> Double Octave + Seventh</TD></TR> <TR> <TD vAlign=top width="33%"> C64</TD> <TD vAlign=top width="33%"> 8th</TD> <TD vAlign=top width="33%"> Triple Octave</TD></TR> <TR> <TD vAlign=top width="33%"> D66</TD> <TD vAlign=top width="33%"> 9th</TD> <TD vAlign=top width="33%"> Triple Octave + Second</TD></TR> <TR> <TD vAlign=top width="33%"> E68</TD> <TD vAlign=top width="33%"> 10th</TD> <TD vAlign=top width="33%"> Triple Octave + = Third</TD></TR></TBODY></TABLE> Important or Interesting Comments on the Chart Above Please note distinctions between the terms partial, interval, and = chord member. The note G37 in relation to C28, for instance, is the 3rd partial of C28, a chord fifth in a major = or minor C chord, and an interval of a 12th from C28. It is also interesting to note the natural science of music theory = that a single string demonstrates. In our example, the first 10 partials = include 4 C’s, 2 E’s, 2 G’s, a B(, and a D. So we have a C major chord in the = natural harmonics of the string, i.e., C-E-G. Add the B( and you have a C7 chord; = add the D and you have a C9 chord. The same relationships hold for any string = played. Note: It is only a coincidence that the chord seventh, here, is the = 7th partial and the 9th partial is a chord = ninth. In fact, the 3rd partial is a chord fifth, the 5th = partial is a chord third. Don’t be confused. It is the relative strength or weakness of each sounding partial = (and the higher ones not here named) that, mostly, account for the string’s = timbre (pronounced "tam·br"), that is to say, it’s particular character = of sound. Middle C has different characteristic sounds in pianos, harps, = guitars, and cellos because of the way string materials, lengths, masses (weights), = & tensions—as well as differing soundboard and resonating chamber constructions—impede or encourage the strength of each partial. = Similarly, it is the reason an oboe, a clarinet, a flute, and a saxophone can play = the same note (fundamental) yet sound distinctly different. This likewise = explains why two human voices singing the same note sound different, especially if = there are significant physical differences between the two persons, e.g., a = tenor and a soprano each singing middle C. Further examples include organ = "stops," reproduction of sound through two different hi-fi speakers, the same instrument played in two different concert halls, etc. Demonstration At a tuned piano, hold down the C28 key (without sounding it). Use = no pedals. Strike and instantly release C40 so the damper immediately = stops this note. You will continue to hear C40 because, through what is called "sympathetic resonance," the energy you put into the piano has caused = C28 to vibrate at it’s 2nd partial (1st = overtone)--the C40 pitch! To prove that this is so, strike and release the C40, as above, = then release C28 and note that the middle C tone of C40 stops instantly. = Instantly, that is, if your C28 damper is working properly. Just for fun, hold down C28 as above and quickly strike and release = any or all of the notes above C28 listed in the chart above. They will all = sound until they decay or until you release C28. Now, holding down C28, try striking and releasing a key not = in the above chart. Any tones that are picked up by the C28 strings are from overtones (partials above the 1st) of that struck = key, not from its fundamental. These overtones, have less energy than the = fundamental of that key. This explains, in part, why sympathetic vibrations picked = up by the C28 strings are relatively weak and somewhat out of tune, in this = case. The other reason is that the C28 strings are naturally sympathetic = only to their own partial series, as per the chart above. Try the experiment with G35. This is the first natural fifth of the = C major chord built on C28. So one might expect it to produce a loud = sympathetic ring in C28. But it doesn’t. In fact compare it to what is generated by = G47 at the 12th. G47 is in the partial series (chart) and G35 is not. = The energy put into C28 by G35 is at G35's second partial, not at its = strong fundamental, and therefore has the pitch of G47—but not with the = amount of energy the G47 key will impart—at its fundamental pitch—if = it is struck. The beats between strings of different intervals (or out-of-tune = unisons) are caused by the interactions of closely--but not = identically—aligned partials of the respective strings. Two strings in a unison provide = the easiest example: When they are in tune (and presuming they have = identical mass, tension, and length—with no nicks, kinks, rust, or other = flaws), every partial will, in theory, line up exactly. Each partial will be exactly = in phase, meaning the highs and lows of their generated sound waves will = occur at precisely the same instant. If the strings differ in any way, = something will change, some of the partials will be out of phase. When two tones are near each other but not in phase, their = respective sound waves will sometimes reinforce each other (we hear louder) and at = other times interfere with each other (we hear softer). These are the proverbial = "beats" we tune with or try to tune out. Beats are a real, physical = phenomenon—a change in the way sound reaches our eardrums—not a psychological = trick of the brain, as some believe. As an interesting aside, multi-engine aircraft can also be tuned = with beats. When the beats get slower, the prop speeds are closer; when the = beats stop, the two propellers are spinning at exactly the same speed = ("rotational velocity," to be precise). If the plane has more than two engines, you = have to "tune" two of them, then start and "tune" the third, etc. The same = principle applies to tuning strings: you can really only tune one at a time. = Even if you aren’t muting out other strings, you are only listening to and = tuning one string at a time. Also, if the propellers differ in some way (not a = good idea), would you have trouble tuning them to beats? Yes. It would be = like tuning two badly mismatched strings in a bass unison (Oh, Mercy, = don’t you know: Been there, done that, got the souvenir T-shirt.). If you want to see this effect, take some stones of differing mass = or size and find some still water (a pond, not a river). Start dropping stones = near each other and watch how the ripples interact. This little phenomenon also explains why string "level" is = important to tone quality in unisons. If the strings are not in exactly the same = plane with respect to the hammer face, one string will start sounding slightly = ahead of the other, i.e., out of phase. So if the hammer shape is uneven, the = hammer "travels" and strikes at an angle to the string plane, or the strings themselves are not exactly level, it is not possible to align all the = partials of those two (or three) strings. Even if each string is precisely, stop-the-lights, in tune at the fundamental pitch, out-of-phase higher = partials will make the note sound whiney, or worse. (Hello Betsy Ross = and all your cheap little friends.) Ghost Tuning ("Finally," Many Will Say) or, More Precisely, Ghost = Tone Interval Testing This part, I will just present as "how to’s" and examples. The = idea, in each case, is to isolate exactly the partials we are trying to match = in the two notes of the interval without having to listen to—or = through—the fundamentals or any other partials of the notes. Octaves Please note that this is not a treatise on tuning, per se, nor on = what size octave to use in what part of the piano or anything like it. This is = simply a way to isolate the pitch of string interactive beats—for training = purposes, if nothing else. Often times, the "best" tuning for a bass note, = especially in poorly scaled or tired pianos, will be somewhere between a = perfect this and a perfect that—a process known as "evening out = the growls." To test a 6:3 octave, hold the two octave keys down, silently, = (remember, no pedals) while striking and releasing the 19th (two = octaves + fifth) from the lower note. This will excite the lower string of the = octave at it’s 6th partial and the higher one at its = 3rd. The resulting tone will have a beat or a slow roll unless the two octave = notes are exactly in tune at the 6:3 interval or so far out of tune that they = are not picking up the vibrations of the "energy" key, the 19th. = If our octave sounds like an octave and this test produce no = beat or roll, you have a perfect 6:3 octave. For many pianos, = especially smaller ones, this makes a fairly clean, nicely "stretched" octave in = the bass. The double octave, in this case, will have about a ½ second = roll that you can isolate by using the double octave note as your energy = key. In our chart example, the C28-C40 octave 6:3 test will use the G52 = key. Don’t forget to immediately dampen the "energy" key after playing = it. We don’t want to listen to the sound of the G52 key at all! We just want it to = put some energy into the other strings, via the soundboard and bridges. Also, = if your "energy" key is above the dampers, be prepared to mash your right = thumb or, better, a chunk of felt onto that unison as soon as you release the = key. To hear the double octave in our example, use C52 as the energy = key. If the octave is "in tune" and you hear no beat using C52 for energy, guess = what! You have a perfect 4:2 octave. The fundamental of C52 is the = 4th partial of C28 and the 2nd partial of C40. This is, of = course, the approximate octave size we want for the temperament and on up into the = treble. I will note, at this time, that it gets harder to hear octave ghost = tones as you go higher in the piano. Sometimes the lowest bass notes are = hard to excite with "ghosts," also. I don’t know why, but I expect it is = because of their mass. In fact, my theory is that "tubbiness" in big and fat = and/or tired and dirty strings is just a reflection of their inability to generate = or sustain higher partials. (Comments welcome.) Anyway, ghost tones are = really most useful in the lower tenor and bichord bass regions, in my = experience. <DIR> In the "To err is human, to really screw it up takes a computer." department: I had to correct my own error in the last paragraph. My = spell checker wasn’t the least bit bothered by the phrase "… to hear = octave ghost towns ...")</DIR> Tuning a Steinway D or a Böesendorfer Imperial? Try C64 with the = C28-C40 octave. See how close the piano will let you stretch for 8:4 = octaves. Unisons When string pairs are very noisy, especially in the bass, it is = sometimes helpful to tune or test with ghosts. The usual culprit or "bad boy" in = the mix is the 15th. The energy key for this is at the octave + = fifth. In our example, if we were tuning two strings of the C28 unison we would = strike G47 and try for no beat, no roll. Not that this always produces the = "best" unison: As always, listen carefully—then judge, nudge, or = fudge, as necessary. Other Intervals Though not as useful as for octaves and unisons, other intervals = can be tested with ghost tones. The beat we listen for in fifths is found = one octave above the higher note of the interval. The beat of = the fourth is found two octaves above the lower note of the interval. For example: The F33-C40 (fifth) roll can be isolated and = energized by striking the C52 key. For the F33-A# (fourth) beat/roll, strike = F57. Ghosts for other intervals are, in my opinion, hard to hear, hard = to remember (where they are), and not any help to the tuner. Well, that’s it for now, boys and girls. This is Uncle Al, the = kiddies’ pal, saying: So long, and thanks for listening. Disclaimer If this information is correct, coherent, and useful, I wrote it. Otherwise, it’s someone else’s fault, entirely. Alan R. Barnard Salem, MO  </DIV> <HR> _______________________________________________ pianotech = list info: = https://www.moypiano.com/resources/#archives </BLOCKQUOTE></BODY></HT= ML>