=========================================================================== Instrument Builders FAQ rec.music.makers.builders Original Compilation: Clark Battle Past Maintainers: Gary Watts Jeff Rice Currently erratically maintained by: Eric Nicolich =========================================================================== Last Update: 19 December 1996 =========================================================================== Index: Introduction: Charter: Organizations: Internet Mailing Lists WWW Sites of Interest Bibliography: (Books and reviews by topic) Guitar Stringed Instruments (other than guitar) Electronic Wind Instruments Percussion Keyboard Instruments Misc. Periodicals: (none listed yet) Supplies: Questions: Q1: Where do I put the holes in a flute? Q2: How does a truss rod work? Q3: What frequencies are the notes of the standard diatonic scale? Qc: String Mathematics: pitch, gauge, length, & tension. Q5: What is the difference between Quarter sawn wood and Slab sawn wood? Q6: Where do the frets go? (C, BASIC, & Fortran programs) Q7: Why don't the bridge saddles line up? Unindexed questions: (I'll give them numbers on the next update) =========================================================================== Introduction: This FAQ was compiled mainly from posts on rec.music.makers.builders and the defunct mail group ==Instrument Builders Digest==. I have begun to add information gained from other sources (books, periodicals, and e-mail). While I attempt to provide accurate information, nothing here is guaranteed; addresses, phone numbers, version numbers, prices, etc. may or may not be correct. There are many other questions which should be addressed such as the strengths and weaknesses of different types of glues. Feel free to suggest new FAQs, answers, and other sordid comments to: eric.nicolich@worldnet.att.net The following charter was in place long before I even dreamt about such a group as rec.music.makers.builders. While most traffic in this group focuses naturally enough on guitar issues, please realize that postings relative to other instruments are not only welcomed, but encouraged. =========================================================================== Charter: The group will be dedicated to the discussion of designing, building, & repairing musical instruments. The discussion will involve the design, building, and repair of any device intended to make music: percussive, string, wind, keyboard, experimental, acoustic, electric, electronic, amplificatory, robotic, and ridiculous. The group is unmoderated. =========================================================================== Organizations: Guild of American Luthiers 8222 South Park Avenue Tacoma, WA 98408 (206)472-7853 Membership is are US$36 per year; Canada and Mexico $40; overseas $46. And include quarterly journal and discounts on back issues, guitar plans, etc. ----------------------------------------------------------------------- International Society of Folk Harpers & Craftsmen (ISFHC), 4718 Maychelle Dr. Anaheim, CA 92807-3040 (714)998-5717. Membership is $22/yr which includes the quarterly Journal. =========================================================================== Internet Mailing Lists: Lute Builders and Players: To subscribe send mail to: lute-request@cs.dartmouth.edu To send mail to the list: lute@cs.dartmouth.edu ----------------------------------------------------------------------- Bagpipe Makers bagpipe-request@cs.dartmouth.edu has pipe makers on the list ----------------------------------------------------------------------- Pipe Organ Send a message to LISTSERV@ALBNYVM1.BITNET and put the message SUBSCRIBE in the body of the message. ----------------------------------------------------------------------- Analog Synthesizers Subscribe to analogue-request@magnus.acs.ohio-state.edu to post, leave off the -request part in the address. Subscription requests take a couple of days sometimes because they are all handled manually. ----------------------------------------------------------------------- Harmonica / Concertinas To subscribe send to: accordion-request@cs.cmu.edu To post send to: accordion-request@cs.cmu.edu =========================================================================== WWW Sites of Interest Schematics - Electric Guitar Effects and Amps. http://rowlf.cc.wwu.edu:8080/~n9343176/schems.html ----------------------------------------------------------------------- Guitar Manufacturers / Luthiers Gibson - USA http://www.gibson.com ----------------------------------------------------------------------- Acoustic Guitar (RMMGA) http://pentagon.io.com:8001/galvis/rmmga ----------------------------------------------------------------------- The hurdy-gurdy web site, at http://weber.u.washington.edu/~darkstar/HGhome.html ----------------------------------------------------------------------- Guitar building http://www.cis.tu-graz.ac.at/iwb/martin/welcome.html http://falcon.jmu.edu/~dehartcg/cdhome.htm =========================================================================== Bibliography *************************************************************************** GUITAR *************************************************************************** G1. Build Your Own Electric Guitar by Melvin Hiscock Blandford Press - 1986 159pp B&W ISBN: Real good info (even if the writing and editing is a bit amateurish as well as distinctly British) - from scratch, he builds 3 electrics in that book: 1. Lefty archtop body with glued-on maple neck with rosewood finger board - painted. 2. Tele copy body with binding and veneer maple face, bolt-on one-piece maple neck - sunburst. 3. Neck-through-body 8 string bass, multiple wood body, maple neck with laminated accent stripes, I think ebony fingerboard - natural oiled finish. In other words, he covers a range of styles so you can get a feel for most options one might consider in the construction of a solid body. And he covers truss rods, neck and bridge angles and their interaction, fingerboards, wood, etc. very well. Pleny-o-pictures. He only lightly covers pickup wiring, you may need another reference (and there are many) to get expertise in that. From reading this book, I am actually under the impression that I am capable of building a decent guitar on my own. The book is that dangerous... ;-) This is an excellent book, and has been my "bible" for a lot of info that I could find nowhere else. Step by step, lotso pics, different variations in bodies, necks, etc. You'll love it. -------------------------------------------------------------------- G2. Constucting a Solid Body Guitar by Roger H. Siminoff. Hal Leanord Books - 1986 60pp B&W (2 color pages on staining) ISBN: Decent book, IMHO, not as good as Hiscock's book in technical detail, or in breadth of issues mentioned/covered. Siminoff was the editor of Frets, methinks, for a while, and has a lengthy history in the field as a general luthier. He has other books on building mandolins, etc. He builds and finishes one electric guitar in the book. This is an excellent book as well, but kinda odd IMHO. Some techniques are different from standard building. It does have a great section on inlay work, and another great section on staining. It also has some full size templates for neck, headstock, body, but once again-kinda odd IMHO) -------------------------------------------------------------------- G3. Guitar Player Repair Guide By Dan Erlewine GPI Books - 1994, 1990 (second edition; there may be an update out) 309pp B&W ISBN: 0-87930-291-7 $22.95 US This book is not exactly on the building process, but is absolutely required. It is so full of completely anal details and imformation regarding setup, repair, mods, retrofitting, finishing, etc. You HAVE to have this one. Dan does the column in Guitar Player about repairing, and has a vested interest in Stewart McDonald Guitar Supply. ----------------------------------------------------------------- G4. Guitarmaking: Tradition and Technology. by William Cumpiano & Jonathan Natelson. Hadley MA: Rosewood Press, 1897. ISBN: Detailed instructions for building a classical & a steel-string guitar. Much of the information is relevant to other necked, plucked strings, such as lutes (my interest). ----------------------------------------------------------------- G5. Lutherie Tools: Making Hand and Power Tools for String Instrument Building. Tim Olsen & Cyndy Burton, eds., Guild of American Luthiers Resource Book 1, 1990. ISBN: Plans and details on the construction of many lutherie tools. ----------------------------------------------------------------- G6. Digital Guitar Digest Internet newsletter To subscribe, send email to Paolo Valladolid pvallado@sdcc5.ucsd.edu Dedicated to the discussion of music technology as applied to guitar and other stringed intruments. *************************************************************************** STRINGS *************************************************************************** S1. Making Stringed Instruments: A Workshop Guide by George Buchanan Sterling Publishing Co., ISBN 0-80696-7464-8 This book gives plans and instructions for making a violin, classical guitar, viola, cello, mandolin, and mandola. It assumes you have some woodworking skills. ----------------------------------------------------------------- S2. A Fiddlemaker's Worksheets by William K. Robertson Argus Books Limited The Robertson book is a very good book (although I believe it is now out of print) which concentrates on the building of a violin. It goes through every step with illustrations for everything. The publisher is Argus Books Limited should you wish to find out if they will be printing it again. *************************************************************************** ELECTRONICS *************************************************************************** E1. Digital Projects for Musicians by Craig Anderton et. al. ----------------------------------------------------------------------- E2. Electronic Musical Projects by R.A. Penfold ISBN 0-900162-94-5 ----------------------------------------------------------------------- E3. Electronic Project for Musicians by Craig Anderton. PAiA, as you may know, is the supplier of kits associated with this book and has a free catalog that lists, among other things, the book itself. We accept email catalog requests and answer questions at the address paia@aol.com. EPFM projects use several components that are extinct and others that are difficult to find. For example, the CLM6000 optoisolators that Craig used are right up there with living brontosaurs in availability, but a current replacement is the NSL32 and they're available from JAMECO. 4739 opamps are a different story. To the best of my knowledge there are none available and no other amp with the same footprint. A current subsitute is the 5532, but they're in an 8 pin package. PAiA has an adapter consisting of 16 pin wire wrap socket, small circuit board (the size of a 16 pin DIP) and a 5532 for $4.50. The small board mounts on the socket, the pins of the socket go in the 4739 footprint on the application board and the 5532 plugs in the lower group of 8 pins on the socket. *************************************************************************** WIND *************************************************************************** W1. The Irish Bagpipes: Their Construction and Maintenance by Wilbert Garvin ISBN: *************************************************************************** PERCUSSION *************************************************************************** P1. How To Make a Bodhran (traditional Celtic goatskin drum) by Brent Santin. Email document. Send requests to bsantin@TrentU.CA or send regular post to Brent Santin, 6 Jerome Crescent, Bramalea, Ontario, Canada, L6S-2H1. *************************************************************************** MISC *************************************************************************** M1. The Encyclopedia of Wood. ISBN: Color slides of hundreds of woods along with descriptions, warnings, common uses, and ratings of hardness, stiffness strength, and workability. Source unknown but Stewart Macdonald sells it & the Buffalo, NY public Library has a copy. ----------------------------------------------------------------- M2. Making and Playing Musical Instruments. by Jack Botermans, Herman Dewit and Hans Goddefroy. University of Washington Press, 1989 ----------------------------------------------------------------- M3. Making Folk Instruments in Wood. by Dennis Waring. Sterling Publishing, 1979 ISBN: ----------------------------------------------------------------- M4. Folk Instruments: Make Them and Play Them by Dennis Waring ISBN: 0-920534-06-6 This a book that shows how to make both instruments simple enough for children to make to more advanced instruments for the beginning instrument maker with some wood working experienc (e.g. Hammered Dulcimer, Celtic Harp) ----------------------------------------------------------------- M5. Experimental Musical Instruments PO box 784 Nicasio, CA 94946 415 662-2182 $24/year - 4 issues Its a really great journal... well worth the cost for anyone interested in new instruments of all type. The layout and art work are outstanding. =========================================================================== Supplies: ***** IMPORTAANT NOTE ******* The following addresses are accurate to the best of my knowledge. The fact that a particular buisness does or does not appear here should not be construed as any kind of recommendation, pro or con. Editorial comments after addresses were provided by submitters. This list is intended to save folks some leg-work. Please let me know if there are inacurracies in any of the information. ******************************* ----------------------------------------------------------------- GUITAR Stewart MacDonald's Guitar Shop Supply Athens OH (800)848-2273 Catalogs are free. Luthier's Mercantile PO Box 774 412 Moore Lane Healdsburg CA, 95448 (800)477-4437. (707)433-1823 Catalog $19.95 Their catalog is so full of information it is worth the $19.95 even if you never buy anything from it. Note: most of the non-catalog information is targeted towards builders of acoustic guitars. Martin Guitar: Guitar Makers Connection & The 1833 Shop Box 329 510 Sycamore Street Nazareth, PA 18064 (215)759-2837 (800)247-6931 KIT Factory San Diego, CA. See the classifieds in Acoustic Guitar mag or call information for the address ----------------------------------------------------------------- HARP Markwood Musical Strings 809 W. First St. Phoenix, OR 97535 (505)535-7700. Custom Strings. Markwood also does RELIABLE computerized string analysis on any harp whether real or in design phase. I have built several small harps using their harmonic curves and can attest to their accuracy. Robinson's Harp Shop 33908 Mount Laguna Drive Mount Laguna, CA 91948 (619) 473-8556 For strings, pins, sharping levers, plans, etc. Vermont Strings RD1 Box 8790 Waterbury Center, VT 05677 (802)244-8564 East coast affiliate to Robinson's. Musicmakers Kits Box 2117 Stillwater MN. 55082 612-439-9120 Here Inc. Rural route 4 Box 38 34000 205 Ave. Red Wing, MN 55066 612-423-4709 ----------------------------------------------------------------- HARPSICHORD Lark in the Morning 707-964-5569 Harpsicord kits from $1000 to $3000. Almost a hundred pages of instruments you never heard of (or thought no one else had) Zuckermann Harpsichords, Inc. 15 Williams St. Box 151 Stonington, CT 06378 (203) 535-1715 Hubbard Harpsichords 31 Union Ave Sudbury, MA 01776 (508) 443-3417 ----------------------------------------------------------------- ACORDIAN The Button Box Amherst, MA Castigione Detroit, MI ALAS Accordion-O-Rama 16th Street (or thereabouts) Manhattan NY,NY Hohner (you have to be a dealer. No retail) Richmond, VA For concertina parts I use Marcus Music in Wales. ----------------------------------------------------------------- MISC Timeless Instruments Box 51 Tugaske, Saskatchewan, CAN S0H 4B0 (306) 759-2042 Fax:(306) 759-2729 A & M Wood Specialty, Inc. 358 Eagle Street North Box 32040 Cambridge, Ontario, CANADA N3H 5M2 Ph. (519)653-9322 These people have everything! If you need exotic wood make a trip there. They close at 12am on saturdays though :( ----------------------------------------------------------------- FLUTE Shakuhachi (japaneese flute): Tai Hei Shakuhachi Monty H. Levenson P.O. Box 294, Willits, CA 95490 FAX 707.459.3434 The catalogue includes many books on everything from playing Japanese music to making the flutes. There are sources for bamboo and tools included. ----------------------------------------------------------------- ELECTRONICS PAiA (405) 340-6300 One neat example of the projects they offer is a MIDI finger drum kit for $99. There are 10 finger pads, one for each finger, which respond to taps like a MIDI drum and send pulse out to your pulse to MIDI converter! Is there a musician out there who DOESNT tap their fingers? They also offer most of the projects from Craig Anderton's book _electronics Projects for Musicians_ in kit form. =========================================================================== Where do I put the holes in a flute? Quite inexpensive flutes can be made (with very fine sound) from PVC hot water pipe --- the cold water pipe is too thin. For a pretty good approximation of where to place the holes measure from the embouchure (sp?) to the end of the pipe. Divide this distance by five. Mark the first fifth (from the open end) and the third fifth. divide this distance by five and mark every fifth. Drill the holes small and tune them by gradually enlarging them starting with the lowest. On this basis the third hole will be quite small and the second will be the biggest. I find that fudging the highest three holes down a little bit helps. The precise location of the holes will depend on the thickness of the materials, the diameter of the bore, and the nature of the embouchure (I gotta find out how that's spelled) some times it seems to be dependent on the day of the week. ------------------------------------------------------------------- Hey a REAL good idea is....instead of "thinking" where the holes should be, take a lagre vessel of water (deeper than the flute) and blow through to get basic pitch, then submerse the end piece, till you get to the next note (it will sound strange, but you will hear the tone) then mark it....and complete the scale....this method really works great if you are trying to make "exact-scales" from materials that are not uniform such as bamboo. This is a scale of A-flat-Maj Flute (piccolo) total length:14 1/2" width:7/8th" hole starting from mouth piece (not center of hole, but side closest to mouth end) 1st hole: 5 1/4" 2) 5 3/4" 3) 6 5/8" 4) 7 1/2" 5) 8 3/8" 6) 9 5/8" 7) 10 5/8" =========================================================================== How does a truss rod work? The rod is tapped at one end and anchored at the other (the other end may also be reverse tapped for a really efficient truss rod). Initially the rod is straight but it is pressed into a curved truss channel. The curve is concave facing the fingerboard (the middle of the channel is further from the fingerboard than the ends. The rod is then forced into the curved truss channel and held in place with a wood strip. The fingerboard is then attached. Fender's rear mounted truss channels work the same way but the rod is inserted into the back of the neck (harder to do IMHO). When the neck is complete the tapped end sticks out at the nut (or the end of the fingerboard in some instruments). A nut is screwed on to the tap. Now, think what will happen when the nut is tightened. The other end of the rod can not move so the rod will attempt to straighten itself. An easy way to see this is to hold a string slack with one end in each hand. Now move one hand away from the other, the string will straighten. In other words, the center of the string will move outwards. This is exactly the kind of movement that is necessary to straighten a neck contrary to string tension which is trying to make the rod *more* concave. If we go back to the example, pretend there is a force attracting your two hands (string tension). The string will become more slack and need to become *less* concave in order to regain its original curvature. Although there are several ways to mount a truss rod most of them involve a curved rod. Notice that the rod itself does little for the *stiffness* of the neck. It only provides a way to counter the force of string tension. A well built neck will only need the rod to be finger tight! If youre looking for stiffness remember that the rod can vibrate just as much as anything else in the neck; perhaps even more since it is not really attached to anything besides at each end. Imbedded steel or graphite bars or multiple laminated necks are the best bet for stiffness. ------------------------------------------------------------------- The compression type of truss rod exists, but is generally not effective when a warp becomes severe. The original type of adjustable truss rod developed by Gibson is indeed curved. A channel is routed in the center of the neck (before the fingerboard is glued on) that is deeper in the middle of the neck than at the ends. The truss rod is set in the channel and fixed at the body end, threaded at the headstock end. (The rod used to be encased in a flexible plastic tube to prevent binding with glue overflow that might fill the channel - I'm not sure this is done anymore) A fillet of hardwood is glued into the channel, pressing the rod into a curve. The neck is planed flat, the fingerboard applied etc. When the rod is tightened it tries to straighten out the curved channel, thus causing the neck to bow backward. There is a good cutaway drawing of this (as well as other designs) in Don Teeter's book "The Acoustic Guitar Adjustment, Care, Maintenance, and Repair." I have replaced these truss rods myself and used a similar design on my personal instrument. In my opinion it is still the best. (In my opinion, nobody has built a better mousetrap than those old spring mechanisms either. :-) =========================================================================== What frequencies are the notes of the standard diatonic scale? pick your starting frequency (e.g. 440 A) and keep multiplying by the 12th root of 2 until you have an octave's worth. Then you can get the other octaves by multiplying or dividing by powers of 2. ------------------------------------------------------------------- There are lots of possible frequencies, depending on what you use as your reference point (There is a scientific scale, using 256Hz as C), but probably the most common is the chromatic scale built around A=440Hz. If you have a good calculator, or a computer, calculate the 1/12th root of 2, which gives the frequency ratio of a halftone, and then start out by multiplying (or dividing) the 440 by that value. This gives you the next halftone up (or down) from A. Keep doing this, and by the time you reach 880Hz (or 220Hz), you will have an octave worth of frequencies. Acoustically-derived scales will be somewhat different, with the greatest difference being between D# and Eb. The chromatic note for these will be halfway between the two notes, which wind up at around 12 cents sharp and flat compsred to the chromatic (if my memory is correct). The old brass-reed English concertinas were so tuned, and you could hear a major difference between D# and Eb when they were sounded together, or even close in time. It sounds very nice in keys not too far from C, but as you go away from C, it eventually gets terrible. =========================================================================== Is there a way, given a string gauge, a tension, and a pitch that we can mathematically determine the strings length? How about functions for the other factors (given tension, pitch, & length what is the gauge? etc.)? The following is THE equation for EVERYTHING you desire (and then some): n * sqrt(T/u) f = ------------ 2L f = the frequency of a streched string (or wire) n = 1 for FUNDAMENTAL frequency (which is what we want) T = Tension in wire u = (actually a greek mu) mass per unit length of wire Solve this for T and we get T = 4 L^2 F^2 u The mass per unit length (mu) is defined as R A u = --- g R = (rho in greek) = density of wire material steel = 0.283 lb/in^3 brass = 0.310 lb/in^3 A = cross-sectional area of the wire (pi * r^2) or (pi * (d/2)^2) r = wire radius or d = wire diameter g = gravitational constant (32.2 ft/sec^2) This reduces to pi * (d/2)^2 * R * F^2 * L^2 T = ------------------------------ 96.6 (the 96.6 is (32.2 * 12 in/ft) / 4 ) so, for #8 steel wire (d = 0.020"), 16 in long, tuned to A (440 hz) it will be under 45.6 lbs tension! You will need to dig up a table of string #s to find the diameter (#6 = 0.016" #8 = 0.020" #10 = 0.024" #12 = 0.029") and other densities if you don't use steel or brass wire. ANY college physics book should also have these equations as well as the wire diameter table and the wire densities. I have used this MANY times to calulate the total tension in my Hammer Dulcimer I built (58 strings = 1.4 TONS!) to see why it was bending by 1/4" when I strung it. ---------------------------------------------------------------- Your very basic equation is l = 1/(2*f*r)*SQRT(T/(pi*d)) where: l=length (cm) f = frequency (hz) r = radius of string (meters) T = Tension (newtons) aka kg force (kg*meters/seconds^2) d = density (kg/meter^3) This is ok for roughing things out since you usually don't know things like the tension very precisely. The fun begins when you want to consider what radius to use for a wound string, what is the sounding length of the string as opposed to the bridge to nut or fret distance etc.... =========================================================================== What is the difference between Quarter sawn wood and Slab sawn wood? Most hardwood is slab-sawn. This is what you typically think of as the way a lumbermill cuts wood. The log is sawn into slabs from top to bottom. Slab sawing is an efficient way to cut up a log, but you end up with pieces that can warp, owing to the way the grain pattern runs. Quarter-sawing involves cutting the log *radially* abound the center. You get a grain pattern that minimizes warping, and a finer, more attractive grain pattern, too. But quarter sawing is wasteful compared to slab sawing, so the wood costs more. ---------------------------------------------------------------- A lot of times if you know what to look for you can get quarter sawn boards which were actually slab sawn. With a slab sawn log the pieces near the center of the log will be quarter sawn. Go to a *good* lumber yard and ask them to help you find a board with a radially sawn grain. ---------------------------------------------------------------- The easiest way to tell if a board is quartersawn is to look at the end of the board. Quartersawn boards have end grain that is perpendicular to the width of the board. (Martin, I believe, considers anything between 75 degrees and 90 degrees to be quartersawn.) Slab-sawn boards have end grain somewhere between 75 degrees and 0 degrees relative to the board's width. Here's a crude illustration showing the difference (viewing the end of the board): Quartersawn: ---------------------- |||||||||||||||||||||| ---------------------- Slab-sawn: ---------------------- ---------------------- ///////////////////// or ====================== ---------------------- ---------------------- =========================================================================== Where do the frets go? This is some simple C code I wrote that computes the locations of frets for any scale length. /*= Computes fret locations for any scale. = The syntax is: scale length [frets] = "length" is the scale length of the fingerboard. = It is given in any units (dont include the units). = The optional argument "frets" is the number of frets. = The default number of frets is 24. = Example: for a standard bass: "scale 34 24" or "scale 34" = = To compile it use: "cc -g -o scale scale.c" */ #include #define RULE 17.819 main(argc, argv) int argc; char *argv[]; { float scale, fromNut, offset; int frets, fret; /*==Get scale==================*/ if(argc < 2) { printf("Scale (cm): "); scanf("%f", &scale); } else sscanf(argv[1],"%f", &scale); /*==Get frets=================*/ if(argc < 3) frets = 24; else sscanf(argv[2],"%d", &frets); /*==Compute===================*/ fromNut=0.0; offset=0.0; for(fret=0; fret<=frets; fret++) { printf("Fret %d: \tFrom nut: %5.3f \tOffset: %5.3f\n", fret, fromNut, offset); offset = scale/RULE; fromNut = fromNut + offset; scale = scale - offset; } } ------------------------------------------------------------- The following is a simple Basic programme for finding the approporiate fret spacing for guitars (or any other freted instrument). It is the easiest way that I know of to get the exact measurements, to a greater degree of accuracy than you can mark out or cut. The program comes from a back issue of Guitar Maker (the journal for the Association of Stringed Instrument Artisans in the US) and was written by Bill Cumpiano. 90 DIM X(45) 100 REM 110 REM (GET THE FRET CONSTANT) 120 REM 130 K = 17.818 140 PRINT "Fret constant is "; K; " is this ok"; 150 INPUT A$ 160 IF ((A$ = "Y") OR (A$ = "y") OR (A$ = "yes") OR (A$ = "YES")) THEN GOTO 210 170 INPUT "What constant would you like"; K 180 IF ABS(K - 17.818) <= .3 THEN GOTO 210 190 PRINT "Invalid constant" 200 GOTO 170 210 REM 220 REM get number of frets 230 REM 240 INPUT "How many frets"; F 250 IF ((F >= 12) AND (F <= 45)) THEN GOTO 280 260 PRINT "Inappropriate number of frets" 270 GOTO 240 280 F = F + 1 290 REM 300 REM (get scale length) 310 INPUT "What is the scale length"; S 320 IF ((S >= 200) AND (S <= 750) THEN GOTO 350 330 PRINT "Inappropriate scale length" 340 GOTO 310 350 REM 360 REM (Calculate fret positions) 370 REM 380 PRINT 390 PRINT 400 X(0) = 0 420 FOR I = 1 TO F 430 X(I) = (S - X(I - 1)) / K + X(I - 1) 440 NEXT I 445 F$ = "Fret ## ##.## " 450 N = F - INT(F / 2) 460 FOR I = 1 TO N 470 PRINT USING F$; I; X(I); 480 IF I + N <= F THEN PRINT USING F$; I + N; X(I + N); 490 PRINT 500 NEXT I 510 PRINT 520 PRINT 530 END The value [17.818] come from mathematical manipulations involving the 12th root of 2. This is to give equal temperment in a 12 (semitone) scale, with similar named notes an octave apart (ie double or half the frequency). ------------------------------------------------------------- Hi, I've built 4 so far, all to homemade plans. For fret spacing I use the following Fortran program missing out the inappropriate frets. program fret C integer*2 i,s real*4 l,r,d C r = 0.5**(1.0/12.0) read(5,'(i4)') s write(6,'(x,a,i3,a)') 'Open string length ',s,'mm.' write(6,'(x)') write(6,'(x,a)') 'Distance from nut to fret' write(6,'(x)') l = s do i = 0, 29 d = l - (l*(r**i)) write(6,'(x,i2,x,f10.2)') i,d end do end Just supply the open string length. I use a moveable bridge which usually needs placing a few mm beyond it's theoretical position to take into account the sharpening effect caused by the increase in tension of a fretted string. =========================================================================== Why dont the bridge saddles line up? The derivation of the ideal formula that relates string length, mass/unit length, tension, and frequency involves at least two unrealistic assumptions: First, it is assumed that the string does not have to be stretched to push it down to the fret. Second, it is assumed that the string has zero bending stiffness. Consider the difference between a piece of cooked spaghetti (low bending stiffness) and a steel string (higher bending stiffness). Then there are (at least) two phenomena that cause a string to go sharp when it is fretted: 1) The string must be stretched a little to push it down to the fret. This increases the tension in the string and thus makes the fretted string go sharp. 2) The string's finite stiffness makes the "effective" vibrating length of the string shorter than its "measured" length. This makes a given string's frequency at a given tension and length higher than what would be predicted by the ideal formula. In addition, the stiffness of a string makes the partials (harmonics) successively more out of tune with the fundamental the further up the harmonic series you go. This is because the stiffness shortens the effective length of the partials (1/2, 1/3, 1/4, ...) more and more, the further up the harmonic series you go. So while it would be possible, for example, to replace the low E on a steel-string acoustic guitar with a plain string with the same tension, this string would a) need to be intonation-compensated even more than the wound string, and b) sound pretty bad due to the partials being out-of-tune with the fundamental. There should be a dimensionless parameter defined something like this: (d^p)*(E^q) ----------- (T^r)*(L^s) (d = string diameter E = string material modulus of elasticity T = string tension L = string length p, q, r, s = exponents necessary to make the expression dimensionless) which should be kept _less_than_ some value in order to produce a string that doesn't need "too much" intonation compensation and whose partials are not "too far" out of tune with the fundamental. Exponents p, q, r, s that will make this parameter dimensionless are d^3 E ----- T L This will work with any consistent set of units, e.g., d in ft, E in psf, T in lb, L in ft. For a 25.4" scale, 0.012" steel string tuned to E330, this parameter is about 0.088. For a 0.016" dia B-string, it is about 0.21. Maybe greater than about 0.2 - 0.25, we would want to start wrapping the strings to achieve greater mass per unit length without adding stiffness? (Using a wrapped string vs. a plain string for a given pitch/tension/length decreases d, which is just the core diameter, while keeping E, T, and L constant, thus decreasing the value of the dimensionless parameter.) Has anyone else out there heard of this dimensionless parameter? Does my formulation make sense? Does anyone have properties for nylon strings? And would like to do the calculation for the unwound 1st & second strings? There is at least one other phenomenon I can think of that is unaccounted for in the derivation of the ideal string equation: the string tension is assumed constant. This assumption is bad for large vibrations of low-tension strings. To demonstrate this, tune a string way down (e.g., tune a steel-string acoustic (light gauge) sixth string down to C. Then pluck it real hard. You should hear a tone that starts high and descends in pitch. Somehow the "average tension" of the string is being increased by the large amplitude of the vibration. As the amplitude dies down, the increase in the "average tension" decreases, causing the pitch to settle down to a constant value. ----------------------------------------------------------------------- Q) I want to play around with piezoelectric transducers, but I can't afford to buy a really expensive pickup system. A) You can get cheap transducers from many places, including Radio Shack and All Electronics (1-800-826-5432). They cost less than a dollar each in small quantities (~10). The inexpensive piezos often have a very high output level, so you don't need a preamp for them; however, a high-impedence FET amplifer will allow you to adjust the volume, mix multiple piezos, and will make the output more even. ----------------------------------------------------------------------- Q) How can I make a magnetic pickup to experiment with? A) A pickup consists of a solid metal core with a magnet at one end, and surrounded by windings of wire. The cheapest & easiest way to make a pickup is to buy some surplus relays or solenoids. File or cut both ends of the core so that it is nearly flush with the coil; then, attach a magnet to one end of the core. The end without the magnet can then be placed near a vibrating piece of metal* and the 2 wires from the coil will output a signal which can be amplified. * = The metal must be attracted to magnets for this to work; I forget the name of this property. [try ferromagnetic. Eric Nicolich] ----------------------------------------------------------------------- Q) I can't afford to buy rosewood or ebony for my fingerboard. Besides, this is my first project and I don't want to butcher a lot of good wood. What else can I use? A) Many instrument makers use pau ferro. It is less expensive than either rosewood or ebony, and it is very easy to work. However, it can irritate your skin (<- massive understatement, and I have several square feet of rash to attest to this!), so be sure to cover up as much as possible before making a lot of dust from it while sanding or sawing.