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The Helmholtz Resonance

The Helmholtz Resonance

A Brief and Not-Too-Technical Introduction to the History and Theory of the Lowest Sound-Producing Mode, and Some Practical Considerations for Instrument Designers

by R.M. Mottola

Originally published in American Lutherie #82, 2005 and Big Red Book of American Lutherie Volume Seven, 2015



Research in physics and acoustics of stringed instruments shows us the mechanism by which sound is produced by those instruments. The plates of the instruments and the air inside vibrate in various patterns, each pattern producing sound in a range around a certain frequency. Each of these patterns can be considered to be a resonator, each with its own characteristics. Some of these resonators exist as modes of vibration of different areas of the plates of an instrument, and some are modes of vibration of the air inside the instrument.

One of the air resonators is composed of the mass of air inside the instrument and the mass of air within and around the soundhole. The natural frequency of this resonator is near the lowest note that an instrument can make. It is generally labeled the A0 resonance, the letter A standing for the word “air” and the numeral 0 indicating that this is the first in a series of air resonances. This resonance is also referred to as the so-called Helmholtz resonance. Understanding how this resonance works in stringed instruments is not difficult, particularly given a historical perspective. Complete understanding involves some math, but a practical understanding can be had without it. Therefore, I am putting off presenting the formulae in the main article and have included them in a sidebar.

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The Helmholtz Formula

The Helmholtz Formula

by R.M. Mottola

Originally published in American Lutherie #82, 2005 and Big Red Book of American Lutherie Volume Seven, 2015



The resonant frequency of a mass spring resonator can be determined by the following formula:

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Product Review: Colorado Soft Cases

Product Review: Colorado Soft Cases

by R.M. Mottola

Originally published in American Lutherie #75, 2003 and Big Red Book of American Lutherie Volume Seven, 2015



The item reviewed in the following paragraphs was purchased by the author at full price through normal sales channels. A draft of this review was sent to the manufacturer/seller prior to publication so that any factual errors could be corrected.


Colorado Soft Cases

High-quality soft instrument cases (gig bags) and case covers are readily available for most standard-size instruments. There are dozens of manufacturers of these off-the-shelf items, and it is pretty easy to find bags for your instruments in a wide range of price and quality. Since the inside dimensions of soft cases are, well, softer than those of hard cases, it is even likely that you can make an off-the-shelf case fit a nonstandard instrument, at least if the instrument is not too nonstandard. But if you’ve got something way out of the ordinary, you’ll need a custom-made bag for it. It is probably safe to say that any bag manufacturer will make cases to your specs if you order enough of them. If you make one-of-a-kind instruments and need just one though, the number of manufacturers that are willing to accommodate your needs drops precipitously. Colorado Case of Fort Collins, Colorado, (coloradocase.com) is one case company that does make custom cases in any quantity, and their cases are the subject of this review.

First, a word or two about soft cases. Why would you want to use a soft case in the first place, when a hard case offers considerably better protection? Probably the most compelling reason is that your customers want the option. In my experience this is particularly the case if the instrument in question is either a solidbody instrument or is particularly large, like an upright bass. Solidbody instruments are pretty robust to begin with and so protection from scratches and abrasions may be all the user wants out of a case. Really large acoustic instruments are no less delicate than their smaller counterparts, but the weight of a large hard case can sometimes compel a user to trade off some amount of protection for some reduction in weight.

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Plywood

Plywood

Some Observations and a Report on the Use of Laminated Wood in Lutherie

by R.M. Mottola

Originally published in American Lutherie #73, 2003 and Big Red Book of American Lutherie Volume Seven, 2015



Considering that most stringed instruments are made in factories by large companies, and that the instruments at the low-priced end of these companies’ product lines are sold in great quantity, and that these low-priced instruments are frequently constructed of laminated wood (i.e., plywood), it is not at all unreasonable to assume that most of the instruments made are probably constructed from plywood. Further, as plywood is a physically robust material, it may be reasonable to conclude that the majority of the stringed instruments extant are made of plywood. For some reason, plywood is associated only with cheap instruments, although there are some exceptions. A cursory review of the lutherie literature reveals not too much in the way of scientific experimentation that would change that association, but it does provide a number of interesting anecdotes and observations that may indicate that plywood could be a far more useful material for high-end instruments than generally thought.

The very first issue of The Guild of American Luthiers Newsletter (Vol. 1 #1) contains a letter by R.E. Bruné describing the construction of classical guitar ribs made of rosewood/maple laminate, a construction which the author claims to increase volume. In his review of a harp kit in American Lutherie #69 (Big Red Book of American Lutherie Volume Six), John Calkin compared the tone of two dissimilar harps, one with a solid top and the other with one of plywood, and found the plywood one to sound “bolder and a bit louder.” An interesting observation can be found in the bible of flattop guitar making, Cumpiano and Natelson’s Guitarmaking: Tradition and Technology. They opine that lateral stiffness of a guitar top will greatly influence the tonal response of the instrument and state that superior lateral stiffness will allow the top to be worked thinner, thus reducing mass. Now, they’re not talking about plywood here per se. A top made of, say, three-ply spruce with the center ply oriented at 90° to the outside plies should be stiffer across the grain than a solid top of similar thickness. Kevin B. Reilly described small-bodied guitars he made using birch ply for the tops and backs in AL#61 (BRBAL6), and found these instruments to have considerable volume and sustain.

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Fall Collection 2024

Articles Online
Fall Collection 2024

GAL Members – Login first before clicking on article titles to read the full articles.
Not a member? You can join or renew here.

 

Radiation from Lower Guitar Modes by Graham Caldersmith (1985)
▪ Caldersmith discusses the efficiency and pattern of sound radiation in the classic guitar produced by the four lower resonance modes, which he calls monopole, cross dipole, long dipole, and tripole.

Inside Pacific Rim Tonewoods by Steve McMinn (1993)
▪ McMinn’s lutherie wood business has turned out to be a pretty big deal. Here we gain perspective by seeing it at the very beginning.

The Great White Sitka by Jeffrey R. Elliott (1993)
▪ Holy Moby Spruce! How does one hack a log that’s eleven feet wide into 4000 guitar tops? Very carefully! By the way, this is a log that Steve McMinn rescued from the pulp mill.

Meet the Maker: Bernard Millant by Jonathon Peterson (2006)
▪ Millant is a violin maker, a bow maker, an appraiser, an author, and a man of high repute within the violin world. The depth of training behind many old-school fiddle people will astonish most guitar makers, and it makes for entrancing reading.

Meet the Maker: Dmitry Zhevlakov by Federico Sheppard (2007)
▪ This is not only the story of a Russian luthier who also makes beautiful rosettes for other builders, but is another example of how the Internet has changed the world — in this case for better.

Aluminum Sonatas: A Brief History of Aluminum Stringed Instruments in the Last 120 Years by James Condino (2007)
▪Every luthier knows how fickle and finicky the market is, so it’s no wonder that musical instruments made of aluminum didn’t catch on. Examined here are a violin, a mandolin, and a pair of bass viols. Fun stuff!

Mechanical Compliance for Soundboard Optimization by David Hurd (2007)
▪ Hurd believes that the fastest way to great instruments is science, and it’s hard to argue with such a rational man. His jigs measure the deflection of top plates while under tension, and once he carves the top and braces to the numbers he wants, he’s done. This could be math heavy, but he offers an Internet spread sheet to ease the pain.

Construction of the Colombian Tiple by Anamaria Paredes Garcia and R.M. Mottola (2007)
▪ Cross a 12-string flattop with a classical guitar and you get the Colombian tiple. The tiple has four courses of three steel strings, but on the inside, it’s a classical. Follow Alberto Paredes as he builds the instrument in this photo tour. See GAL Plan #51.

Meet the Maker: Mervyn Davis by Rodney Stedall (2007)
▪ Davis’ South African upbringing inspires a wonderful decorative sense in his instruments. He’s built a ton of different stuff but may end up best known for his wildly unique modular guitars called Smooth Talkers.

Cricket: A Reclaimed Salvage Recovery by James Condino (2007)
▪ Condino’s mandolin is made from recycled materials, mostly Douglas fir and katalox. It is unique and beautiful, and the story behind it is pretty cool, too.

Grading on the Curves: Fitting Bars and Bridges on Archtop Guitars by Steve Andersen (2007)
▪ This is a very detailed look at how a notable builder of archtop guitars fits tone bars and bridges to his instruments.

The Venezuelan Cuatro by Aquiles Torres (2008)
▪ Traditionally, this instrument is a small 4-string guitar with 14 frets clear, no frets over the body, a flush fretboard, and a large veneer tap plate. Note that the cuatro built for the article has 17 frets clear of the body. See GAL Plan #58.

The MacRostie Mandolin Deflection Jig by Don MacRostie (2008)
▪ MacRostie’s clever jig measures the top deflection of a carved mandolin under string load at any stage of its construction. It is a valuable tool within the reach of any luthier.

The “Corker” Guitar: A Sideport Experiment by Alan Carruth (2008)
▪ Carruth built a classical guitar with many small ports drilled in the side. By plugging the ports in various combinations he investigated the usefulness and physics behind them. Though this guitar did not make a believer out of him, he admits that his results are somewhat inconclusive.

Electric Guitar Setup by Erick Coleman and Elliot John-Conry (2009)
▪ Two disciples of Dan Erlewine explain the latest techniques of setting up the electric guitar. All the details and specs are there, as well as a bit of philosophy.

Dulcimer 101 by John Calkin (2009)
▪ Dulcimers are needlessly maligned and in need of advocates, and the author is a strong one. Tools and jiggery are kept to a minimum to make construction of this entry level instrument as accessible as possible.

The Guitar as a Structure and Some Practical Information on Bracing by James Blilie (2009)
▪ A structural engineer and guitar builder sees the guitar as a thing buffeted by forces and stresses.

Total Flame Out: Retopping a Harp Guitar by Harry Fleishman (2009)
▪ Harry replaces the failed soundboard on a complicated instrument with as little refinishing and other stress as possible.

Strings: The (Often) Forgotten Accessory by Fan Tao (2010)
▪ D’Addario's resident scientist Fan Tao helps us understand string issues in relation to custom instruments and customized tuning.

Practical Acoustics by Michael Cone (2010)
▪ Cone describes his advanced apparatus and method for acoustically testing classical guitars.

Meet the Maker: James Ham by Roger Alan Skipper (2010)
▪ Ham operates from a shop in Victoria, B.C. where he repairs and restores violin family instruments and constructs world class double basses.

It’s All About the Core or How to Estimate Compensation by Sjaak Elmendorp (2010)
▪ Mathematics and parameters used to address the problem of string compensation estimation.

Articles Online
Fall Collection 2024

Radiation from Lower Guitar Modes by Graham Caldersmith (1985)
▪ Caldersmith discusses the efficiency and pattern of sound radiation in the classic guitar produced by the four lower resonance modes, which he calls monopole, cross dipole, long dipole, and tripole.

Inside Pacific Rim Tonewoods by Steve McMinn (1993)
▪ McMinn's lutherie wood business has turned out to be a pretty big deal. Here we gain perspective by seeing it at the very beginning.

The Great White Sitka by Jeffrey R. Elliott (1993)
▪ Holy Moby Spruce! How does one hack a log that’s eleven feet wide into 4000 guitar tops? Very carefully! By the way, this is a log that Steve McMinn rescued from the pulp mill.

Meet the Maker: Bernard Millant by Jonathon Peterson (2006)
▪ Millant is a violin maker, a bow maker, an appraiser, an author, and a man of high repute within the violin world. The depth of training behind many old-school fiddle people will astonish most guitar makers, and it makes for entrancing reading.

Meet the Maker: Dmitry Zhevlakov by Federico Sheppard (2007)
▪ This is not only the story of a Russian luthier who also makes beautiful rosettes for other builders, but is another example of how the Internet has changed the world — in this case for better.

Aluminum Sonatas: A Brief History of Aluminum Stringed Instruments in the Last 120 Years by James Condino (2007)
▪ Every luthier knows how fickle and finicky the market is, so it’s no wonder that musical instruments made of aluminum didn’t catch on. Examined here are a violin, a mandolin, and a pair of bass viols. Fun stuff!

Mechanical Compliance for Soundboard Optimization by David Hurd (2007)
▪ Hurd believes that the fastest way to great instruments is science, and it’s hard to argue with such a rational man. His jigs measure the deflection of top plates while under tension, and once he carves the top and braces to the numbers he wants, he’s done. This could be math heavy, but he offers an Internet spread sheet to ease the pain.

Construction of the Colombian Tiple by Anamaria Paredes Garcia and R.M. Mottola (2007)
▪ Cross a 12-string flattop with a classical guitar and you get the Colombian tiple. The tiple has four courses of three steel strings, but on the inside, it’s a classical. Follow Alberto Paredes as he builds the instrument in this photo tour. See GAL Plan #51.

Meet the Maker: Mervyn Davis by Rodney Stedall (2007)
▪ Davis’ South African upbringing inspires a wonderful decorative sense in his instruments. He’s built a ton of different stuff but may end up best known for his wildly unique modular guitars called Smooth Talkers.

Cricket: A Reclaimed Salvage Recovery by James Condino (2007)
▪ Condino’s mandolin is made from recycled materials, mostly Douglas fir and katalox. It is unique and beautiful, and the story behind it is pretty cool, too.

Grading on the Curves: Fitting Bars and Bridges on Archtop Guitars by Steve Andersen (2007)
▪ This is a very detailed look at how a notable builder of archtop guitars fits tone bars and bridges to his instruments.

The Venezuelan Cuatro by Aquiles Torres (2008)
▪ Traditionally, this instrument is a small 4-string guitar with 14 frets clear, no frets over the body, a flush fretboard, and a large veneer tap plate. Note that the cuatro built for the article has 17 frets clear of the body. See GAL Plan #58.

The MacRostie Mandolin Deflection Jig by Don MacRostie (2008)
▪ MacRostie’s clever jig measures the top deflection of a carved mandolin under string load at any stage of its construction. It is a valuable tool within the reach of any luthier.

The “Corker” Guitar: A Sideport Experiment by Alan Carruth (2008)
▪ Carruth built a classical guitar with many small ports drilled in the side. By plugging the ports in various combinations he investigated the usefulness and physics behind them. Though this guitar did not make a believer out of him, he admits that his results are somewhat inconclusive.

Electric Guitar Setup by Erick Coleman and Elliot John-Conry (2009)
▪ Two disciples of Dan Erlewine explain the latest techniques of setting up the electric guitar. All the details and specs are there, as well as a bit of philosophy.

Dulcimer 101 by John Calkin (2009)
▪ Dulcimers are needlessly maligned and in need of advocates, and the author is a strong one. Tools and jiggery are kept to a minimum to make construction of this entry level instrument as accessible as possible.

The Guitar as a Structure and Some Practical Information on Bracing by James Blilie (2009)
▪ A structural engineer and guitar builder sees the guitar as a thing buffeted by forces and stresses.

Total Flame Out: Retopping a Harp Guitar by Harry Fleishman (2009)
▪ Harry replaces the failed soundboard on a complicated instrument with as little refinishing and other stress as possible.

Strings: The (Often) Forgotten Accessory by Fan Tao (2010)
▪ D'Addario's resident scientist Fan Tao helps us understand string issues in relation to custom instruments and customized tuning.

Practical Acoustics by Michael Cone (2010)
▪ Cone describes his advanced apparatus and method for acoustically testing classical guitars.

Meet the Maker: James Ham by Roger Alan Skipper (2010)
▪ Ham operates from a shop in Victoria, B.C. where he repairs and restores violin family instruments and constructs world class double basses.

It’s All About the Core or How to Estimate Compensation by Sjaak Elmendorp (2010)
▪ Mathematics and parameters used to address the problem of string compensation estimation.