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The Truth about Temperaments

The Truth about Temperaments

by Edward Kottick

originally published in Guild of American Luthiers Quarterly Volume 12, #2, 1984 and Big Red Book of American Lutherie Volume #1, 2000



There is a good deal of misinformation in print about consonance, dissonance, scales, harmonics, intervals, tuning, and temperaments. Even textbooks and scientific journals have gotten these subjects wrong, and I hope to correct the situation.

Let us begin with the terms “consonance” and “dissonance.” These words have two separate sets of meanings, one musical and psychological, the other acoustical and physical; and they are often confused. From the musical point of view a dissonance is a combination of tones which, dictated by usage, projects a quality of restlessness, motion, direction, or instability. Dissonances want to go somewhere; that is, they want to resolve to consonances, which have, of course, the opposite effect. Consonances are combinations of tones to which we ascribe the qualities of restfulness, stability, and a feeling of arrival. Note that I have described the character of these terms as something dictated by usage, rather than as qualities inherent in the combination of tones. Since around 1450 (the beginning of the Renaissance) major and minor thirds and sixths, perfect fourths, fifths, and octaves have been considered consonances, although a distinction is made between perfect consonances (fourths, fifths, and octaves) and the others, which are imperfect consonances. Every other combination of tones is considered dissonant, including the fourth if it appears above the lowest sounding note.

Music needs both consonance and dissonance. Without the latter it would be bland, dull, and lacking in direction. Although we may not think of composers such as Palestrina, Bach, and Chopin (to pull some names out of the air) as dissonant composers, there is an enormous amount of dissonance, as we just defined it, in their music. Furthermore, a dissonance is a dissonance only if we all say so. In the music of John Phillip Sousa a major chord with an added sixth (which makes a dissonant second to the fifth) is a dissonance; but in a jazz style that same combination of tones is treated as a consonance and is perceived in that way. In polyphonic music (music of more than one part) of the Middle Ages the third was considered dissonant, but around 1450 it began to be perceived as a consonance. This is an apparent contradiction only if the interval itself is considered in vacuo; but in the context of the music, medieval composers treated thirds and sixths as unstable combinations that needed to be resolved to perfect consonances, while Renaissance composers, and all those who followed up to the 20th century, considered thirds and sixths consonant and the building blocks of music.

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Meet the Maker: Norman Pickering

Meet the Maker: Norman Pickering

by N.P., with Barbara Goldowsky

previously published in American Lutherie #95, 2008



Norman Pickering does not understand the concept of retirement. He celebrated his ninety-second birthday on July 9, 2008, and he is still immersed in studying the properties of violin, viola, and cello bows. This is a logical follow-up to his lifelong study of the acoustics of bowed instruments, as a player, maker, and scientist.

Though musical acoustics is his overriding passion, there have been lengthy, but fascinating detours along the way into fields as various as medical ultrasound, aircraft instrument design, and his most famous invention, the Pickering phonograph tonearm and cartridge.

Rather than trying to condense his multiple careers and achievements into a question-and-answer interview, Norman agreed to share his life story — so far — in an essay he wrote after moving to our current home in East Hampton. I think AL readers will enjoy it. With characteristic modesty, he calls it simply “Biography.”

— Barbara Goldowsky

I was born in 1916 in a small fishing and farming town where both sides of my family had lived for at least three generations. Just at that time it was on the way to being submerged in the borough of Brooklyn by development and road building. By the time I was seven years old it was no longer the integrated semi-isolated village my parents and grandparents had known.

My mother’s family were farmers and my father and his father were engineers. My future education was decreed almost from birth: I would follow my father’s plan for me. And so I did; after a happy and successful time in grammar and high school, I entered Newark College of Engineering and finished in 1936, a few weeks before my twentieth birthday. I enjoyed engineering, but found that my interest in music was much too strong to be ignored.

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Herr Helmholtz’ Tube

Herr Helmholtz’ Tube

by Mike Doolin

previously published in American Lutherie #91, 2007

See also,
“There’s a Hole in the Bucket” by Cyndy Burton
“Sideways” by John Monteleone
“Three Holes are Better than One” by Robert Ruck



Design innovator Mike Doolin tried an interesting experiment. Mike’s guitars have the distinctive double-cutaway feature and they don’t lend themselves to a port up in the neck/cutaway region for reasons of underlying structure. So Mike put one in the lower bout and very unexpectedly found his Helmholtz resonance had raised something like a major third. He felt that compromised the responses of the guitar. His solution was to “tube it.”

The side was ported before I assembled the guitar. After gluing the back on, I realized the change in the Helmholtz when I tapped on the guitar with the port open. It seemed obvious that a shift of a major third up was going to radically change the sound of the guitar, probably killing most of the bass response. I knew that ports in bass reflex speakers are often tubes, where the longer the tube the lower the resonant frequency. I also knew that the tube could be either inside or outside the box. So I initially held a roll of toilet paper against the port, letting the cardboard core of the roll form a tube that extended the port. That dropped the main air resonance back down, showing me that I was on the right track. Then I turned a tube of wood on my lathe to fit the hole and experimented with the length until the air resonance moved less than a half-step with the port closed or open. I recall the port being 1 1/4" in diameter and the tube being about 2 1/4" long, but that’s just from memory.

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The Colombian Andean Bandola

The Colombian Andean Bandola

by Luis Alberto Paredes Rodríguez and Manuel Bernal Martínez

previously published in American Lutherie #96, 2008



The Colombian Andean bandola is a transcultural product similar to plectrum-played antecedents from Asia and Europe. It is a 12-string, 6-course soprano instrument with “flat” top and back, and is the solo melodic instrument in the Colombian Andean quartet, which consists of two bandolas, a tiple (see Big Red Book Volume Seven, previously published in AL#82), and a classical guitar.

The name “bandola” comes from the old Persian-Arabic word pandura. Derived from the name of the European lute, the word refers to a great variety of instruments of medium and high register with melodic functions. The direct ancestor of the bandola is the guitar through the Spanish bandurria and the soprano guitars, and which after taking its form in Colombia during the 19th and 20th centuries, continues to undergo transformations in its morphology and usage.

The Colombian Andean bandola has two developmental lineages: on one hand, the denomination line which makes reference to its name, and on the other, the construction line which makes reference to its morphological features (Bernal, 2003). The name of the bandola comes from the pandura (known since the 10th century) following the European lute, and one of its families known as the “mandoras family.” These 4- to 6-course instruments with thin bodies had a variety of pitches (a mixture of perfect fourths and fifths) and scale lengths ranging between 37CM and 42CM. By the year 1700, the mandolines emerged in Italy when the size of the mandola was reduced, prevailing and persisting in Italy in two different models: the Milanese mandoline with a thin, slightly arched body, and six courses of either gut or metal strings tuned in perfect fourths; and the Neapolitan mandolin with a bowl back body, a cranked (bent) soundboard just where the bridge is placed, four courses of metal strings tuned like a violin, and strings fastened to the end of the body by way of a tailpiece. The scale for both models is about 32CM to 34CM. In the 18th century, mandolins began to be manufactured with flat or slightly arched sides and back, especially in France, Germany, and Portugal.

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Letter: Circles in Classical Violin Design

Letter: Circles in Classical Violin Design

by Jim Blilie

Originally published in American Lutherie #89, 2007



Hi Tim,

I’m sure Michael Darnton has infinitely more experience with violin design and a much more sensitive eye for the form of violins than I do (See The Power of Circles). That being said, I was really bothered by his article.

Mr. Darnton writes that his theory of circles in the design of classic Cremonese violins seems to be the only one that will produce aesthetically pleasing shapes. I have no doubt that circles were used extensively in the design of violins, since they are much easier to draw than parabolic, hyperbolic, or elliptical curves. But he goes on to say that essentially all the extant violins of the height of the Cremonese school do not follow his plan. He posits various reasons for this, but in engineering, if the data don’t match your theory, you go back to the drawing board and find a new theory!

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