Posted on June 6, 2024May 14, 2025 by Dale Phillips Google Calculator and the Guitar’s Magic Number Google Calculator and the Guitar’s Magic Number by William Leirer Originally published in American Lutherie #96, 2008 Since the frequency of the octave note at fret 12 is two times the frequency of the open string, the fret positions can be determined by finding a number that can be multiplied by itself 12 times to get 2. That’s the guitar’s magic number: the 12th root of 2. In one form or another, it is a part of every calculation related to scales, fret placement, intonation, compensation, and much more. When Google perceives an entry in its search field to be math, it switches from search mode to calculator mode and displays the answer. Any calculator can solve a math problem, and there are plenty of online fret calculators. But with Google Calculator we can view the entire equation at once and see the effect of substituting one part at a time, helping us to understand the “why” behind the numbers. Become A Member to Continue Reading This Article This article is part of our premium web content offered to Guild members. To view this and other web articles, join the Guild of American Luthiers. Members also receive 4 annual issues of American Lutherie and get discounts on products. For details, visit the membership page. If you are already a member, login for access or contact us to setup your account.
Posted on August 11, 2021May 16, 2025 by Dale Phillips Taking the Guitar Beyond Equal Temperament Taking the Guitar Beyond Equal Temperament by Don Musser Originally published in American Lutherie #30, 1991 and Big Red Book of American Lutherie Volume Three, 2004 If someone were to tell you that the simple C chord you just played on your perfectly intonated, handmade guitar was in fact significantly out of tune with itself, you might have a few doubts and perhaps some curiosity about just what he was talking about. If that person were Mark Rankin and he happened to have his little Martin set up with the just intonation, key-of-C fretboard, and you compared a C chord on that guitar to the C chord on your guitar, instead of doubts and curiosity you would have something else: the beginning of a revelation, a revelation not only about the guitar itself, but about the foundation of the music we play on it. Back in 1987, David Ouellette, a Eugene, Oregon musician for whom I had built several guitars in the early 1980s called and wanted a new, unconventional instrument built. It was to be a special guitar with magnetic interchangeable fretboards having staggered frets set up for alternative tunings of the scale steps within the octave. The standard guitar fretboard we all play on is based on the equal-tempered scale where the octave is divided into twelve equal half-step intervals. This equal division of the octave is good in that it allows modulation from key to key without intolerable dissonance. Its drawback, though, is that the scale intervals are tempered, i.e., harmonically inaccurate and slightly out of tune with one another. Become A Member to Continue Reading This Article This article is part of our premium web content offered to Guild members. To view this and other web articles, join the Guild of American Luthiers. Members also receive 4 annual issues of American Lutherie and get discounts on products. For details, visit the membership page. If you are already a member, login for access or contact us to setup your account.
