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\viewkind4\uc1\pard\f0\fs28 A "Just Intonation" issue with some tunings\par
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\f1 Some very popular tunings ... utilize the root, 2nd, 5th and 6th notes together.\par
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This sets up a "problem" when tuning the steel guitar using "Just Intonation"\par
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Basically a tuning with the 1, 2, 5 & 6 notes in it ... cannot be made "\b beatless\b0 ".\par
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EX: E13/9 (lo to hi) E F# G# B C# E\par
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The F# note can't be in tune with B and the C# at the same time ... somethings gonna beat ... . \par
\f0 In the key of E ... the following deviations for "Just Intonation" from "Equal Temperament" is as follows:\f2\fs24 \par
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E = root = 0 cents\f2\fs24 \par
\f0\fs20 F# = 2nd = + 4 cents sharp\f2\fs24 \par
\f0\fs20 G# = 3rd = -14 cents flat\f2\fs24 \par
\f0\fs20 A = 4th = - 2 cents flat\f2\fs24 \par
\f0\fs20 B = 5th = + 2 cents sharp\f2\fs24 \par
\f0\fs20 C# = 6th = -16 cents flat\f2\fs24 \par
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Heres the "problem"\f2\fs24 \par
\b\f0\fs20 F# is the fifth of B\b0 ... 5ths need to be +2 cents sharp of their ET value to fit in with their roots overtone series ... so tuning the F# to the B ... in this particular tunin' ... will put that F# + 4 cents sharp ... \par
Why ... \f2\fs24\par
\f0\fs20 Because the B is already +2 cents sharp ... because its the 5th of E... so (+2) + (+2) = +4 ... exactly where it needs to be to fit in with the root E overtone series ...\f2\fs24 \par
\f0\fs20 So far so good ...\f2\fs24 \par
\f0\fs20 The problem is ...\b F# is the fourth of C# \b0 ... so if you tune your F# to the C # ... it needs to be -2 cents flat ... 4ths need to be - 2 cents flat of their ET value to fit in with their roots overtone series.\f2\fs24 \par
\f0\fs20 Since C# is already the sixth of E (-16 cents flat) ... that would put the F# ... -18 cents flat of its ET value.\f2\fs24 \par
\f0\fs20 There's the problem ... to get F# to "fit in" the key of E and agree with E's overtone series and the fifth B ... it needs to be +4 cents sharp.\f2\fs24 \par
\f0\fs20 But to "fit in" with the C# in this particular tuning ... it would have to be -18 cents flat.\f2\fs24 \par
\f0\fs20 Strumming E, F#, B and C# ... will produce a mess of nasty beats.\f2\fs24 \par
\f0\fs20 Most folks that use this E13/9 tuning ... tune the second (F#) to the fifth (B) ... and the sixth (C#) gets tuned to third (G#) ... \f2\fs24\par
\f0\fs20 And the player just avoids hitting the F#, B and C# ... together.\f2\fs24 \par
\f0\fs20 Or you could just tune up "Equal Temperament" ... ha, ha\f2\fs24 \par
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