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Dante Rosati
Arbor Low for 21-Tone Just Intonation Guitar
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2/1 octave
15/8 classic major seventh9/5 just minor seventh16/9 Pythagorean minor seventh7/4 harmonic seventh12/7 septimal major sixth5/3 major sixth8/5 minor sixth14/9 septimal minor sixth3/2 perfect fifth10/7 Euler's tritone7/5 septimal tritone4/3 perfect fourth9/7 septimal major third5/4 major third6/5 minor third7/6 septimal minor third8/7 septimal whole tone
9/8 major whole tone10/9 minor whole tone16/15 minor diatonic semitone1/1 unison
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Notes on setup and tuning
The 21-Tone Just Intonation Guitar uses a standard set of guitar strings, although the lowest strings will be tuned slightly below their customary ranges, and the upper strings above theirs. Tuning the guitar toC or C# produces the best results. If we tune the lowest (6 th) string to C, which then becomes 1/1, thenthe 4 th and 2 nd strings are also tuned to 1/1, with the 4 th string being an octave above the 6th, and the 2 nd
an octave above the 4th. The 5 th string is then tuned to G (3/2), with the 3 rd string tuned to 3/2 an octavehigher, and the 1 st string 3/2 an octave above that.
Thus the tuning, from 6 th string to 1 st is literally:
1/1 – 3/2 – 2/1 – 3/1 – 4/1 – 6/1
or, more simply,
1/1 – 3/2 – 1/1 – 3/2 – 1/1 – 3/2
which, if we take the note “C” as our 1/1, gives:
C – G – c – g – c' – g'
The strings tuned to 1/1 will give the 21 note scale from the open string to the halfway point of theneck (the “12 th fret” position on a standard guitar):
1/1 16/15 10/9 9/8 8/7 7/6 6/5 5/4 9/7 4/3 7/5 10/7 3/2 14/9 8/5 5/3 12/7 7/4 16/9 9/5 15/8 1/1*
The strings tuned to 3/2 will continue up the scale as follows:
3/2 14/9 8/5 5/3 12/7 7/4 16/9 9/5 15/8 1/1 16/15 10/9 9/8 8/7 7/6 6/5 5/4 9/7 4/3 7/5 10/7 3/2*
Notice that in each case, the octave of the open string, lying at the midpoint of the string, is markedwith an asterisk (“*”) to distinguish it in the tablature from the open string. Any notes lying above theoctave are similarly marked.
The colors for each ratio were chosen to highlight its prime limit factor. Thus, ratios in red have a prime number limit of 2 or 3, green is 5 and blue is 7. For more information on this and how the scalewas derived, see my website: danterosati.com.
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© 2005 Dante Rosati
Arbor Low
Dante Rosati for 21-Tone Just Intonation Guitar
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