Tuning vs intonation

[Richard Moody]

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Maybe you should check out Jim Coleman´s Sr. pure fifths
temperament.

Kristinn Leifsson


I have (tried), but I'll leave that for the machines. : ) This has
to be the "hyper modern" of tuning theory.  
	To get pure fifths (on paper) the octaves must be stretched by
2.003875...   This will give C4--C5 a beat of 1 bps. The C4-G4 of
course is pure, but the G4-C5 is 3 bps.  A spread sheet will give
the beats of thirds, sixths etc, and even then it is daunting to
figure out how to lay the bearings.  Jim did give step by step
aural instructions, but it takes quite a while to go through the 
first time(s).   And knowing the machine can be set up to knock out
the temp in 5 min. it becomes an issue of waiting for a machine to
show up. 
	In the meantime it is fun to play with the spread sheet making the
wide octave not so wide.  The fifths won't be pure but what is one
beat in 5 seconds? And noticing  with pure fifths the 6ths, m3rds,
m6ths are virtually the same from the same root. Talk about "equal
beating".   The 3rd is 1bps slower. 
	Since octaves are stretched naturally it might be that fifths on
the piano are actually purer than on paper. It still amazes me how
close the fifths are to pure but what a huge difference it makes. 
I would not be surprised that most, if not all musicians listening
to a piano fifth do not realize they are flat unless told, and
would need to hear that slight difference of intonation to believe
it. ---ric