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Further examples of Zeta function tunings

🔗genewardsmith@juno.com

8/27/2001 6:22:15 PM

This came up on the other list. A "Gram tuning" is a tuning derived
from the Gram point associated to the large value of |Z(t)|
assoicated to an et--in practice, this seems to mean the nearest Gram
point. A "Z tuning" is the tuning derived from the actual value where
|Z(t)| achieves its large local maximum near the n-et referred to
before. Here are some further examples:

15

Gram point 45
Gram tuning = 15.052, 4.14 cents flat
Z tuning = 15.053, 4.26 cents flat

19

Gram point 63
Gram tuning = 18.954, 2.93 cents sharp
Z tuning = 18.948, 3.29 cents sharp

22

Gram point 78
Gram tuning = 22.025, 1.35 cents flat
Z tuning = 22.025, 1.37 cents flat

72

Gram point 378
Gram tuning = 71.954, .763 cents sharp
Z tuning = 71.951, .823 cents sharp

It would be interesting to compare this tunings to those arrived at
by other methods.