back to list

Re: circulating meantones -- that ~6.07 cents (erratum)

🔗mschulter <MSCHULTER@VALUE.NET>

8/11/2001 10:48:44 PM

Hello, there, and I just wanted to correct a line in my table relating to
the sizes of major thirds in 19-tET -- obviously not the same as in
31-tET, despite my omission of this change in using the first part of the
table to finish the second:

-------------------------------------------------------------------
31 notes: 1/4-comma meantone or 31-tET
-------------------------------------------------------------------
1/4-comma 31-tET
...................................................................
31-comma ~-6.07 cents 0 cents
(31 5ths - 18 8ves)
...................................................................
Fifths 30 at ~696.57 cents ~696.77 cents
(~5.38 cents narrow) (~5.18 cents narrow)
....................
1 at ~702.65 cents
(~0.69 cents wide)
...................................................................
Major 3rds 27 at ~386.31 cents ~387.10 cents
(pure 5:4) (~0.78 cents wide)
,,,,,,,,,,,,,,,,,,,
4 at ~392.38 cents
(~6.07 cents wide)
...................................................................
minor 3rds 28 at ~310.26 cents ~309.68 cents
(~5.38 cents narrow) (~5.96 cents narrow)
....................
3 at ~304.20 cents
(~11.45 cents narrow)
-------------------------------------------------------------------
19 notes: 1/3-comma meantone or 19-tET
-------------------------------------------------------------------
1/3-comma 19-tET
...................................................................
19-comma ~+0.94 cents 0 cents
(19 5ths - 11 8ves)
...................................................................
Fifths 18 at ~694.79 cents ~694.74 cents
(~7.17 cents narrow) (~7.22 cents narrow)
....................
1 at ~693.85 cents
(~8.11 cents wide)
...................................................................
Major 3rds 15 at ~379.14 cents ~378.95 cents
(~7.17 cents narrow) (~7.37 cents narrow)
,,,,,,,,,,,,,,,,,,,
4 at ~378.21 cents
(~8.11 cents narrow)
...................................................................
minor 3rds 16 at ~315.64 cents ~315.79 cents
(pure 6:5) (~0.15 cents wide)
....................
3 at ~316.58 cents
(~0.94 cents wide)
-------------------------------------------------------------------

The correct data on the 19-tET major thirds appears near the end of the
article, but a corrected version of the table might not be a bad idea.

Most respectfully,

Margo Schulter
mschulter@value.net