The stretched 12 TET

I derived the following stretched 12 TET scale and will appreciate your comments about it:

1
4922 / 4645 --- 100.279 cents
7999 / 7124 --- 200.558
4805 / 8241 --- 300.835
20671 / 16396 --- 401.117
10686 / 7999 --- 501.396
13826 / 9767 --- 601.675
3/2 -- 701.955
24379 / 15338 --- 802.234
13708 / 8139 --- 902.513
9805 / 5494 --- 1002.793
19658 / 10395 --- 1103.072
(47053 / 23481) = (2.003875) --- 3.3514

Despite this scale is close to 12 TET, there are some features to be considered:

1) Apparently it works with 12 perfect fifths.

2 ) 3/2 is better than the corresponding 12 TET G.

3 ) The 3.3514 cents that exceeds the normal 2 of the octave can be disregarded since
the ear don´t distinguish the difference between 1200 and 1203.3514 cents. Besides, it seems that this difference wouldn´t exist since the stretched scale tuning inserts the adjustments mentioned in paragraph (4).

4 ) The frequency adjustments that are done in the middle octave and the remaining piano octaves to compensate the ear imperfection are practically assumed by the stretched scale.

This might be an alternate equal tempered tuning where all major thirds are 1.2607 which is about the same of 12 TET.

Thanks

Mario Pizarro

Lima, April 26.
piagui@...

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