In my opinion

Steve Martin, Sorry, the latest toctave scale I sent you is not the one I wanted to send. Here you have the corrected data. Note....Cell#....Tone factor....Frequency....Cents ......Fifths C.........0 ........... 1 ...............0 ...............0 .............1.5 C# .....49 .......... P .....1.057072991 .... 96.09 ...... 1.5 D .......101 ........ K .....1.121195220 .... 198.05 .... 1.5 Eb .....153 ......... K .... 1.189207115 .... 300 ..........1.5 E...... 205 ......... K .... 1.261344622 .... 401.955 ...1.5 F .......257 ......... K .... 1.337858004 .... 503.91......1.5 F# ....306 .......... P .... 2^(1/2) ............ 600 ......... 1.5 G ..... 358 .......... K ..... 1.5 ....................701.955 ...1.5 Ab .... 407 .......... P ..... 1.585609486.... 798.045 ...1.50509 A ...... 459 .......... K ..... 1.681792830.... 900 ..........1.50509 Bb .....511 .......... K ..... 1.783810672 ...1001.955....1.50509 B ...... 563 .......... K ..... 1.892016934 ...1103.91 .....1.5 & ...... 615 .......... K ..... 2.006787006 ...1205.865 .. 1.5 &*C# ... 664 ...... P ...... 2.121320343 ......................1.5 &*D.......716........ K ..... 2.25 ................................... 1.5 &*Eb.....768 ........ K ......2.386485386 ..................... 1.5 &*E ......820 ........K ......2.53125 .............................. 1.5 &*F ......872 ........K ......2.684796059....................... 1.5 &*F#....921 .........P.......2.838025401 ...................... 1.5 &*G .....973 .........K ..... 3.010180509 ...................... 1.5 Steve, This toctaved scale has the particularity of generating the toctave on cell # 615 by intervention of K and P tone factors which were derived mathematically to get the three Piagui scales as you can see in my folder. As far as I know nobody has proved that 2/1 is the true octave. I made many mistakes in my former two messages. Regards Mario September, 19
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