May the 4ths be with you

[David Andersen]

>"Two contiguous musical intervals are intervals that touch
>each other, in other words, share the note in the middle. 
>Tests that use contiguous intervals are easy to learn and
>use, and tell the tuner explicitly which notes are at fault
>and what to do to correct them.
>Contiguous major thirds will beat in the ratio of four to
>five because the major third itself consists of two notes
>whose frequencies are in the ratio of four to five. 
>Displacing any interval up the keyboard will speed it up
>theoretically in the ratio of the frequencies of the two
>root notes involved.  Therefore two contiguous major thirds
>should beat in the ratio of four to five, two contiguous
>minor thirds in the ratio of five to six.Similarly, two
>contiguous fourths should beat in the ratio of three to four
>and two contiguous fifths in the
>ratio of two to three.  However, on the piano this
>theoretical relationship holds well only for the major and
>minor  thirds.    The  fourths  and  fifths  are  so 
>strongly  affected  by  inharmonicity  that  these 
>contiguous intervals beat at almost the same speeds"

Yowee zowee, Ric.......that is SO cool: we're both right.
I appreciate your effort on this, and your passion about tuning......
David A