>"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
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