List. The following is an except from appendix F of the SAT manual. It gives an explanation by Dr Sanderson that shows why David Anderson was "correct" about 4ths having the same slow beat rates, and why I was "correct" in stating that 4ths should have a contiguous relationship as 3rds do. "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" Cheers ! Ricb
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