![]() It gives you an easy way to remember the relative placements of accidentals. When I was young, I was told the comma model of the occidental scale and I think it is a good first approach of these issues in most classical music, even if it is theoretical and limited. I will not quantify them as there are already other answers on this area. When you are playing fretless string instruments, especially bowed instruments in small groups, you become very sensitive to these differences. This ensures that enharmonic equivalent notes have the same frequencies, but it also means that no interval is "perfect" in the whole-number ratio sense. Where n is the number of half-steps above or below the A440 reference pitch. Rather, you use the formula: frequency = 440 * 2^(n/12) In Equal Temperament, pitches aren't determined by whole-number ratios. Not close enough not to be noticeable, though. In the end, and adjusting for octaves, you get that Gb = 366.25 Hz while F# = 371.25 Hz. Meanwhile, the D below the A440 is tuned to 440 * 2/3 = 293.333 Hz, the G below the D is tuned to 293.333 * 2/3 = 195.555 Hz, and so on. The F♯ above the B is tuned to 990 * 3/2 = 1485 Hz. The B above the E is tuned to 660 * 3/2 = 990 Hz. Then the E above the A is tuned to 440 * 3/2 = 660 Hz. ![]() intervals in which the ratios of the frequencies are in whole-number pairs, then Gb isn't exactly the same as F#.įor example, say you're tuning to A440 and using perfect intervals. If you're tuning by perfect intervals, i.e. It depends on the tuning system being used.
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