My intuition about which intervals are major / minor and which are diminished comes from the intervals that create the differences between the major and minor scales. The major interval is what you'd get if you're measuring the intervals on a major (Ionian) scale minor is -1 half step, dimished -2, augmented +1. The other intervals (2nd, 3rd, 6th, 7th) can be either diminished, minor, major, or augmented. If your fret spacing is introducing that much error, it's going to be tough to tune the instrument for more than maybe one chord at a time.Ī little more info for those who are curious: The perfect intervals (unison, 4th, 5th, 8ve) can be modified by being diminished or augmented, which shrinks or expands the interval by one half step.
For reference, the distance between that B and the Bb below it is about 27.72Hz. There's about a 4.5 Hz difference between just-tuned Bs in those two chords. > equal_E * perfect_fifth_ratio # B as fifth of E chord > equal_G * major_third_ratio # B as third of G major chord return basenote * (2 ** (semitones/12.0)) > def alterBySemitones(basenote, semitones): Type "help", "copyright", "credits" or "license" for more information. But since we're talking about the math, I thought I'd try to put some numbers behind my experience. When I tune by ear, I spend a lot of time compromising to get even a few basic chords to all sound good.
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