Meantone was used for several centuries and is still enjoyed by connoisseurs of early music, but it had one problem: since four of the less-common thirds were very discordant (and one fifth, the wolf fifth, was really awful), meantone didn’t allow the free use of all the intervals in all the keys. This Pythagorean tuning was the basis of organ tuning and music theory until around the late 14th or early 15th century, which is why thirds and sixths were regarded before that time as dissonant intervals.īut when musicians began to want to use the consonant third a compromise had to be found, and they responded by tuning that troublesome D to the mean (average) of the two that were needed, which produced a system in which most of the thirds were very good and most of the fifths were only slightly off this we now call meantone temperament (to “temper” an interval means to adjust its tuning a little bit away from perfect). The first solution was to tune the fifths exactly right and not to worry about the thirds and sixths, just as Pythagoras, the semi-legendary discoverer of musical mathematics, had done. This problem was solved in many ways over the years.
In other words, it doesn’t come out even you can’t tune all the consonances to be simultaneously exactly right unless you have two different keys for some of the notes, such as one D tuned to agree with G and another D made to work with A. For example, you can tune your A so that it will make a very nice sixth above your C, and the G as a good fifth above the C, and the D to make a good fifth below A, but then you’ll find that the G will be out of tune with the D. Indeed, many musicians have long regarded this as sort of ideal, but it doesn’t work out very well on a keyboard with only twelve keys to the octave.
You would think that the ideal way to tune your piano would be to make each of the consonant intervals sound exactly in tune, so that no beating could be heard.
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