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Appreciating 1/6-comma — Temperament Part III

1件のコメント / Early Music, Essays / Koji Otsuki

(Originally posted in March, 2010) By now we hopefully understand that the Pythagorean temperament is really a stack of pure perfect 5ths (Pythagorean 5ths) and can bring out melodic beauty, and the temperament based on the narrow 5ths, each tampered by a quarter of a syntonic comma (mean-tone 5ths), can bring out chordal beauty. Then what about those so-called well-temperaments like Kirnberger, Werckmeister, Vallotti and Young? What is the 1/6-comma mean-tone that we hear about lately? How different is that from the Vallotti or the Young temperaments? Before we get to the discussion of 1/6-Pythagorean-comma systems vs. 1/6-comma mean-tone, let’s take a look at the 1/4-comma systems. Among those well-temperaments, […]

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Hating and loving 1/6-comma — Temperament Part II

1件のコメント / Early Music, Essays / Koji Otsuki

(Originally posted in March, 2010) In the previous blog entry, I mentioned that you can characterize those temperament systems as either harmonic systems or melodic systems. The Pythagorean tuning is suited for monophonic lines because of the sharper mediants and leading tones, and thus it is a typical example of a melodic system. Not great at all for playing harmonies it is though. On the other hand, the mean-tone has just intonation major 3rds for harmonic purity; because of low mediants and leading tones, its melodic contours often suffer, but it is a harmonically pleasing temperament. The biggest problem of mean-tone is, because of the fact that twelve of those

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1/6-Pythagorean-comma mean-tone?? — Temperament Part I

1件のコメント / Early Music, Essays / Koji Otsuki

(Originally posted in March, 2010) If you just thought this title didn’t make sense, no, it does not make sense, at least to you and me. Perhaps some of you can help me understand this stuff better — I don’t have a mathematical mind and I can only go so far as to understand the temperament issues, but I don’t think I’m too stupid to understand the basics. Some of those claims out there doesn’t quite make sense to me…. Now, those of you who are thinking you’ll be in over your head talking temperament, you’ve got to stay with me. Let’s clarify what the mean-tone temperament is. Well,

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