Tour of regular temperaments: Difference between revisions
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Wikispaces>hstraub **Imported revision 10836951 - Original comment: Meantone link** |
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This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
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Magic is based on a chain of major thirds. It's optimal, in a sense, for 9-limit harmony with a tuning close to 41-EDO. It's more accurate than meantone and simpler than schismatic. It works with 19 and 22 note scales. Five major thirds approximate 3/1. Twelve major thirds, less an octave, approximate 7/1. It's a little tricky to work with because 3/2 fifths are a relatively complex interval and it doesn't naturally work with scales of around 7 notes to the octave. | Magic is based on a chain of major thirds. It's optimal, in a sense, for 9-limit harmony with a tuning close to 41-EDO. It's more accurate than meantone and simpler than schismatic. It works with 19 and 22 note scales. Five major thirds approximate 3/1. Twelve major thirds, less an octave, approximate 7/1. It's a little tricky to work with because 3/2 fifths are a relatively complex interval and it doesn't naturally work with scales of around 7 notes to the octave. | ||
===Meantone[[#meantone]]=== | ===[[Meantone]][[#meantone]]=== | ||
This is the most familiar of the rank 2 temperaments. The syntonic comma, 81/80 is tempered out; any intervals that differ by 81/80 in just intonation are tempered to the same interval in meantone temperament. This means four fiths approximate 5/1. | This is the most familiar of the rank 2 temperaments. The syntonic comma, 81/80 is tempered out; any intervals that differ by 81/80 in just intonation are tempered to the same interval in meantone temperament. This means four fiths approximate 5/1. | ||
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Magic is based on a chain of major thirds. It's optimal, in a sense, for 9-limit harmony with a tuning close to 41-EDO. It's more accurate than meantone and simpler than schismatic. It works with 19 and 22 note scales. Five major thirds approximate 3/1. Twelve major thirds, less an octave, approximate 7/1. It's a little tricky to work with because 3/2 fifths are a relatively complex interval and it doesn't naturally work with scales of around 7 notes to the octave.<br /> | Magic is based on a chain of major thirds. It's optimal, in a sense, for 9-limit harmony with a tuning close to 41-EDO. It's more accurate than meantone and simpler than schismatic. It works with 19 and 22 note scales. Five major thirds approximate 3/1. Twelve major thirds, less an octave, approximate 7/1. It's a little tricky to work with because 3/2 fifths are a relatively complex interval and it doesn't naturally work with scales of around 7 notes to the octave.<br /> | ||
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This is the most familiar of the rank 2 temperaments. The syntonic comma, 81/80 is tempered out; any intervals that differ by 81/80 in just intonation are tempered to the same interval in meantone temperament. This means four fiths approximate 5/1.<br /> | This is the most familiar of the rank 2 temperaments. The syntonic comma, 81/80 is tempered out; any intervals that differ by 81/80 in just intonation are tempered to the same interval in meantone temperament. This means four fiths approximate 5/1.<br /> | ||