12edo: Difference between revisions
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<span style="display: block; text-align: right;">[[12平均律|日本語]]</span> | <span style="display: block; text-align: right;">[[12平均律|日本語]]</span> | ||
'''12edo''', perhaps better known as '''12et''' since it really is a temperament, is the predominating tuning system in the world today. It achieved that position because it is the smallest equal division of the octave ([[EDO]]) which can seriously claim to represent [[5-limit]] harmony, and because as 1/12 Pythagorean comma (approximately 1/11 syntonic comma or full schisma) meantone, it represents [[meantone]]. | |||
It divides the octave into twelve equal parts, each of exactly 100 cents each unless octave shrinking or stretching is employed. Its has a fifth which is quite good at two cents flat. It has a major third which is 13+2/3 cents sharp, which works well enough for some styles of music and is not really adequate for others, and a minor third which is flat by even more, 15+2/3 cents. It is probably not an accident that as tuning in European music became increasingly close to 12et, the style of the music changed so that the defects of 12et appeared less evident, though it should be borne in mind that in actual performance these are often reduced by the tuning adaptations of the performers. | It divides the octave into twelve equal parts, each of exactly 100 cents each unless octave shrinking or stretching is employed. Its has a fifth which is quite good at two cents flat. It has a major third which is 13+2/3 cents sharp, which works well enough for some styles of music and is not really adequate for others, and a minor third which is flat by even more, 15+2/3 cents. It is probably not an accident that as tuning in European music became increasingly close to 12et, the style of the music changed so that the defects of 12et appeared less evident, though it should be borne in mind that in actual performance these are often reduced by the tuning adaptations of the performers. | ||
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| {{Monzo| -19 12 }} | | {{Monzo| -19 12 }} | ||
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| {{Monzo| 3 4 -4 }} | | {{Monzo| 3 4 -4 }} | ||
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| {{Monzo| 7 0 -3 }} | | {{Monzo| 7 0 -3 }} | ||
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| {{Monzo| -4 4 -1 }} | | {{Monzo| -4 4 -1 }} | ||
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| style="text-align:center;" | 32805/32768 | | style="text-align:center;" | [[32805/32768]] | ||
| {{Monzo| -15 8 1 }} | | {{Monzo| -15 8 1 }} | ||
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| style="text-align:center;" | 36/35 | | style="text-align:center;" | [[36/35]] | ||
| {{Monzo| 2 2 -1 -1 }} | | {{Monzo| 2 2 -1 -1 }} | ||
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| style="text-align:center;" | 50/49 | | style="text-align:center;" | [[50/49]] | ||
| {{Monzo| 1 0 2 -2 }} | | {{Monzo| 1 0 2 -2 }} | ||
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| style="text-align:center;" | 64/63 | | style="text-align:center;" | [[64/63]] | ||
| {{Monzo| 6 -2 0 -1 }} | | {{Monzo| 6 -2 0 -1 }} | ||
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| style="text-align:center;" | 126/125 | | style="text-align:center;" | [[126/125]] | ||
| {{Monzo| 1 2 -3 1 }} | | {{Monzo| 1 2 -3 1 }} | ||
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| {{Monzo| -5 2 2 -1 }} | | {{Monzo| -5 2 2 -1 }} | ||
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| style="text-align:center;" | 99/98 | | style="text-align:center;" | [[99/98]] | ||
| {{Monzo| -1 2 0 -2 1 }} | | {{Monzo| -1 2 0 -2 1 }} | ||
| style="text-align:right;" | 17.58 | | style="text-align:right;" | 17.58 | ||
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| style="text-align:center;" | 100/99 | | style="text-align:center;" | [[100/99]] | ||
| {{Monzo| 2 -2 2 0 -1 }} | | {{Monzo| 2 -2 2 0 -1 }} | ||
| style="text-align:right;" | 17.40 | | style="text-align:right;" | 17.40 | ||