Comparison of the bell data with five tuning models |
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The
models, given in Cent values for single and cumulative intervals, are: |
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1)
Phytagorean (phyt) |
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D |
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E |
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F |
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G |
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A |
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C |
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0 |
204 |
204 |
90 |
294 |
204 |
498 |
204 |
702 |
294 |
996 |
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2)
Just intonation (just) |
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D |
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E |
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F |
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G |
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A |
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C |
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0 |
182 |
182 |
134 |
316 |
182 |
498 |
204 |
702 |
316 |
1018 |
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3)
12-tone equal temperament (12ET) |
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D |
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E |
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F |
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G |
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A |
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C |
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0 |
200 |
200 |
100 |
300 |
200 |
500 |
200 |
700 |
300 |
1000 |
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4)
1/3 komma mean-tone temperament (1/3ko) |
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D |
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E |
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F |
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G |
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A |
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C |
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0 |
190 |
190 |
126 |
316 |
190 |
505 |
190 |
695 |
316 |
1010 |
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5)
Equally tempered fifths CGDAE of 696.2 tuned from D, based on pure minor
third D-F (696.2) |
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D |
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E |
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F |
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G |
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A |
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C |
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0 |
192 |
192 |
123 |
316 |
188 |
504 |
192 |
696 |
311 |
1008 |
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Results
of statistical analysis: |
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1)
Phytagorean tuning must definitely be excluded as a model for the bell
casters (p<0.002). |
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2)
12-tone equal temperament is highly improbable as a model (p<0.05). |
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3)
The best-fitting model is "Equally tempered fifths CGDAE of 696.2 tuned
from D, based on pure minor third D-F". |
4)
Just intonation and 1/3 komma mean-tone also fit the data, but the detailed
results suggest |
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that
they are less probable than the best-fitting model. |
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