5040edo: Difference between revisions
→Prime harmonics: add continued as I talk on the page a lot about high prime limit |
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=== Regular temperament theory === | === Regular temperament theory === | ||
From the regular temperament theory perspective, 5040edo is not as impressive, as for example zeta EDOs. It does offer unique harmonies, although they are not simple. Since having errors less than 25% guarantees "naive consistency" to distance 1, this means that the best subgroup for 5040edo is 2.3.7.13.17.23.29.31.41. | From the regular temperament theory perspective, 5040edo is not as impressive, as for example zeta EDOs. It does offer unique harmonies, although they are not simple. Since having errors less than 25% guarantees "naive consistency" to distance 1, this means that the best subgroup for 5040edo is 2.3.7.13.17.23.29.31.41.43.53.59.61.73.89. | ||
There's an interesting property that arises in | There's an interesting property that arises in the subgroup, 2.7.13.17.29.31.41.47.61.67. In this subgroup, it makes a rank two temperament with 1111edo (1111 & 5040), which brings two notable number classes together - a repunit and a highly composite number. | ||
Using the patent val, 5040edo tempers out [[9801/9800]] in the 11-limit. | Using the patent val, 5040edo tempers out [[9801/9800]] in the 11-limit. | ||