988edo: Difference between revisions
→Theory: about the notablity of 988 & 2016... I also know the year 988 as the year of baptism of Kyiv Rus so I just casually stumbled upon 988 & 2016 temperament while composing, i think it's interesting |
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== Theory == | == Theory == | ||
988edo provides excellent tuning for the 2, 3, 5, 11, 13, 19, 37, 43, 47, 53, and | 988edo provides excellent tuning for the 2, 3, 5, 11, 13, 19, 37, 43, 47, 53, 59th harmonics and a reasonable tuning for 23, 31, 41st harmonics, making a strong higher-limit system. In lower limits, it is [[enfactored]] in the [[17-limit]], with the same tuning as 494edo, which is notable for being a zeta edo. If considered in the 19-limit, it provides a good correction for the 19th harmonic over 494edo. The comma basis for 988edo in the 19-limit is {1156/1155, 1275/1274, 1445/1444, 1716/1715, 2080/2079, 2431/2430, 4096/4095}. | ||
An alternate mapping for 17 would be the 988g val, where it tempers out 2025/2023, 13013/13005, 15625/15606, 31213/31212. | An alternate mapping for 17 would be the 988g val, where it tempers out 2025/2023, 13013/13005, 15625/15606, 31213/31212. | ||
=== Higher limits === | |||
In the 2.5.11.13.19.29.31 it supports period-52 temperament called [[french deck]], with the tempering out of [[6656/6655]] inherited from 494edo. | |||
988edo is similar to [[2016edo]] in the fact that both tune well the 2.5.11.13.19.41.47 subgroup. The result is the 988 & 2016 temperament, which reaches [[13/8]] in four generators and has a comma basis {7943/7942, 322465/322373, 16777475/16777216, 22151168/22150865, 12998046875/12994428928}. | |||
=== As an interval size measure === | |||
One step of 988edo is named ''semisqub'', given the strong relation to 494edo and the fact that 1 step of 494edo is called a squb. | |||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|988|columns=11}} | {{Harmonics in equal|988|columns=11}} | ||