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 |
→Theory: +quadritikleismic |
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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}. | 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. In addition, in the 988ccd val it is a tuning for [[quadritikleismic]] temperament in the 7-limit. | ||
=== Higher limits === | === 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. | 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. | ||
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== Regular temperament properties == | == Regular temperament properties == | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
Note: temperaments represented by 494edo are not included. | |||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
!Periods<br>per 8ve | !Periods<br>per 8ve | ||
| Line 23: | Line 24: | ||
! Associated<br>Ratio | ! Associated<br>Ratio | ||
! Temperaments | ! Temperaments | ||
|- | |||
|1 | |||
|261\988 | |||
|317.004 | |||
|6/5 | |||
|[[Quadritikleismic]] (988ccd) | |||
|- | |- | ||
| 52 | | 52 | ||
| Line 28: | Line 35: | ||
| 394.736<br>(2.429) | | 394.736<br>(2.429) | ||
| 134560000/107132311<br>(?) | | 134560000/107132311<br>(?) | ||
| [[French deck]] | |[[French deck]] | ||
|} | |} | ||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||