198edo: Difference between revisions
Jump to navigation
Jump to search
+some info about semicanou since this is the OPV |
+error table |
||
| Line 2: | Line 2: | ||
It is the [[optimal patent val]] for the rank five temperament tempering out 352/351, plus other temperaments of lower rank also tempering it out, such as [[Misty family #Hemimist|hemimist]], [[Hemifamity family #Namaka|namaka]] and [[Canou family #Semicanou|semicanou]]. It is distinctly [[consistent]] through the 15-limit, and has divisors 2, 3, 6, 9, 11, 18, 22, 33, 66 and 99. | It is the [[optimal patent val]] for the rank five temperament tempering out 352/351, plus other temperaments of lower rank also tempering it out, such as [[Misty family #Hemimist|hemimist]], [[Hemifamity family #Namaka|namaka]] and [[Canou family #Semicanou|semicanou]]. It is distinctly [[consistent]] through the 15-limit, and has divisors 2, 3, 6, 9, 11, 18, 22, 33, 66 and 99. | ||
== Just approximation == | |||
{| class="wikitable center-all" | |||
! colspan="2" | | |||
! prime 2 | |||
! prime 3 | |||
! prime 5 | |||
! prime 7 | |||
! prime 11 | |||
! prime 13 | |||
! prime 17 | |||
! prime 19 | |||
! prime 23 | |||
! prime 29 | |||
! prime 31 | |||
|- | |||
! rowspan="2" |Error | |||
! absolute (¢) | |||
| 0.00 | |||
| +1.08 | |||
| +1.57 | |||
| +0.87 | |||
| +0.20 | |||
| +1.90 | |||
| -1.93 | |||
| -0.54 | |||
| +2.03 | |||
| +0.73 | |||
| +0.42 | |||
|- | |||
! [[Relative error|relative]] (%) | |||
| 0.0 | |||
| +17.7 | |||
| +25.8 | |||
| +14.4 | |||
| +3.3 | |||
| +31.3 | |||
| -31.8 | |||
| -9.0 | |||
| +33.5 | |||
| +12.0 | |||
| +6.9 | |||
|} | |||
[[Category:Edo]] | [[Category:Edo]] | ||
Revision as of 08:53, 5 October 2020
The 198 equal temperament divides the octave into 198 parts of 6.061 cents each. It is contorted in the 7-limit, with the same tuning as 99edo, but makes for a good 11- and 13-limit system. Like 99, it tempers out 2401/2400, 4375/4374, 3136/3125, 5120/5103 and 6144/6125 in the 7-limit; in the 11-limit it tempers 3025/3024, 9801/9800 and 14641/14580; and in the 13-limit 352/351, 676/675, 847/845, 1001/1000, 1716/1715 and 2080/2079.
It is the optimal patent val for the rank five temperament tempering out 352/351, plus other temperaments of lower rank also tempering it out, such as hemimist, namaka and semicanou. It is distinctly consistent through the 15-limit, and has divisors 2, 3, 6, 9, 11, 18, 22, 33, 66 and 99.
Just approximation
| prime 2 | prime 3 | prime 5 | prime 7 | prime 11 | prime 13 | prime 17 | prime 19 | prime 23 | prime 29 | prime 31 | ||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | 0.00 | +1.08 | +1.57 | +0.87 | +0.20 | +1.90 | -1.93 | -0.54 | +2.03 | +0.73 | +0.42 |
| relative (%) | 0.0 | +17.7 | +25.8 | +14.4 | +3.3 | +31.3 | -31.8 | -9.0 | +33.5 | +12.0 | +6.9 | |