User:Xenwolf/Fifthspan: Difference between revisions
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{{Primes in edo|columns=9|title=[[46edo]]|46}} | {{Primes in edo|columns=9|title=[[46edo]]|46}} | ||
{{Primes in edo|columns=9|title=[[53edo]]|53}} | {{Primes in edo|columns=9|title=[[53edo]]|53}} | ||
== Separate mod steps == | |||
Shown on the example of [[17edo]]. | |||
All fifthspans are given as positive values. (This can be transformed into mixed mode by subtracting <code>17</code> from all values <code> > 17/2 == 8.5</code>) | |||
{| class="wikitable center-all" | |||
! colspan="2" | <!-- empty cell --> | |||
! prime 2 | |||
! prime 3 | |||
! prime 5 | |||
! prime 7 | |||
! prime 11 | |||
! prime 13 | |||
! prime 17 | |||
! prime 19 | |||
! prime 23 | |||
|- | |||
! rowspan="2" | Error | |||
! absolute ([[cent|¢]]) | |||
| 0.0 | |||
| +3.9 | |||
| -33.4 | |||
| +19.4 | |||
| +13.4 | |||
| +6.5 | |||
| -34.3 | |||
| -15.2 | |||
| +7.0 | |||
|- | |||
! [[Relative error|relative]] (%) | |||
| 0 | |||
| +6 | |||
| -47 | |||
| +27 | |||
| +19 | |||
| +9 | |||
| -49 | |||
| -21 | |||
| +10 | |||
|- | |||
! rowspan="2" | [[nearest edomapping|Mapping]] | |||
! steps | |||
| '''17''' | |||
| 27 | |||
| 39 | |||
| 48 | |||
| 59 | |||
| 63 | |||
| 69 | |||
| 72 | |||
| 77 | |||
|- | |||
! [[octave reduction|mod 17]] | |||
| 0 | |||
| '''10''' | |||
| 5 | |||
| 14 | |||
| 8 | |||
| 12 | |||
| '''1''' | |||
| 4 | |||
| 9 | |||
|- | |||
! colspan="2" | [[fifthspan]] (steps) | |||
| 0 | |||
| '''1''' | |||
| 9 | |||
| 15 | |||
| 11 | |||
| 8 | |||
| '''12''' | |||
| 14 | |||
| 6 | |||
|- | |||
! rowspan="2" colspan="2" | fifthspan explained | |||
| rowspan="2" | - | |||
| 10= '''1''' *10 %17 | |||
| 5= '''9''' *10 %17 | |||
| 14= '''15''' *10 %17 | |||
| 8= '''11''' *10 %17 | |||
| 12= '''8''' *10 %17 | |||
| 1= '''12''' *10 %17 | |||
| 4= '''14''' *10 %17 | |||
| 9= '''6''' *10 %17 | |||
|- | |||
| 1= 10 *12 %17 | |||
| 9= 5 *12 %17 | |||
| 15= 14 *12 %17 | |||
| 11= 8 *12 %17 | |||
| 8= 12 *12 %17 | |||
| 12= 1 *12 %17 | |||
| 14= 4 *12 %17 | |||
| 6= 9 *12 %17 | |||
|} | |||
Revision as of 19:03, 13 January 2021
Fifthspan examples
| Prime → | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|
| EDO ↓ |
Mapping ↓ |
(1/1) | (3/2) | (5/4) | (7/4) | (11/8) | (13/8) | (17/16) | (19/16) | (23/16) |
| 5edo | 3\5 | 0 | +1 | -1 | -2 | -1 | -2 | 0 | +2 | |
| 7edo | 4\7 | 0 | +1 | -3 | -2 | -1 | +3 | |||
| 8edo | 5\8 | 0 | +1 | -1 | -2 | +4 | -2 | -3 | +2 | |
| 9edo | 5\9 | 0 | +1 | -3 | -4 | -1 | +3 | +2 | +4 | |
| 11edo | 6\11 | 0 | +1 | -3 | -4 | -1 | +5 | +2 | -5 | |
| 12edo | 7\12 | 0 | +1 | +4 | -2 | +6 | -4 | -5 | -3 | |
| 13edo | 8\13 | 0 | +1 | +7 | -2 | +4 | +6 | +5 | +2 | -4 |
| 16edo | 9\16 | 0 | +1 | -3 | +5 | -1 | +3 | -7 | +4 | |
| 17edo | 10\17 | 0 | +1 | -8 | -2 | -6 | +8 | -5 | -3 | +6 |
| 18edo | 11\18 | 0 | +1 | -6 | +3 | +4 | -7 | |||
| 19edo | 11\19 | 0 | +1 | +4 | -9 | +6 | -4 | -6 | ||
| 22edo | 13\22 | 0 | +1 | +9 | -2 | -6 | -4 | -10 | ||
| 23edo | 13\23 | 0 | +1 | -3 | +5 | -8 | +3 | +9 | +4 | +8 |
| 26edo | 15\26 | 0 | +1 | +4 | -9 | +6 | -4 | -12 | -10 | -6 |
| 27edo | 16\27 | 0 | +1 | +9 | -2 | -6 | +13 | -10 | -8 | |
| 29edo | 17\29 | 0 | +1 | -8 | -14 | +11 | +8 | |||
| 31edo | 18\31 | 0 | +1 | +4 | +10 | -13 | +15 | -5 | -3 | -6 |
| 39edo | 23\39 | 0 | +1 | -13 | -19 | -6 | -9 | +12 | +14 | |
| 41edo | 24\41 | 0 | +1 | -8 | -14 | -18 | +20 | +7 | -3 | |
| 46edo | 27\46 | 0 | +1 | +21 | +15 | +11 | +8 | -22 | -3 | +6 |
| 53edo | 31\53 | 0 | +1 | -8 | -14 | +23 | +20 | +7 | -3 | +18 |
EDO information
Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo". Script error: No such module "primes_in_edo".
Separate mod steps
Shown on the example of 17edo.
All fifthspans are given as positive values. (This can be transformed into mixed mode by subtracting 17 from all values > 17/2 == 8.5)
| prime 2 | prime 3 | prime 5 | prime 7 | prime 11 | prime 13 | prime 17 | prime 19 | prime 23 | ||
|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | 0.0 | +3.9 | -33.4 | +19.4 | +13.4 | +6.5 | -34.3 | -15.2 | +7.0 |
| relative (%) | 0 | +6 | -47 | +27 | +19 | +9 | -49 | -21 | +10 | |
| Mapping | steps | 17 | 27 | 39 | 48 | 59 | 63 | 69 | 72 | 77 |
| mod 17 | 0 | 10 | 5 | 14 | 8 | 12 | 1 | 4 | 9 | |
| fifthspan (steps) | 0 | 1 | 9 | 15 | 11 | 8 | 12 | 14 | 6 | |
| fifthspan explained | - | 10= 1 *10 %17 | 5= 9 *10 %17 | 14= 15 *10 %17 | 8= 11 *10 %17 | 12= 8 *10 %17 | 1= 12 *10 %17 | 4= 14 *10 %17 | 9= 6 *10 %17 | |
| 1= 10 *12 %17 | 9= 5 *12 %17 | 15= 14 *12 %17 | 11= 8 *12 %17 | 8= 12 *12 %17 | 12= 1 *12 %17 | 14= 4 *12 %17 | 6= 9 *12 %17 | |||