Hahn distance: Difference between revisions
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This makes the 9.5.7.11.13 sublattice symmetrical, corresponded to even distance values from the origin, with the full lattice corresponding to all positive integer distances. | This makes the 9.5.7.11.13 sublattice symmetrical, corresponded to even distance values from the origin, with the full lattice corresponding to all positive integer distances. | ||
== Examples == | |||
{| class="wikitable" | |||
|+ style="font-size: 105%;" | Hahn distance of 5-limit intervals | |||
|- | |||
! Ratio | |||
! 5-odd-limit | |||
! 9-odd-limit | |||
! 15-odd-limit | |||
! 25-odd-limit | |||
! 27-odd-limit | |||
|- | |||
| [[6/5]] | |||
| 1 | |||
| 1 | |||
| 1 | |||
| 1 | |||
| 1 | |||
|- | |||
| [[10/9]] | |||
| 2 | |||
| 1 | |||
| 1 | |||
| 1 | |||
| 1 | |||
|- | |||
| [[16/15]] | |||
| 2 | |||
| 2 | |||
| 1 | |||
| 1 | |||
| 1 | |||
|- | |||
| [[25/24]] | |||
| 2 | |||
| 2 | |||
| 2 | |||
| 1 | |||
| 1 | |||
|- | |||
| [[27/25]] | |||
| 3 | |||
| 2 | |||
| 2 | |||
| 2 | |||
| 1 | |||
|- | |||
| [[45/32]] | |||
| 3 | |||
| 2 | |||
| 2 | |||
| 2 | |||
| 2 | |||
|- | |||
| [[75/64]] | |||
| 3 | |||
| 3 | |||
| 2 | |||
| 2 | |||
| 2 | |||
|- | |||
| [[81/80]] | |||
| 4 | |||
| 2 | |||
| 2 | |||
| 2 | |||
| 2 | |||
|- | |||
| [[135/128]] | |||
| 4 | |||
| 3 | |||
| 2 | |||
| 2 | |||
| 2 | |||
|} | |||
[[Category:Math]] | [[Category:Math]] | ||