Tenney–Euclidean temperament measures: Difference between revisions

The different definitions yield different results, but they are related to each other by a factor derived only from the rank and limit. A meaningful comparison of temperaments in the same rank and limit can be provided by picking any one of them.  

Here is a demonstration from [[7-limit]] [[magic]] and [[meantone]], comparing each of the definitions.  

 

{| class="wikitable center-all"

|+ style="font-size: 105%;" | 7-limit magic (left) vs. meantone (right) in TE temperament measures

! {{W|Norm (mathematics) #Euclidean norm|Standard ''L''² norm}}

| 1.799 : 1.350

| 1.074 : 1.382

| 1.610×10⁻³ : 1.554×10⁻³

| 2.937 : 2.204

| 2.631 : 3.384

| 6.441×10⁻³ : 6.218×10⁻³