Septimal ennealimma: Difference between revisions

| Name = septimal ennealimma, septiennealimma, no-five ennealimma

The '''septimal ennealimma''', '''septiennealimma''' or '''no-five ennealimma''' is an [[unnoticeable comma|unnoticeable]] [[7-limit]] [[comma]] measuring 1.838 [[cent]]s. It is the difference between a stack of nine [[7/6|septimal minor thirds (7/6)]] and two [[2/1|octaves]], or ([[7/6]])⁹ / ([[2/1]])².  

In the 2.3.7 subgroup, tempering it out leads to the 2.3.7-subgroup [[restriction]] of the [[ennealimmal]] temperament, which is the head of the [[septiennealimmal clan]]. It can only possibly be tempered out in an edo if that edo is a multiple of 9.  

In the full 7-limit, tempering it out leads to the '''septiennealimmal temperament''' (''cf''. septimal ennealimmal temperament). You may find a list of good equal temperaments that support this temperament below.  

{{Mapping|legend=1| 9 0 0 11 | 0 1 0 1 | 0 0 1 0 }}

: mapping generators: ~2592/2401, ~3, ~5

: [[error map]]: {{val| 0.0000 +0.0494 0.0000 -0.1549 }}

* [[CWE]]: ~2592/2401 = 133.3333, ~3/2 = 701.9833, ~5/4 = 386.2877

: error map: {{val| 0.0000 +0.0283 -0.0260 -0.1759 }}

 

[[Badness]] (Smith): 0.502 × 10^-3

* [[Ennealimma]]