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=== A temperament with multiple commas ===

We could repeat this experiment but with septimal meantone, {{ket|{{val|1 0 -4 -13}} {{val|0 1 4 10}}}}, which is still [[rank]]-2 but due to the one extra [[dimensionality]] according to the [[rank-nullity theorem]] is nullity-2. The additional comma it ~~tempers out~~ is [[126/125]] {{vector|1 2 -3 1}}, the starling comma. Here, 10/9 {{vector|1 -2 1 0}} and 9/8 {{vector|-3 2 0 0}} both still map to [-1 2}, so they are still members of [-1 2}'s preimage, along with all the intervals listed in the previous section. But here we have some additional members which are off by multiples of the second comma as well, such as {{vector|1 -2 1 0}} + {{vector|1 2 -3 1}} = {{vector|2 0 -2 1}}, which is 28/25, or {{vector|-3 2 0 0}} - {{vector|1 2 -3 1}} = {{vector|-4 0 3 -1}}, which is 125/112.

We could repeat this experiment but with septimal meantone, {{ket|{{val|1 0 -4 -13}} {{val|0 1 4 10}}}}, which is still [[rank]]-2 but due to the one extra [[dimensionality]] according to the [[rank-nullity theorem]] is nullity-2. The additional comma it makes to vanish is [[126/125]] {{vector|1 2 -3 1}}, the starling comma. Here, 10/9 {{vector|1 -2 1 0}} and 9/8 {{vector|-3 2 0 0}} both still map to [-1 2}, so they are still members of [-1 2}'s preimage, along with all the intervals listed in the previous section. But here we have some additional members which are off by multiples of the second comma as well, such as {{vector|1 -2 1 0}} + {{vector|1 2 -3 1}} = {{vector|2 0 -2 1}}, which is 28/25, or {{vector|-3 2 0 0}} - {{vector|1 2 -3 1}} = {{vector|-4 0 3 -1}}, which is 125/112.

So in this case the full member set of the preimage for any mapped interval of this temperament such as [-1 2} could be arranged as a 2D grid, with members differing by a meantone comma along one axis and members differing by a starling comma along the other axis.

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 === A temperament with multiple commas ===
-We could repeat this experiment but with septimal meantone, {{ket|{{val|1 0 -4 -13}} {{val|0 1 4 10}}}}, which is still [[rank]]-2 but due to the one extra [[dimensionality]] according to the [[rank-nullity theorem]] is nullity-2. The additional comma it tempers out is [[126/125]] {{vector|1 2 -3 1}}, the starling comma. Here, 10/9 {{vector|1 -2 1 0}} and 9/8 {{vector|-3 2 0 0}} both still map to [-1 2}, so they are still members of [-1 2}'s preimage, along with all the intervals listed in the previous section. But here we have some additional members which are off by multiples of the second comma as well, such as {{vector|1 -2 1 0}} + {{vector|1 2 -3 1}} = {{vector|2 0 -2 1}}, which is 28/25, or {{vector|-3 2 0 0}} - {{vector|1 2 -3 1}} = {{vector|-4 0 3 -1}}, which is 125/112.
+We could repeat this experiment but with septimal meantone, {{ket|{{val|1 0 -4 -13}} {{val|0 1 4 10}}}}, which is still [[rank]]-2 but due to the one extra [[dimensionality]] according to the [[rank-nullity theorem]] is nullity-2. The additional comma it makes to vanish is [[126/125]] {{vector|1 2 -3 1}}, the starling comma. Here, 10/9 {{vector|1 -2 1 0}} and 9/8 {{vector|-3 2 0 0}} both still map to [-1 2}, so they are still members of [-1 2}'s preimage, along with all the intervals listed in the previous section. But here we have some additional members which are off by multiples of the second comma as well, such as {{vector|1 -2 1 0}} + {{vector|1 2 -3 1}} = {{vector|2 0 -2 1}}, which is 28/25, or {{vector|-3 2 0 0}} - {{vector|1 2 -3 1}} = {{vector|-4 0 3 -1}}, which is 125/112.
 So in this case the full member set of the preimage for any mapped interval of this temperament such as [-1 2} could be arranged as a 2D grid, with members differing by a meantone comma along one axis and members differing by a starling comma along the other axis.