Generator form manipulation: Difference between revisions

Let's begin with the simple example of 5-limit meantone. The following table demonstrates how to obtain mingen form from various starting positions, by synthesizing the two generator size manipulation tricks explained in the previous section.

|+mapping manipulations to where where period <span><math>p</math></span> is the first mapping row r₁ in cents and generator <span><math>g</math></span> is the second mapping row r₂ in cents

!current <span><math>p</math></span> and <span><math>g</math></span>

!required r₂ change

|<nowiki>{{1,0,-4},{0,-1,-4}}</nowiki>

|{1201.4,-1898.4}

|<nowiki>{{1,1,0},{0,-1,-4}}</nowiki>

|{1201.4,-697.049}

|<nowiki>{{1,2,4},{0,1,4}}</nowiki>

|{1201.4,-504.348}

|<nowiki>{{1,2,4},{0,-1,-4}}</nowiki>

|{1201.4,504.4}

|<nowiki>{{1,1,0},{0,1,4}}</nowiki>

|{1201.4,697.049}

|<nowiki>{{1,0,-4},{0,1,4}}</nowiki>

|{1201.4,1898.4}