7-limit tempered scale possibilities

I give the name of the temperament, the wedgie, the Graham complexity,
the chroma and the scale size, in that order. These all have scale
size more than 50% larger than Graham complexity. Will Carl stretch a
point and include Kleismic[11]? I'm betting against.

["Duodecimal", [0, 12, 24, 19, 38, 22], 24, 49/48, 48]

["Hemikleismic", [12, 10, -9, -12, -48, -49], 21, 28/27, 45]

["Kleismic", [6, 5, 3, -6, -12, -7], 6, 28/27, 15]

["Kleismic", [6, 5, 3, -6, -12, -7], 6, 16/15, 11]

["Tripletone", [3, 0, -6, -7, -18, -14], 9, 28/27, 15]

["Tripletone", [3, 0, -6, -7, -18, -14], 9, 49/48, 15]

["Hemifourth", [2, 8, 1, 8, -4, -20], 8, 25/24, 14]

["Meantone", [1, 4, 10, 4, 13, 12], 10, 49/48, 19]

["Hemithird", [15, -2, -5, -38, -50, -6], 20, 28/27, 50]

["Injera", [2, 8, 8, 8, 7, -4], 8, 25/24, 14]

["Injera", [2, 8, 8, 8, 7, -4], 8, 49/48, 14]

["Double wide", [8, 6, 6, -9, -13, -3], 8, 16/15, 14]

["Double wide", [8, 6, 6, -9, -13, -3], 8, 28/27, 18]

["Hemithird", [15, -2, -5, -38, -50, -6], 20, 36/35, 37]

["Superpythagorean", [1, 9, -2, 12, -6, -30], 11, 25/24, 17]

["Muggles", [5, 1, -7, -10, -25, -19], 12, 28/27, 22]

["Hemififth", [2, 25, 13, 35, 15, -40], 25, 25/24, 48]

["Muggles", [5, 1, -7, -10, -25, -19], 12, 49/48, 19]

["Hemiwuerschmidt", [16, 2, 5, -34, -37, 6], 16, 28/27, 43]

["Beatles", [2, -9, -4, -19, -12, 16], 11, 25/24, 20]

["Beatles", [2, -9, -4, -19, -12, 16], 11, 36/35, 17]

["Wizard", [12, -2, 20, -31, -2, 52], 22, 21/20, 34]

["Hemiwuerschmidt", [16, 2, 5, -34, -37, 6], 16, 36/35, 25]

["Ennealimmal", [18, 27, 18, 1, -22, -34], 27, 16/15, 45]

["Magic", [5, 1, 12, -10, 5, 25], 12, 49/48, 19]

["Nonkleismic", [10, 9, 7, -9, -17, -9], 10, 16/15, 19]

["Nonkleismic", [10, 9, 7, -9, -17, -9], 10, 28/27, 23]

["Decimal", [4, 2, 2, -6, -8, -1], 4, 28/27, 10]

["Orwell", [7, -3, 8, -21, -7, 27], 11, 21/20, 18]

["Diminished", [4, 4, 4, -3, -5, -2], 4, 16/15, 8]

["Diminished", [4, 4, 4, -3, -5, -2], 4, 28/27, 8]

["Miracle", [6, -7, -2, -25, -20, 15], 13, 25/24, 20]

["Miracle", [6, -7, -2, -25, -20, 15], 13, 36/35, 21]

["Blackwood", [0, 5, 0, 8, 0, -14], 5, 25/24, 10]

["Miracle", [6, -7, -2, -25, -20, 15], 13, 28/27, 20]

["Quartaminorthirds", [9, 5, -3, -13, -30, -21], 12, 28/27, 30]

["Supermajor seconds", [3, 12, -1, 12, -10, -36], 13, 25/24, 21]

["Schismic", [1, -8, -14, -15, -25, -10], 15, 49/48, 29]

["Schismic", [1, -8, -14, -15, -25, -10], 15, 36/35, 24]

["Superkleismic", [9, 10, -3, -5, -30, -35], 13, 15/14, 22]

["Pajara", [2, -4, -4, -11, -12, 2], 6, 28/27, 10]

["Pajara", [2, -4, -4, -11, -12, 2], 6, 25/24, 10]

["Pajara", [2, -4, -4, -11, -12, 2], 6, 36/35, 12]

["Superkleismic", [9, 10, -3, -5, -30, -35], 13, 28/27, 30]

["Pajara", [2, -4, -4, -11, -12, 2], 6, 49/48, 10]

["Squares", [4, 16, 9, 16, 3, -24], 16, 25/24, 28]

["Diaschismic", [2, -4, -16, -11, -31, -26], 18, 49/48, 34]

["Octafifths", [8, 18, 11, 10, -5, -25], 18, 25/24, 28]

["Tritonic", [5, -11, -12, -29, -33, 3], 17, 36/35, 33]

["Tritonic", [5, -11, -12, -29, -33, 3], 17, 28/27, 27]

["Tritonic", [5, -11, -12, -29, -33, 3], 17, 25/24, 27]

["Tritonic", [5, -11, -12, -29, -33, 3], 17, 49/48, 29]

["Supersupermajor", [3, 17, -1, 20, -10, -50], 18, 25/24, 31]

["Catakleismic", [6, 5, 22, -6, 18, 37], 22, 49/48, 38]

>I give the name of the temperament, the wedgie, the Graham complexity,
>the chroma and the scale size, in that order. These all have scale
>size more than 50% larger than Graham complexity.

That's a good criterion, but (even with a max scale size) was it
sufficient to close this list?

>Will Carl stretch a point and include Kleismic[11]? I'm betting
>against.

Yeah, Kleismic[11] came up long ago, and I rejected it in favor of
Kleismic[8]. ;)

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> >I give the name of the temperament, the wedgie, the Graham complexity,
> >the chroma and the scale size, in that order. These all have scale
> >size more than 50% larger than Graham complexity.
>
> That's a good criterion, but (even with a max scale size) was it
> sufficient to close this list?

Not really; I simply used a list of temperaments I already had.
However, if we bound badness and insist on "validity" the list is
finite, since it involves vals which have one or more of the "good"
chromas as commas. After a while we would only get things with scale
degrees out of order, like my "invalid" Ennealimmal[45] example.