Nine gold medal seven limit rank two temperaments

Here are nine temperaments which are not cangwu dominated by anything on my list, which means very likely they cannot be dominated at all. To the probable distress of many, the list is short and overrun with high complexity temperaments, but here it is:

ennealimmal: <<18 27 18 1 -22 -34||
supermajor: <<37 46 75 -13 15 45||
enneadecal: <<19 19 57 -14 37 79||
sesquiquartififths: <<4 -32 -15 -60 -35 55||
tertiaseptal: <<22 -5 3 -59 -57 21||
meantone: <<1 4 10 4 13 12||
pontiac: <<1 -8 39 -15 59 113||
miracle: <<6 -7 -2 -25 -20 15||
beep: <<2 3 1 0 -4 -6||

The new fact which emerges from this is that meantone and miracle are good temperaments, which you probably didn't know.

On 08/07/2010, genewardsmith <genewardsmith@sbcglobal.net> wrote:
> Here are nine temperaments which are not cangwu dominated by anything on my list, which means very likely they cannot be dominated at all. To the probable distress of many, the list is short and overrun with high complexity temperaments, but here it is:
>
>
> ennealimmal: <<18 27 18 1 -22 -34||
> supermajor: <<37 46 75 -13 15 45||
> enneadecal: <<19 19 57 -14 37 79||
> sesquiquartififths: <<4 -32 -15 -60 -35 55||
> tertiaseptal: <<22 -5 3 -59 -57 21||
> meantone: <<1 4 10 4 13 12||
> pontiac: <<1 -8 39 -15 59 113||
> miracle: <<6 -7 -2 -25 -20 15||
> beep: <<2 3 1 0 -4 -6||

That looks right, yes. How does it compare with a logflat badness list?

> The new fact which emerges from this is that meantone and miracle
> are good temperaments, which you probably didn't know.

And ennealimmal. That's a corker -- numerically speaking. And magic,
while good, is only silver.

Graham

--- In tuning-math@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> > ennealimmal: <<18 27 18 1 -22 -34||
> > supermajor: <<37 46 75 -13 15 45||
> > enneadecal: <<19 19 57 -14 37 79||
> > sesquiquartififths: <<4 -32 -15 -60 -35 55||
> > tertiaseptal: <<22 -5 3 -59 -57 21||
> > meantone: <<1 4 10 4 13 12||
> > pontiac: <<1 -8 39 -15 59 113||
> > miracle: <<6 -7 -2 -25 -20 15||
> > beep: <<2 3 1 0 -4 -6||
>
> That looks right, yes. How does it compare with a logflat badness list?

It was already in wedgie logflat badness order, and the first nine temperaments on the list are exactly the undominated ones. Number ten is magic, dominated by meantone.

--- In tuning-math@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> > ennealimmal: <<18 27 18 1 -22 -34||
> > supermajor: <<37 46 75 -13 15 45||
> > enneadecal: <<19 19 57 -14 37 79||
> > sesquiquartififths: <<4 -32 -15 -60 -35 55||
> > tertiaseptal: <<22 -5 3 -59 -57 21||
> > meantone: <<1 4 10 4 13 12||
> > pontiac: <<1 -8 39 -15 59 113||
> > miracle: <<6 -7 -2 -25 -20 15||
> > beep: <<2 3 1 0 -4 -6||

> And ennealimmal. That's a corker -- numerically speaking. And magic,
> while good, is only silver.

And the runners-up are:

Silver medals

magic <<5 1 12 -10 5 25||
dicot <<2 1 3 -3 -1 4||
term <<3 -24 -54 -45 -94 -58||
pajara <<2 -4 -4 -11 -12 2||
hemiwürschmidt <<16 2 5 -34 -37 6||
dominant <<1 4 -2 4 -6 -16||
orwell <<7 -3 8 -21 -7 27||
father <<1 -1 3 -4 2 10||
catakleismic <<6 5 22 -6 18 37||
sharp <<2 1 6 -3 4 11||
gamera <<23 40 1 10 -63 -110||

Bronze medals

garibaldi <<1 -8 -14 -15 -25 -10||
hemififths <<2 25 13 35 15 -40||
diminished <<4 4 4 -3 -5 -2||
neptune <<40 22 21 -58 -79 -13||
mother <<1 -1 -2 -4 -6 -2||
augene <<3 0 -6 -7 -18 -14||
sharptone <<1 4 3 4 2 -4||
mitonic <<17 35 -21 16 -81 -147||
sensi <<7 9 13 -2 1 5||
negri <<4 -3 2 -14 -8 13||
semaphore <<2 8 1 8 -4 -20||
myna <<10 9 7 -9 -17 -9||