The marvel family

family name: marvel
generators: 2, 3, 5

7-limit

name: marvel
comma: 225/224
mapping: [<1 0 0 -5], <0 1 0 2|, <0 0 1 2|]
TOP tuning: [1200.494, 1901.173, 2785.167, 3370.212]
its generators very expeditiously.
possible et tunings: 156 , 175, 228; 384 and 403 using other than the
best JI tuning.
other tunings: 1/4-kleismic is the tuning which leaves octaves and 7s
pure and flattens
3 and 5 by (225/224)^(1/4) (225/224 being termed the septimal
kleisma.) This is
analogous to 1/4-comma meantone, and like 1/4-comma is the minimax
tuning. A
tuning using only 5-limit intervals retunes 3 to |15 -7 -1>, 5 to |15
-8 0> and 7 to
|55 -30 -2>. While not very good so far as 7-limit intervals are
concerned, a tuning
which keeps 2, 3, and 5 pure and uses the sharp value 225/32 in place
of 7 is
theoretically very important; it expresses the marvel-tempered tone
group in terms of
supporting linear temperaments: miracle, waage, hanson, wizard; orwell
and garibaldi
at a slightly lesser accuracy.

11-limit

name: marvel
commas: {225/224, 385/384}
planar wedgie: <<<1 2 -3 -2 1 -4 -5 12 9 -19|||
mapping: [<1 0 0 -5 12|, <0 1 0 2 -1|, <0 0 1 2 -3|]
TOP tuning: [1200.509, 1901.149, 2785.133, 3370.019, 4149.558]
possible et tunings: 72, 238, 310
minimax tuning: (26873856/1375)^(1/9) for 3, (2097152000/1089)^(1/9) for 5
supporting temperaments: miracle, wizard, hanson, slender

name: prodigy
commas: {225/224, 441/440}
planar wedgie: <<<1 -2 3 -2 6 -6 5 -13 11 -4|||
mapping: [<1 0 0 -5 -13|, <0 1 0 2 6|, <0 0 1 2 3|]
TOP tuning: [1200., 1900.058168, 2783.119618]
possible et tunings: 72, 780
supporting temperaments: miracle, waage

thanks, Gene!

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

> family name: marvel
> generators: 2, 3, 5
>
> 7-limit
>
> name: marvel
> comma: 225/224
> mapping: [<1 0 0 -5], <0 1 0 2|, <0 0 1 2|]
> TOP tuning: [1200.494, 1901.173, 2785.167, 3370.212]
> its generators very expeditiously.

is something missing there?

-monz

--- In tuning-math@yahoogroups.com, "monz" <monz@a...> wrote:
> thanks, Gene!
>
> --- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
>
> > family name: marvel
> > generators: 2, 3, 5
> >
> > 7-limit
> >
> > name: marvel
> > comma: 225/224
> > mapping: [<1 0 0 -5], <0 1 0 2|, <0 0 1 2|]
> > TOP tuning: [1200.494, 1901.173, 2785.167, 3370.212]
> > its generators very expeditiously.
>
>
> is something missing there?

It wandered off to the wrong line.

family name: marvel
generators: 2, 3, 5

7-limit

name: marvel
comma: 225/224
mapping: [<1 0 0 -5], <0 1 0 2|, <0 0 1 2|]
TOP tuning: [1200.494, 1901.173, 2785.167, 3370.212]

possible et tunings: 156 , 175, 228; 384 and 403 using other than the
best JI tuning.

other tunings: 1/4-kleismic is the tuning which leaves octaves and 7s
pure and flattens 3 and 5 by (225/224)^(1/4) (225/224 being termed the
septimal kleisma.) This is analogous to 1/4-comma meantone, and like
1/4-comma is the minimax tuning. A tuning using only 5-limit intervals
retunes 3 to |15 -7 -1>, 5 to |15 -8 0> and 7 to |55 -30 -2>. While
not very good so far as 7-limit intervals are concerned, a tuning
which keeps 2, 3, and 5 pure and uses the sharp value 225/32 in place
of 7 is theoretically very important; it expresses the marvel-tempered
tone group in terms of its generators very expeditiously.

supporting linear temperaments: miracle, waage, hanson, wizard; orwell
and garibaldi at a slightly lesser accuracy.

11-limit

name: marvel
commas: {225/224, 385/384}
planar wedgie: <<<1 2 -3 -2 1 -4 -5 12 9 -19|||
mapping: [<1 0 0 -5 12|, <0 1 0 2 -1|, <0 0 1 2 -3|]
TOP tuning: [1200.509, 1901.149, 2785.133, 3370.019, 4149.558]
possible et tunings: 72, 238, 310
minimax tuning: (26873856/1375)^(1/9) for 3,
(2097152000/1089)^(1/9) for 5
supporting temperaments: miracle, wizard, hanson, slender

name: prodigy
commas: {225/224, 441/440}
planar wedgie: <<<1 -2 3 -2 6 -6 5 -13 11 -4|||
mapping: [<1 0 0 -5 -13|, <0 1 0 2 6|, <0 0 1 2 3|]
TOP tuning: [1200., 1900.058168, 2783.119618]
possible et tunings: 72, 780
supporting temperaments: miracle, waage