<2401/2400, 2048/2025> Minkowski reduced

ets: 10, 58, 68

Map (no adjustment needed)

[ 0 2]

[-4 4]

[ 8 3]

[ 3 5]

a = .1030320504 (~15/14) = 7.006179427 / 68; b = 1/2

Error compared to 68:

3: 3.39 3.93

5: 2.79 1.92

7: 2.09 1.76

This system is effectively 58+10

<1029/1024, 686/675> Minkowski reduced

Map (no adjustment)

[ 0 2]

[-3 5]

[ 6 1]

[ 1 5]

Generators a = .3040426304 (~100/81) = 13.985961 / 46; b = 1/2

<4375/4374, 6144/6125>

Minkowski reduction: <4375/4374, 5120/5103>

ets: 7, 39, 46, 53, 99

Map:

[ 1 -2]

[ 3 -1]

[ 6 1]

[-2 13]

Adjusted map:

[ 0 1]

[ -5 3]

[-13 6]

[ 17 -2]

Generators: a = .2828456082 (~17/14, ~~11/9) = 28.00171521 / 99; b=1

This is essentially the 53+46 system of the 99-et; it's also related

to 46+7

Errors compared to 99:

3: 0.9713 1.0753

5: 1.2948 1.5651

7: 1.2245 0.8711

<3136/3125, 49/48>

Minkowski reduction: <3125/3072, 49/48>

Map:

[1 -1]

[0 10]

[2 0]

[2 3]

Adjusted map:

[ 0 1]

[10 0]

[ 2 2]

[ 5 2]

Generator: a = .1584971341 (~10/9, exactly 3^(1/10))

= 3.011445548 / 19

Errors compared to 19:

3: 0 -7.22

5: -5.92 -7.37

7: -17.84 -21.46

This is not your father's 19-et! In fact, with its perfect fifths,

it's not much like either the 19 or 25 et it can be played in. This

one is a genuine original, a temperament best left as a temperament.

Definately worth a look as a way of tempering 19 notes.

--- In tuning-math@y..., genewardsmith@j... wrote:

> <1029/1024, 686/675> Minkowski reduced

>

> Map (no adjustment)

>

> [ 0 2]

> [-3 5]

> [ 6 1]

> [ 1 5]

>

> Generators a = .3040426304 (~100/81) = 13.985961 / 46; b = 1/2

What about the errors?

--- In tuning-math@y..., "Paul Erlich" <paul@s...> wrote:

> --- In tuning-math@y..., genewardsmith@j... wrote:

>

> > <1029/1024, 686/675> Minkowski reduced

> >

> > Map (no adjustment)

> >

> > [ 0 2]

> > [-3 5]

> > [ 6 1]

> > [ 1 5]

> >

> > Generators a = .3040426304 (~100/81) = 13.985961 / 46; b = 1/2

>

> What about the errors?

Did I forget those? I was supposed to include them, with a comparison

to the 46 et:

3: 3.49 2.39

5: 2.79 4.99

7: -3.98 -3.61

There doesn't seem to be much gained by not using 46-et for this. I

like this 686/675 in the kernel--it gives it character. It's also a

good system, with lots of 7-limit stuff in it.