DE scales with the stepwise harmonization property

Here is what I get by the most plausible temperings of the
corresponding JI scales. The DE scales for these are now unique up to
transposition, so all the headaches about correctly ordering the steps
vanish.

Diminished[8]
[28/25, 10/9, 15/14, 21/20] [2, 2, 3, 1]
[28/25, 10/9, 15/14, 25/24] [3, 1, 3, 1]

(28/25)/(10/9) = 126/125
(15/14)/(21/20) = 50/49
(15/14)/(25/24) = 36/35

Augmented[9]
[28/25, 35/32, 15/14, 16/15] [1, 2, 3, 3]

(28/25)/(35/32) = 128/125
(15/14)/(16/15) = 225/224

Blackwood[10]
[10/9, 35/32, 16/15, 36/35] [2, 3, 2, 3]
[10/9, 35/32, 21/20, 36/35] [4, 1, 2, 3]
[10/9, 15/14, 16/15, 21/20] [2, 3, 2, 3]
[35/32, 15/14, 16/15, 21/20] [2, 3, 4, 1,
[35/32, 15/14, 16/15, 36/35] [3, 2, 4, 1]

(10/9)/(35/32) = 64/63
(16/15)/(36/35) = 28/27
(21/20)/(36/35) = 49/48
(10/9)/(15/14) = 28/27
(16/15)/(21/20) = 64/63

Kleismic[11]
[28/25, 10/9, 25/24, 36/35] [3, 1, 4, 3]

(28/25)/(10/9) = 126/125
(25/24)/(36/35) = 876/864

Superpythagorean[12]
[10/9, 35/32, 36/35, 49/48] [4, 1, 5, 2]

(10/9)/(35/32) = 64/63
(36/35)/(49/48) = 1728/1715

Meantone[12]
[15/14, 16/15, 21/20, 25/24] [3, 4, 3, 2]

(15/14)/(16/15) = 225/224
(21/20)/(25/24) = 126/125

Augmented[12]
[15/14, 16/15, 21/20, 49/48] [5, 4, 1, 2]

(15/14)/(16/15) = 225/224
(21/20)/(49/48) = 36/35

Orwell[13]
[15/14, 16/15, 36/35, 49/48] [5, 4, 1, 3]

(15/14)/(16/15) = 225/224
(36/35)/(49/48) = 1728/1715

Porcupine[15]
[16/15, 21/20, 25/24, 36/35] [4, 3, 5, 3]

(16/15)/(21/20) = 64/63
(25/24)/(36/35) = 875/864

>Augmented[9]
>[28/25, 35/32, 15/14, 16/15] [1, 2, 3, 3]
>
>(28/25)/(35/32) = 128/125
>(15/14)/(16/15) = 225/224

Augmented[9], eh? How far is the 7-limit TOP version
from...

!
TOP 5-limit Augmented[9].
9
!
93.15
306.77
399.92
493.07
706.69
799.84
892.99
1106.61
1199.76
!

...?

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >Augmented[9]
> >[28/25, 35/32, 15/14, 16/15] [1, 2, 3, 3]
> >
> >(28/25)/(35/32) = 128/125
> >(15/14)/(16/15) = 225/224
>
> Augmented[9], eh? How far is the 7-limit TOP version
> from...
>
> !
> TOP 5-limit Augmented[9].
> 9
> !
> 93.15
> 306.77
> 399.92
> 493.07
> 706.69
> 799.84
> 892.99
> 1106.61
> 1199.76
> !
>
> ...?
>
> -Carl

Just look at the horagram, Carl!

107.31
292.68
399.99
507.3
692.67
799.98
907.29
1092.66
1199.97

>> Augmented[9], eh? How far is the 7-limit TOP version
>> from...
>>
>> !
>> TOP 5-limit Augmented[9].
>> 9
>> !
>> 93.15
>> 306.77
>> 399.92
>> 493.07
>> 706.69
>> 799.84
>> 892.99
>> 1106.61
>> 1199.76
>> !
>>
>> ...?
>>
>> -Carl
>
>Just look at the horagram, Carl!
>
>107.31
>292.68
>399.99
>507.3
>692.67
>799.98
>907.29
>1092.66
>1199.97

Oh! Where are the 7-limit horagrams?

-C.

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> Augmented[9], eh? How far is the 7-limit TOP version
> >> from...
> >>
> >> !
> >> TOP 5-limit Augmented[9].
> >> 9
> >> !
> >> 93.15
> >> 306.77
> >> 399.92
> >> 493.07
> >> 706.69
> >> 799.84
> >> 892.99
> >> 1106.61
> >> 1199.76
> >> !
> >>
> >> ...?
> >>
> >> -Carl
> >
> >Just look at the horagram, Carl!
> >
> >107.31
> >292.68
> >399.99
> >507.3
> >692.67
> >799.98
> >907.29
> >1092.66
> >1199.97
>
> Oh! Where are the 7-limit horagrams?
>
> -C.

Some of them are in

/tuning-math/files/perlich/

some of them are in

/tuning-math/files/Erlich/sevenlimit.zip

and this one, aug7.gif, is in both.