--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:

> > > > I think it is
> > > > 90:95:101:107:113:120:127:135:143:151:160:169:180

That's made by construction in 5ths:
C = 90 45
G = 3C = 135
D: (3G=405) > 404 202 101
A: (3D=303)> 302 151
E: (3A=453) > 452 226 113
B: (3e=339) > 338 169
F# (3B=507) < 508 254 127 attend the broade layperson's dog-5th
C# (3F#=381) > 380 190 95
G# (3C#=285) < 286 143 another even worser wide dog-5th
Eb (3G#=429) > 428 214 107
Bb (3Eb=321) > 320 160 80 40
F = 3Bb = 120 60 30 15
C = 3F = 45 cycle closed


>... there is the wide fifth 143/95 which is tempered by 286/285,
> about 2/7 comma.
that sound none well, but is still only good,
if you really intend there an 'open' 5th alike in meantonics.
> > >
> > > Noting that 285=3*95, I think the smallest base number that
allows all
> > > fifths to be tempered less than 321/320 will turn out to be over
107.
> > What about ?
> >
> > 125:132:140:148:157:167:176:187:198:210:222:235:250
>
in 5ths cycle:
C 125
G (375) > 374 187
D (561) > 560 280 140 70
A 210 105
E (315) > 314 157
B (471) > 470 235
F# (1175) < 1184 592 148 74 37 even worser wide than the above ex.
C# 222 111
G# (333) < 334 167 another problematic wide 5th
D# (501) > 500 250 125

in order to fix such ugly broade-5th bugs, just consult my:
http://www.strukturbildung.de/Andreas.Sparschuh/Mainz_1999.jpg
without such dog-5ths defects,
as found in some 'esotheric' reinterpretations,
that do not appear in my 1999 original 'discovery' version.

> Wait! There's even better one
> 101:107:113:120:127:135:143:151:160:169:180:191:202
> No fifth differs more than 1/4 pythagorean comma from just.

That's expanded:
C: 101
G: (303) > 302 151
D: (453) > 452 226 113
A: (339) > 338 169
E: (507) < 508 254 127 at least barely only one broade 5th
B: (381) > 382 191
F# (573) > 572 286 143
C# (429) > 428 214 107
G# (312) > 320 160 80 40 20 10 5
Eb 15
Bb 45
F: 135
C: (405) > 404 202 101
>
> And with this
>
> 131:139:147:156:165:175:185:196:208:220:234:247:262
> No fifth differs more than 321/320 from just.
>
C 131
G (393) > 392 196 98 49
D 147
A (441) > 440 220 110 55
E 165
B (495) > 494 247
F# (741) > 740 370 185 {Proposal in order to get rid of the dog}
C# (555) < 556 278 139 { here you'd better let 555 unchanged }
G# (417) > 416 ... 13 {...832 1664 < (1665 = 3*555) }
Eb 39
Bb 117
F: (351) > 350 175 instead W's choice 176=11*2^4
C: (525) > 524 262 131

{considering that little change converts your's originally
'open'-tuning into an
"well"-temperament in the sense of W. & Bach, without the dog}

Attend:
Already Werckmeister used almost about the same ratios in:
http://www.rzuser.uni-heidelberg.de/~tdent/septenarius.html
http://en.wikipedia.org/wiki/Werckmeister_temperament#Werckmeister_IV_.28VI.29:_\
the_Septenarius_tunings

A.S.