--- In tuning@yahoogroups.com, Jacques Dudon <fotosonix@...> wrote:
that he
>...understands absence of harmonic waste in a 12 tones temperament as

1. > having no fifths intervals wider than 3/2,
2. > and no major thirds intervals smaller than 5/4

> Is that right, or can you or someone
> tell me how we should define it ?

Hi Jaques & all others,
Just those 2 conditions define Werckmeister's german term
"wohl-temperiert" = 'well-tempered'

http://dict.leo.org/ende?lp=ende&p=wlqAU.&search=wohltemperiert
http://dict.leo.org/ende?lp=ende&p=wlqAU.&search=wohltemperierte

as used by J.S.Bach in Werckmeister's sense:
http://en.wikipedia.org/wiki/Well-Tempered_Clavier

for example by the following cycle of a dozen 5ths:


110A_2 220A_3 440HzA_4
329 E_4 (< 330 = 3*A_2)
493.5B_4 987B_5 = 3*E_4
185F#_3 370 F#_4 740F#_5...2960F#_7(<2961=3*B_5)
277.5C#_4 555C#_5 = 3*F#_3
104G#_2 208G#_3 416 G#_4 832G#_5 1664G#_6(<1665=3*C#_5)
156Eb_3 312 Eb_4 = 3*G#_2
117Bb_2 234Bb_3 468 Bb_4 = 3*Eb_3
351 F_4 = 3*Bb_2
(65.7 131.4<)131.5C_3 263middleC_4 526C_5 1052C_6 (<1053 = 3*F_4)
65.7*3 = 197.1G_3 394.2 G_4
(441/3=147 294 <) 294.5 D_4 589D_5 (<591.3 = 3*G_3)
440 A_4 (<441 = 3*147)

!wohltemperiert.scl
!for J.S.Bach's WTC invented by Andreas Sparschuh in 2008
12
!
C-major beats C:E:G = 4: 5*(1316/1315): 6*(1314/1315) synchronously
!
555/526 ! C# 277.5/263
589/526 ! D 294.5/263
312/263 ! Eb
329/263 ! E (5/4)*(1316/1315) ~1.316...Cents sharper than JI 5:4
351/263 ! F
370/263 ! F#
1971/1315 ! G 394.2/263 (3/2)*(1314/1315) ~-1.317...C lower than 3:2
416/263 ! G#
440/263 ! A
468/263 ! Bb
987/526 ! B 493.5/263
2/1
!

that's imho my preferred rational temperament,
that i personally do reccomend for playing in modern HIP
http://en.wikipedia.org/wiki/Historically_informed_performance
of J.S.Bach's music in all 24keys
on modern keyboard instruments with
http://en.wikipedia.org/wiki/A440
as choice of absolute pitch.

It replaces all my older proposals.

Quests:
1. Who in that group dares to try out that one on his/hers own piano?
2. Has anybody suggestions for better ratios in order to improve it?

asks sincerely
A.S.