Mailing list post
From: Gene Ward Smith (2005-10-12)
Subject: A synched 5120/5103 scale example
In message
http://groups.yahoo.com/group/tuning-math/message/10065
I noted that the 3x3x3 chord cube, extended to quintads, produces a 47
note scale which is a good candidate for hemififths tempering (to a 46
note scale, eliminating a 2401/2400 step). As an example of the
closeness of hemififths and 5120/5103 synch tuning, here is the
inversion of that scale tuned to that tuning; since the 2401/2400 step
is not eliminated but shrunk, I picked one of the two nearby steps to
produce the scale. It has 20 otonal tetrads and 17 otonal quintads, of
which one is anomalous; it still has synched beating of the major,
minor and fifth components (brat -1), but the 7 is 0.182 cents sharp
rather than 0.423 cents sharp.
! betacub.scl
inverted 3x3x3 9-limit quintad cube beta (5120/5103) synch tempered
46
!
49.729878
85.285706
110.150645
120.600012
135.015584
170.329890
181.020779
205.885718
230.750657
255.615596
266.306484
316.036363
351.350669
386.906496
436.636374
472.192202
497.057141
521.922080
546.787019
582.342847
617.657153
632.072725
667.387031
702.942859
727.807798
752.672737
763.363626
788.228565
813.093504
823.542871
883.963637
898.379209
908.828577
933.693516
969.249343
994.114282
1004.563649
1018.979221
1043.844161
1079.399988
1089.849355
1114.714294
1129.129866
1139.579233
1164.444172
1200.000000
Full thread (5 messages)
From: Gene Ward Smith (2005-10-12)
Subject: A synched 5120/5103 scale example
In message
http://groups.yahoo.com/group/tuning-math/message/10065
I noted that the 3x3x3 chord cube, extended to quintads, produces a 47
note scale which is a good candidate for hemififths tempering (to a 46
note scale, eliminating a 2401/2400 step). As an example of the
closeness of hemififths and 5120/5103 synch tuning, here is the
inversion of that scale tuned to that tuning; since the 2401/2400 step
is not eliminated but shrunk, I picked one of the two nearby steps to
produce the scale. It has 20 otonal tetrads and 17 otonal quintads, of
which one is anomalous; it still has synched beating of the major,
minor and fifth components (brat -1), but the 7 is 0.182 cents sharp
rather than 0.423 cents sharp.
! betacub.scl
inverted 3x3x3 9-limit quintad cube beta (5120/5103) synch tempered
46
!
49.729878
85.285706
110.150645
120.600012
135.015584
170.329890
181.020779
205.885718
230.750657
255.615596
266.306484
316.036363
351.350669
386.906496
436.636374
472.192202
497.057141
521.922080
546.787019
582.342847
617.657153
632.072725
667.387031
702.942859
727.807798
752.672737
763.363626
788.228565
813.093504
823.542871
883.963637
898.379209
908.828577
933.693516
969.249343
994.114282
1004.563649
1018.979221
1043.844161
1079.399988
1089.849355
1114.714294
1129.129866
1139.579233
1164.444172
1200.000000
From: Paul Erlich (2005-10-14)
Subject: Re: A synched 5120/5103 scale example
--- In [email protected], "Gene Ward Smith" <gwsmith@s...>
wrote:
> beta (5120/5103)
Eduardo Sabat-Garibaldi introduced the "beta" terminology for
*different* 'commas'; hence "beta 2" and "beta 5" are different, for
example. "Beta" alone doesn't signify any comma according to Eduardo's
system or any other that I know of.
From: Carl Lumma (2005-10-14)
Subject: Re: [tuning-math] Re: A synched 5120/5103 scale example
>> beta (5120/5103)
>
>Eduardo Sabat-Garibaldi introduced the "beta" terminology for
>*different* 'commas'; hence "beta 2" and "beta 5" are different, for
>example. "Beta" alone doesn't signify any comma according to Eduardo's
>system or any other that I know of.
And Wendy Carlos has a temperament by this name.
-Carl
From: Gene Ward Smith (2005-10-15)
Subject: Re: A synched 5120/5103 scale example
--- In [email protected], "Paul Erlich" <perlich@a...> wrote:
>
> --- In [email protected], "Gene Ward Smith" <gwsmith@s...>
> wrote:
>
> > beta (5120/5103)
>
> Eduardo Sabat-Garibaldi introduced the "beta" terminology for
> *different* 'commas'; hence "beta 2" and "beta 5" are different, for
> example. "Beta" alone doesn't signify any comma according to Eduardo's
> system or any other that I know of.
Beta5 is the only beta Manuel lists, I'll call it something else if
someone has a good suggestion.
From: Paul Erlich (2005-10-17)
Subject: Re: A synched 5120/5103 scale example
--- In [email protected], "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> --- In [email protected], "Paul Erlich" <perlich@a...>
wrote:
> >
> > --- In [email protected], "Gene Ward Smith"
<gwsmith@s...>
> > wrote:
> >
> > > beta (5120/5103)
> >
> > Eduardo Sabat-Garibaldi introduced the "beta" terminology for
> > *different* 'commas'; hence "beta 2" and "beta 5" are different,
for
> > example. "Beta" alone doesn't signify any comma according to
Eduardo's
> > system or any other that I know of.
>
> Beta5 is the only beta Manuel lists,
Really? What happened to Beta2, Manuel? Any others?