24 and 26 et scales

24-et

With thirds the same as the 12-et, and 7s which aren't that great,
this is an easy division to scoff at, given its status as the choice
of those who aren't quite ready to take the real plunge. However it
has its own sort of scales, which are worth considering.

The whole tone generator (4/24) with an interval of repletion 2^(1/4)
gives us 114114114114 for a 12-note alternative to 12-et, which can
be extended to 1113111311131113, for 16 notes, and etc. The 7-limit
complexity is 8, and the 16-note scale has interesting 11 and 13
possibilities.

The 9/24 generator is similar, we have 332332332 giving us a 9-note
scale, and 121121211212112 for a 15-note scale; with a 7-limit
complexity of 6 these are fully equipped, and again the 15-note scale
gets into 11 and 13 territory.

Finally, there is 5/24, which gives us a 9-note scale 141414144 and a
14-note scale 11311311313, with a 7-limit complexity of 8.

26-et

The 26-et makes up for its not very inspiring fifths and thirds by
being an all-around utility division up to the 17-limit, which also
can seem very traditional since it wears one hat as 4/9-comma
meantone temperament, with a diatonic scale of pattern 4434443 and a
12-note scale (or temperament) of pattern 331313313131. It also has
4/26, with a 9-complexity of 8, and scales 222223222223 of 12 notes
and 22222212222221 of 14 notes; 10/26 with a 7-complexity of 8 and
13-complexity of 14, and scales 2323323233 of 10 notes and
2212212222122122 of 16 notes; and 12/26 with a 7-complexity of 8 and
scales 5151151511 of ten notes and 41141114114111 of 14 notes.

Hi, Gene. I have yet to understand the meaning of meantone
temperaments of higher fractional values than 1/4. I believe I
understand 1/6-comma meantone (1/6 is 2/3 of 1/4) to mean that only
2/3's of the comma is distributed to the 4 P5s and 1/3 of it
(7.166... cents)is left on the major third so the fifths are only 3.6
instead of 5.4 cents flat and the thirds are almost twice as pure as
those of 12-tET.

So what are 2/7-comma, 1/3-comma, etc. meantone? Extending my logic,
if it is correct, to these fractions would imply distributing more
than the full comma to the fifths and leaving the thirds flat!...???

--- In tuning@y..., genewardsmith@j... wrote:
> 24-et
>
> With thirds the same as the 12-et, and 7s which aren't that great,
> this is an easy division to scoff at, given its status as the
choice
> of those who aren't quite ready to take the real plunge. However it
> has its own sort of scales, which are worth considering.
>
> The whole tone generator (4/24) with an interval of repletion 2^
(1/4)
> gives us 114114114114 for a 12-note alternative to 12-et, which can
> be extended to 1113111311131113, for 16 notes, and etc. The 7-limit
> complexity is 8, and the 16-note scale has interesting 11 and 13
> possibilities.
>
> The 9/24 generator is similar, we have 332332332 giving us a 9-note
> scale, and 121121211212112 for a 15-note scale; with a 7-limit
> complexity of 6 these are fully equipped, and again the 15-note
scale
> gets into 11 and 13 territory.
>
> Finally, there is 5/24, which gives us a 9-note scale 141414144 and
a
> 14-note scale 11311311313, with a 7-limit complexity of 8.
>
> 26-et
>
> The 26-et makes up for its not very inspiring fifths and thirds by
> being an all-around utility division up to the 17-limit, which also
> can seem very traditional since it wears one hat as 4/9-comma
> meantone temperament, with a diatonic scale of pattern 4434443 and
a
> 12-note scale (or temperament) of pattern 331313313131. It also has
> 4/26, with a 9-complexity of 8, and scales 222223222223 of 12 notes
> and 22222212222221 of 14 notes; 10/26 with a 7-complexity of 8 and
> 13-complexity of 14, and scales 2323323233 of 10 notes and
> 2212212222122122 of 16 notes; and 12/26 with a 7-complexity of 8
and
> scales 5151151511 of ten notes and 41141114114111 of 14 notes.

[Bob Wendell wrote:]
>Hi, Gene. I have yet to understand the meaning of meantone
>temperaments of higher fractional values than 1/4. I believe I
>understand 1/6-comma meantone (1/6 is 2/3 of 1/4) to mean that only
>2/3's of the comma is distributed to the 4 P5s and 1/3 of it
>(7.166... cents)is left on the major third so the fifths are only 3.6
>instead of 5.4 cents flat and the thirds are almost twice as pure as
>those of 12-tET.

>So what are 2/7-comma, 1/3-comma, etc. meantone? Extending my logic,
>if it is correct, to these fractions would imply distributing more
>than the full comma to the fifths and leaving the thirds flat!...???

Sorry to jump in, but...

As you know, x-comma meantone means "temper the fifth by narrowing
it by x". 1/3 comma meantone makes minor thirds exactly 6:5. Anything
that narrows fifths by more than that might be very hard to justify from
a JI perspective. Various different meantones fall out as a result of
various calculations on how to optimize something. I have hit exactly
2/7 and exactly 1/4 comma meantones "by accident" using my tuning
program on simple sequences. Paul E recently hinted at the methods
which produce other "ideal" meantone numbers.

JdL

--- In tuning@y..., BobWendell@t... wrote:
> Hi, Gene. I have yet to understand the meaning of meantone
> temperaments of higher fractional values than 1/4. I believe I
> understand 1/6-comma meantone (1/6 is 2/3 of 1/4) to mean that only
> 2/3's of the comma is distributed to the 4 P5s and 1/3 of it
> (7.166... cents)is left on the major third so the fifths are only
3.6
> instead of 5.4 cents flat and the thirds are almost twice as pure
as
> those of 12-tET.
>
> So what are 2/7-comma, 1/3-comma, etc. meantone? Extending my
logic,
> if it is correct, to these fractions would imply distributing more
> than the full comma to the fifths and leaving the thirds flat!...???

That's quite correct, Bob -- if you mean _major_ thirds. 2/7-comma
meantone was the earliest meantone to be described precisely. It does
the best job of balancing the major thirds with the minor thirds, and
the major sixths with the minor sixths. All these intervals are only
1/7 comma off from JI. Meanwhile, 1/3-comma meantone has pure major
sixths and minor thirds, and closes nicely after 19 notes. If you
minimize the sum of the squared errors of all the 5-limit consonant
intervals, you get 7/26-comma meantone, which was advocated by
Woolhouse.

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

> 26-et
>
> The 26-et makes up for its not very inspiring fifths and thirds by
> being an all-around utility division up to the 17-limit,

It's the first ET consistent through the 13-limit, but 17-limit?

> It also has
> 4/26, with a 9-complexity of 8, and scales 222223222223 of 12 notes
> and 22222212222221 of 14 notes;

The latter also has an "omnitetrachordal" variant: 22222221222221.
I've discussed these scales many times here, including detailed
discussions with Dave Keenan; and they're mentioned in my paper. They
can be seen as two interlaced diatonic scales, each completing the
other's 5-limit triads into 7-limit tetrads. Quite remarkable, if I
may say so! Even better than 26-tET for them is 38-tET: take each of
the diatonic scales in a different 19-tET subset.

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

> > The 26-et makes up for its not very inspiring fifths and thirds
by
> > being an all-around utility division up to the 17-limit,
>
> It's the first ET consistent through the 13-limit, but 17-limit?

It has a 5 which is 17.08 cents sharp and a 9 19.29 cents sharp,
compared to a 17 which is only 12.65 cents sharp, so I would say yes,
17-limit. For that matter 19 at 20.59 cents sharp isn't much worse!

>They
> can be seen as two interlaced diatonic scales, each completing the
> other's 5-limit triads into 7-limit tetrads.

Fascinating! I see I should buy a new cartridge for my printer and
print it out.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > --- In tuning@y..., genewardsmith@j... wrote:
>
> > > The 26-et makes up for its not very inspiring fifths and thirds
> by
> > > being an all-around utility division up to the 17-limit,
> >
> > It's the first ET consistent through the 13-limit, but 17-limit?
>
> It has a 5 which is 17.08 cents sharp and a 9 19.29 cents sharp,
> compared to a 17 which is only 12.65 cents sharp, so I would say yes,
> 17-limit.

Gene, when you're trying to explore 17-limit harmony, you have to consider _all_ the ratios of
17, not just 17:16 (or 17:1).

Also, 24-tET is inconsistent in the 7-limit -- if you try tuning it up, you'll see that this is actually a
serious problem.

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

> > It has a 5 which is 17.08 cents sharp and a 9 19.29 cents sharp,
> > compared to a 17 which is only 12.65 cents sharp, so I would say
yes,
> > 17-limit.

> Gene, when you're trying to explore 17-limit harmony, you have to
consider _all_ the ratios of
> 17, not just 17:16 (or 17:1).

I did--I pointed out that 3, 5, and 17 are all sharp, and that 9 is
sharper than 17, so you can see for yourself that there is not a
problem. If 13 is acceptable to you, being a little flat, then 17 had
better be also, since it's sharp but not too sharp.

> Also, 24-tET is inconsistent in the 7-limit -- if you try tuning it
up, you'll see that this is actually a
> serious problem.

I don't think so, and I think you attach more significance to
consistency than you should. A consistent measure of goodness is a
fine thing, but "consistency" as a fetish I don't understand. If you
take the 24-et in the 7-limit to be defined by the [24, 38, 56, 67]
val, then it is consistent. It's not a problem and consistency as
such is *never* a problem, the problem is how well in tune things
are. In this particular case the problem is that the 5 is sharp and
the 7 is flat so things such as 7/5 are even more out of whack.
However, it still works out as better than the [24, 38, 56, 68]
system of the 12-et taken twice, which you could also use if you
like.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> > > It has a 5 which is 17.08 cents sharp and a 9 19.29 cents
sharp,
> > > compared to a 17 which is only 12.65 cents sharp, so I would
say
> yes,
> > > 17-limit.
>
> > Gene, when you're trying to explore 17-limit harmony, you have to
> consider _all_ the ratios of
> > 17, not just 17:16 (or 17:1).
>
> I did--I pointed out that 3, 5, and 17 are all sharp, and that 9 is
> sharper than 17, so you can see for yourself that there is not a
> problem. If 13 is acceptable to you, being a little flat, then 17
had
> better be also, since it's sharp but not too sharp.

Well, if you're omitting 11, then you may be right . . . is 26
consistent with respect to the set (1,3,5,7,9,13,15) ?
>
> > Also, 24-tET is inconsistent in the 7-limit -- if you try tuning
it
> up, you'll see that this is actually a
> > serious problem.
>
> I don't think so, and I think you attach more significance to
> consistency than you should. A consistent measure of goodness is a
> fine thing, but "consistency" as a fetish I don't understand. If
you
> take the 24-et in the 7-limit to be defined by the [24, 38, 56, 67]
> val, then it is consistent. It's not a problem and consistency as
> such is *never* a problem, the problem is how well in tune things
> are. In this particular case the problem is that the 5 is sharp and
> the 7 is flat so things such as 7/5 are even more out of whack.
> However, it still works out as better than the [24, 38, 56, 68]
> system of the 12-et taken twice, which you could also use if you
> like.

Any consistent measure of goodness will show 24-tET can't
substantially improve on 12-tET in the 7-limit -- hence it's not
really good at all (to my ears). The problem is when people look at
the approximations to all the 7-limit intervals individually, see
that they're good in 24-tET, but fail to realize that they won't
combine in a consistent way. You'll see this over and over again in
the literature.

you are writing to the wrong email address, please stop emailing me!!

you are writing the wrong address, stop emailing me

wrong address agin take me off your mailing address. this is jrtroy65@aol.com
not gene

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

> Well, if you're omitting 11, then you may be right . . . is 26
> consistent with respect to the set (1,3,5,7,9,13,15) ?

I get the following values, in relative cents:

3: -251
5: -444
7: 10.5
11: 66
13: -254
17: -329
19: -535

If we take 66 - 2*(-251) we get 568, which is less than 600, so the
26-et is consistent through the 11-limit; however worrying about
whether the number is or is not more than 600 strikes me as
numerology rather than music theory. The values for 13 and 17, as I
remarked, are not as flat as 9, so there isn't much reason to neglect
them--the 15, at -695, goes over the magic barrier, and we can see
that 13 and 17 are quite a lot better. The conclusion is that it's
consistent through the 13-limit but not up to 15, in case you think
that matters. The real point is how well in tune things are, and that
may not be acceptable to some palates, but that much was true even in
the 5-limit.

> Any consistent measure of goodness will show 24-tET can't
> substantially improve on 12-tET in the 7-limit -- hence it's not
> really good at all (to my ears).

It seems to me you've ended up saying what I started out by saying,
that the 24-et isn't so hot for 7-harmonies. Having said that, and
noted that it is very good for some other primes, what's really left
to say?

The problem is when people look at
> the approximations to all the 7-limit intervals individually, see
> that they're good in 24-tET, but fail to realize that they won't
> combine in a consistent way.

For some value of "good", I suppose. Since I always think in terms of
vals, it's not a problem likely to bite me, at any rate.

In-Reply-To: <9qe1c4+4deb@eGroups.com>
Gene wrote:

> If we take 66 - 2*(-251) we get 568, which is less than 600, so the
> 26-et is consistent through the 11-limit; however worrying about
> whether the number is or is not more than 600 strikes me as
> numerology rather than music theory. The values for 13 and 17, as I
> remarked, are not as flat as 9, so there isn't much reason to neglect
> them--the 15, at -695, goes over the magic barrier, and we can see
> that 13 and 17 are quite a lot better. The conclusion is that it's
> consistent through the 13-limit but not up to 15, in case you think
> that matters. The real point is how well in tune things are, and that
> may not be acceptable to some palates, but that much was true even in
> the 5-limit.

Yes, it's consistent in the 13-limit, but not 15. It is consistent for
the 1.3.5.7.9.13.17.19.21 diamond, and so close for the
1.3.5.7.9.11.13.17.19.21 diamond that we're splitting an even finer hair
than you do above.

Here are my calculations:

>>> import temper
>>> def test26(integers):
... harmonics = []
... for n in integers:
... harmonics.append(temper.factorize(n)[1:])
... sublimit = temper.TonalityDiamond(harmonics)
... et26 = temper.PrimeET(26, temper.primes[:len(sublimit[0])])
... return et26.getWorstError(sublimit)
...
>>> test26((1,3,5,7,9,13,15))
0.58792751232376617
>>> test26((1,3,5,7,9,11,13))
0.4728279529303876
>>> test26((1,3,5,7,9,11,13,17,19))
0.50089326496348008
>>> test26((1,3,5,7,9,11,13,17,19,21))
0.50089326496348008
>>> test26((1,3,5,7,9,13,17,19,21))
0.45488737603550078

Boy, is this still on the main list? The advantage of consistency is that
no interval is closer to JI than the "correct" approximation. That
probably is musically useful, and certainly makes the calculations easier.

Graham

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

> > Any consistent measure of goodness will show 24-tET can't
> > substantially improve on 12-tET in the 7-limit -- hence it's not
> > really good at all (to my ears).
>
> It seems to me you've ended up saying what I started out by saying,
> that the 24-et isn't so hot for 7-harmonies. Having said that, and
> noted that it is very good for some other primes, what's really
left
> to say?

Sorry, Gene -- the only things you wrote about 24-tET were relating
to its 7-limit approximations. But given that 15-tET and 19-tET do
much better in the 7-limit than 24-tET, and you didn't make a post
about 15-tET or 19-tET, I thought the wrong impression was being
given off.

Hi, John! Good to hear from you again! I posted a reply to this
Friday, but it doesn't seem to have made it into the list. You're
more than welcome to "jump in" my friend. I appreciate your
confirmation and Paul's, the latter of which came after my first
attempt to post.

With regard to this reply, I have seen the whole meantone scenario
more clearly, and now Paul Erlich's replies have further confirmed my
conclusions that came after your confirmation, John. I had already
run into Woolhouse at Joe Monz's site. Quite a guy! Impressed that
Paul had concluded the same via another route. Congratulations, Paul!
You're both very benignly monsturous wizards in your own way. I have
a great deal of respect for Margo's and Gene's contibutions, too,
alhtough I'm not so well-acquainted with the algebraic methods Gene
and Paul are perpetually discussing. What a terrific clan you've
gathered here!

IN connection with meantone systems, before either reply I'd been
listening to some 19-tET stuff over the previous days and found it
quite a "trip", if you will. It is very pleasingly close to JI, but
just weirdly different enough from either JI or 12-tET in it's
melodic/harmonic and structural properties to both charm and
fascinate my little musical brain quite a lot. It sort of scratches
some corners that have not previously been musically scratched.

My musical mind has always had a penchant for the exotic if not the
chaotic (if you pardon the slightly funky rhyme, please), so I go for
near-just in at least 5-limit, but have also always savored the
unique melodic colors of 11-limit blues intervals and the 13-limit
Arabic and Persian stuff.

I've always felt a pinch that western 5-limit concepts had to
sacrifice so much melodic variety in the interest of harmonic
compatibilities. I feel the future of music is away from such
compromise and toward a powerful harmonic language or languages that
integrate the whole beautiful thing without demanidng such
compromises. That is the fundamental motivation for being on this
list and I'm finding a lot of nourishment here. Thanks to all!

Now I just need to find both the time and the means to really play
with these ideas musically. I've already started sketching the first
thematic bits for a 19-tET polyphonic piece for voices, synths,
bells, perhaps percussion, even sparing use of trumpets at points,
etc. in an antiphonal arrangement around the audience.

I'm starting with a simple idea of using the basic meantone-implicit
pentatonic scale. Pentatonic tritonality fifths apart implies the
common diatonic scale of seven notes, of course, so tritonality is
fascinating and multi-dimensional, yet its relative simplicity makes
it quite accessible to the unsophisticated ear as well as pleasingly
pure and consonant.

It generates harmonies that tend to be triadic/tetradic, but tend not
to conform to any kind of conventional functional harmony because of
the constraints within any one voice of writing pentatonically in a
particular key (using any scale rotation, that is, melodic mode we
choose). I allow the bass part, however, to use any note of the
complete underlying diatonic scale.

It's been quite fun so far, but have no means as of yet to actually
hear it in 19-tET. I'm working in 12-tET and projecting with the ear
of my imagination into 19-tET. It's a start, but not so very
satisfactory. Although I'm pretty good at mentally projecting with my
ear, I want the tuning medium to start leading more fully my musical
imagination instead of the current inverted situation.

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
> [Bob Wendell wrote:]
> >Hi, Gene. I have yet to understand the meaning of meantone
> >temperaments of higher fractional values than 1/4. I believe I
> >understand 1/6-comma meantone (1/6 is 2/3 of 1/4) to mean that
only
> >2/3's of the comma is distributed to the 4 P5s and 1/3 of it
> >(7.166... cents)is left on the major third so the fifths are only
3.6
> >instead of 5.4 cents flat and the thirds are almost twice as pure
as
> >those of 12-tET.
>
> >So what are 2/7-comma, 1/3-comma, etc. meantone? Extending my
logic,
> >if it is correct, to these fractions would imply distributing more
> >than the full comma to the fifths and leaving the thirds
flat!...???
>
> Sorry to jump in, but...
>
> As you know, x-comma meantone means "temper the fifth by narrowing
> it by x". 1/3 comma meantone makes minor thirds exactly 6:5.
Anything
> that narrows fifths by more than that might be very hard to justify
from
> a JI perspective. Various different meantones fall out as a result
of
> various calculations on how to optimize something. I have hit
exactly
> 2/7 and exactly 1/4 comma meantones "by accident" using my tuning
> program on simple sequences. Paul E recently hinted at the methods
> which produce other "ideal" meantone numbers.
>
> JdL

--- In tuning@y..., BobWendell@t... wrote:

> Now I just need to find both the time and the means to really play
> with these ideas musically. I've already started sketching the
first
> thematic bits for a 19-tET polyphonic piece for voices, synths,
> bells, perhaps percussion, even sparing use of trumpets at points,
> etc. in an antiphonal arrangement around the audience.
>
> I'm starting with a simple idea of using the basic meantone-
implicit
> pentatonic scale. Pentatonic tritonality fifths apart implies the
> common diatonic scale of seven notes, of course, so tritonality is
> fascinating and multi-dimensional, yet its relative simplicity
makes
> it quite accessible to the unsophisticated ear as well as
pleasingly
> pure and consonant.

Whoa, Bob . . . what do you mean by "tritonality" and "tritonality
fifths apart"? You totally lost me here!
>
> It generates harmonies that tend to be triadic/tetradic, but tend
not
> to conform to any kind of conventional functional harmony because
of
> the constraints within any one voice of writing pentatonically in a
> particular key (using any scale rotation, that is, melodic mode we
> choose). I allow the bass part, however, to use any note of the
> complete underlying diatonic scale.

Oh . . . now I think I understand what you mean. "Tritonality"
suggests tritones to my dull mind.

> It's been quite fun so far, but have no means as of yet to actually
> hear it in 19-tET. I'm working in 12-tET and projecting with the
ear
> of my imagination into 19-tET. It's a start, but not so very
> satisfactory. Although I'm pretty good at mentally projecting with
my
> ear, I want the tuning medium to start leading more fully my
musical
> imagination instead of the current inverted situation.

Tune your piano to a meantone or well-temperament where the white
notes are in 19-tET!

Thanks, but I have incredibly limited means microtonally compared to
many of you here. I have a 5-yr-old Casio I picked up at Best Buys
for $450 bucks because it was the cheapest keyboard that had a half-
way decent choral sound on it for feedback on my arrangements and
compositions for choir. It has single-channel midi in and out and
it's 12-tET with no tuning tables or any tuning alternatives
whatsoever.

I recruit avionics engineers for a living and am watching my paycheck
dwindle toward base salary as avionics divisions all over the place
downsize. Ouch! My Argentine wife has never had to work since she
married me and moved to this country, so it's not a simple matter of
just going out and buying what I need. Wish it were.

I'm wondering how easy it would be to use SCALA and what is it? FTS?
or something, just to at least get some kind of funky mechanical
audio sketch of my ideas in 19-tET.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., BobWendell@t... wrote:
>
> > Now I just need to find both the time and the means to really
play
> > with these ideas musically. I've already started sketching the
> first
> > thematic bits for a 19-tET polyphonic piece for voices, synths,
> > bells, perhaps percussion, even sparing use of trumpets at
points,
> > etc. in an antiphonal arrangement around the audience.
> >
> > I'm starting with a simple idea of using the basic meantone-
> implicit
> > pentatonic scale. Pentatonic tritonality fifths apart implies the
> > common diatonic scale of seven notes, of course, so tritonality
is
> > fascinating and multi-dimensional, yet its relative simplicity
> makes
> > it quite accessible to the unsophisticated ear as well as
> pleasingly
> > pure and consonant.
>
> Whoa, Bob . . . what do you mean by "tritonality" and "tritonality
> fifths apart"? You totally lost me here!
> >
> > It generates harmonies that tend to be triadic/tetradic, but tend
> not
> > to conform to any kind of conventional functional harmony because
> of
> > the constraints within any one voice of writing pentatonically in
a
> > particular key (using any scale rotation, that is, melodic mode
we
> > choose). I allow the bass part, however, to use any note of the
> > complete underlying diatonic scale.
>
> Oh . . . now I think I understand what you mean. "Tritonality"
> suggests tritones to my dull mind.
>
> > It's been quite fun so far, but have no means as of yet to
actually
> > hear it in 19-tET. I'm working in 12-tET and projecting with the
> ear
> > of my imagination into 19-tET. It's a start, but not so very
> > satisfactory. Although I'm pretty good at mentally projecting
with
> my
> > ear, I want the tuning medium to start leading more fully my
> musical
> > imagination instead of the current inverted situation.
>
> Tune your piano to a meantone or well-temperament where the white
> notes are in 19-tET!

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

> Sorry, Gene -- the only things you wrote about 24-tET were relating
> to its 7-limit approximations. But given that 15-tET and 19-tET do
> much better in the 7-limit than 24-tET, and you didn't make a post
> about 15-tET or 19-tET, I thought the wrong impression was being
> given off.

Actually, I spent a whole post on 19, but if you want to complain I
haven't talked about 31, 41, 46, 53 or 72--at least not yet!

Why not use software synthesis? If you have a computer you have all
you need .... well a sound card helps.
==John ff

Yes, thanks, John! That's what I was proposing to do at the end of my
last post, but I'm wondering what the most convenient tools might be.
Any suggestions, anyone?

I would prefer something fairly friendly, since I don't want to
invest a lot of ramp-up time in learning how to use unfriendly,
highly "techy" stuff. Thanks in advance for any help on this.

--- In tuning@y..., jpff@c... wrote:
> Why not use software synthesis? If you have a computer you have all
> you need .... well a sound card helps.
> ==John ff

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

>
> I get the following values, in relative cents:
>
> 3: -251
> 5: -444
> 7: 10.5
> 11: 66
> 13: -254
> 17: -329
> 19: -535

Gene, this is bizarre. Shouldn't "relative cents" be defined such that there are
100 "relative cents" in a step of the tuning? That's how ordinary cents are
defined, with respect to 12-tET. Saying "26-tET has an error in the 19th
harmonic of -535 relative cents" will lead to a lot of head-scratching.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., genewardsmith@j... wrote:
>
> >
> > I get the following values, in relative cents:
> >
> > 3: -251
> > 5: -444
> > 7: 10.5
> > 11: 66
> > 13: -254
> > 17: -329
> > 19: -535
>
> Gene, this is bizarre. Shouldn't "relative cents" be defined such
that there are
> 100 "relative cents" in a step of the tuning?

All I need for the idea to work is that there be some fixed
multiplier, so your definition is certainly reasonable, and if you
think it would be less confusing we could adopt it instead. In my
system, to go from relative to absolute cents you divide by n for an
n-et; using your definition we multiply by 12/n rather than by 1/n.
Mine makes relative and absolute cents the same for the 1-et
(octave), and yours makes them the same for the 12-et.

Does anyone have an objection to defining relative cents (rc) in an
n-et to be cents * n /12 ? If not, the motion carries.

--- In tuning@y..., BobWendell@t... wrote:

/tuning/topicId_29076.html#29188

> I'm wondering how easy it would be to use SCALA and what is it?
FTS? or something, just to at least get some kind of funky mechanical
> audio sketch of my ideas in 19-tET.
>

As the "nutty professor" on the other list suggests... buy a used
TX81Z for $200 and a 5-octave MIDI controller for $150.

$350.

Scala is free, and the TX81Z can be wonderfully tuned with it:

http://www.xs4all.nl/~huygensf/scala/

Or... if you just want to experiment with the sounds of 19-tET and
every other conceivable tuning...with just your sound card and the
keyboard MIDI controller:

Use the TOTALLY FREE, Graham Breed MIDI relay... one of the greatest
xenharmonic inventions known to our wonderful breed known as mankind,
for which we (and I) now have such great confidence...:

http://www.cix.co.uk/~gbreed/software.htm

__________ _______ ________
Joseph Pehrson

Thanks, Joe. For now I'll take the sound card approach.

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., BobWendell@t... wrote:
>
> /tuning/topicId_29076.html#29188
>
> > I'm wondering how easy it would be to use SCALA and what is it?
> FTS? or something, just to at least get some kind of funky
mechanical
> > audio sketch of my ideas in 19-tET.
> >
>
> As the "nutty professor" on the other list suggests... buy a used
> TX81Z for $200 and a 5-octave MIDI controller for $150.
>
> $350.
>
> Scala is free, and the TX81Z can be wonderfully tuned with it:
>
> http://www.xs4all.nl/~huygensf/scala/
>
> Or... if you just want to experiment with the sounds of 19-tET and
> every other conceivable tuning...with just your sound card and the
> keyboard MIDI controller:
>
> Use the TOTALLY FREE, Graham Breed MIDI relay... one of the
greatest
> xenharmonic inventions known to our wonderful breed known as
mankind,
> for which we (and I) now have such great confidence...:
>
>
> http://www.cix.co.uk/~gbreed/software.htm
>
>
> __________ _______ ________
> Joseph Pehrson

Hi Gene,

Yes. I like the term Relative Cents,and I've called it that
in the new FTS.

It's up and running, and if you want to try it out,
usual beta download page:
http://members.tripod.com/~robertinventor/ftsbeta.htm

I've done it so that you can decide to call any of the
notations cents proper, and enter values in the usual decimal point
fashion as for Scala except now it is maybe 1700 cents
to an octave, or 612, or maybe to base 12, or whatever
one has decided one wants to call cents.

See File | Number options. I've updated the help for the window
(which you get if you click on ? icon at top right) - though there
is a little bit of that still to do for the very newest options
in the section.

Robert