A composing challenge

I've been writing Wikipedia articles on equal temperaments (19, 31,
53, 72 with 22 left to do) and find that a lot of excellent
temperaments are not good subjects for such an article because not
enough people write music in them. I'm thinking of 41, 46, 58 and
maybe even 99 here. Why is a beautiful temperament like 46-et left to
languish in obscurity? It's marvelous in a lot of ways--it's
diaschismic, supports starling, and tempers out many other useful
commas. The exact same is true of 58, incidentally. 41 is ideal for
magic temperament. 99 is killer in the 7-limit.

Who wants to write something in 46 equal?

Erv was a big fan of 41 over 31

Gene Ward Smith wrote:

>I've been writing Wikipedia articles on equal temperaments (19, 31,
>53, 72 with 22 left to do) and find that a lot of excellent
>temperaments are not good subjects for such an article because not
>enough people write music in them. I'm thinking of 41, 46, 58 and
>maybe even 99 here. Why is a beautiful temperament like 46-et left to
>languish in obscurity? It's marvelous in a lot of ways--it's
>diaschismic, supports starling, and tempers out many other useful
>commas. The exact same is true of 58, incidentally. 41 is ideal for
>magic temperament. 99 is killer in the 7-limit.
>
>Who wants to write something in 46 equal?
>
>
>
>
>
> >Yahoo! Groups Links
>
>
>
> >
>
>
>
> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

> Gene Ward Smith wrote:
>
> >I've been writing Wikipedia articles on equal temperaments (19, 31,
> >53, 72 with 22 left to do) and find that a lot of excellent
> >temperaments are not good subjects for such an article because not
> >enough people write music in them. I'm thinking of 41, 46, 58 and
> >maybe even 99 here. Why is a beautiful temperament like 46-et left to
> >languish in obscurity? It's marvelous in a lot of ways--it's
> >diaschismic, supports starling, and tempers out many other useful
> >commas. The exact same is true of 58, incidentally. 41 is ideal for
> >magic temperament. 99 is killer in the 7-limit.
> >
> >Who wants to write something in 46 equal?

If there's a crash course on 46= intervals out there, I'll gladly
write something. I've yet to write for a non-meantone (5 limit)
temperament, though, so I'll need a little help.

--- In MakeMicroMusic@yahoogroups.com, Rozencrantz the Sane
<rozencrantz@g...> wrote:

> If there's a crash course on 46= intervals out there, I'll gladly
> write something. I've yet to write for a non-meantone (5 limit)
> temperament, though, so I'll need a little help.

Should I put up such a crash course on tuning-math?

46 is a good 5-limit system, but it misses the point a bit to stop
there; it's consistent through the 13-limit and can reasonably go
higher if you don't mind inconsistency. I'd at least use it as a
7-limit system, where it tempers out 126/125, 245/243, 686/675 and
1029/1024.

At 12:47 PM 1/2/2006, you wrote:
>> Gene Ward Smith wrote:
>>
>> >I've been writing Wikipedia articles on equal temperaments (19, 31,
>> >53, 72 with 22 left to do) and find that a lot of excellent
>> >temperaments are not good subjects for such an article because not
>> >enough people write music in them. I'm thinking of 41, 46, 58 and
>> >maybe even 99 here. Why is a beautiful temperament like 46-et left to
>> >languish in obscurity? It's marvelous in a lot of ways--it's
>> >diaschismic, supports starling, and tempers out many other useful
>> >commas. The exact same is true of 58, incidentally. 41 is ideal for
>> >magic temperament. 99 is killer in the 7-limit.
>> >
>> >Who wants to write something in 46 equal?
>
>If there's a crash course on 46= intervals out there, I'll gladly
>write something. I've yet to write for a non-meantone (5 limit)
>temperament, though, so I'll need a little help.

Here are two good starting points:

!
Gene Smith's "nova" scale in 46-tet.
8
!
130.435 !....5
313.043 !...12
391.304 !...15
626.087 !...24
704.348 !...27
886.956 !...34
1017.391 !..39
2/1 !.......46
!

!
Gene Smith's "star" scale in 46-tet.
8
!
78.261 !.....3
313.044 !...12
391.305 !...15
626.087 !...24
704.348 !...27
886.957 !...34
1017.392 !..39
2/1 !.......46
!

-Carl

> Here are two good starting points:

Thanks. I'll start writing in these, and as I learn more I'll branch out.

At http://www.soundclick.com/mockingbirdfranklin you can hear my first
attempt at playing in 46-EDO. I improvised each instrument while
playing along to the one that came before, in the order guitar, bells,
flute.

I used Smith's Star mode, as given on MMM, which is slightly different
from the one bundled with Scala.

This is only my first try, and a bit of a sprint. Because I recorded
each track seperately, it's hard for me to hear how they go together,
so if people could tell me how coherent it feels, that would be
helpful. I'm hoping to make an album's worth of 46-EDO music, and I
want each track to be better than the last.

--- In MakeMicroMusic@yahoogroups.com, "lmtbl" <rozencrantz@g...> wrote:

> I used Smith's Star mode, as given on MMM, which is slightly different
> from the one bundled with Scala.

Good scale. Alas, we can't download it until tomorrow.

> This is only my first try, and a bit of a sprint. Because I recorded
> each track seperately, it's hard for me to hear how they go together,
> so if people could tell me how coherent it feels, that would be
> helpful. I'm hoping to make an album's worth of 46-EDO music, and I
> want each track to be better than the last.

A worthy ambition! I think I'll dust off my uncompleted sensi
temperament project, finish it, tune it to 46-et, and join you in this
orgy of 46-equality. Sensi is the temperament with a sharp septimal
third (9/7) as generator, with two making up a major sixth. 17 steps
out of 46.

On 1/2/06, Gene Ward Smith <gwsmith@...> wrote:
> --- In MakeMicroMusic@yahoogroups.com, "lmtbl" <rozencrantz@g...> wrote:
>
> > I used Smith's Star mode, as given on MMM, which is slightly different
> > from the one bundled with Scala.
>
> Good scale. Alas, we can't download it until tomorrow.
>
> > This is only my first try, and a bit of a sprint. Because I recorded
> > each track seperately, it's hard for me to hear how they go together,
> > so if people could tell me how coherent it feels, that would be
> > helpful. I'm hoping to make an album's worth of 46-EDO music, and I
> > want each track to be better than the last.
>
> A worthy ambition! I think I'll dust off my uncompleted sensi
> temperament project, finish it, tune it to 46-et, and join you in this
> orgy of 46-equality. Sensi is the temperament with a sharp septimal
> third (9/7) as generator, with two making up a major sixth. 17 steps
> out of 46.

Hm. I'll try to find a better host. Until then, thanks for the encouragement

--- In MakeMicroMusic@yahoogroups.com, Rozencrantz the Sane
<rozencrantz@g...> wrote:
>
> > Gene Ward Smith wrote:
> >
> > >I've been writing Wikipedia articles on equal temperaments (19,
31,
> > >53, 72 with 22 left to do) and find that a lot of excellent
> > >temperaments are not good subjects for such an article because
not
> > >enough people write music in them. I'm thinking of 41, 46, 58 and
> > >maybe even 99 here. Why is a beautiful temperament like 46-et
left to
> > >languish in obscurity? It's marvelous in a lot of ways--it's
> > >diaschismic, supports starling, and tempers out many other useful
> > >commas. The exact same is true of 58, incidentally. 41 is ideal
for
> > >magic temperament. 99 is killer in the 7-limit.
> > >
> > >Who wants to write something in 46 equal?
>
> If there's a crash course on 46= intervals out there, I'll gladly
> write something. I've yet to write for a non-meantone (5 limit)
> temperament, though, so I'll need a little help.

46 doesn't work for meantone, but for one thing it works great
for 'srutal' (where 2048:2025 vanishes) . . . Expressed in degrees of
46-equal, the 10-note srutal modes would include the rotations of
3353333533 and 3533333533. These scales allow a consistent pattern of
steps ("1-4-7" instead of "1-3-5") in the scale to produce a wealth
of nice 5-limit major and minor triads. Let's discuss this more on
one of the other (tuning or tuning-math) lists, shall we?

On Tue, 03 Jan 2006, Tristan Parker wrote:
>
> At http://www.soundclick.com/mockingbirdfranklin you can hear my first
> attempt at playing in 46-EDO. I improvised each instrument while
> playing along to the one that came before, in the order guitar, bells,
> flute.
>
> I used Smith's Star mode, as given on MMM, which is slightly different
> from the one bundled with Scala.
>
> This is only my first try, and a bit of a sprint. Because I recorded
> each track seperately, it's hard for me to hear how they go together,
> so if people could tell me how coherent it feels, that would be
> helpful. I'm hoping to make an album's worth of 46-EDO music, and I
> want each track to be better than the last.

Hi Tristan,

It coheres.

Regards,
Yahya

--
No virus found in this outgoing message.
Checked by AVG Free Edition.
Version: 7.1.371 / Virus Database: 267.14.11/219 - Release Date: 2/1/06

--- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, Rozencrantz the Sane
> <rozencrantz@g...> wrote:
> >
> > > Gene Ward Smith wrote:
> > >
> > > >I've been writing Wikipedia articles on equal temperaments (19,
> 31,
> > > >53, 72 with 22 left to do) and find that a lot of excellent
> > > >temperaments are not good subjects for such an article because
> not
> > > >enough people write music in them. I'm thinking of 41, 46, 58 and
> > > >maybe even 99 here. Why is a beautiful temperament like 46-et
> left to
> > > >languish in obscurity? It's marvelous in a lot of ways--it's
> > > >diaschismic, supports starling, and tempers out many other useful
> > > >commas. The exact same is true of 58, incidentally. 41 is ideal
> for
> > > >magic temperament. 99 is killer in the 7-limit.
> > > >
> > > >Who wants to write something in 46 equal?
> >
> > If there's a crash course on 46= intervals out there, I'll gladly
> > write something. I've yet to write for a non-meantone (5 limit)
> > temperament, though, so I'll need a little help.
>
> 46 doesn't work for meantone, but for one thing it works great
> for 'srutal' (where 2048:2025 vanishes) . . . Expressed in degrees of
> 46-equal, the 10-note srutal modes would include the rotations of
> 3353333533 and 3533333533. These scales allow a consistent pattern of
> steps ("1-4-7" instead of "1-3-5") in the scale to produce a wealth
> of nice 5-limit major and minor triads. Let's discuss this more on
> one of the other (tuning or tuning-math) lists, shall we?

But 3353333533 and 3533333533 are modes of 34-equal. Those should be
4474444744 and 4744444744.

Kalle

Gene,

I will try to compose something in 46 equal.
Joel

--- Gene Ward Smith <gwsmith@...> wrote:

> I've been writing Wikipedia articles on equal
> temperaments (19, 31,
> 53, 72 with 22 left to do) and find that a lot of
> excellent
> temperaments are not good subjects for such an
> article because not
> enough people write music in them. I'm thinking of
> 41, 46, 58 and
> maybe even 99 here. Why is a beautiful temperament
> like 46-et left to
> languish in obscurity? It's marvelous in a lot of
> ways--it's
> diaschismic, supports starling, and tempers out many
> other useful
> commas. The exact same is true of 58, incidentally.
> 41 is ideal for
> magic temperament. 99 is killer in the 7-limit.
>
> Who wants to write something in 46 equal?
>
>
>
>

--- In MakeMicroMusic@yahoogroups.com, Joel Hickman
<joelhickman_1999@y...> wrote:
>
> Gene,
>
> I will try to compose something in 46 equal.
> Joel

Great! We've been discussing it of late on tuning-math if you want to
check that out.

--- In MakeMicroMusic@yahoogroups.com, "Kalle Aho" <kalleaho@m...>
wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <paul@s...>
wrote:
> >
> > --- In MakeMicroMusic@yahoogroups.com, Rozencrantz the Sane
> > <rozencrantz@g...> wrote:
> > >
> > > > Gene Ward Smith wrote:
> > > >
> > > > >I've been writing Wikipedia articles on equal temperaments
(19,
> > 31,
> > > > >53, 72 with 22 left to do) and find that a lot of excellent
> > > > >temperaments are not good subjects for such an article
because
> > not
> > > > >enough people write music in them. I'm thinking of 41, 46,
58 and
> > > > >maybe even 99 here. Why is a beautiful temperament like 46-
et
> > left to
> > > > >languish in obscurity? It's marvelous in a lot of ways--it's
> > > > >diaschismic, supports starling, and tempers out many other
useful
> > > > >commas. The exact same is true of 58, incidentally. 41 is
ideal
> > for
> > > > >magic temperament. 99 is killer in the 7-limit.
> > > > >
> > > > >Who wants to write something in 46 equal?
> > >
> > > If there's a crash course on 46= intervals out there, I'll
gladly
> > > write something. I've yet to write for a non-meantone (5 limit)
> > > temperament, though, so I'll need a little help.
> >
> > 46 doesn't work for meantone, but for one thing it works great
> > for 'srutal' (where 2048:2025 vanishes) . . . Expressed in
degrees of
> > 46-equal, the 10-note srutal modes would include the rotations of
> > 3353333533 and 3533333533. These scales allow a consistent
pattern of
> > steps ("1-4-7" instead of "1-3-5") in the scale to produce a
wealth
> > of nice 5-limit major and minor triads. Let's discuss this more
on
> > one of the other (tuning or tuning-math) lists, shall we?
>
> But 3353333533 and 3533333533 are modes of 34-equal. Those should be
> 4474444744 and 4744444744.
>
> Kalle

Yes, thanks for the correction Kalle! I had a problem reading my own
horagrams!

--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, Joel Hickman
> <joelhickman_1999@y...> wrote:
> >
> > Gene,
> >
> > I will try to compose something in 46 equal.
> > Joel
>
> Great! We've been discussing it of late on tuning-math if you want to
> check that out.

Unfortunately, the 4474444744 and 4744444744 scales (and their
rotations) I suggested (thanks Kalle for the correction) for 46-equal
haven't been mentioned there. These may be the most viable scales for a
5-limit approach to 46-equal.

>> But 3353333533 and 3533333533 are modes of 34-equal. Those should be
>> 4474444744 and 4744444744.
>>
>> Kalle
>
>Yes, thanks for the correction Kalle! I had a problem reading my own
>horagrams!

Would it have helped to make every-other band shaded?

-Carl

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
> >> But 3353333533 and 3533333533 are modes of 34-equal. Those should
be
> >> 4474444744 and 4744444744.
> >>
> >> Kalle
> >
> >Yes, thanks for the correction Kalle! I had a problem reading my own
> >horagrams!
>
> Would it have helped to make every-other band shaded?

I don't think so; my problem was that I put 46 as an additional extra-
large scale *outside* the outer circle of the horagram, but forgot to
count the dotted lines that represent the additional notes (without
cents values given) that srutal-46 has but srutal-34 (the one right
inside the outer circle) doesn't.

if you go to
http://anaphoria.com/hrgm.PDF
the first places for 46 to appear out of the horogram tree are
horogram 20 on page 22
and
horogram 26 on page 28
like looking at these as rhythms, on can look at any ring as being equal ( or not) . It still works

I have cause most of the misspelling of Horogram but i should point out that Erv spelled it with O no As. sorry to steer you wrong on the spelling

Paul Erlich wrote:

>--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> >wrote:
> >
>>--- In MakeMicroMusic@yahoogroups.com, Joel Hickman
>><joelhickman_1999@y...> wrote:
>> >>
>>>Gene,
>>>
>>>I will try to compose something in 46 equal.
>>> Joel
>>> >>>
>>Great! We've been discussing it of late on tuning-math if you want to
>>check that out.
>> >>
>
>Unfortunately, the 4474444744 and 4744444744 scales (and their >rotations) I suggested (thanks Kalle for the correction) for 46-equal >haven't been mentioned there. These may be the most viable scales for a >5-limit approach to 46-equal.
>
>
>
>
>
> >Yahoo! Groups Links
>
>
>
> >
>
>
> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

--- In MakeMicroMusic@yahoogroups.com, Kraig Grady <kraiggrady@a...>
wrote:
>
> if you go to
> http://anaphoria.com/hrgm.PDF
> the first places for 46 to appear out of the horogram tree are
> horogram 20 on page 22

Up to 46, this agrees with the sensipent (78732:78125 vanishes) and
especially sensisept (126:125 and 245:243 vanish) temperaments.

> and
> horogram 26 on page 28

Basically the chain-of-fifths scales in 46 . . .

The horagram for srutal temperament (2048:2025), which I was talking
about below, is something that wouldn't arise from Wilson's methods,
but is found in my paper. Its series of distributionally even scales
is 2, 4, 6, 8, 10, 12, 22, 34, 46 . . . Each of these scales can be
altered slightly so as to make them omnitetrachordal (instead of
having a 'bitonal' symmetry at the half-octave as they do in the
horagram); the resulting omnitetrachordal 12- and 22-note scales are
very similar to the theoretical scales of Indian music. For some,
this may be the best approach to 46. Others may be interested in 11-
limit or 13-limit harmony; I think some such approaches to 46 will
come up in the forthcoming second part of my paper . . .

> like looking at these as rhythms, on can look at any ring as being
equal
> ( or not) . It still works
>
> I have cause most of the misspelling of Horogram but i should
point
> out that Erv spelled it with O no As. sorry to steer you wrong on
the
> spelling

Oops -- OK, apology accepted! I guess I'll have to stop
thinking "dance the Hora" in connection with these . . . :)

i have the next set of 32 horograms to put up which includes some more 46.
.
As noted it is usually the most common ones that pop up first with these horograms.
It is to my own liking that the two level patterns are for me the most interesting

Paul Erlich wrote:

>--- In MakeMicroMusic@yahoogroups.com, Kraig Grady <kraiggrady@a...> >wrote:
> >
>>if you go to
>>http://anaphoria.com/hrgm.PDF
>>the first places for 46 to appear out of the horogram tree are
>>horogram 20 on page 22
>> >>
>
>Up to 46, this agrees with the sensipent (78732:78125 vanishes) and >especially sensisept (126:125 and 245:243 vanish) temperaments.
>
> >
>> and
>>horogram 26 on page 28
>> >>
>
>Basically the chain-of-fifths scales in 46 . . .
>
>The horagram for srutal temperament (2048:2025), which I was talking >about below, is something that wouldn't arise from Wilson's methods, >but is found in my paper. Its series of distributionally even scales >is 2, 4, 6, 8, 10, 12, 22, 34, 46 . . . Each of these scales can be >altered slightly so as to make them omnitetrachordal (instead of >having a 'bitonal' symmetry at the half-octave as they do in the >horagram); the resulting omnitetrachordal 12- and 22-note scales are >very similar to the theoretical scales of Indian music. For some, >this may be the best approach to 46. Others may be interested in 11-
>limit or 13-limit harmony; I think some such approaches to 46 will >come up in the forthcoming second part of my paper . . .
>
> >
>>like looking at these as rhythms, on can look at any ring as being >> >>
>equal > >
>>( or not) . It still works
>>
>> I have cause most of the misspelling of Horogram but i should >> >>
>point > >
>>out that Erv spelled it with O no As. sorry to steer you wrong on >> >>
>the > >
>>spelling
>> >>
>
>Oops -- OK, apology accepted! I guess I'll have to stop >thinking "dance the Hora" in connection with these . . . :)
>
>
>
>
>
> >Yahoo! Groups Links
>
>
>
> >
>
>
> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

--- In MakeMicroMusic@yahoogroups.com, Kraig Grady <kraiggrady@a...>
wrote:
>
> i have the next set of 32 horograms to put up which includes some
more 46.
> .
> As noted it is usually the most common ones that pop up first with
> these horograms.

? What does that mean?

> It is to my own liking that the two level patterns are for me the
most
> interesting

Can you give an example (I may know what you mean but I'm not sure)?

>
> Paul Erlich wrote:
>
> >--- In MakeMicroMusic@yahoogroups.com, Kraig Grady
<kraiggrady@a...>
> >wrote:
> >
> >
> >>if you go to
> >>http://anaphoria.com/hrgm.PDF
> >>the first places for 46 to appear out of the horogram tree are
> >>horogram 20 on page 22
> >>
> >>
> >
> >Up to 46, this agrees with the sensipent (78732:78125 vanishes)
and
> >especially sensisept (126:125 and 245:243 vanish) temperaments.
> >
> >
> >
> >> and
> >>horogram 26 on page 28
> >>
> >>
> >
> >Basically the chain-of-fifths scales in 46 . . .
> >
> >The horagram for srutal temperament (2048:2025), which I was
talking
> >about below, is something that wouldn't arise from Wilson's
methods,
> >but is found in my paper. Its series of distributionally even
scales
> >is 2, 4, 6, 8, 10, 12, 22, 34, 46 . . . Each of these scales can
be
> >altered slightly so as to make them omnitetrachordal (instead of
> >having a 'bitonal' symmetry at the half-octave as they do in the
> >horagram); the resulting omnitetrachordal 12- and 22-note scales
are
> >very similar to the theoretical scales of Indian music. For some,
> >this may be the best approach to 46. Others may be interested in
11-
> >limit or 13-limit harmony; I think some such approaches to 46 will
> >come up in the forthcoming second part of my paper . . .
> >
> >
> >
> >>like looking at these as rhythms, on can look at any ring as
being
> >>
> >>
> >equal
> >
> >
> >>( or not) . It still works
> >>
> >> I have cause most of the misspelling of Horogram but i should
> >>
> >>
> >point
> >
> >
> >>out that Erv spelled it with O no As. sorry to steer you wrong on
> >>
> >>
> >the
> >
> >
> >>spelling
> >>
> >>
> >
> >Oops -- OK, apology accepted! I guess I'll have to stop
> >thinking "dance the Hora" in connection with these . . . :)
> >
> >
> >
> >
> >
> >
> >Yahoo! Groups Links
> >
> >
> >
> >
> >
> >
> >
> >
> >
>
> --
> Kraig Grady
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
> The Wandering Medicine Show
> KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles
>

--- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:

> Each of these scales can be
> altered slightly so as to make them omnitetrachordal (instead of
> having a 'bitonal' symmetry at the half-octave as they do in the
> horagram); the resulting omnitetrachordal 12- and 22-note scales are
> very similar to the theoretical scales of Indian music.

It might be interesting to look at those as tempered by 46 or 58
equal. I may post something on another group about that.

>Each of these scales can be
>altered slightly so as to make them omnitetrachordal (instead of
>having a 'bitonal' symmetry at the half-octave as they do in the
>horagram);

What is the method for doing so?

-Carl

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
> >Each of these scales can be
> >altered slightly so as to make them omnitetrachordal (instead of
> >having a 'bitonal' symmetry at the half-octave as they do in the
> >horagram);
>
> What is the method for doing so?
>
> -Carl

If you understand, in 22-equal, how to change a symmetrical decatonic
to a pentachordal decatonic, and a symmetrical dodecatonic to a
hexachordal dodecatonic, you're most of the way there. If you want more
on this, please post a question to one of the other lists.