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Compact 5-limit MOS

🔗Gene Ward Smith <genewardsmith@...>

2/13/2007 8:57:11 PM

Speaking of the 5-limit, there are all these reasonably sized 5-limit
MOS scales which don't seem to be getting any attention, despite
their formal similarity with the diatonic scale. I think an
interesting challenge would be to take a break from doing goofy equal
divisions and give one a try. Diatonic, of course, is famous, and
porcupine and dischismci have I think gotten some attention, but what
about these:

Magic in 7 or 10 notes.

I've given magic a shot--anyone else? The 10 note scale ought to give
considerable scope for 5-limit fun and games. Recommended tuning:
13deg41.

Hanson in 7 or 11 notes.

I guess Hanson must have used it. Who else? 11 notes of it look like
a great way to do 5-limit stuff, with the option of smuggling in some
cheesy 7-limit stuff also. Recommended tuning: 14deg53

Sensi, 11 notes.

As a bonus, some 7-limit stuff. Recommended tuning: 31deg84, though
46deg17 would be just fine if you want to work with a smaller
division.

Schismatic, 12 notes

It worked for the late middle ages. Recommended tuning: 31deg53. Or
hell, Pythagorean if you like.

Surely someone out there could take a break from 13edo and do a Magic
[10]?

🔗Aaron Krister Johnson <aaron@...>

2/13/2007 10:18:17 PM

See my questions/comments below...

--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
<genewardsmith@...> wrote:
>
> Speaking of the 5-limit, there are all these reasonably sized 5-limit
> MOS scales which don't seem to be getting any attention, despite
> their formal similarity with the diatonic scale. I think an
> interesting challenge would be to take a break from doing goofy equal
> divisions and give one a try. Diatonic, of course, is famous, and
> porcupine and dischismci have I think gotten some attention, but what
> about these:
>
> Magic in 7 or 10 notes.
>
> I've given magic a shot--anyone else? The 10 note scale ought to give
> considerable scope for 5-limit fun and games. Recommended tuning:
> 13deg41.

So this means the 13th degree of 41-edo as a generator, right?

> Hanson in 7 or 11 notes.
>
> I guess Hanson must have used it. Who else? 11 notes of it look like
> a great way to do 5-limit stuff, with the option of smuggling in some
> cheesy 7-limit stuff also. Recommended tuning: 14deg53
>
> Sensi, 11 notes.
>
> As a bonus, some 7-limit stuff. Recommended tuning: 31deg84, though
> 46deg17 would be just fine if you want to work with a smaller
> division.

You lost me here---is that the 46th degree of 17-edo, or the 17th
degree of 46-edo? HUH?

> Schismatic, 12 notes
>
> It worked for the late middle ages. Recommended tuning: 31deg53. Or
> hell, Pythagorean if you like.
>
> Surely someone out there could take a break from 13edo and do a Magic
> [10]?

Sounds interesting....right now I'm looking at the properties of 171
and 441 as JI approximations in my 'micro_composer' (old alias:
'et_compose' (as you know those divisions are great for 7-limit, but
they are good in general one would think)...care to paste .scl files
of the above suggestions?

-A.

🔗Gene Ward Smith <genewardsmith@...>

2/14/2007 4:56:49 AM

--- In MakeMicroMusic@yahoogroups.com, "Aaron Krister Johnson"
<aaron@...> wrote:

> You lost me here---is that the 46th degree of 17-edo, or the 17th
> degree of 46-edo? HUH?

It's 17deg46. I picked this up from Ozan, but maybe I shoulf go back to
saying 17/46.

🔗Aaron Krister Johnson <aaron@...>

2/14/2007 5:59:20 AM

--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
<genewardsmith@...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "Aaron Krister Johnson"
> <aaron@> wrote:
>
> > You lost me here---is that the 46th degree of 17-edo, or the 17th
> > degree of 46-edo? HUH?
>
> It's 17deg46. I picked this up from Ozan, but maybe I shoulf go back to
> saying 17/46.

I prefer the compactness of x/y notation, but perhaps XdegY is less
ambiguous because the x/y notation might be mistaken out of context as
linear ratios instead of exponents of two.

So, I think Ozan is onto something. What confused me is that you meant
17th degree of 46-edo, whic would be 17deg46, but you wrote 46deg17.

-A.

🔗c.m.bryan <chrismbryan@...>

2/14/2007 6:14:41 AM

Hello Gene, thanks for pointing these out. I'm currently playing with
different MOS. I'm looking at the tuning encyclopedia for magic, but
having trouble deciphering some of the lingo. Poptimal generator?
TOP period/generator? One-sentence definitions of these would be
helpful.

Hanson and sensi I can't find in the encyclopedia, so i'll search the
tuning archives.

-Chris Bryan

On 14/02/07, Gene Ward Smith <genewardsmith@...> wrote:
>
>
>
>
>
>
> Speaking of the 5-limit, there are all these reasonably sized 5-limit
> MOS scales which don't seem to be getting any attention, despite
> their formal similarity with the diatonic scale. I think an
> interesting challenge would be to take a break from doing goofy equal
> divisions and give one a try. Diatonic, of course, is famous, and
> porcupine and dischismci have I think gotten some attention, but what
> about these:
>
> Magic in 7 or 10 notes.
>
> I've given magic a shot--anyone else? The 10 note scale ought to give
> considerable scope for 5-limit fun and games. Recommended tuning:
> 13deg41.
>
> Hanson in 7 or 11 notes.
>
> I guess Hanson must have used it. Who else? 11 notes of it look like
> a great way to do 5-limit stuff, with the option of smuggling in some
> cheesy 7-limit stuff also. Recommended tuning: 14deg53
>
> Sensi, 11 notes.
>
> As a bonus, some 7-limit stuff. Recommended tuning: 31deg84, though
> 46deg17 would be just fine if you want to work with a smaller
> division.
>
> Schismatic, 12 notes
>
> It worked for the late middle ages. Recommended tuning: 31deg53. Or
> hell, Pythagorean if you like.
>
> Surely someone out there could take a break from 13edo and do a Magic
> [10]?
>
> --
Rop tú mo baile,
a Choimdiu cride:
ní ní nech aile
acht Rí secht nime.

🔗Carl Lumma <ekin@...>

2/14/2007 8:02:30 AM

>Hanson in 7 or 11 notes.
>
>I guess Hanson must have used it. Who else? 11 notes of it look like
>a great way to do 5-limit stuff, with the option of smuggling in some
>cheesy 7-limit stuff also. Recommended tuning: 14deg53

I don't think Hanson did, but I could be wrong. I wrote some
chord progressions in the 8-tone chain. Herman may have done
some stuff with it.

-Carl

🔗Carl Lumma <ekin@...>

2/14/2007 8:14:36 AM

At 06:14 AM 2/14/2007, you wrote:
>Hello Gene, thanks for pointing these out. I'm currently playing with
>different MOS. I'm looking at the tuning encyclopedia for magic, but
>having trouble deciphering some of the lingo. Poptimal generator?

Gene's been over this a hundred times, but I'm still not sure I
get it. I think it's like, how do you decided whether you're
minimizing the error, or the squared error, or the cubed error,
etc.? Poptimal doesn't decide, it just says there is some
exponent for which this generator minimizes the error. Or
something. I think there are an infinite number of poptimal
generators for any tuning. But I could be wrong. It's never
seemed terribly useful to me.

>TOP period/generator? One-sentence definitions of these would be
>helpful.

TOP is Paul Erlich's scheme for tempering all the consonances
in proportion to their complexity. Octaves the least, ratios
of 3 next, and so on. It's generally what I'd recommend.

>Hanson and sensi I can't find in the encyclopedia, so i'll search the
>tuning archives.

Hanson used to be called kleismic. Don't forget Google web search.

-Carl

🔗Gene Ward Smith <genewardsmith@...>

2/14/2007 12:33:27 PM

--- In MakeMicroMusic@yahoogroups.com, "Aaron Krister Johnson"
<aaron@...> wrote:

> I prefer the compactness of x/y notation, but perhaps XdegY is less
> ambiguous because the x/y notation might be mistaken out of context as
> linear ratios instead of exponents of two.

It is a ratio: it's a fraction of an octave.

> So, I think Ozan is onto something. What confused me is that you meant
> 17th degree of 46-edo, whic would be 17deg46, but you wrote 46deg17.

Yeah, well, rub it in already.

🔗monz <monz@...>

2/14/2007 12:56:58 PM

Hi Gene,

--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
<genewardsmith@...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "Aaron Krister Johnson"
> <aaron@> wrote:
>
> > You lost me here---is that the 46th degree of 17-edo, or the 17th
> > degree of 46-edo? HUH?
>
> It's 17deg46. I picked this up from Ozan, but maybe I
> shoulf go back to saying 17/46.

No, please don't do that!-- it's too easy to confuse
that with a frequency-ratio.

I personally really like the long-winded (but absolutely
accurate) way of notating it: 2^(17/46) ... but that's
just me.

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗monz <monz@...>

2/14/2007 1:22:12 PM

Hi Chris and Gene,

--- In MakeMicroMusic@yahoogroups.com, c.m.bryan <chrismbryan@...> wrote:
>
> Hello Gene, thanks for pointing these out. I'm currently
> playing with different MOS. I'm looking at the tuning
> encyclopedia for magic, but having trouble deciphering
> some of the lingo. Poptimal generator? TOP period/generator?
> One-sentence definitions of these would be helpful.

They're in the Encyclopedia:

http://tonalsoft.com/enc/p/poptimal.aspx

http://tonalsoft.com/enc/t/top.aspx

... but unfortunately they are pretty much one-sentence
definitions, which doesn't really explain them fully
enough. Problem is that i myself have not taken the
time to understand either of them enough to flesh out
the webpages.

For most types of temperaments, where the octave (2:1 ratio)
is the Identity Interval, "TOP" really simply means that
the octaves are tempered as well as the 3rds and 5ths.

"Poptimal" i really can't help you with -- Gene is the
one to explain that.

> Hanson and sensi I can't find in the encyclopedia,
> so i'll search the tuning archives.

There was a time a couple of years ago where i was in
the process of getting good basic definitions of all
the main temperament families into the Encyclopedia.
I didn't get very far, but here are the ones i got in
there:

http://tonalsoft.com/enc/k/kwazy.aspx

http://tonalsoft.com/enc/m/magic.aspx

http://tonalsoft.com/enc/m/marvel.aspx

http://tonalsoft.com/enc/m/meantone.aspx

http://tonalsoft.com/enc/m/miracle.aspx

http://tonalsoft.com/enc/m/mutt.aspx

http://tonalsoft.com/enc/m/mystery.aspx

http://tonalsoft.com/enc/o/orwell.aspx

http://tonalsoft.com/enc/s/schismic.aspx

http://tonalsoft.com/enc/s/semisixths.aspx

"Meantone" is by far the most complete of these
webpages, because that is by far the family i'm most
familiar with (and i would guess that's the case with
nearly everyone else too, except maybe Gene).

The "miracle" page is also pretty good, because i
was in on the day-to-day rediscovery of it on the
tuning list back in 2001.

For the others, i posted a template here with all
the labels filled in and all the data areas blank,
and Gene filled out several of them and sent them
to me, Herman Miller did a few others.

But i really haven't explored these families myself
at all, except for a little bit of magic and kleisma,
because 19-edo belongs to those, and in my improvs
with Jonathan Glasier and Brink at Sonic Arts we make
it a point to avoid sounding like meantone when we
play in 19.

When the categorizing of these temperament families
first began a few years ago, there was a lot of
discussion of how we would name them, and several
of the names did change, so i'm not sure how current
my "family" webpage is:

http://tonalsoft.com/enc/f/family.aspx

If "sensi" means the same as "semisixths", then
i've already got a page on that (the last one in the
above list).

First thing we should do is clarify the list of names,
and make it as complete as we can.

Gene, can we pick up the process of putting these
definitions into the Encyclopedia? We could start
with "Hanson" ... and i'm also very unclear what
people mean by "pajara".

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗Aaron Krister Johnson <aaron@...>

2/14/2007 2:17:02 PM

--- In MakeMicroMusic@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Gene,

> > Gene wrote:
> > It's 17deg46. I picked this up from Ozan, but maybe I
> > shoulf go back to saying 17/46.
>
> Monz wrote:
> No, please don't do that!-- it's too easy to confuse
> that with a frequency-ratio.
>
> I personally really like the long-winded (but absolutely
> accurate) way of notating it: 2^(17/46) ... but that's
> just me.

Monz, you must have missed my message (#16072) that made the same point!

BTW, did you get my email correspondence regarding the ET page of your
encyclopedia?

-A.

🔗monz <monz@...>

2/14/2007 2:37:35 PM

Hi Aaron,

--- In MakeMicroMusic@yahoogroups.com, "Aaron Krister Johnson"
<aaron@...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "monz" <monz@> wrote:
> >
> > Hi Gene,
>
> > > Gene wrote:
> > > It's 17deg46. I picked this up from Ozan, but maybe I
> > > shoulf go back to saying 17/46.
> >
> > Monz wrote:
> > No, please don't do that!-- it's too easy to confuse
> > that with a frequency-ratio.
> >
> > I personally really like the long-winded (but absolutely
> > accurate) way of notating it: 2^(17/46) ... but that's
> > just me.
>
> Monz, you must have missed my message (#16072) that made
> the same point!

I read yours right after i sent mine. ;-)

> BTW, did you get my email correspondence regarding the ET
> page of your encyclopedia?

Yes, i got emails from you and several other folks,
but have been too busy to update the page yet ... my
precalculus course started a couple of weeks ago, and
i'm still struggling to remember the algebra i need.

I'll get around to it hopefully on Friday or Monday
... reminders are always good with me.

(When Paul Erlich was around, he would periodically
send me a "friendly reminder" every few months about
something i had wrong on my website that was bugging
him ... and some of those *still* haven't been fixed
after several years! ... i really do need to find some
time for the website ...)

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗Gene Ward Smith <genewardsmith@...>

2/14/2007 2:36:46 PM

--- In MakeMicroMusic@yahoogroups.com, "Aaron Krister Johnson"
<aaron@...> wrote:
>
> See my questions/comments below...

Replied to on tuning:
/tuning/topicId_69789.html#69789

🔗Aaron Krister Johnson <aaron@...>

2/14/2007 3:51:51 PM

--- In MakeMicroMusic@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Aaron,
>
>
> --- In MakeMicroMusic@yahoogroups.com, "Aaron Krister Johnson"
> <aaron@> wrote:
> >
> > --- In MakeMicroMusic@yahoogroups.com, "monz" <monz@> wrote:
> > >
> > > Hi Gene,
> >
> > > > Gene wrote:
> > > > It's 17deg46. I picked this up from Ozan, but maybe I
> > > > shoulf go back to saying 17/46.
> > >
> > > Monz wrote:
> > > No, please don't do that!-- it's too easy to confuse
> > > that with a frequency-ratio.
> > >
> > > I personally really like the long-winded (but absolutely
> > > accurate) way of notating it: 2^(17/46) ... but that's
> > > just me.
> >
> > Monz, you must have missed my message (#16072) that made
> > the same point!
>
>
> I read yours right after i sent mine. ;-)
>
>
> > BTW, did you get my email correspondence regarding the ET
> > page of your encyclopedia?
>
>
> Yes, i got emails from you and several other folks,
> but have been too busy to update the page yet ... my
> precalculus course started a couple of weeks ago, and
> i'm still struggling to remember the algebra i need.
>
> I'll get around to it hopefully on Friday or Monday
> ... reminders are always good with me.
>
> (When Paul Erlich was around, he would periodically
> send me a "friendly reminder" every few months about
> something i had wrong on my website that was bugging
> him ... and some of those *still* haven't been fixed
> after several years! ... i really do need to find some
> time for the website ...)

OR---you could wiki-fy the encyclopedia, which could make such
corrections and maintainence much easier!

Best,
Aaron

🔗Gene Ward Smith <genewardsmith@...>

2/14/2007 4:37:09 PM

--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
<genewardsmith@...> wrote:

> Magic in 7 or 10 notes.

Magic tempers out the magic comma of 3125/3072, which means that five
major thirds make up a twelvth: (5/4)^5/3 = 3125/3072. The major
thirds of 41-et are flat by about 1/5 of a magic comma, which would
be analogous to 1/4 comma meantone. It bears the same relationship to
magic as 31 does to meantone. The scales are constant structure MOS,
but don't mess with them if you insist on propriety.

! magic7.scl
Magic[7] in 41-et tuning
7
!
321.951220
380.487805
702.439024
760.975610
819.512195
1141.463415
1200.000000

! magic10.scl
Magic[10] in 41-et tuning
10
!
263.414634
321.951220
380.487805
439.024390
702.439024
760.975610
819.512195
1082.926829
1141.463415
1200.000000

> Hanson in 7 or 11 notes.

Hanson tempers out the kleisma of 15625/15552, so you may also call
it kleismic. (5/2)/(6/5)^5 = 3/(6/5)^6 = 15625/15552, which shows how
triads are formed. 53 has minor thirds about 1/6-kleisma sharp,
connected to its nearly pure fifths. Once again, both scales are
improper. The cycle of minor thirds closes with a fourth for the 7-
note scale, and with a 9/7 (supermajor third) for the 11-note scale.
The latter is a "catakleismic temperament" interval popping up in a
mostly 5-limit (unless you want to use keemun approximations)
context. It can be made exact by using (56/9)^(1/10) for the minor
third. Another nice feature of the 11-note scale is its circle of six
major thirds and five fourths, which could certainly be made use of
structurally.

! hanson7.scl
Hanson[7] in 53-et tuning
7
!
67.924528
316.981132
384.905660
633.962264
701.886792
950.943396
1200.000000

! hanson11.scl
Hanson[11] in 53-et tuning
11
!
67.924528
135.849057
316.981132
384.905660
566.037736
633.962264
701.886792
883.018868
950.943396
1018.867925
1200.000000

> Sensi, 11 notes.

Sensi, or semisixths, tempers out the semisixths comma of
78732/78125. While I'm just considering the 5-limit, it makes a lot
of sense to view sensi as a basically 7-limit temperament, in which
case the 9/7 generator is 7.77 cents sharp in the 84edo tuning I
used. A feature Sensi[11] has in common with the diatonic scale is a
circle of major/minor thirds--9 minor and 2 major in this case.
Another very characteristic feature is the huge number of diminished
seventh chords.

! sensi11.scl
Sensi[11] (Semisixths[11]) in 84edo tunig
11
!
128.571429
257.142857
385.714286
442.857143
571.428571
700.000000
828.571429
885.714286
1014.285714
1142.857143
1200.000000

> Schismatic, 12 notes

Since Aaron is interested in 171-et, I give this in 171-et, an
excellent schismatic tuning close to 1/10-schisma. For extra fun,
treat it as a circulating temperament.

! schismatic12.scl
Schismatic[12] in 171-et tuning
12
!
91.228070
203.508772
294.736842
385.964912
498.245614
589.473684
701.754386
792.982456
884.210526
996.491228
1087.719298
1200.000000

Here's someone steps up to the plate and takes a swing.

🔗monz <monz@...>

2/14/2007 8:36:58 PM

--- In MakeMicroMusic@yahoogroups.com, "Aaron Krister Johnson"
<aaron@...> wrote:

> OR---you could wiki-fy the encyclopedia, which could make such
> corrections and maintainence much easier!

I had the idea to do something like that before Wikipedia
existed ... but at this point i plan to eventually
incorporate the whole Encyclopedia into Tonescape's
menu system, so making it a wiki could cause problems,
from editing to copyrights.

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗Gene Ward Smith <genewardsmith@...>

2/14/2007 8:36:32 PM

--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
<genewardsmith@...> wrote:

I'm getting way outside of my knowledge area here, but it occurred to
me to wonder about tuning guitars (and perhaps other stringed
instruments) to these MOS. It seems fourths and major thirds are
popular intervals, and I wonder if anyone can tell me if the thoughts
below make any sense.

> > Magic in 7 or 10 notes.

Magic has a flat major fourth as a generator, and how would that work
as an interval for tuning a guitar? It might be possible to make
either a 19 or a 22 tone guitar on this principle, correct? Six major
thirds and a tone give a complete cycle.

> > Hanson in 7 or 11 notes.

> Another nice feature of the 11-note scale is its circle of six
> major thirds and five fourths, which could certainly be made use of
> structurally.

Could this be used for tuning purposes? 19 and even 34 tone guitars
have been made, but I don't know if in four octaves, which six major
thirds and five fourths would give you. Of course minor thirds would
be an alternative.

> > Sensi, 11 notes.

The sensi generator is around 443 cents, which may be a good size.

🔗Carl Lumma <ekin@...>

2/14/2007 8:51:45 PM

Dave Keenan is good at this.

It's a qustion for Tuning, though, not MMM.

-Carl

>I'm getting way outside of my knowledge area here, but it occurred to
>me to wonder about tuning guitars (and perhaps other stringed
>instruments) to these MOS. It seems fourths and major thirds are
>popular intervals, and I wonder if anyone can tell me if the thoughts
>below make any sense.
>
>> > Magic in 7 or 10 notes.
>
>Magic has a flat major fourth as a generator, and how would that work
>as an interval for tuning a guitar? It might be possible to make
>either a 19 or a 22 tone guitar on this principle, correct? Six major
>thirds and a tone give a complete cycle.
>
>> > Hanson in 7 or 11 notes.
>
>> Another nice feature of the 11-note scale is its circle of six
>> major thirds and five fourths, which could certainly be made use of
>> structurally.
>
>Could this be used for tuning purposes? 19 and even 34 tone guitars
>have been made, but I don't know if in four octaves, which six major
>thirds and five fourths would give you. Of course minor thirds would
>be an alternative.
>
>> > Sensi, 11 notes.
>
>The sensi generator is around 443 cents, which may be a good size.

🔗Carl Lumma <ekin@...>

2/14/2007 8:53:13 PM

>i plan to eventually
>incorporate the whole Encyclopedia into Tonescape's
>menu system, so making it a wiki could cause problems,
>from editing to copyrights.

Do you consider the copyright to the quoted material in
the encyclopedia Tonalsoft property?

-Carl

🔗Herman Miller <hmiller@...>

2/14/2007 9:16:57 PM

Carl Lumma wrote:
>> Hanson in 7 or 11 notes.
>>
>> I guess Hanson must have used it. Who else? 11 notes of it look like >> a great way to do 5-limit stuff, with the option of smuggling in some >> cheesy 7-limit stuff also. Recommended tuning: 14deg53
> > I don't think Hanson did, but I could be wrong. I wrote some
> chord progressions in the 8-tone chain. Herman may have done
> some stuff with it.

All of my experimentation with the 11-note chain-of-minor-thirds scale was with the 7-limit version (keemun). I played Lecuona's _Malague�a_ in that tuning and it mostly worked pretty well. But then I discovered lemba temperament and haven't gone back to doing much with keemun in a while.

🔗Gene Ward Smith <genewardsmith@...>

2/15/2007 12:34:33 AM

--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
<genewardsmith@...> wrote:

> Magic has a flat major fourth as a generator,

Major third.

🔗Graham Breed <gbreed@...>

2/15/2007 1:14:15 AM

On 15/02/07, Gene Ward Smith <genewardsmith@...> wrote:
>
> I'm getting way outside of my knowledge area here, but it occurred to
> me to wonder about tuning guitars (and perhaps other stringed
> instruments) to these MOS. It seems fourths and major thirds are
> popular intervals, and I wonder if anyone can tell me if the thoughts
> below make any sense.
>
> > > Magic in 7 or 10 notes.
>
> Magic has a flat major fourth as a generator, and how would that work
> as an interval for tuning a guitar? It might be possible to make
> either a 19 or a 22 tone guitar on this principle, correct? Six major
> thirds and a tone give a complete cycle.

I've thought that magic might make for a good guitar temperament, but
not worked out the details. Meantone is good but inaccurate,
especially on the fourths and fifths which are important for a guitar
style. Magic's the next simplest 9-limit temperament *waves hand*.
It's better tuned, and I think 9-limit harmony on a guitar would sound
cool. There are folks who've managed JI with guitars, of course, but
I've always been frightened off by the commas.

One thing, as you corrected yourself in another message, is that the
generator's a major third. Perfect fourths are a relatively distant
interval (five thirds down) and so a conventional tuning probably
wouldn't work at all. (But maybe a lute tuning?) That means you'd
have to learn a new fingering as well as getting the frets moved
around. I don't expect anybody to be crazy enough to try that in the
near future, but perhaps I will one day ;-)

Without checking the details, I'm guessing it'd be my first choice if
I got a new re-fretted guitar. I've done meantone, and tuned the
strings to copy the blackjack fretting we were talking about at the
time. That sort of worked, and magic should be simpler and good
enough. A 29-equal fretting to get mystery is also worth a thought,
but that's more of a freaky fairground tuning. I had it on my ZTar
for a while.

Anyway, as I'm not planning to mutilate another guitar it's not
something I've thought through.

Graham

🔗Aaron Krister Johnson <aaron@...>

2/15/2007 10:30:32 AM

--- In MakeMicroMusic@yahoogroups.com, "monz" <monz@...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "Aaron Krister Johnson"
> <aaron@> wrote:
>
> > OR---you could wiki-fy the encyclopedia, which could make such
> > corrections and maintainence much easier!
>
>
> I had the idea to do something like that before Wikipedia
> existed ... but at this point i plan to eventually
> incorporate the whole Encyclopedia into Tonescape's
> menu system, so making it a wiki could cause problems,
> from editing to copyrights.

hmm....legally, ethically, community-wise, putting it into Tonescape's
menu seems like a bad idea, just on the surface of it. It just seems
too much going against the grain of an open community of contributors,
which is de facto how the encyclopedia stands. Granted, Tonescape is a
corporation I suppose, and you *are* after all, the maintainer and
host of the encyclopedia, but the tuning community has contributed
enormous amounts of material to it---I don't understand how your
company could 'own' it to the point of actually coding it into non
open-source software; in fact, I would think, although I'm not a
lawyer, that it would have to be defined as an open-source project of
sorts, unless you got permission from each and every contributer to
profit from it's existence.

Maybe I'm not privy to certain information, and all the authors and
quoted sources have already conceded that the encyclopedia is owned by
Tonalsoft, since you host it....

Anyway, why not just have a helper app open a local file version with
a local browser? This way, as the online excyclopedia gets updated,
you can zip it into an archive, and have your users download it.

My wish and hope would be that the encyclopedia *not* disappear from
the web once you do that, if you do that!

Best,
Aaron.

🔗monz <monz@...>

2/15/2007 2:10:04 PM

Hi Aaron,

I don't want to get too far into this yet, because Tonescape
is far from ready for the Encyclopedia to be included
into it. But basically we intended to ask contributors
to sign license agreements with us which allow us to
include their contributions into the version of the
Encyclopedia that lives inside Tonescape.

The main reason i want to include the Encyclopedia
into the software is because, instead of having
static graphics which just give one "bird's eye view"
of a tuning, you would get the complete 3-D rotatable
Lattice-with-sound which is a part of Tonescape.
The idea is to link the Encyclopedia pages directly
into the way Tonescape operates. You'd be able to
read the Encyclopedia page about a tuning topic, see
and play with the Lattice of it, as well as any
musical illustrations that are there, and then
actually compose your own examples, without needing
any extraneous browsers, text editors, etc. etc.

Anyway, as i said, Tonalsoft needs some serious investor
interest to proceed any farther than what we are offering
right now, and what we have right now still needs a little
fixing up. So i'll bring this up again later when the
time is appropriate.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In MakeMicroMusic@yahoogroups.com, "Aaron Krister Johnson"
<aaron@...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "monz" <monz@> wrote:
> >
> > --- In MakeMicroMusic@yahoogroups.com, "Aaron Krister Johnson"
> > <aaron@> wrote:
> >
> > > OR---you could wiki-fy the encyclopedia, which could make such
> > > corrections and maintainence much easier!
> >
> >
> > I had the idea to do something like that before Wikipedia
> > existed ... but at this point i plan to eventually
> > incorporate the whole Encyclopedia into Tonescape's
> > menu system, so making it a wiki could cause problems,
> > from editing to copyrights.
>
> hmm....legally, ethically, community-wise, putting it into Tonescape's
> menu seems like a bad idea, just on the surface of it. It just seems
> too much going against the grain of an open community of contributors,
> which is de facto how the encyclopedia stands. Granted, Tonescape is a
> corporation I suppose, and you *are* after all, the maintainer and
> host of the encyclopedia, but the tuning community has contributed
> enormous amounts of material to it---I don't understand how your
> company could 'own' it to the point of actually coding it into non
> open-source software; in fact, I would think, although I'm not a
> lawyer, that it would have to be defined as an open-source project of
> sorts, unless you got permission from each and every contributer to
> profit from it's existence.
>
> Maybe I'm not privy to certain information, and all the authors and
> quoted sources have already conceded that the encyclopedia is owned by
> Tonalsoft, since you host it....
>
> Anyway, why not just have a helper app open a local file version with
> a local browser? This way, as the online excyclopedia gets updated,
> you can zip it into an archive, and have your users download it.
>
> My wish and hope would be that the encyclopedia *not* disappear from
> the web once you do that, if you do that!
>
> Best,
> Aaron.
>

🔗Aaron Krister Johnson <aaron@...>

2/15/2007 2:24:11 PM

Hey Monz!

What ou say makes sense. And the software sounds awfully cool!

-A.

--- In MakeMicroMusic@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Aaron,
>
>
> I don't want to get too far into this yet, because Tonescape
> is far from ready for the Encyclopedia to be included
> into it. But basically we intended to ask contributors
> to sign license agreements with us which allow us to
> include their contributions into the version of the
> Encyclopedia that lives inside Tonescape.
>
> The main reason i want to include the Encyclopedia
> into the software is because, instead of having
> static graphics which just give one "bird's eye view"
> of a tuning, you would get the complete 3-D rotatable
> Lattice-with-sound which is a part of Tonescape.
> The idea is to link the Encyclopedia pages directly
> into the way Tonescape operates. You'd be able to
> read the Encyclopedia page about a tuning topic, see
> and play with the Lattice of it, as well as any
> musical illustrations that are there, and then
> actually compose your own examples, without needing
> any extraneous browsers, text editors, etc. etc.
>
> Anyway, as i said, Tonalsoft needs some serious investor
> interest to proceed any farther than what we are offering
> right now, and what we have right now still needs a little
> fixing up. So i'll bring this up again later when the
> time is appropriate.
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>
>
> --- In MakeMicroMusic@yahoogroups.com, "Aaron Krister Johnson"
> <aaron@> wrote:
> >
> > --- In MakeMicroMusic@yahoogroups.com, "monz" <monz@> wrote:
> > >
> > > --- In MakeMicroMusic@yahoogroups.com, "Aaron Krister Johnson"
> > > <aaron@> wrote:
> > >
> > > > OR---you could wiki-fy the encyclopedia, which could make such
> > > > corrections and maintainence much easier!
> > >
> > >
> > > I had the idea to do something like that before Wikipedia
> > > existed ... but at this point i plan to eventually
> > > incorporate the whole Encyclopedia into Tonescape's
> > > menu system, so making it a wiki could cause problems,
> > > from editing to copyrights.
> >
> > hmm....legally, ethically, community-wise, putting it into Tonescape's
> > menu seems like a bad idea, just on the surface of it. It just seems
> > too much going against the grain of an open community of contributors,
> > which is de facto how the encyclopedia stands. Granted, Tonescape is a
> > corporation I suppose, and you *are* after all, the maintainer and
> > host of the encyclopedia, but the tuning community has contributed
> > enormous amounts of material to it---I don't understand how your
> > company could 'own' it to the point of actually coding it into non
> > open-source software; in fact, I would think, although I'm not a
> > lawyer, that it would have to be defined as an open-source project of
> > sorts, unless you got permission from each and every contributer to
> > profit from it's existence.
> >
> > Maybe I'm not privy to certain information, and all the authors and
> > quoted sources have already conceded that the encyclopedia is owned by
> > Tonalsoft, since you host it....
> >
> > Anyway, why not just have a helper app open a local file version with
> > a local browser? This way, as the online excyclopedia gets updated,
> > you can zip it into an archive, and have your users download it.
> >
> > My wish and hope would be that the encyclopedia *not* disappear from
> > the web once you do that, if you do that!
> >
> > Best,
> > Aaron.
> >
>

🔗Jon Szanto <jszanto@...>

2/15/2007 5:26:24 PM

Dan,

{you wrote...}
>for anyone out of the loop that's interested in playing along at home, is there a neat and orderly place where all these names--"lemba" et al--are compiled along with their definitions?

Son, you must be joking.

Cheers,
Jon

🔗Carl Lumma <ekin@...>

2/15/2007 7:55:09 PM

At 04:52 PM 2/15/2007, you wrote:
>for anyone out of the loop that's interested in playing along at home,
>is there a neat and orderly place where all these names--"lemba" et
>al--are compiled along with their definitions?
>
>http://www.myspace.com/danstearns

The short answer is, sadly, no. Google web search is your best
bet. Herman Miller does have a great page on lemba in particular.
It remains for someone with the passion, time, and knowledge to
put this all together in a way that mortals can understand.

-Carl

🔗Jacob <jbarton@...>

2/15/2007 8:02:48 PM

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@...> wrote:
>
> At 04:52 PM 2/15/2007, you wrote:
> >for anyone out of the loop that's interested in playing along at home,
> >is there a neat and orderly place where all these names--"lemba" et
> >al--are compiled along with their definitions?
> >
> >http://www.myspace.com/danstearns
>
> The short answer is, sadly, no. Google web search is your best
> bet. Herman Miller does have a great page on lemba in particular.
> It remains for someone with the passion, time, and knowledge to
> put this all together in a way that mortals can understand.
>
> -Carl
>

Ok, I'll start, at least, over at xenharmonic.wikispaces.com . I
can't promise I'll get very far, or that I actually understand
anything properly, but by golly this is something that should have
happened by now if the linear-temperament contingent ever expects its
neologisms to make a dent in the language.

roger,
jacob

🔗monz <monz@...>

2/15/2007 8:26:58 PM

Hey guys, did you miss this?

/makemicromusic/topicId_16064.html#16081

I just renewed my call for those who know to help me
put more about temperament families into the Encyclopedia.
But at least you can get a start from the links i put
into that message.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In MakeMicroMusic@yahoogroups.com, "Jacob" <jbarton@...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, Carl Lumma <ekin@> wrote:
> >
> > At 04:52 PM 2/15/2007, you wrote:
> > >
> > > for anyone out of the loop that's interested in
> > > playing along at home, is there a neat and orderly
> > > place where all these names--"lemba" et al--are
> > > compiled along with their definitions?
> > >
> > > http://www.myspace.com/danstearns
> >
> > The short answer is, sadly, no. Google web search
> > is your best bet. Herman Miller does have a great page
> > on lemba in particular.
> > It remains for someone with the passion, time, and
> > knowledge to put this all together in a way that mortals
> > can understand.
> >
> > -Carl
> >
>
> Ok, I'll start, at least, over at xenharmonic.wikispaces.com .
> I can't promise I'll get very far, or that I actually
> understand anything properly, but by golly this is
> something that should have happened by now if the
> linear-temperament contingent ever expects its
> neologisms to make a dent in the language.
>
> roger,
> jacob
>

🔗Herman Miller <hmiller@...>

2/15/2007 8:18:35 PM

daniel_anthony_stearns wrote:
> for anyone out of the loop that's interested in playing along at home,
> is there a neat and orderly place where all these names--"lemba" et
> al--are compiled along with their definitions?

Paul Erlich's "Middle Path" paper is probably the best reference at the moment. As far as the web, there's a list of 7-limit temperaments on Gene's page, but the definitions (in the form of wedgies) are of limited use.

http://66.98.148.43/~xenharmo/sevnames.htm

I thought there were better references than that, but I can't find them. In the meantime, I threw together a quick list of regular temperaments based on an old document (some of the names may be out of date, and this is by no means a complete list).

http://www.io.com/~hmiller/music/temp-list.html

Not all of these names are in current use (some of them may have been suggested once and subsequently forgotten).

The period and generator shown represents the TOP tuning of each temperament -- some temperaments have a large tolerance for tuning, but others need to be tuned more precisely. I made some charts which give a rough idea of how various 5-limit temperaments hold up when the tuning of the generator and the period is changed: they're in the files section of the tuning-math Yahoo group.

/tuning-math/files/Rank%202%20Consistency/

(Generally speaking the darker areas are better, and the more accurate temperaments require more precise tuning.)

🔗Graham Breed <gbreed@...>

2/16/2007 12:14:56 AM

On 16/02/07, daniel_anthony_stearns <daniel_anthony_stearns@...> wrote:
>
> for anyone out of the loop that's interested in playing along at home,
> is there a neat and orderly place where all these names--"lemba" et
> al--are compiled along with their definitions?

My catalog's here:

http://x31eq.com/catalog.htm

but I gave up a long time ago because there were so many new names
being minted. So it doesn't have lemba. I thought about setting up a
database with definition, name, theoretical and musical references and
the like, but it's too big a job for this holiday.

Graham

🔗Herman Miller <hmiller@...>

2/16/2007 6:33:16 PM

Carl Lumma wrote:
> At 04:52 PM 2/15/2007, you wrote:
>> for anyone out of the loop that's interested in playing along at home,
>> is there a neat and orderly place where all these names--"lemba" et
>> al--are compiled along with their definitions?
>>
>> http://www.myspace.com/danstearns > > The short answer is, sadly, no. Google web search is your best
> bet. Herman Miller does have a great page on lemba in particular.
> It remains for someone with the passion, time, and knowledge to
> put this all together in a way that mortals can understand.

Are you thinking of the porcupine temperament page?

http://www.io.com/~hmiller/music/temp-porcupine.html

I have the start of a lemba page, but haven't got around to making it usable yet. Still, the chart showing the mixed Sagittal lemba notation, and the comparison of TOP lemba with just intervals, may be useful.

http://www.io.com/~hmiller/music/lemba.html

🔗Carl Lumma <ekin@...>

2/16/2007 7:24:11 PM

>>> for anyone out of the loop that's interested in playing along at home,
>>> is there a neat and orderly place where all these names--"lemba" et
>>> al--are compiled along with their definitions?
>>>
>>> http://www.myspace.com/danstearns
>>
>> The short answer is, sadly, no. Google web search is your best
>> bet. Herman Miller does have a great page on lemba in particular.
>> It remains for someone with the passion, time, and knowledge to
>> put this all together in a way that mortals can understand.
>
>Are you thinking of the porcupine temperament page?
>
>http://www.io.com/~hmiller/music/temp-porcupine.html

I was thinking of:

http://www.io.com/~hmiller/music/zireen-music.html

>I have the start of a lemba page, but haven't got around to making it
>usable yet. Still, the chart showing the mixed Sagittal lemba notation,
>and the comparison of TOP lemba with just intervals, may be useful.
>
>http://www.io.com/~hmiller/music/lemba.html

This is all overlapping in IE6 'n shit.

-Carl

🔗Herman Miller <hmiller@...>

2/17/2007 1:26:42 PM

Carl Lumma wrote:

>> I have the start of a lemba page, but haven't got around to making it >> usable yet. Still, the chart showing the mixed Sagittal lemba notation, >> and the comparison of TOP lemba with just intervals, may be useful.
>>
>> http://www.io.com/~hmiller/music/lemba.html
> > This is all overlapping in IE6 'n shit.
> > -Carl

I have no idea what your problem might be, unless you're viewing it through some kind of proxy that alters the formatting of the page or something. It's nothing more than plain text and images. The main chart was missing "width" and "height", but that shouldn't cause any trouble, once the image is loaded...

The only other thing I can think of is the "meta" header that sets the character set to UTF-8, but IE6 shouldn't have any problem at all with that. Still, I don't need it for that page, so I took it out.

🔗Carl Lumma <ekin@...>

2/17/2007 1:53:38 PM

At 01:26 PM 2/17/2007, you wrote:
>Carl Lumma wrote:
>
>>> I have the start of a lemba page, but haven't got around to making it
>>> usable yet. Still, the chart showing the mixed Sagittal lemba notation,
>>> and the comparison of TOP lemba with just intervals, may be useful.
>>>
>>> http://www.io.com/~hmiller/music/lemba.html
>>
>> This is all overlapping in IE6 'n shit.
>>
>> -Carl
>
>I have no idea what your problem might be,

Hm, it's working fine now.

-Carl

🔗George D. Secor <gdsecor@...>

2/22/2007 1:00:55 PM

--- In MakeMicroMusic@yahoogroups.com, "Aaron Krister Johnson"
<aaron@...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
> <genewardsmith@> wrote:
> >
> > --- In MakeMicroMusic@yahoogroups.com, "Aaron Krister Johnson"
> > <aaron@> wrote:
> >
> > > You lost me here---is that the 46th degree of 17-edo, or the
17th
> > > degree of 46-edo? HUH?
> >
> > It's 17deg46. I picked this up from Ozan, but maybe I shoulf go
back to
> > saying 17/46.
>
> I prefer the compactness of x/y notation, but perhaps XdegY is less
> ambiguous because the x/y notation might be mistaken out of context
as
> linear ratios instead of exponents of two.
>
> So, I think Ozan is onto something. What confused me is that you
meant
> 17th degree of 46-edo, whic would be 17deg46, but you wrote 46deg17.

I believe that Oz got it from me (look thru the old Sagittal "A
Common Notation for ..." messages on tuning-math beginning in 2002
and you'll see that Dave Keenan and I used it extensively). I
proposed the idea of using a degree-sign instead of a slash over 30
years ago, and you'll find it in the documentation on the Sagittal
website, and also in my 17-tone XH18 paper (written late in 2001).

Unfortunately, since the degree sign isn't a member of the usual
ASCII set, we've had to substitute the more cumbersome "deg" in text
messages.

--George