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Message: 6750 - Contents - Hide Contents

Date: Mon, 14 Apr 2003 16:44:02

Subject: Re: Canonical homomorphisms revisted

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:


> what do you make of monz's use of the term "internal homomorphism" on 
> this page:
> 
> more on the duodene * [with cont.]  (Wayb.)


It makes no sense to me. Oh well. :)


> anyway, so miracle doesn't want to have 2 as a generator? then what 
> does the scale "really" look like?


72-et with slightly flattened octaves, perhaps.

Message: 6751 - Contents - Hide Contents

Date: Mon, 14 Apr 2003 05:23:36

Subject: Re: Canonical homomorphisms revisted

From: wallyesterpaulrus

what do you make of monz's use of the term "internal homomorphism" on 
this page:

more on the duodene * [with cont.]  (Wayb.)

?

anyway, so miracle doesn't want to have 2 as a generator? then what 
does the scale "really" look like?

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> 
wrote:

> The problem with my first definition is that it works beautifully 
when
> it works, but it doesn't always work (1/2 time in the 5-limit, 1/4 
of
> the time in the 7-limit, and so forth.) Taking it as a source of
> inspiration, here is a definition which works in general.
> Unfortunately it no longer is as slick as goose grease.
> 
> If T is a temperament, call q a "subgroup comma" for T if q>1 is 
not a
> power of anything else, and if only three primes are involved in its
> factorization (these commas are easily found from the wedgie.) Call 
a
> prime "reducible" if it appears by itself in either numerator or
> denominator for the factorization of a subgroup comma. If T is
> p-limit, let P be the set of primes <= p, and let R be the set of
> reducible primes. Then N = P\R is the set of non-reducible primes. 
If
> card(N) = g, where g is the number of generators (2 for a linear
> temperament, 3 for a planar temperament, and so forth) then set G = 
N.
> If card(N)<g, then fill it out by adding the smallest of the 
remaining
> primes, and set the result to G; if card(N)>g, then reduce it by
> removing the largest of the primes in N, and call that G. We end 
with
> a set G of primes such that card(G)=g, and we may use G as a set of
> generators for the temperament T.
> 
> Strange as it may seem, this definition actually corresponds to my
> previous one in those cases where the previous one gives a
> homomorphism. It also seems to give us reasonable results, or at 
least
> so it seems to me, YMMV. Here is what we get for meantone and 
miracle;
> I give the mapping of the generators (2 and 3/2 in the case of
> meantone, 2 and 16/15 in the case of miracle), and the mapping 
applied
> to primes:
> 
> 5-limit meantone 81/80
> Generators [2, 5^(1/4)]
> Prime mapping [2, 2*5^(1/4), 5]
> 
> 7-limit meantone [1, 4, 10, 4, 13, 12]
> Generators [2, 2^(3/10)*7^(1/10)]
> Prime mapping [2, 2*2^(3/10)*7^(1/10), 2*2^(1/5)*7^(2/5), 7]
> 
> 11-limit meantone [1, 4, 10, 18, 4, 13, 25, 12, 28, 16]
> Generators [2, 2^(3/10)*7^(1/10)]
> Prime mapping [2, 2*2^(3/10)*7^(1/10), 2*2^(1/5)*7^(2/5), 7,
> 7/4*2^(2/5)*7^(4/5)]
> 
> 11-limit meanpop [1, 4, 10, -13, 4, 13, -24, 12, -44, -71]
> Generators [7^(13/71)*11^(10/71), 7^(11/71)*11^(3/71)]
> Prime mapping [7^(13/71)*11^(10/71), 7^(24/71)*11^(13/71),
> 7^(44/71)*11^(12/71), 7, 11]
> 
> 5-limit miracle 34171875/33554432
> Generators [3^(7/25)*5^(6/25), 1/5*3^(3/25)*5^(24/25)]
> Prime mapping [3^(7/25)*5^(6/25), 3, 5]
> 
> 7-limit miracle [6, -7, -2, -25, -20, 15]
> Generators [3^(7/25)*5^(6/25), 1/5*3^(3/25)*5^(24/25)]
> Prime mapping [3^(7/25)*5^(6/25), 3, 5, 3^(3/5)*5^(4/5)]
> 
> 11-limit miracle [6, -7, -2, 15, -25, -20, 3, 15, 59, 49]
> Generators [5^(15/59)*11^(7/59), 1/5*5^(57/59)*11^(3/59)]
> Prime mapping [5^(15/59)*11^(7/59), 5^(3/59)*11^(25/59), 5,
> 5^(49/59)*11^(15/59), 11]

Message: 6752 - Contents - Hide Contents

Date: Mon, 14 Apr 2003 21:08:06

Subject: Re: Canonical homomorphisms revisted

From: wallyesterpaulrus

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> 
wrote:

> --- In tuning-math@xxxxxxxxxxx.xxxx "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
> 

>> what do you make of monz's use of the term "internal 
homomorphism" on 
>> this page:
>> 
>> more on the duodene * [with cont.]  (Wayb.)
> 

> It makes no sense to me. Oh well. :)
> 

>> anyway, so miracle doesn't want to have 2 as a generator? then 
what 
>> does the scale "really" look like?
> 

> 72-et with slightly flattened octaves, perhaps.


no, i meant something with about as many notes per octave as 
blackjack or canasta, but using the generators you posted instead of 
2 . . . are those just the secor and a flattened octave? i didn't 
bother to check . . .

Message: 6753 - Contents - Hide Contents

Date: Wed, 16 Apr 2003 05:59:22

Subject: Ennealimmal[45]

From: Gene Ward Smith

The standard 45-et val, h45 = [45, 71, 104, 126], has 81/80,
2401/2400 and 4375/4374 as a comma basis. The Fokker block for this is

[1, 49/48, 36/35, 21/20, 200/189, 27/25, 54/49, 10/9, 245/216, 8/7, 
7/6, 25/21, 6/5, 49/40, 100/81, 63/50, 9/7, 35/27, 324/245, 4/3,
49/36, 243/175,7/5, 10/7, 350/243, 72/49, 3/2, 245/162, 54/35, 14/9,
100/63, 81/50, 80/49, 5/3, 42/25, 12/7, 7/4, 432/245, 9/5, 49/27,
50/27, 189/100, 40/21, 35/18, 96/49]

which in terms of the 612 et, is

[0, 18, 25, 43, 50, 68, 86, 93, 111, 118, 136, 154, 161, 179, 186,
204,222, 229, 247, 254, 272, 290, 297, 315, 322, 340, 358, 365, 383,
390, 408, 426, 433, 451, 458, 476, 494, 501, 519, 526, 544, 562, 569,
587, 594]

All of this is nicely regular, but adjusting by an 81/80 has some
interest but not as much as some smaller chromas. 

However, 16/15 as a chroma also works in a sense; we have instead of
the standard val ennealimmal ^ 16/15 = [45, 73, 107, 128] as a val.
The corresponding Fokker block for [16/15, 2401/2400, 4375/4374] is

[1, 36/35, 200/189, 49/48, 21/20, 27/25, 10/9, 8/7, 54/49, 245/216, 
7/6, 6/5, 216/175, 25/21, 60/49, 63/50, 35/27, 4/3, 9/7, 324/245,
49/36, 7/5, 36/25, 25/18, 10/7, 72/49, 245/162, 14/9, 3/2, 54/35,
100/63, 49/30, 42/25, 175/108, 5/3, 12/7, 432/245, 49/27, 7/4, 9/5,
50/27, 40/21, 96/49, 189/100, 35/18]

which in terms of the 612-et is

[0, 25, 50, 18, 43, 68, 93, 118, 86, 111, 136, 161, 186, 154, 179,
204,229, 254, 222, 247, 272, 297, 322, 290, 315, 340, 365, 390, 358,
383, 408, 433, 458, 426, 451, 476, 501, 526, 494, 519, 544, 569, 594,
562, 587]

Here things are not ordered by increasing size; in terms of Paul
theory this is not a valid val. However, if we reorder the above, we
see that the two scales, in 612-et, are identical. Ordering it as
above leads to 16/15 as a chroma in terms of circulating chords, and
we could, if we chose, approach the scale in this way.

Message: 6754 - Contents - Hide Contents

Date: Wed, 16 Apr 2003 07:31:09

Subject: 7-limit tempered scale possibilities

From: Gene Ward Smith

I give the name of the temperament, the wedgie, the Graham complexity,
the chroma and the scale size, in that order. These all have scale
size more than 50% larger than Graham complexity. Will Carl stretch a
point and include Kleismic[11]? I'm betting against.


["Duodecimal", [0, 12, 24, 19, 38, 22], 24, 49/48, 48]

["Hemikleismic", [12, 10, -9, -12, -48, -49], 21, 28/27, 45]

["Kleismic", [6, 5, 3, -6, -12, -7], 6, 28/27, 15]

["Kleismic", [6, 5, 3, -6, -12, -7], 6, 16/15, 11]

["Tripletone", [3, 0, -6, -7, -18, -14], 9, 28/27, 15]

["Tripletone", [3, 0, -6, -7, -18, -14], 9, 49/48, 15]

["Hemifourth", [2, 8, 1, 8, -4, -20], 8, 25/24, 14]

["Meantone", [1, 4, 10, 4, 13, 12], 10, 49/48, 19]

["Hemithird", [15, -2, -5, -38, -50, -6], 20, 28/27, 50]

["Injera", [2, 8, 8, 8, 7, -4], 8, 25/24, 14]

["Injera", [2, 8, 8, 8, 7, -4], 8, 49/48, 14]

["Double wide", [8, 6, 6, -9, -13, -3], 8, 16/15, 14]

["Double wide", [8, 6, 6, -9, -13, -3], 8, 28/27, 18]

["Hemithird", [15, -2, -5, -38, -50, -6], 20, 36/35, 37]

["Superpythagorean", [1, 9, -2, 12, -6, -30], 11, 25/24, 17]

["Muggles", [5, 1, -7, -10, -25, -19], 12, 28/27, 22]

["Hemififth", [2, 25, 13, 35, 15, -40], 25, 25/24, 48]

["Muggles", [5, 1, -7, -10, -25, -19], 12, 49/48, 19]

["Hemiwuerschmidt", [16, 2, 5, -34, -37, 6], 16, 28/27, 43]

["Beatles", [2, -9, -4, -19, -12, 16], 11, 25/24, 20]

["Beatles", [2, -9, -4, -19, -12, 16], 11, 36/35, 17]

["Wizard", [12, -2, 20, -31, -2, 52], 22, 21/20, 34]

["Hemiwuerschmidt", [16, 2, 5, -34, -37, 6], 16, 36/35, 25]

["Ennealimmal", [18, 27, 18, 1, -22, -34], 27, 16/15, 45]

["Magic", [5, 1, 12, -10, 5, 25], 12, 49/48, 19]

["Nonkleismic", [10, 9, 7, -9, -17, -9], 10, 16/15, 19]

["Nonkleismic", [10, 9, 7, -9, -17, -9], 10, 28/27, 23]

["Decimal", [4, 2, 2, -6, -8, -1], 4, 28/27, 10]

["Orwell", [7, -3, 8, -21, -7, 27], 11, 21/20, 18]

["Diminished", [4, 4, 4, -3, -5, -2], 4, 16/15, 8]

["Diminished", [4, 4, 4, -3, -5, -2], 4, 28/27, 8]

["Miracle", [6, -7, -2, -25, -20, 15], 13, 25/24, 20]

["Miracle", [6, -7, -2, -25, -20, 15], 13, 36/35, 21]

["Blackwood", [0, 5, 0, 8, 0, -14], 5, 25/24, 10]

["Miracle", [6, -7, -2, -25, -20, 15], 13, 28/27, 20]

["Quartaminorthirds", [9, 5, -3, -13, -30, -21], 12, 28/27, 30]

["Supermajor seconds", [3, 12, -1, 12, -10, -36], 13, 25/24, 21]

["Schismic", [1, -8, -14, -15, -25, -10], 15, 49/48, 29]

["Schismic", [1, -8, -14, -15, -25, -10], 15, 36/35, 24]

["Superkleismic", [9, 10, -3, -5, -30, -35], 13, 15/14, 22]

["Pajara", [2, -4, -4, -11, -12, 2], 6, 28/27, 10]

["Pajara", [2, -4, -4, -11, -12, 2], 6, 25/24, 10]

["Pajara", [2, -4, -4, -11, -12, 2], 6, 36/35, 12]

["Superkleismic", [9, 10, -3, -5, -30, -35], 13, 28/27, 30]

["Pajara", [2, -4, -4, -11, -12, 2], 6, 49/48, 10]

["Squares", [4, 16, 9, 16, 3, -24], 16, 25/24, 28]

["Diaschismic", [2, -4, -16, -11, -31, -26], 18, 49/48, 34]

["Octafifths", [8, 18, 11, 10, -5, -25], 18, 25/24, 28]

["Tritonic", [5, -11, -12, -29, -33, 3], 17, 36/35, 33]

["Tritonic", [5, -11, -12, -29, -33, 3], 17, 28/27, 27]

["Tritonic", [5, -11, -12, -29, -33, 3], 17, 25/24, 27]

["Tritonic", [5, -11, -12, -29, -33, 3], 17, 49/48, 29]

["Supersupermajor", [3, 17, -1, 20, -10, -50], 18, 25/24, 31]

["Catakleismic", [6, 5, 22, -6, 18, 37], 22, 49/48, 38]

Message: 6755 - Contents - Hide Contents

Date: Wed, 16 Apr 2003 00:38:19

Subject: Re: 7-limit tempered scale possibilities

From: Carl Lumma

>I give the name of the temperament, the wedgie, the Graham complexity,
>the chroma and the scale size, in that order. These all have scale
>size more than 50% larger than Graham complexity.


That's a good criterion, but (even with a max scale size) was it
sufficient to close this list?


>Will Carl stretch a point and include Kleismic[11]? I'm betting
>against.


Yeah, Kleismic[11] came up long ago, and I rejected it in favor of
Kleismic[8].  ;)

-Carl

Message: 6756 - Contents - Hide Contents

Date: Wed, 16 Apr 2003 15:32:32

Subject: Re: 7-limit tempered scale possibilities

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:


>> I give the name of the temperament, the wedgie, the Graham complexity,
>> the chroma and the scale size, in that order. These all have scale
>> size more than 50% larger than Graham complexity.
> 

> That's a good criterion, but (even with a max scale size) was it
> sufficient to close this list?


Not really; I simply used a list of temperaments I already had.
However, if we bound badness and insist on "validity" the list is
finite, since it involves vals which have one or more of the "good"
chromas as commas. After a while we would only get things with scale
degrees out of order, like my "invalid" Ennealimmal[45] example.

Message: 6757 - Contents - Hide Contents

Date: Thu, 17 Apr 2003 21:19:41

Subject: Re: Ennealimmal[45]

From: wallyesterpaulrus

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> 
wrote:

> The standard 45-et val, h45 = [45, 71, 104, 126], has 81/80,
> 2401/2400 and 4375/4374 as a comma basis. The Fokker block for this 
is
> 
> [1, 49/48, 36/35, 21/20, 200/189, 27/25, 54/49, 10/9, 245/216, 8/7, 
> 7/6, 25/21, 6/5, 49/40, 100/81, 63/50, 9/7, 35/27, 324/245, 4/3,
> 49/36, 243/175,7/5, 10/7, 350/243, 72/49, 3/2, 245/162, 54/35, 14/9,
> 100/63, 81/50, 80/49, 5/3, 42/25, 12/7, 7/4, 432/245, 9/5, 49/27,
> 50/27, 189/100, 40/21, 35/18, 96/49]
> 
> which in terms of the 612 et, is
> 
> [0, 18, 25, 43, 50, 68, 86, 93, 111, 118, 136, 154, 161, 179, 186,
> 204,222, 229, 247, 254, 272, 290, 297, 315, 322, 340, 358, 365, 383,
> 390, 408, 426, 433, 451, 458, 476, 494, 501, 519, 526, 544, 562, 
569,
> 587, 594]
> 
> All of this is nicely regular, but adjusting by an 81/80 has some
> interest but not as much as some smaller chromas. 
> 
> However, 16/15 as a chroma also works in a sense; we have instead of
> the standard val ennealimmal ^ 16/15 = [45, 73, 107, 128] as a val.
> The corresponding Fokker block for [16/15, 2401/2400, 4375/4374] is
> 
> [1, 36/35, 200/189, 49/48, 21/20, 27/25, 10/9, 8/7, 54/49, 245/216, 
> 7/6, 6/5, 216/175, 25/21, 60/49, 63/50, 35/27, 4/3, 9/7, 324/245,
> 49/36, 7/5, 36/25, 25/18, 10/7, 72/49, 245/162, 14/9, 3/2, 54/35,
> 100/63, 49/30, 42/25, 175/108, 5/3, 12/7, 432/245, 49/27, 7/4, 9/5,
> 50/27, 40/21, 96/49, 189/100, 35/18]
> 
> which in terms of the 612-et is
> 
> [0, 25, 50, 18, 43, 68, 93, 118, 86, 111, 136, 161, 186, 154, 179,
> 204,229, 254, 222, 247, 272, 297, 322, 290, 315, 340, 365, 390, 358,
> 383, 408, 433, 458, 426, 451, 476, 501, 526, 494, 519, 544, 569, 
594,
> 562, 587]
> 
> Here things are not ordered by increasing size; in terms of Paul
> theory this is not a valid val.


can you fill me in on what i need to know about paul theory to 
understand this last assertion?

Message: 6758 - Contents - Hide Contents

Date: Thu, 24 Apr 2003 18:28:31

Subject: Re: Canonical homomorphisms revisted

From: Carl Lumma

I have nothing to say, but I wish I did.  Does anybody
else have anything to say?  If so, you may say it now.

-Carl

Message: 6759 - Contents - Hide Contents

Date: Thu, 24 Apr 2003 18:34:11

Subject: Re: Canonical homomorphisms revisted

From: Carl Lumma

>I have nothing to say,


Other than, if I understand this, it's what I've been pining
for all along -- defining temperaments with maps.  Unforch,
I haven't tracked the reasoning behind what why maps found
with this technique should be canonical.  Would anybody
besides Gene consider them natural mappings for their fav.
temperament(s)?

-Carl

Message: 6760 - Contents - Hide Contents

Date: Thu, 24 Apr 2003 18:35:58

Subject: Re: Doing 12-equal within 133-et

From: Carl Lumma

>Retuning any 12-et piece into this tuning is a straightforward task,
>and I hope to get around to actually doing it soon. (I've either got
>to boot up DOS, which I seldom do now, or get my Linux up to speed.)


Any progress on this?

I can't say I see how applying a temperament to any 12-et piece would
be "straightforward"?  Do you do this in maple?

-Carl

Message: 6761 - Contents - Hide Contents

Date: Sat, 26 Apr 2003 10:16:44

Subject: Re: Doing 12-equal within 133-et

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:


>> Retuning any 12-et piece into this tuning is a straightforward task,
>> and I hope to get around to actually doing it soon. (I've either got
>> to boot up DOS, which I seldom do now, or get my Linux up to speed.)
> 

> Any progress on this?


I'm still not happy about how Scala works under Linux for me, but I
don't really need it. 


> I can't say I see how applying a temperament to any 12-et piece would
> be "straightforward"?  Do you do this in maple?


Eh? Wasn't this exactly what you were doing with the shootout?

Maple is what I'd use for my example though, and calling it
straightforward is a stretch, since I'd take a midi file, turn it into
a Csound score file, edit that into a Maple file, then work with the
Maple file and then create a Scala file using Maple. Since Scala under
Linux seems very fussy about what files it will read, and I can't get
Maple to work on my chip under Windows, I'll probably need to copy the
.seq file over to the DOS part of the disk under Linux, and then
reboot to finish in Windows.

Like I said, straightforward.

Message: 6762 - Contents - Hide Contents

Date: Sat, 26 Apr 2003 13:20:08

Subject: Re: Doing 12-equal within 133-et

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...>
wrote:


> Maple is what I'd use for my example though, and calling it
> straightforward is a stretch, since I'd take a midi file, turn it into
> a Csound score file, edit that into a Maple file, then work with the
> Maple file and then create a Scala file using Maple. Since Scala under
> Linux seems very fussy about what files it will read, and I can't get
> Maple to work on my chip under Windows, I'll probably need to copy the
> .seq file over to the DOS part of the disk under Linux, and then
> reboot to finish in Windows.
> 
> Like I said, straightforward.


I converted the 4th movement of the Brahms string quartet #2 to a
Scala seq file in 132 (which is to say, 12) et, and Scala rendered it
as a midi file with no trouble. When I changed "0 equal 132" to "0
equal 133" it told me there were not enough midi channels; depite it
being a quartet Brahms uses a lot of double stops.

Drat midi. When is someone going to fix it? Isn't the midi tuning
standard supposed to deal with this stuff?

Message: 6763 - Contents - Hide Contents

Date: Sat, 26 Apr 2003 10:18:56

Subject: Re: Canonical homomorphisms revisted

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:

>> I have nothing to say,
> 

> Other than, if I understand this, it's what I've been pining
> for all along -- defining temperaments with maps.  Unforch,
> I haven't tracked the reasoning behind what why maps found
> with this technique should be canonical. 


Maybe I shouldn't call them that anymore.

Message: 6764 - Contents - Hide Contents

Date: Sat, 26 Apr 2003 17:15:28

Subject: Re: Doing 12-equal within 133-et

From: Manuel Op de Coul

Gene wrote:


>Since Scala under
> Linux seems very fussy about what files it will read,


The scale files? Then see readme.txt. I could save the archive
in Unix format, but then there'll be Windows editors to
become fussy.


>Drat midi. When is someone going to fix it? Isn't the midi tuning
>standard supposed to deal with this stuff?


You could use Audio Compositor as Carl did with his temperament
exercise. AC has been fixed recently. Convert the seq file to
a midi file first, then use example/midi/mts.
Or use a tunable softsynth with a MIDI loopback, only that will affect
the timing a bit.
In 133-tET there are two fifths you can use.

Manuel

Message: 6765 - Contents - Hide Contents

Date: Sat, 26 Apr 2003 10:57:38

Subject: Re: Doing 12-equal within 133-et

From: Carl Lumma

>> > can't say I see how applying a temperament to any 12-et piece would
>> be "straightforward"?  Do you do this in maple?
>

>Eh? Wasn't this exactly what you were doing with the shootout?


I'm mapping 12 pitches to 12 other pitches.  I was under the impression
this conversion required mapping intervals to intervals.

-Carl

Message: 6766 - Contents - Hide Contents

Date: Sat, 26 Apr 2003 11:11:01

Subject: Re: Canonical homomorphisms revisted

From: Carl Lumma

>> >ther than, if I understand this, it's what I've been pining
>> for all along -- defining temperaments with maps.  Unforch,
>> I haven't tracked the reasoning behind what why maps found
>> with this technique should be canonical. 
>

>Maybe I shouldn't call them that anymore.

Why?

-Carl

Message: 6767 - Contents - Hide Contents

Date: Sat, 26 Apr 2003 18:52:28

Subject: Esurientes implevit from Bach's Magnificat

From: Gene Ward Smith

I did this in both 12-et and in 133-et, using 132 steps of it as a flat 
octave, and so approximating the "canonical" Dominant Seventh
temperament mapping. The files 

Yahoo groups: /tuning-math/files/gene/magni132... * [with cont.] 

and

The Proxomitron Reveals... * [with cont.]  (Wayb.)

I prefer the canonical version with flat octaves. Anyone else have an
opinion?

Message: 6768 - Contents - Hide Contents

Date: Sat, 26 Apr 2003 18:57:44

Subject: Re: Doing 12-equal within 133-et

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "Manuel Op de Coul"
<manuel.op.de.coul@e...> wrote:

> 
> Gene wrote:
> 

>> Since Scala under
>> Linux seems very fussy about what files it will read,
> 

> The scale files? Then see readme.txt. I could save the archive
> in Unix format, but then there'll be Windows editors to
> become fussy.


They both seem fussy. I'm finding the Linux version works fine as long
as everything is created in a native Linux environment, with *no*
cutting and pasting of anything taken from a Windows file. The midi
files for my examples were created on the Linux side.


>> Drat midi. When is someone going to fix it? Isn't the midi tuning
>> standard supposed to deal with this stuff?
> 

> You could use Audio Compositor as Carl did with his temperament
> exercise. AC has been fixed recently. Convert the seq file to
> a midi file first, then use example/midi/mts.


It's the conversion of a seq to a midi file which is the problem. 


> In 133-tET there are two fifths you can use.


For this canonical map business, I must use the meantone fifth.

Message: 6769 - Contents - Hide Contents

Date: Sat, 26 Apr 2003 19:00:32

Subject: Re: Canonical homomorphisms revisted

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:

>>> Other than, if I understand this, it's what I've been pining
>>> for all along -- defining temperaments with maps.  Unforch,
>>> I haven't tracked the reasoning behind what why maps found
>>> with this technique should be canonical. 
>> 

>> Maybe I shouldn't call them that anymore.


My nice, clean, overwhelmingly nifty definition only worked part of
the time, and its replacement does the same job, but the definition is
hardly nifty anymore.

In practical terms the darn thing works, however.

Message: 6771 - Contents - Hide Contents

Date: Sat, 26 Apr 2003 12:40:39

Subject: Re: Esurientes implevit from Bach's Magnificat

From: Carl Lumma

>Yahoo groups: /tuning-math/files/gene/magni132... * [with cont.] 
>
>and
>
>The Proxomitron Reveals... * [with cont.]  (Wayb.)
>
>I prefer the canonical version with flat octaves. Anyone else have
>an opinion?


Yahoo's case-sensitive -- "Gene".  Must run on unix...

Gene, you might try converting your Scala files from Windows to
Unix linebreaks before opening them, using a text editor such as
EditPad Lite.

I think the canonical version sounds more just in some sense,
though it seems slightly melodically warped.

So this is done with a simple 12-to-12 mapping?  Can you upload
the scala file you used?

-Carl

Message: 6772 - Contents - Hide Contents

Date: Sat, 26 Apr 2003 19:52:14

Subject: Re: Esurientes implevit from Bach's Magnificat

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:


> So this is done with a simple 12-to-12 mapping?  Can you upload
> the scala file you used?


Here's the Scala .scl file. To get the 12-et version, simply change
the line "0 equal 133" to "0 equal 132".


0 tempo 135 pm
0 exclude 10
0 velocity 110
0 frequency 85
0 equal 133

0 track 1
0 program 68

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0 track 2
0 program 69

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0 track 3
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0 track 4
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Message: 6773 - Contents - Hide Contents

Date: Sat, 26 Apr 2003 13:02:54

Subject: Re: Esurientes implevit from Bach's Magnificat

From: Carl Lumma

>> >o this is done with a simple 12-to-12 mapping?  Can you upload
>> the scala file you used?
>

>Here's the Scala .scl file. To get the 12-et version, simply change
>the line "0 equal 133" to "0 equal 132".


That's a .seq file, no?

-Carl

Message: 6774 - Contents - Hide Contents

Date: Sat, 26 Apr 2003 20:12:55

Subject: Re: Esurientes implevit from Bach's Magnificat

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:


>>> So this is done with a simple 12-to-12 mapping?  Can you upload
>>> the scala file you used?
>> 

>> Here's the Scala .scl file. To get the 12-et version, simply change
>> the line "0 equal 133" to "0 equal 132".
> 

> That's a .seq file, no?


Sorry, yes! Scala will convert it to a midi file if you save it as
something.scl, load an abitrary scale file, and under "tools" invoke
the transform to midi file.

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