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Message: 10750 - Contents - Hide Contents

Date: Mon, 05 Apr 2004 23:38:02

Subject: Re: 126 7-limit linears

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:



> So do I -- particularly the projects that mean most to me. This is 
> why I have composed so little. You've done me better -- many, many 
> better -- in this regard. I applaud you, Gene, and your compositions 
> will receive due notice in my paper. Which website would you like me 
> to reference?



Thanks, Paul. I only have one website: www.xenharmony.org
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Message: 10751 - Contents - Hide Contents

Date: Mon, 05 Apr 2004 00:39:50

Subject: The 18 qujus scales

From: Gene Ward Smith

By a qujus scale I mean a Fokker block with commas a QUartertone of 
36/35, a JUbilee comma of 50/49, and a Septimal comma of 64/63. Below 
I list all 18 of them, in order of decreasing Lumma stability. On the 
line describing it, the first number is the minimum maximum Tenney 
height over all the transpositions, where the transposition chosen is 
the unique one giving the minimax height. The next four numbers, 
seperated by commas, are the number of o/utonal tetrads and 
supermajor/subminor tetrads. There are always two each of the otonal 
and utonal tetrads, but some scales have one subminor and supermajor, 
and some have two. Following this is the ratio between the largest 
and smallest scale step, then the lumma stability and finally 
propriety. The first listed scale, qujus1, is clearly the most 
regular, and is equivalent under transposition to 
parizekj1.scl, "Petr Parizek, 12-tone septimal tuning, 2002" in 
Manuel's database.


! qujus1.scl
scale 1 420 2,2,2,2 1.897095 0.538729 strictly proper
12
!
21/20
10/9
7/6
5/4
4/3
7/5
3/2
14/9
5/3
7/4
28/15
2

! qujus2.scl
scale 2 840 2,2,2,2 2.330127 0.344658 strictly proper
12
!
21/20
8/7
6/5
9/7
4/3
10/7
3/2
8/5
12/7
9/5
40/21
2

! qujus3.scl
scale 3 840 2,2,2,2 2.330127 0.344658 strictly proper
12
!
21/20
10/9
7/6
5/4
4/3
7/5
3/2
14/9
5/3
7/4
40/21
2

! qujus4.scl
scale 4 840 2,2,2,2 2.330127 0.308814 strictly proper
12
!
21/20
8/7
6/5
9/7
4/3
7/5
3/2
8/5
12/7
9/5
40/21
2

! qujus5.scl
scale 5 840 2,2,2,2 2.330127 0.308814 strictly proper
12
!
21/20
10/9
7/6
5/4
4/3
10/7
3/2
14/9
5/3
7/4
40/21
2

! qujus6.scl
scale 6 420 2,2,2,2 2.330127 0.272970 strictly proper
12
!
21/20
8/7
6/5
9/7
4/3
7/5
3/2
8/5
12/7
9/5
28/15
2

! qujus7.scl
scale 7 840 2,2,1,1 4.109804 0.266088 strictly proper
12
!
21/20
8/7
7/6
5/4
4/3
7/5
3/2
8/5
5/3
7/4
40/21
2

! qujus8.scl
scale 8 840 2,2,1,1 4.109804 0.266088 strictly proper
12
!
21/20
8/7
6/5
5/4
4/3
10/7
3/2
8/5
12/7
7/4
40/21
2

! qujus9.scl
scale 9 420 2,2,1,1 4.109804 0.27795 strictly proper
12
!
21/20
8/7
7/6
5/4
4/3
7/5
3/2
8/5
5/3
7/4
28/15
2

! qujus10.scl
scale 10 840 2,2,1,1 4.109804 0.207795 strictly proper
12
!
21/20
8/7
7/6
5/4
4/3
10/7
3/2
8/5
5/3
7/4
40/21
2

! qujus11.scl
scale 11 840 2,2,1,1 4.109804 0.207795 strictly proper
12
!
21/20
8/7
6/5
5/4
4/3
7/5
3/2
8/5
12/7
7/4
40/21
2

! qujus12.scl
scale 12 840 2,2,1,1 4.109804 0.207795 strictly proper
12
!
15/14
8/7
6/5
5/4
4/3
10/7
3/2
8/5
12/7
7/4
40/21
2

! qujus13.scl
scale 13 420 2,2,1,1 4.109804 0.194943 strictly proper
12
!
21/20
8/7
6/5
5/4
4/3
7/5
3/2
8/5
12/7
7/4
28/15
2

! qujus14.scl
scale 14 840 2,2,1,1 4.109804 0.194943 strictly proper
12
!
15/14
8/7
7/6
5/4
4/3
10/7
3/2
8/5
5/3
7/4
40/21
2

! qujus15.scl
scale 15 1568 2,2,1,1 2.801371 0.193741 impropriety 0.044238
12
!
21/20
35/32
7/6
5/4
21/16
10/7
3/2
49/32
5/3
7/4
15/8
2

! qujus16.scl
scale 16 1568 2,2,1,1 4.109804 0.193741 impropriety 0.044238
12
!
25/24
35/32
7/6
5/4
21/16
10/7
35/24
49/32
5/3
7/4
15/8
2

! qujus17.scl
scale 17 1568 2,2,1,1 4.109804 0.135448 impropriety 0.044238
12
!
15/14
35/32
7/6
5/4
21/16
10/7
3/2
49/32
5/3
7/4
15/8
2

! qujus18.scl
scale 18 1960 2,2,1,1 4.109804 0.135448 improriety 0.044238
12
!
21/20
8/7
7/6
49/40
4/3
7/5
3/2
8/5
49/30
7/4
28/15
2
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Message: 10752 - Contents - Hide Contents

Date: Mon, 05 Apr 2004 19:22:18

Subject: Re: Comma names

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx Graham Breed <graham@m...> wrote:


> Gene Ward Smith wrote:
> 
>>> 121/120
>> 


>> Naming it after linear temperaments, this could be the undecimal
>> schrutar-orwell-valentine comma, or unisov for short.
> 


> That's the neutral second comma, because it's between 12:11 and 
11:10.



Sounds good, except for the part about "between". I'd call it a ratio.



>>> 225/224 septimal kleisma (is this the best we can do?)



> If it does need a new one, how about some permutation of "secor"?  
It's 
> the comma between 16:15 and 15:14, the two simple rationalizations 
of a 
> secor.  And George doesn't have a comma yet.



Again, sounds good. Secorisma?



>>> 441/440
>> 


>> It's a comma of miracle and unidec, but there are other linear
>> temperaments involved here which are pretty good but not yet 
named.
> 


> I don't see a "Wilson's comma" either.  Surely Erv must have run 
into 
> this somwhere.



Kind of hard not to, which is the point of naming all the 11-limit 
superparticulars. It would be nice to have a better excuse than this 
for naming this particular comma after Erv, but we are running out of 
11-limit commas, and that may do as a reason.

Where did the names "ragisma" and "kalisma" come from, and why?
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Message: 10753 - Contents - Hide Contents

Date: Mon, 05 Apr 2004 00:45:15

Subject: Re: 126 7-limit linears

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
wrote:


> Hi Gene,
> 
> Would you be so kind as to produce a file like the one below, but 
> instead of culling to 126 lines, leave all 32201 in there? That 
would 
> be great. If that's too much, you could cut off the error and 
> complexity wherever you see fit. The idea, though, is to produce a 
> graph, and as most pieces of paper are rectangular, the data should 
> fill a rectangular region. I'm *not* arguing for a rectangular 
> badness function.



I could either upload something or email it. Which is better?



> Also could you provide the TM-reduced kernel bases -- at least for 
> the 126 below?



Not unless I write code to fully automate the process first.

Are we getting serious about the paper again? It's not as if the 
marklet is flooded with good math-heavy theory papers or books. 
Haluska's book is something of a mess, and the Diderot Forum book is 
in some respects rather appalling, but they got published.
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Message: 10754 - Contents - Hide Contents

Date: Mon, 05 Apr 2004 19:25:45

Subject: Re: Comma names

From: Gene Ward Smith

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


> 
> Gene wrote:
> 


>> 15/14 major diatonic semitone (should be septimal diatonic 
semitone)
> 


> I wouldn't say "should be", it's another possibility. This list
> wasn't intended to be systematic but more as a list of historical
> usage.



Which is why I was objecting--isn't diatonic semitone the 
historically established name for 16/15?



>> 22/21 no name--unidecimal minor semitone?
> 


> You mean "undecimal", looks ok to me.
> 


>> 33/32 unidecimal comma (bad name! Schoenberg's diesis?)
> 


> Why Schönberg's diesis and not undecimal 1/4-tone for example?



Because "undecimal 1/4-tone" is kind of ugly, and Schoenberg seems to 
have considered this comma according to Monzo's analysis.



>> 540/539 Swets' comma (who is Swet?)
> 


> Wouter Swets is a Dutch ethnomusicologist. He mentioned this
> comma to me personally. I can't say more about it since he
> still has to publish his results.



Ah. Surprising if this makes an ethnomusicological appearance.
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Message: 10755 - Contents - Hide Contents

Date: Mon, 05 Apr 2004 01:23:19

Subject: Re: 126 7-limit linears

From: Paul Erlich

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


> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
> wrote:
>> Hi Gene,
>> 


>> Would you be so kind as to produce a file like the one below, but 
>> instead of culling to 126 lines, leave all 32201 in there? That 
> would 


>> be great. If that's too much, you could cut off the error and 
>> complexity wherever you see fit. The idea, though, is to produce 
a 
>> graph, and as most pieces of paper are rectangular, the data 
should 
>> fill a rectangular region. I'm *not* arguing for a rectangular 
>> badness function.
> 


> I could either upload something or email it. Which is better?



Uploading keeps things public. If that doesn't work, e-mail.



>> Also could you provide the TM-reduced kernel bases -- at least 
for 
>> the 126 below?
> 


> Not unless I write code to fully automate the process first.
> 
> Are we getting serious about the paper again?



John Chalmers just reneged on his much earlier reneging of having a 
paper by me in XH18. He's putting a serious time-clamp on me, so 
there's absolutely no way we can iron out our differences in time. 
Right now I have 7.5 pages of text, 2 pages of endnotes, and I'm 
planning to have loads of those horagrams (which look much nicer 
printed directly to paper than as .jpgs or .gifs). Many people are 
thanked, especially you, Graham, and Dave. The main concern at this 
point is *understandability*. If the importance of the results can't 
be communicated to the average xenharmonicist, then all is lost. My 
XH17 paper was too hard for most people, and this one is much more 
ambitious. It's still only going to scratch the surface, leaving out 
most of the math, lattices, keyboard designs etc. that one would 
ideally like to see. Only so much space (not to mention time).



> It's not as if the 
> marklet is flooded with good math-heavy theory papers or books.



Gene, you've done work of such breadth and depth. Is it going to 
remain unorganized, spread across thousands of posts, forever?
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Message: 10756 - Contents - Hide Contents

Date: Mon, 05 Apr 2004 02:40:43

Subject: Re: 126 7-limit linears

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:



> Gene, you've done work of such breadth and depth. Is it going to 
> remain unorganized, spread across thousands of posts, forever?



A little has been organized on my web site. I'm wondering again about
what and where to publish, after having seen what's gotten published
lately. There's enough material for a book, if I could get myself up
to speed and actually do it; but I started a book on Chebyshev
functions and never finished it, and in general have a problem
finishing projects.
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Message: 10757 - Contents - Hide Contents

Date: Mon, 05 Apr 2004 03:12:28

Subject: Re: Why AMT (amity)?

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
wrote:



> Another question -- why "semisixths" but "hemifourths"? Why 
> not "semifourths"? A hyphenated use of the latter word is found 
here:
> 
> http://www.anaphoria.com/xen3a.PDF - Type Ok * [with cont.]  (Wayb.)



I presume the lack of a response means "no reason"?
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Message: 10758 - Contents - Hide Contents

Date: Mon, 05 Apr 2004 03:16:12

Subject: Comma names

From: Gene Ward Smith

Manuel's list is closing in on listing and having a name for every
11-limit superparticular, which t seems to me an excellent thing. 

We have

9/8 major whole tone
10/9 minor whole tone
11/10 Ptolemy's second
12/11 unidecimal neutral second
15/14 major diatonic semitone (should be septimal diatonic semitone)
16/15 minor diatonic semitone (should be diatonic semitone)
21/20 minor semitone
22/21 no name--unidecimal minor semitone?
25/24 classic chromatic semitone, minor chroma
28/27 Archytas' 1/3-tone
33/32 unidecimal comma (bad name! Schoenberg's diesis?)
36/35 septimal diesis, 1/4-tone
45/44 1/5-tone (needs improvement)
49/48 slendro diesis, 1/6-tone
50/49 Erlich's decatonic comma, tritonic diesis, jubilee comma
55/54 major unidecimal comma?
56/55 minor unidecimal comma?
64/63 septimal comma
81/80 syntonic comma, Didymus comma
99/98 small unidecimal comma
100/99 Ptolemy's comma
121/120
126/125 small septimal comma (is this the best we can do?)
176/175
225/224 septimal kleisma (is this the best we can do?)
243/242 neutral third comma
385/384 unidecimal kleisma
441/440
540/539 Swets' comma (who is Swet?)
2401/2400 breedsma
3025/3024 lehmerisma
4375/4374 ragisma
9801/9800 kalisma (Gauss' comma)
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Message: 10759 - Contents - Hide Contents

Date: Mon, 05 Apr 2004 03:19:52

Subject: Re: Why AMT (amity)?

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:


> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
> wrote:
> 


>> Another question -- why "semisixths" but "hemifourths"? Why 
>> not "semifourths"? A hyphenated use of the latter word is found 
> here:
>> 
>> http://www.anaphoria.com/xen3a.PDF - Type Ok * [with cont.]  (Wayb.)
> 


> I presume the lack of a response means "no reason"?



Actually it meant "I liked the sound better, and hadn't read xen3a.pdf".
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Message: 10760 - Contents - Hide Contents

Date: Mon, 05 Apr 2004 05:15:56

Subject: Re: Comma names

From: Gene Ward Smith

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



> 121/120



Naming it after linear temperaments, this could be the undecimal
schrutar-orwell-valentine comma, or unisov for short.



> 126/125 small septimal comma (is this the best we can do?)



This is the starling comma if named after a planar temperament, or
meantone-nonkleismic if we use linear temperaments



> 176/175



Unidecimal nonkleismic-orwell-valentine comma, or uninov for short.



> 225/224 septimal kleisma (is this the best we can do?)



The marvel comma (not to be confused with Marvel Comics) or the
miracle-orwell comma.



> 441/440



It's a comma of miracle and unidec, but there are other linear
temperaments involved here which are pretty good but not yet named.
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Message: 10761 - Contents - Hide Contents

Date: Mon, 05 Apr 2004 09:45:04

Subject: Re: Comma names

From: Graham Breed

Gene Ward Smith wrote:



>> 121/120
> 


> Naming it after linear temperaments, this could be the undecimal
> schrutar-orwell-valentine comma, or unisov for short.



That's the neutral second comma, because it's between 12:11 and 11:10.



>> 225/224 septimal kleisma (is this the best we can do?)
> 


> The marvel comma (not to be confused with Marvel Comics) or the
> miracle-orwell comma.



I though it was already established as a kleisma.  The only reason the 
name "marvel" had to be thought up is that there's already a "kleismic". 
  Of course, it is the marvel comma, but it's mostly the septimal 
kleisma.  What's wrong with that name?

If it does need a new one, how about some permutation of "secor"?  It's 
the comma between 16:15 and 15:14, the two simple rationalizations of a 
secor.  And George doesn't have a comma yet.



>> 441/440
> 


> It's a comma of miracle and unidec, but there are other linear
> temperaments involved here which are pretty good but not yet named.



I don't see a "Wilson's comma" either.  Surely Erv must have run into 
this somwhere.


                         Graham


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Message: 10762 - Contents - Hide Contents

Date: Tue, 06 Apr 2004 21:53:58

Subject: The five 16/15 27/25 Fokker pentatonics

From: Gene Ward Smith

[1, 6/5, 4/3, 3/2, 5/3]
[1, 6/5, 4/3, 3/2, 9/5]
[1, 6/5, 5/4, 3/2, 5/3]
[1, 6/5, 4/3, 8/5, 5/3]
[1, 6/5, 4/3, 8/5, 9/5]
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Message: 10763 - Contents - Hide Contents

Date: Tue, 06 Apr 2004 21:59:24

Subject: Re: The five 16/15 27/25 Fokker pentatonics

From: Paul Erlich

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


> [1, 6/5, 4/3, 3/2, 5/3]
> [1, 6/5, 4/3, 3/2, 9/5]
> [1, 6/5, 5/4, 3/2, 5/3]
> [1, 6/5, 4/3, 8/5, 5/3]
> [1, 6/5, 4/3, 8/5, 9/5]



Thanks for finally getting around to these! I enjoyed when you listed 
Scala names, when available . . .
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Message: 10764 - Contents - Hide Contents

Date: Tue, 06 Apr 2004 22:09:23

Subject: Re: The five 16/15 27/25 Fokker pentatonics

From: Paul Erlich

--- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
wrote:


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


>> [1, 6/5, 4/3, 3/2, 5/3]
>> [1, 6/5, 4/3, 3/2, 9/5]
>> [1, 6/5, 5/4, 3/2, 5/3]
>> [1, 6/5, 4/3, 8/5, 5/3]
>> [1, 6/5, 4/3, 8/5, 9/5]
> 


> Thanks for finally getting around to these! I enjoyed when you 
listed 
> Scala names, when available . . .



Why doesn't [1, 6/5, 5/4, 3/2, 9/5] qualify? I forgot your 
conventions . . .
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Message: 10765 - Contents - Hide Contents

Date: Tue, 06 Apr 2004 22:32:41

Subject: The five 27/25 81/80 Fokker pentatonics

From: Gene Ward Smith

[1, 10/9, 4/3, 3/2, 9/5]
[1, 10/9, 27/20, 3/2, 9/5]
[1, 6/5, 4/3, 3/2, 9/5]
[1, 6/5, 4/3, 8/5, 9/5]
[1, 10/9, 27/20, 3/2, 5/3]
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Message: 10766 - Contents - Hide Contents

Date: Tue, 06 Apr 2004 22:21:28

Subject: The five 16/15 81/80 Fokker pentatonics

From: Gene Ward Smith

[1, 9/8, 4/3, 3/2, 16/9]
[1, 9/8, 4/3, 3/2, 9/5]
[1, 6/5, 4/3, 3/2, 9/5]
[1, 6/5, 4/3, 8/5, 9/5]
[1, 9/8, 4/3, 3/2, 5/3]
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Message: 10767 - Contents - Hide Contents

Date: Tue, 06 Apr 2004 08:21:40

Subject: Re: 126 7-limit linears

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:


> Hi Gene,
> 
> Would you be so kind as to produce a file like the one below, but 
> instead of culling to 126 lines, leave all 32201 in there?



I presume you want TOP error, but what complexity do you want? Should
I use logflat badness?

This will take some amount of time to compute, so I want to get it
right the first time.
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Message: 10768 - Contents - Hide Contents

Date: Tue, 06 Apr 2004 22:54:35

Subject: Re: The five 16/15 27/25 Fokker pentatonics

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> wrote:


> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
> wrote:


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


>>> [1, 6/5, 4/3, 3/2, 5/3]
>>> [1, 6/5, 4/3, 3/2, 9/5]
>>> [1, 6/5, 5/4, 3/2, 5/3]
>>> [1, 6/5, 4/3, 8/5, 5/3]
>>> [1, 6/5, 4/3, 8/5, 9/5]
>> 


>> Thanks for finally getting around to these! I enjoyed when you 
> listed 


>> Scala names, when available . . .
> 


> Why doesn't [1, 6/5, 5/4, 3/2, 9/5] qualify? I forgot your 
> conventions . . .



It does qualify--it is a transposed version of [1,6/5,4/3,8/5,5/3]. I
used that form because the Tenney height of 8/5 is less than that of
9/5, but your version is a more likely mode for it.
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Message: 10769 - Contents - Hide Contents

Date: Tue, 06 Apr 2004 15:12:47

Subject: Re: Comma names

From: George D. Secor

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


> Manuel's list is closing in on listing and having a name for every
> 11-limit superparticular, which t seems to me an excellent thing. 
> 
> We have
> 
> 28/27 Archytas' 1/3-tone



Nice, or perhaps Archytas' diesis, since Dave Keenan's work in 
defining small-interval categories resulted in an upper boundary of 
~68.57c for a diesis.



> 33/32 unidecimal comma (bad name! Schoenberg's diesis?)



Unidecimal diesis.  Dave's comma/diesis boundary is ~35.19c.



> 64/63 septimal comma
> 81/80 syntonic comma, Didymus comma
> 100/99 Ptolemy's comma

What about:


64/63 septimal comma, Archytas' comma

Margo, Dave, and I have been using this term for a couple of years.  
The comma is the difference between the largest intervals (7:8 and 
8:9) in Archytas' diatonic tetrachord, in exact analogy to those (8:9 
and 9:10) in Didymus' diatonic tetrachord.

Besides, in a very short time it will be revealed that the ancients 
(at the direction of the gods) have already named 63:64 after 
Archytas, so you would merely be recognizing a _fait accompli_.  ;-)



> 2401/2400 breedsma
> 3025/3024 lehmerisma
> 4375/4374 ragisma
> 9801/9800 kalisma (Gauss' comma)



Conspicuous by its absence is:

4096/4095 tridecimal schisma or schismina

When Dave and I went about devising the Sagittal symbols, the schisma 
(or schismina) 4095:4096 (which we are presently calling the 
tridecimal schismina) was the first to be discovered (about 2/3 of 
the way through the following message):

Yahoo groups: /tuning-math/message/3679 * [with cont.] 

This is the difference between the sum (product) of the 5 and 7 
commas (80:81 and 63:64) and the 13 diesis (1024:1053), three of the 
principal commas that define the semantics of the notation.  (The 
large 13 diesis, 26:27, is also symbolized in the notation, being the 
apotome complement of 1024:1053.)

Perhaps you will want to suggest another name for 4095:4096 that 
would acknowledge it as the linchpin of the Sagittal symbol-flag 
economy.

--George

P.S. - I'm not really back on the lists yet (not reading everything), 
only peeking in from time to time to scan the subject lines.
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Message: 10771 - Contents - Hide Contents

Date: Tue, 06 Apr 2004 18:12:10

Subject: Re: Comma names

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "George D. Secor" <gdsecor@y...> 
wrote:


> Conspicuous by its absence is:
> 
> 4096/4095 tridecimal schisma or schismina



That's because it is 13-limit, of course, but Manuel does have it 
listed as "tridecimal schisma". There are no names for a lot of other 
13-limit supers, such as 2080/2079, 4225/4224, 6656/6655, and 
123201/123200, but he has 10648/10647 down as the "harmonisma".



> Perhaps you will want to suggest another name for 4095:4096 that 
> would acknowledge it as the linchpin of the Sagittal symbol-flag 
> economy.



I think you should do that, if you wish. Of course "sagittal schisma" 
suggests itself.
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Message: 10772 - Contents - Hide Contents

Date: Tue, 06 Apr 2004 20:25:00

Subject: Re: Comma names

From: George D. Secor

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


> --- In tuning-math@xxxxxxxxxxx.xxxx "George D. Secor" 
<gdsecor@y...> 
> wrote:


>> Conspicuous by its absence is:
>> 
>> 4096/4095 tridecimal schisma or schismina
> 


> That's because it is 13-limit, of course, but Manuel does have it 
> listed as "tridecimal schisma". There are no names for a lot of 
other 
> 13-limit supers, such as 2080/2079, 4225/4224, 6656/6655, and 
> 123201/123200, but he has 10648/10647 down as the "harmonisma".
> 


>> Perhaps you will want to suggest another name for 4095:4096 that 
>> would acknowledge it as the linchpin of the Sagittal symbol-flag 
>> economy.
> 


> I think you should do that, if you wish. Of course "sagittal 
schisma" 
> suggests itself.



Looks as if that's the name to go with.  A 13-limit schisma would be 
very appropriate to associate with Sagittal, because all of the 11-
limit consonances (relative to a Pythagorean chain of fifths) are 
notated *exactly*.  Hence, 11-limit schismas enter into the picture 
only when primes 5, 7, and/or 11 have exponent > 1.

Two other small schismas that figure prominently in the notation are:
4374:4375 (2*3^7:5^4*7), ~0.396 cents (ragisma)
184528125:184549376 (3^10*5^5:2^24*11), ~0.199 cents
But the second one is not superparticular.

--George




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Message: 10773 - Contents - Hide Contents

Date: Tue, 06 Apr 2004 19:33:01

Subject: Re: 126 7-limit linears

From: Paul Erlich

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


> --- In tuning-math@xxxxxxxxxxx.xxxx "Paul Erlich" <perlich@a...> 
wrote:
>> Hi Gene,
>> 


>> Would you be so kind as to produce a file like the one below, but 
>> instead of culling to 126 lines, leave all 32201 in there?
> 


> I presume you want TOP error, but what complexity do you want? 



The same complexity you used there, when you culled to 126 (just 
click "up thread" repeatedly if you forgot). It was the L1 kind.



>Should
> I use logflat badness?



No badness figure required.



> This will take some amount of time to compute, so I want to get it
> right the first time.



Well, if you can't reproduce the results you posted when you culled 
to 126, it'll be a good sign something's wrong. Of course, I should 
do an independent check myself, but time is running out.
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Message: 10774 - Contents - Hide Contents

Date: Wed, 07 Apr 2004 19:17:54

Subject: Fokker pentatonics, known and unknown

From: Gene Ward Smith

Below I list what the Scala scl database knows about the Fokker 
pentatonics I computed. Two scales appeared as all three kinds of 
blocks; tranh-prime_5 and its inverse. It surprises me that such an 
evidently important pentatonic as tranh-inverse was not listed.


16/15 27/25
[1, 6/5, 4/3, 3/2, 5/3] harrison_min.scl
From Lou Harrison, a symmetrical pentatonic with minor thirds   

[1, 6/5, 4/3, 3/2, 9/5] tranh.scl inverse equal key 0
[1, 6/5, 5/4, 3/2, 5/3] unknown
[1, 6/5, 4/3, 8/5, 5/3] unknown

[1, 6/5, 4/3, 8/5, 9/5] tranh.scl key 4, prime_5.scl key 2
Bac Dan Tranh scale, Vietnam
What Lou Harrison calls "the Prime Pentatonic", a widely used scale   

16/15 81/80

[1, 9/8, 4/3, 3/2, 16/9] hexany16.scl, chin_5.scl key 3
1.3.9.27 Hexany, a degenerate pentatonic form
Chinese pentatonic from Zhou period 

[1, 9/8, 4/3, 3/2, 9/5] korea_5.scl
According to Lou Harrison, called "the Delightful" in Korea 

[1, 6/5, 4/3, 3/2, 9/5] same as first 16/15 27/25 scale, inverse tranh
[1, 6/5, 4/3, 8/5, 9/5] same as fifth 16/15 27/25 scale, tranh and 
prime_5
[1, 9/8, 4/3, 3/2, 5/3] inverse korea_5, key 3

27/25 81/80

[1, 10/9, 4/3, 3/2, 9/5] unknown
[1, 10/9, 27/20, 3/2, 9/5] unknown, inverse of fifth scale below
[1, 6/5, 4/3, 3/2, 9/5] same as first 16/15 27/25 and second 16/15 
81/80, inverse tranh
[1, 6/5, 4/3, 8/5, 9/5] same as fifth 16/15 27/25 and fourth 16/15 
81/80, tranh&prime_5
[1, 10/9, 27/20, 3/2, 5/3] unknown, inverse of second scale above
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