request for temperament family datasheets

Hi Gene, Herman, or anyone else who can provide,

I posted on this not too long and either got no
(or not much) response, or don't remember.
(hey, i've been busy ...)

I'd like to really expand on the Encyclopedia's coverage
of the multitude of temperament families. Specifically,
i would like to provide datasheets similar to the ones
already included -- these are the only ones i have so far:

aristoxenean (now officially compton?)
atomic
augmented/diesic
ennealimmal
kwazy
magic
marvel
meantone
minerva
miracle
mutt
mystery
orwell
schismic/skhismic (now officially helmholtz?)
semisixths (now officially sensipent?)

for any important families that are still missing.

Also, as can be seen from my list above, i'd like to
clarify the names. If an older name has definitely
been superceded, i'll put the datasheet webpage under
the consensus name and make the older names link to
the newer one.

Thanks.

Also, Gene, i'd appreciate more clarification of the
daughter, cousing, illegitimate uncle, etc. relationships,
so that i can draw more family-trees along the lines of
the one that's on my "family" Encyclopedia page.

To facilitate the process, here's a template that
sets up the tables as they appear in my webpages.
Just replace "[data]" with the real data, and reproduce
the "name, comma, ..." tables as many times as necessary
for different "daughters" and "cousins" in the higher limits.

------ temperament family datasheet template -----------

family name: [data]
period: [data]
generator: [data]

5-limit

name: [data]
comma: [data]
mapping: [data]
poptimal generator: [data]
TOP period: [data]
TOP generator: [data]
MOS: [data]

7-limit

name: [data]
wedgie: [data]
mapping: [data]
7-limit poptimal generator: [data]
9-limit poptimal generator: [data]
TOP period: [data]
TOP generator: [data]
TM basis: [data]
MOS: [data]

name: [data]
wedgie: [data]
mapping: [data]
7-limit poptimal generator: [data]
9-limit poptimal generator: [data]
TOP period: [data]
TOP generator: [data]
TM basis: [data]
MOS: [data]

name: [data]
wedgie: [data]
mapping: [data]
7-limit poptimal generator: [data]
9-limit poptimal generator: [data]
TOP period: [data]
TOP generator: [data]
TM basis: [data]
MOS: [data]

11 limit

name: [data]
wedgie: [data]
mapping: [data]
poptimal generator: [data]
TOP period: [data]
TOP generator: [data]
TM basis: [data]
MOS: [data]

-------------------------------------------------

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

Monz wrote:

> I'd like to really expand on the Encyclopedia's coverage
> of the multitude of temperament families. Specifically,
> i would like to provide datasheets similar to the ones
> already included -- these are the only ones i have so far:

1. I'm missing hanson.
2. I'm missing keemun.
3. If I choose a period of 2/1 and a generator of 30^(1/19), how do you call
this?
4. If I choose a period of 2/1 and a generator of sqrt(11/8), how do you
call this?
5. If I choose a period of 2/1 and a generator of cbrt(3/2), how do you call
this? ("cbrt" means third root).

Petr

I wrote:

> 4. If I choose a period of 2/1 and a generator of sqrt(11/8), how do you
> call this?

Actually, a much better generator would be cbrt(8/5) or (11/5)^(1/5) in this
case.

Petr

monz wrote:
> Hi Gene, Herman, or anyone else who can provide,
> > > I posted on this not too long and either got no
> (or not much) response, or don't remember.
> (hey, i've been busy ...)
> > > I'd like to really expand on the Encyclopedia's coverage
> of the multitude of temperament families. Specifically,
> i would like to provide datasheets similar to the ones
> already included -- these are the only ones i have so far:
> > aristoxenean (now officially compton?)
Compton is the name in Paul's "Middle Path" paper for the 5-limit temperament (12&48). There's a 7-limit temperament that's also had that name, although one of the other names (waage, duodecimal) may be better to avoid confusion.

> schismic/skhismic (now officially helmholtz?)
Helmholtz is the 5-limit schismatic temperament, and garibaldi is the 7-limit one. I like to use "schismatic" to refer to this group of related temperaments in general, as with "kleismic" for the group of temperaments including hanson, keemun, etc.

> semisixths (now officially sensipent?)
Assuming that a distinction between sensipent and sensisept is useful. I tend to call them both "sensi".

> for any important families that are still missing.

Define "important". :-)

I've written music in father and bug, but whether they count as important or not is debatable. Paul Erlich's paper mentions these temperaments by name:

5-limit: father, bug, dicot, meantone, augmented, mavila, porcupine, blackwood, dimipent, srutal, magic, ripple, hanson, negripent, tetracot, superpyth, helmholtz, sensipent, passion, w�rschmidt, compton, amity, orson, vishnu, luna.

7-limit: blacksmith, dimisept, dominant, august, pajara, semaphore, meantone, injera, negrisept, augene, keemun, catler, hedgehog, superpyth, sensisept, lemba, porcupine, flattone, magic, doublewide, nautilus, beatles, liese, cynder, orwell, garibaldi, myna, miracle, ennealimmal.

Note that augene and august are two different 7-limit extensions of augmented temperament.

If you're including mystery you might as well include other higher limit temperaments like peppermint. And besides marvel there are other named rank 3 temperaments such as starling. Various other temperaments have had names given to them, and some of those have had musical uses; it's hard to know when to stop.

If I get the time, I can look up the data for these, although I only have the TOP period and generator, not the poptimal generators. In some cases the MOS patterns will depend on the exact tuning of the generators, and it becomes necessary to pick a representative tuning.

Hi Herman,

Thanks for your response. I think i'll just quote that on
the "family" page, and when the links are finally back in
the Encyclopedia, they will all be links to the individual
pages containing the data.

One more comment ...

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:

> <sniop> ... Various other temperaments have had names
> given to them, and some of those have had musical uses;
> it's hard to know when to stop.

Well, my whole point is that we don't *have* to stop! ;-)
Just keep naming them, give me the data, and i'll put
them into the Encyclopedia, so that folks have a place
to look them up.

Eventually, i hope to have examples of all these families
as .tonescape files, so that users can see and hear how
various tunings from a single family intersect.

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

Hi Gene,

Can you put Herman's post into context, and hopefully
provide filled-out datasheets for the families he
mentions and which i don't yet have in the Encyclopedia?

I'd particularly like to form the family-tree diagrams
to connect e.g. compton/waage/duodecimal, helmholtz/garibaldi,
hanson/keemun, etc.

The only relationships i can see from Herman's post are:

augmented family:
5-limit grandmother: augmented
7-limit mothers: augene, august

schismatic family:
5-limit grandmother: helmholtz
7-limit mother: garibaldi

(Note: i've tried to eliminate the confusion of using
both "schismic" and "schismatic" by defining each of
those names for separate things: "schismic" for the
temperament family and "schismatic" for the 15th-century
tuning practice of using e.g. pythagorean Db for JI C# etc.
But apparently it hasn't caught on.)

Of course the Encyclopedia already has a datasheet for
the schismic family, so i've used the data you provided
to make a tentative family-tree:

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

You can see that i'm not sure about the names of the
relationships (mother, illegitimate uncle, etc.), so
i'd appreciate clarification on that.

I'd like to make a tree like this for all of the
Encyclopedia temperament family webpages.

I don't have a copy of Paul's "Middle Path" paper handy,
but would like to know where each of those names fits
in the larger picture.

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

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> monz wrote:
> > Hi Gene, Herman, or anyone else who can provide,
> >
> >
> > I posted on this not too long and either got no
> > (or not much) response, or don't remember.
> > (hey, i've been busy ...)
> >
> >
> > I'd like to really expand on the Encyclopedia's coverage
> > of the multitude of temperament families. Specifically,
> > i would like to provide datasheets similar to the ones
> > already included -- these are the only ones i have so far:
> >
> > aristoxenean (now officially compton?)
> Compton is the name in Paul's "Middle Path" paper for
> the 5-limit temperament (12&48). There's a 7-limit
> temperament that's also had that name, although one of
> the other names (waage, duodecimal) may be better to
> avoid confusion.
>
> > schismic/skhismic (now officially helmholtz?)
> Helmholtz is the 5-limit schismatic temperament, and
> garibaldi is the 7-limit one. I like to use "schismatic"
> to refer to this group of related temperaments in general,
> as with "kleismic" for the group of temperaments including
> hanson, keemun, etc.
>
> > semisixths (now officially sensipent?)
> Assuming that a distinction between sensipent and sensisept
> is useful. I tend to call them both "sensi".
>
> > for any important families that are still missing.
>
> Define "important". :-)
>
> I've written music in father and bug, but whether they
> count as important or not is debatable. Paul Erlich's
> paper mentions these temperaments by name:
>
> 5-limit: father, bug, dicot, meantone, augmented, mavila,
> porcupine, blackwood, dimipent, srutal, magic, ripple,
> hanson, negripent, tetracot, superpyth, helmholtz,
> sensipent, passion, würschmidt, compton, amity, orson,
> vishnu, luna.
>
> 7-limit: blacksmith, dimisept, dominant, august, pajara,
> semaphore, meantone, injera, negrisept, augene, keemun,
> catler, hedgehog, superpyth, sensisept, lemba, porcupine,
> flattone, magic, doublewide, nautilus, beatles, liese,
> cynder, orwell, garibaldi, myna, miracle, ennealimmal.
>
> Note that augene and august are two different 7-limit
> extensions of augmented temperament.
>
> If you're including mystery you might as well include
> other higher limit temperaments like peppermint. And
> besides marvel there are other named rank 3 temperaments
> such as starling. Various other temperaments have
> had names given to them, and some of those have had
> musical uses; it's hard to know when to stop.
>
> If I get the time, I can look up the data for these,
> although I only have the TOP period and generator, not
> the poptimal generators. In some cases the MOS patterns
> will depend on the exact tuning of the generators, and
> it becomes necessary to pick a representative tuning.

monz wrote:

> I don't have a copy of Paul's "Middle Path" paper handy,
> but would like to know where each of those names fits
> in the larger picture.

I use the same temperaments and names in the appendix of my prime errors and complexities PDF:

http://x31eq.com/primerr.pdf

Graham

monz wrote:

> Well, my whole point is that we don't *have* to stop! ;-)
> Just keep naming them, give me the data, and i'll put
> them into the Encyclopedia, so that folks have a place
> to look them up.

Some 5-limit temperaments:

name: bug
comma: [0, 3, -2> 27/25
mapping: [<1, 2, 3], <0, -2, -3]>
TOP period: 1200.000000
TOP generator: 260.256797
MOS: 1+1, 1+2, 1+3, 4+1, 5+4, 9+5

name: father
comma: [4, -1, -1> 16/15
mapping: [<1, 2, 2], <0, -1, 1]>
TOP period: 1185.869125
TOP generator: 447.386341
MOS: 1+1, 2+1, 3+2, 5+3

name: supersharp
comma: [5, -6, 2> 800/729
mapping: [<2, 3, 4], <0, 1, 3]>
TOP period: 595.799819
TOP generator: 127.869801
MOS: 2+2, 2+4, 2+6, 8+2, 10+8

name: dicot
comma: [-3, -1, 2> 25/24
mapping: [<1, 1, 2], <0, 2, 1]>
TOP period: 1207.657798
TOP generator: 353.217263
MOS: 1+1, 1+2, 3+1, 3+4, 7+3

name: gorgo
comma: [-4, 7, -3> 2187/2000
mapping: [<1, 1, 1], <0, 3, 7]>
TOP period: 1207.014515
TOP generator: 227.940914
MOS: 1+1, 1+2, 1+3, 1+4, 5+1, 5+6, 5+11

name: mavila
comma: [-7, 3, 1> 135/128
mapping: [<1, 2, 1], <0, -1, 3]>
TOP period: 1206.548265
TOP generator: 521.520283
MOS: 1+1, 2+1, 2+3, 2+5, 7+2, 7+9, 7+16

name: blackwood
comma: [8, -5, 0> 256/243
mapping: [<5, 8, 12], <0, 0, -1]>
TOP period: 238.866863
TOP generator: 80.088638
MOS: 5+5

name: lemba
comma: [-17, 2, 6> 140625/131072
mapping: [<2, 2, 5], <0, 3, -1]>
TOP period: 601.785732
TOP generator: 230.907633
MOS: 2+2, 4+2, 6+4, 10+6

name: diminished, dimipent
comma: [3, 4, -4> 648/625
mapping: [<4, 6, 9], <0, 1, 1]>
TOP period: 299.160315
TOP generator: 101.669634
MOS: 4+4

name: ripple, superchrome
comma: [-1, 8, -5> 6561/6250
mapping: [<1, 2, 3], <0, -5, -8]>
TOP period: 1203.324382
TOP generator: 101.992557
MOS: 1+1, 1+2, 1+3, ..., 1+11, 11+1

name: porcupine
comma: [1, -5, 3> 250/243
mapping: [<1, 2, 3], <0, -3, -5]>
TOP period: 1196.905960
TOP generator: 162.317661
MOS: 1+1, 1+2, 1+3, 1+4, 1+5, 1+6, 7+1, 7_8, 15+7

name: augmented
comma: [7, 0, -3> 128/125
mapping: [<3, 5, 7], <0, -1, 0]>
TOP period: 399.020013
TOP generator: 93.145064
MOS: 3+3, 3+6, 3+9

name: beatles
comma: [19, -9, -2> 524288/492075
mapping: [<1, 1, 5], <0, 2, -9]>
TOP period: 1197.104145
TOP generator: 354.720338
MOS: 1+1, 1+2, 3+1, 3+4, 7+3, 10+7

name: superpyth
comma: [12, -9, 1> 20480/19683
mapping: [<1, 2, 6], <0, -1, -9]>
TOP period: 1197.596121
TOP generator: 489.427183
MOS: 1+1, 2+1, 2+3, 5+2, 5+7, 5+12, 5+17

name: negri(pent)
comma: [-14, 3, 4> 16875/16384
mapping: [<1, 2, 2], <0, -4, 3]>
TOP period: 1201.822936
TOP generator: 126.145039
MOS: 1+1, 1+2, ..., 1+8, 9+1, 10+9

name: meantone
comma: [-4, 4, -1> 81/80
mapping: [<1, 2, 4], <0, -1, -4]>
TOP period: 1201.698520
TOP generator: 504.134131
MOS: 1+1, 2+1, 2+3, 5+2, 7+5, 12+7, 19+12

name: passion
comma: [18, -4, -5> 262144/253125
mapping: [<1, 2, 2], <0, -5, 4]>
TOP period: 1198.313984
TOP generator: 98.400139
MOS: 1+1, 1+2, 1+3, ..., 1+11, 12+1, 12+13, 12+25, 12+37, 12+49

name: magic
comma: [-10, -1, 5> 3125/3072
mapping: [<1, 0, 2], <0, 5, 1]>
TOP period: 1201.276744
TOP generator: 380.795718
MOS: 1+1, 1+2, 3+1, 3+4, 3+7, 3+10, 3+13, 3+16, 19+3

name: tetracot
comma: [5, -9, 4> 20000/19683
mapping: [<1, 1, 1], <0, 4, 9]>
TOP period: 1199.031259
TOP generator: 176.114790
MOS: 1+1, 1+2, 1+3, 1+4, 1+5, 6+1, 7+6, 7+13, 7+20

name: srutal, diaschismic
comma: [11, -4, -2> 2048/2025
mapping: [<2, 3, 5], <0, 1, -2]>
TOP period: 599.555294
TOP generator: 104.698803
MOS: 2+2, 2+4, 2+6, 2+8, 10+2, 12+10, 12+22

name: compton
comma: [-19, 12, 0> 531441/524288
mapping: [<12, 19, 28], <0, 0, -1]>
TOP period: 100.051421
TOP generator: 15.126072
MOS: 12+12, 12+24, 12+36, 12+48, 12+60, 72+12

name: semisixths, sensi(pent)
comma: [2, 9, -7> 78732/78125
mapping: [<1, -1, -1], <0, 7, 9]>
TOP period: 1199.587953
TOP generator: 442.984268
MOS: 1+1, 2+1, 3+2, 3+5, 8+3, 8+11, 19+8, 19+27

name: misty
comma: [26, -12, -3> 67108864/66430125
mapping: [<3, 5, 6], <0, -1, 4]>
TOP period: 399.887155
TOP generator: 96.944209
MOS: 3+3, 3+6, 3+9, 12+3, 12+15, 12+27, 12+39, 12+51, 12+63, 12+75

name: w�rschmidt
comma: [17, 1, -8> 393216/390625
mapping: [<1, -1, 2], <0, 8, 1]>
TOP period: 1199.692003
TOP generator: 387.644855
MOS: 1+1, 1+2, 3+1, 3+4, 3+7, 3+10, 3+13, 3+16, 3+19, 3+22, 3+25, 3+28, 31+3, 34+31

name: hanson, kleismic
comma: [-6, -5, 6> 15625/15552
mapping: [<1, 0, 1], <0, 6, 5]>
TOP period: 1200.291038
TOP generator: 317.069381
MOS: 1+1, 1+2, 3+1, 4+3, 4+7, 4+11, 15+4

name: orson (orwell)
comma: [-21, 3, 7> 2109375/2097152
mapping: [<1, 0, 3], <0, 7, -3]>
TOP period: 1200.239500
TOP generator: 271.653629
MOS: 1+1, 1+2, 1+3, 4+1, 4+5, 9+4, 9+13, 22+9, 31+22

name: amity
comma: [9, -13, 5> 1600000/1594323
mapping: [<1, 3, 6], <0, -5, -13]>
TOP period: 1199.850693
TOP generator: 339.472087
MOS: 1+1, 1+2, 3+1, 4+3, 7+4, 7+11, 7+18, 7+25, 7+32, 7+39

name: helmholtz, schism(at)ic
comma: [-15, 8, 1> 32805/32768
mapping: [<1, 2, -1], <0, -1, 8]>
TOP period: 1200.065120
TOP generator: 498.278454
MOS: 1+1, 2+1, 2+3, 5+2, 5+7, 12+5, 12+17, 12+29, 12+41

name: vishnu, semisuper
comma: [23, 6, -14> 6115295232/6103515625
mapping: [<2, 4, 5], <0, -7, -3]>
TOP period: 599.974330
TOP generator: 71.146242
MOS: 2+2, 2+4, 2+6, 2+8, 2+10, 2+12, 2+14, 16+2, 16+18

name: luna, hemithirds
comma: [38, -2, -15> 274877906944/274658203125
mapping: [<1, 4, 2], <0, -15, 2]>
TOP period: 1199.981785
TOP generator: 193.196218
MOS: 1+1, 1+2, 1+3, 1+4, 1+5, 6+1, 6+7, 6+13, 6+19, 25+6, 31+25, 31+56

Wow Herman, thanks! Just what i wanted!

One question ...

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:

> Some 5-limit temperaments:
>
> name: bug
> comma: [0, 3, -2> 27/25
> mapping: [<1, 2, 3], <0, -2, -3]>
> TOP period: 1200.000000
> TOP generator: 260.256797
> MOS: 1+1, 1+2, 1+3, 4+1, 5+4, 9+5
>
> <etc. - snip>

What's with the double MOS numbers and plus sign?

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

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:

> Also, Gene, i'd appreciate more clarification of the
> daughter, cousing, illegitimate uncle, etc. relationships,
> so that i can draw more family-trees along the lines of
> the one that's on my "family" Encyclopedia page.

For that purpose, it might be best to include the Hermite comma
sequence as a part of the data. As for instance:

<<1 4 10 18 4 13 25 12 28 16||

[81/80, 59049/57344, 387420489/369098752]

or

[|-4 4 -1 0 0>, |-13 10 0 -1 0>, |-25 18 0 0 -1>]

<<1 4 10 -13 4 13 -24 12 -44 -71||

[81/80, 59049/57344, 17537553/16777216]

<<2 8 -11 -26 8 -23 -48 -48 -88 -35||

[81/80, 8680203/8388608, 17537553/16777216]

<<3 12 -1 -8 12 -10 -23 -36 -60 -19||

[81/80, 1029/1024, 2079/2048]

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Gene,
>
>
> Can you put Herman's post into context, and hopefully
> provide filled-out datasheets for the families he
> mentions and which i don't yet have in the Encyclopedia?

Would Hermite comma sequences help?

monz wrote:
> Wow Herman, thanks! Just what i wanted!
> > One question ...
> > > --- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
> >> Some 5-limit temperaments:
>>
>> name: bug
>> comma: [0, 3, -2> 27/25
>> mapping: [<1, 2, 3], <0, -2, -3]>
>> TOP period: 1200.000000
>> TOP generator: 260.256797
>> MOS: 1+1, 1+2, 1+3, 4+1, 5+4, 9+5
>>
>> <etc. - snip>
> > What's with the double MOS numbers and plus sign?

Number of large steps + number of small steps (in an octave). E.g. mavila has the pelog-like scale with 2 large steps and 5 small steps, while on the other hand meantone has the diatonic scale with 5 large steps and 2 small steps.

Some 7-limit (rank 2 / "linear") temperaments

name: beep
wedgie: <<2, 3, 1, 0, -4, -6]]
mapping: [<1, 2, 3, 3], <0, -2, -3, -1]>
TOP period: 1206.049627
TOP generator: 266.306424
MOS: 1+1, 1+2, 1+3, 4+1, 5+4

name: hexadecimal
wedgie: <<1, -3, 5, -7, 5, 20]]
mapping: [<1, 2, 1, 5], <0, -1, 3, -5]>
TOP period: 1208.959293
TOP generator: 530.163729
MOS: 1+1, 2+1, 2+3, 2+5, 7+2, 9+7

name: supersharp
wedgie: <<2, 6, 6, 5, 4, -3]]
mapping: [<2, 3, 4, 5], <0, 1, 3, 3]>
TOP period: 595.799819
TOP generator: 127.869801
MOS: 2+2, 2+4, 2+6, 8+2, 10+8

name: decimal
wedgie: <<4, 2, 2, -6, -8, -1]]
mapping: [<2, 4, 5, 6], <0, -2, -1, -1]>
TOP period: 603.828899
TOP generator: 250.611636
MOS: 2+2, 4+2, 4+6, 10+4, 10+14

name: superpelog
wedgie: <<2, -6, 1, -14, -4, 19]]
mapping: [<1, 2, 1, 3], <0, -2, 6, -1]>
TOP period: 1206.548265
TOP generator: 260.760141
MOS: 1+1, 1+2, 1+3, 4+1, 5+4, 9+5

name: gorgo
wedgie: <<3, 7, -1, 4, -10, -22]]
mapping: [<1, 1, 1, 3], <0, 3, 7, -1]>
TOP period: 1205.820043
TOP generator: 228.199305
MOS: 1+1, 1+2, 1+3, 1+4, 5+1, 5+6, 5+11

name: blacksmith
wedgie: <<0, 5, 0, 8, 0, -14]]
mapping: [<5, 8, 12, 14], <0, 0, -1, 0]>
TOP period: 239.178693
TOP generator: 83.830599
MOS: 5+5, 10+5

name: diminished, dimisept
wedgie: <<4, 4, 4, -3, -5, -2]]
mapping: [<4, 6, 9, 11], <0, 1, 1, 1]>
TOP period: 298.532115
TOP generator: 101.456140
MOS: 4+4, 8+4

name: august
wedgie: <<3, 0, 6, -7, 1, 14]]
mapping: [<3, 5, 7, 9], <0, -1, 0, -2]>
TOP period: 399.992210
TOP generator: 107.311173
MOS: 3+3, 3+6, 9+3

name: dominant
wedgie: <<1, 4, -2, 4, -6, -16]]
mapping: [<1, 2, 4, 2], <0, -1, -4, 2]>
TOP period: 1195.228951
TOP generator: 495.881015
MOS: 1+1, 2+1, 2+3, 5+2, 5+7, 12+5, 12+17, 12+29

name: lemba
wedgie: <<6, -2, -2, -17, -20, 1]]
mapping: [<2, 2, 5, 6], <0, 3, -1, -1]>
TOP period: 601.700493
TOP generator: 230.874926
MOS: 2+2, 4+2, 6+4, 10+6, 16+10

name: semaphore, hemifourths
wedgie: <<2, 8, 1, 8, -4, -20]]
mapping: [<1, 2, 4, 3], <0, -2, -8, -1]>
TOP period: 1203.668841
TOP generator: 252.480358
MOS: 1+1, 1+2, 1+3, 4+1, 5+4, 5+9, 5+14

name: injera
wedgie: <<2, 8, 8, 8, 7, -4]]
mapping: [<2, 3, 4, 5], <0, 1, 4, 4]>
TOP period: 600.888907
TOP generator: 93.609825
MOS: 2+2, 2+4, 2+6, 2+8, 2+10, 12+2, 12+14

name: catler
wedgie: <<0, 0, 12, 0, 19, 28]]
mapping: [<12, 19, 28, 34], <0, 0, 0, -1]>
TOP period: 99.806172
TOP generator: 24.583958
MOS: 12+12, 12+24

name: nautilus
wedgie: <<6, 10, 3, 2, -12, -21]]
mapping: [<1, 2, 3, 3], <0, -6, -10, -3]>
TOP period: 1202.659696
TOP generator: 82.974671
MOS: 1+1, 1+2, 1+3, ... 1+13, 14+1

name: doublewide
wedgie: <<8, 6, 6, -9, -13, -3]]
mapping: [<2, 5, 6, 7], <0, -4, -3, -3]>
TOP period: 599.276941
TOP generator: 272.312338
MOS: 2+2, 4+2, 4+6, 4+10, 4+14

name: negri(sept)
wedgie: <<4, -3, 2, -14, -8, 13]]
mapping: [<1, 2, 2, 3], <0, -4, 3, -2]>
TOP period: 1203.187309
TOP generator: 124.841963
MOS: 1+1, 1+2, 1+3, ..., 1+8, 9+1, 10+9

name: keemun
wedgie: <<6, 5, 3, -6, -12, -7]]
mapping: [<1, 0, 1, 2], <0, 6, 5, 3]>
TOP period: 1203.187309
TOP generator: 317.834461
MOS: 1+1, 1+2, 3+1, 4+3, 4+7, 4+11, 15+4

name: muggles
wedgie: <<5, 1, -7, -10, -25, -19]]
mapping: [<1, 0, 2, 5], <0, 5, 1, -7]>
TOP period: 1203.148011
TOP generator: 379.393104
MOS: 1+1, 1+2, 3+1, 3+4, 3+7, 3+10, 3+13

name: pajara
wedgie: <<2, -4, -4, -11, -12, 2]]
mapping: [<2, 3, 5, 6], <0, 1, -2, -2]>
TOP period: 598.446711
TOP generator: 106.566546
MOS: 2+2, 2+4, 2+6, 28, 10+2, 12+10, 22+12

name: hedgehog
wedgie: <<6, 10, 10, 2, -1, -5]]
mapping: [<2, 4, 6, 7], <0, -3, -5, -5]>
TOP period: 598.4467109
TOP generator: 162.3159606
MOS: 2+2, 2+4, 6+2, 8+6, 8+14

name: porcupine
wedgie: <<3, 5, -6, 1, -18, -28]]
mapping: [<1, 2, 3, 2], <0, -3, -5, 6]>
TOP period: 1196.905960
TOP generator: 162.317661
MOS: 1+1, 1+2, 1+3, ..., 1+6, 7+1, 7+8, 15+7, 22+15

name: augene, tripletone
wedgie: <<3, 0, -6, -7, -18, -14]]
mapping: [<3, 5, 7, 8], <0, -1, 0, 2]>
TOP period: 399.020013
TOP generator: 90.593035
MOS: 3+3, 3+6, 3+9

name: beatles
wedgie: <<2, -9, -4, -19, -12, 16]]
mapping: [<1, 1, 5, 4], <0, 2, -9, -4]>
TOP period: 1197.104145
TOP generator: 354.720338
MOS: 1+1, 1+2, 3+1, 3+4, 7+3

name: liese, gawel
wedgie: <<3, 12, 11, 12, 9, -8]]
mapping: [<1, 3, 8, 8], <0, -3, -12, -11]>
TOP period: 1202.624742
TOP generator: 569.049147
MOS: 1+1, 2+1, 2+3, 2+5, 2+7, 2+9, 2+11, 2+13, 2+15, 17+2

name: flattone
wedgie: <<1, 4, -9, 4, -17, -32
mapping: [<1, 2, 4, -1], <0, -1, -4, 9]>
TOP period: 1202.536419
TOP generator: 507.137966
MOS: 1+1, 2+1, 2+3, 5+2, 7+5, 7+12

name: superpyth
wedgie: <<1, 9, -2, 12, -6, -30]]
mapping: [<1, 2, 6, 2], <0, -1, -9, 2]>
TOP period: 1197.596121
TOP generator: 489.427183
MOS: 1+1, 2+1, 2+3, 5+2, 5+7, 5+12, 5+17

name: meantone
wedgie: <<1, 4, 10, 4, 13, 12]]
mapping: [<1, 2, 4, 7], <0, -1, -4, -10]>
TOP period: 1201.698520
TOP generator: 504.13413
MOS: 1+1, 2+1, 2+3, 5+2, 7+5, 12+7, 19+12

name: cynder, mothra
wedgie: <<3, 12, -1, 12, -10, -36]]
mapping: [<1, 1, 0, 3], <0, 3, 12, -1]>
TOP period: 1201.698520
TOP generator: 232.521463
MOS: 1+1, 1+2, 1+3, 1+4, 5+1, 5+6, 5+11, 5+16, 5+21

name: sensi(sept), semisixths
wedgie: <<7, 9, 13, -2, 1, 5]]
mapping: [<1, -1, -1, -2], <0, 7, 9, 13]>
TOP period: 1198.389531
TOP generator: 443.160293
MOS: 1+1, 2+1, 3+2, 3+5, 8+3, 8+11, 19+8, 27+19

name: peppermint
wedgie: <<1, 21, 15, 31, 21, -24]]
mapping: [<1, 2, 11, 9], <0, -1, -21, -15]>
TOP period: 1200.114945
TOP generator: 495.775687
MOS: 1+1, 2+1, 2+3, 5+2, 5+7, 12+5, 17+12, 29+17

name: superkleismic
wedgie: <<9, 10, -3, -5, -30, -35]]
mapping: [<1, 4, 5, 2], <0, -9, -10, 3]>
TOP period: 1201.371918
TOP generator: 322.373137
MOS: 1+1, 1+2, 3+1, 4+3, 4+7, 11+4, 15+11

name: magic
wedgie: <<5, 1, 12, -10, 5, 25]]
mapping: [<1, 0, 2, -1], <0, 5, 1, 12]>
TOP period: 1201.276744
TOP generator: 380.795718
MOS: 1+1, 1+2, 3+1, 3+4, 3+7, 3+10, 3+13, 3+16

name: hemififths
wedgie: <<18, -7, 1, -53, -49, 22]]
mapping: [<1, 5, 1, 3], <0, -18, 7, -1]>
TOP period: 1198.747107
TOP generator: 227.210819
MOS: 1+1, 1+2, 1+3, 1+4, 5+1, 5+6, 5+11, 16+5, 21+16, 37+21

name: myna
wedgie: <<10, 9, 7, -9, -17, -9]]
mapping: [<1, -1, 0, 1], <0, 10, 9, 7]>
TOP period: 1198.828458
TOP generator: 309.892661
MOS: 1+1, 1+2, 3+1, 4+3, 4+7, 4+11, 4+15, 4+19, 4+23, 27+4, 31+27

name: valentine
wedgie: <<9, 5, -3, -13, -30, -21]]
mapping: [<1, 1, 2, 3], <0, 9, 5, -3]>
TOP period: 1199.792743
TOP generator: 77.833153
MOS: 1+1, 1+2, ..., 1+14, 15+1, 15+16, 31+15, 31+46

name: orwell
wedgie: <<7, -3, 8, -21, -7, 27]]
mapping: [<1, 0, 3, 1], <0, 7, -3, 8]>
TOP period: 1199.532657
TOP generator: 271.493647
MOS: 1+1, 1+2, 1+3, 4+1, 4+5, 9+4, 9+13, 22+9, 31+22

name: garibaldi
wedgie: <<1, -8, -14, -15, -25, -10]]
mapping: [<1, 2, -1, -3], <0, -1, 8, 14]>
TOP period: 1200.760624
TOP generator: 498.119330
MOS: 1+1, 2+1, 2+3, 5+2, 5+7, 12+5, 12+17, 12+29, 41+12, 41+53

name: rodan
wedgie: <<3, 17, -1, 20, -10, -50]]
mapping: [<1, 1, -1, 3], <0, 3, 17, -1]>
TOP period: 1200.231587
TOP generator: 234.380469
MOS: 1+1, 1+2, 1+3, 1+4, 5+1, 5+6, 5+11, 5+16, 5+21, 5+26, 5+31, 5+36

name: vulture
wedgie: <<4, 21, -3, 24, -16, -66]]
mapping: [<1, 0, -6, 4], <0, 4, 21, -3]>
TOP period: 1199.274449
TOP generator: 475.411671
MOS: 1+1, 2+1, 3+2, 5+3, 5+8, 5+13, 5+18, 5+23, 5+28, 5+33, 5+38, 5+43, 5+48, 53+5

name: miracle
wedgie: <<6, -7, -2, -25, -20, 15]]
mapping: [<1, 1, 3, 3], <0, 6, -7, -2]>
TOP period: 1200.631014
TOP generator: 116.720642
MOS: 1+1, 1+2, ..., 1+9, 10+1, 10+11, 10+21, 31+10

name: compton
wedgie: <<0, 12, 24, 19, 38, 22]]
mapping: [<12, 19, 28, 34], <0, 0, -1, -2]>
TOP period: 100.051421
TOP generator: 15.126072
MOS: 12+12, 12+24, 12+36, 12+48, 12+60, 72+12

name: hemikleismic
wedgie: <<12, 10, -9, -12, -48, -49]]
mapping: [<1, 0, 1, 4], <0, 12, 10, -9]>
TOP period: 1199.411231
TOP generator: 158.574015
MOS: 1+1, 1+2, 1+3, ..., 1+6, 7+1, 8+7, 15+8, 15+23, 15+38

name: catakleismic
wedgie: <<6, 5, 22, -6, 18, 37]]
mapping: [<1, 0, 1, -3], <0, 6, 5, 22]>
TOP period: 1200.536355
TOP generator: 316.906396
MOS: 1+1, 1+2, 3+1, 4+3, 4+7, 4+11, 15+4, 19+15, 19+34, 53+19

name: guiron
wedgie: <<3, -24, -1, -45, -10, 65]]
mapping: [<1, 1, 7, 3], <0, 3, -24, -1]>
TOP period: 1200.486331
TOP generator: 233.998391
MOS: 1+1, 1+2, 1+3, 1+4, 5+1, 5+6, 5+11, 5+16, 5+21, 5+26, 5+31, 36+5

name: misty
wedgie: <<3, -12, -30, -26, -56, -36]]
mapping: [<3, 5, 6, 6], <0, -1, 4, 10]>
TOP period: 399.887155
TOP generator: 96.944209
MOS: 3+3, 3+6, 3+9, 12+3, 12+15, 12+27, 12+39, 12+51, 12+75

name: kwai
wedgie: <<1, 33, 27, 50, 40, -30]]
mapping: [<1, 2, 16, 14], <0, -1, -33, -27]>
TOP period: 1199.680495
TOP generator: 497.252002
MOS: 1+1, 2+1, 2+3, 5+2, 5+7, 12+5, 12+17, 29+12

name: hemiw�rschmidt
wedgie: <<16, 2, 5, -34, -37, 6]]
mapping: [<1, -1, 2, 2], <0, 16, 2, 5]>
TOP period: 1199.692003
TOP generator: 193.822428
MOS: 1+1, 1+2, 1+3, 1+4, 1+5, 6+1, 6+7, 6+13, 6+19, 6+25

name: amity
wedgie: <<5, 13, -17, 9, -41, -76]]
mapping: [<1, 3, 6, -2], <0, -5, -13, 17]>
TOP period: 1199.723894
TOP generator: 339.355813
MOS: 1+1, 1+2, 3+1, 4+3, 7+4, 7+11, 7+18, 7+25, 7+32, 7+39, 46+7, 53+46

name: gamera
wedgie: <<23, 40, 1, 10, -63, -110]]
mapping: [<1, 6, 10, 3], <0, -23, -40, -1]>
TOP period: 1199.851847
TOP generator: 230.313719
MOS: 1+1, 1+2, 1+3, 1+4, 5+1, 5+6, 5+11, 5+16, 21+5, 26+21, 26+47, 26+73

name: ennealimmal
wedgie: <<18, 27, 18, 1, -22, -34]]
mapping: [<9, 15, 22, 26], <0, -2, -3, -2]>
TOP period: 133.337375
TOP generator: 49.023986
MOS: 9+9, 18+9, 27+18, 27+45, 72+27

Hi Herman,

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> monz wrote:

> > What's with the double MOS numbers and plus sign?
>
> Number of large steps + number of small steps (in an octave).
> E.g. mavila has the pelog-like scale with 2 large steps and
> 5 small steps, while on the other hand meantone has the
> diatonic scale with 5 large steps and 2 small steps.

Thanks for the clarification. I like that! It's much more
informative than simply giving the cardinality.

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

Hi Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@> wrote:
>
> > Also, Gene, i'd appreciate more clarification of the
> > daughter, cousing, illegitimate uncle, etc. relationships,
> > so that i can draw more family-trees along the lines of
> > the one that's on my "family" Encyclopedia page.
>
> For that purpose, it might be best to include the Hermite comma
> sequence as a part of the data. As for instance:
>
> <<1 4 10 18 4 13 25 12 28 16||
>
> [81/80, 59049/57344, 387420489/369098752]
>
> or
>
> [|-4 4 -1 0 0>, |-13 10 0 -1 0>, |-25 18 0 0 -1>]
>
>
>
> <<1 4 10 -13 4 13 -24 12 -44 -71||
>
> [81/80, 59049/57344, 17537553/16777216]
>
>
>
> <<2 8 -11 -26 8 -23 -48 -48 -88 -35||
>
> [81/80, 8680203/8388608, 17537553/16777216]
>
>
>
> <<3 12 -1 -8 12 -10 -23 -36 -60 -19||
>
> [81/80, 1029/1024, 2079/2048]

Thanks for those, but ... your post is so cryptic
that i don't have enough info to know what you're
showing me.

First off, the Encyclopedia needs a page explaining
"Hermite comma sequence", which i assume goes along
with "Hermite reduction". Would you please write some
definitions and illustrations for me?

It looks like you're describing 7-limit temperaments
here, given that you list 3 commas for each example.
How about some family names?

Also, i've begun making separate Encyclopedia pages
for each of the families which Herman tabulated in
his posts. But i'd like to make them conform to the
ones which are already in the Encyclopedia and which
were mostly done by you. To do that, i need to know
which 7-limit temperaments go with which 5-limit ones.

How useful is this attempt by Keenan Pepper to illustrate
the relationships? Please point out which of the follow-ups
(if any) contribute pertinent info.

/tuning/topicId_63413.html#63413

Thanks.

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

monz wrote...
> How useful is this attempt by Keenan Pepper to illustrate
> the relationships? Please point out which of the follow-ups
> (if any) contribute pertinent info.
>
> /tuning/topicId_63413.html#63413

Have you read the page Keenan links to?

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

It explains comma sequences a bit.

-Carl

Which one is 79/80 MOS 2deg159tET?

----- Original Message -----
From: "Herman Miller" <hmiller@IO.COM>
To: <tuning@yahoogroups.com>
Sent: 01 Haziran 2007 Cuma 6:22
Subject: Re: [tuning] Re: request for temperament family datasheets

> Some 7-limit (rank 2 / "linear") temperaments
>
> name: beep
> wedgie: <<2, 3, 1, 0, -4, -6]]
> mapping: [<1, 2, 3, 3], <0, -2, -3, -1]>
> TOP period: 1206.049627
> TOP generator: 266.306424
> MOS: 1+1, 1+2, 1+3, 4+1, 5+4
>
> name: hexadecimal
> wedgie: <<1, -3, 5, -7, 5, 20]]
> mapping: [<1, 2, 1, 5], <0, -1, 3, -5]>
> TOP period: 1208.959293
> TOP generator: 530.163729
> MOS: 1+1, 2+1, 2+3, 2+5, 7+2, 9+7
>
> name: supersharp
> wedgie: <<2, 6, 6, 5, 4, -3]]
> mapping: [<2, 3, 4, 5], <0, 1, 3, 3]>
> TOP period: 595.799819
> TOP generator: 127.869801
> MOS: 2+2, 2+4, 2+6, 8+2, 10+8
>
> name: decimal
> wedgie: <<4, 2, 2, -6, -8, -1]]
> mapping: [<2, 4, 5, 6], <0, -2, -1, -1]>
> TOP period: 603.828899
> TOP generator: 250.611636
> MOS: 2+2, 4+2, 4+6, 10+4, 10+14
>
> name: superpelog
> wedgie: <<2, -6, 1, -14, -4, 19]]
> mapping: [<1, 2, 1, 3], <0, -2, 6, -1]>
> TOP period: 1206.548265
> TOP generator: 260.760141
> MOS: 1+1, 1+2, 1+3, 4+1, 5+4, 9+5
>
> name: gorgo
> wedgie: <<3, 7, -1, 4, -10, -22]]
> mapping: [<1, 1, 1, 3], <0, 3, 7, -1]>
> TOP period: 1205.820043
> TOP generator: 228.199305
> MOS: 1+1, 1+2, 1+3, 1+4, 5+1, 5+6, 5+11
>
> name: blacksmith
> wedgie: <<0, 5, 0, 8, 0, -14]]
> mapping: [<5, 8, 12, 14], <0, 0, -1, 0]>
> TOP period: 239.178693
> TOP generator: 83.830599
> MOS: 5+5, 10+5
>
> name: diminished, dimisept
> wedgie: <<4, 4, 4, -3, -5, -2]]
> mapping: [<4, 6, 9, 11], <0, 1, 1, 1]>
> TOP period: 298.532115
> TOP generator: 101.456140
> MOS: 4+4, 8+4
>
> name: august
> wedgie: <<3, 0, 6, -7, 1, 14]]
> mapping: [<3, 5, 7, 9], <0, -1, 0, -2]>
> TOP period: 399.992210
> TOP generator: 107.311173
> MOS: 3+3, 3+6, 9+3
>
> name: dominant
> wedgie: <<1, 4, -2, 4, -6, -16]]
> mapping: [<1, 2, 4, 2], <0, -1, -4, 2]>
> TOP period: 1195.228951
> TOP generator: 495.881015
> MOS: 1+1, 2+1, 2+3, 5+2, 5+7, 12+5, 12+17, 12+29
>
> name: lemba
> wedgie: <<6, -2, -2, -17, -20, 1]]
> mapping: [<2, 2, 5, 6], <0, 3, -1, -1]>
> TOP period: 601.700493
> TOP generator: 230.874926
> MOS: 2+2, 4+2, 6+4, 10+6, 16+10
>
> name: semaphore, hemifourths
> wedgie: <<2, 8, 1, 8, -4, -20]]
> mapping: [<1, 2, 4, 3], <0, -2, -8, -1]>
> TOP period: 1203.668841
> TOP generator: 252.480358
> MOS: 1+1, 1+2, 1+3, 4+1, 5+4, 5+9, 5+14
>
> name: injera
> wedgie: <<2, 8, 8, 8, 7, -4]]
> mapping: [<2, 3, 4, 5], <0, 1, 4, 4]>
> TOP period: 600.888907
> TOP generator: 93.609825
> MOS: 2+2, 2+4, 2+6, 2+8, 2+10, 12+2, 12+14
>
> name: catler
> wedgie: <<0, 0, 12, 0, 19, 28]]
> mapping: [<12, 19, 28, 34], <0, 0, 0, -1]>
> TOP period: 99.806172
> TOP generator: 24.583958
> MOS: 12+12, 12+24
>
> name: nautilus
> wedgie: <<6, 10, 3, 2, -12, -21]]
> mapping: [<1, 2, 3, 3], <0, -6, -10, -3]>
> TOP period: 1202.659696
> TOP generator: 82.974671
> MOS: 1+1, 1+2, 1+3, ... 1+13, 14+1
>
> name: doublewide
> wedgie: <<8, 6, 6, -9, -13, -3]]
> mapping: [<2, 5, 6, 7], <0, -4, -3, -3]>
> TOP period: 599.276941
> TOP generator: 272.312338
> MOS: 2+2, 4+2, 4+6, 4+10, 4+14
>
> name: negri(sept)
> wedgie: <<4, -3, 2, -14, -8, 13]]
> mapping: [<1, 2, 2, 3], <0, -4, 3, -2]>
> TOP period: 1203.187309
> TOP generator: 124.841963
> MOS: 1+1, 1+2, 1+3, ..., 1+8, 9+1, 10+9
>
> name: keemun
> wedgie: <<6, 5, 3, -6, -12, -7]]
> mapping: [<1, 0, 1, 2], <0, 6, 5, 3]>
> TOP period: 1203.187309
> TOP generator: 317.834461
> MOS: 1+1, 1+2, 3+1, 4+3, 4+7, 4+11, 15+4
>
> name: muggles
> wedgie: <<5, 1, -7, -10, -25, -19]]
> mapping: [<1, 0, 2, 5], <0, 5, 1, -7]>
> TOP period: 1203.148011
> TOP generator: 379.393104
> MOS: 1+1, 1+2, 3+1, 3+4, 3+7, 3+10, 3+13
>
> name: pajara
> wedgie: <<2, -4, -4, -11, -12, 2]]
> mapping: [<2, 3, 5, 6], <0, 1, -2, -2]>
> TOP period: 598.446711
> TOP generator: 106.566546
> MOS: 2+2, 2+4, 2+6, 28, 10+2, 12+10, 22+12
>
> name: hedgehog
> wedgie: <<6, 10, 10, 2, -1, -5]]
> mapping: [<2, 4, 6, 7], <0, -3, -5, -5]>
> TOP period: 598.4467109
> TOP generator: 162.3159606
> MOS: 2+2, 2+4, 6+2, 8+6, 8+14
>
> name: porcupine
> wedgie: <<3, 5, -6, 1, -18, -28]]
> mapping: [<1, 2, 3, 2], <0, -3, -5, 6]>
> TOP period: 1196.905960
> TOP generator: 162.317661
> MOS: 1+1, 1+2, 1+3, ..., 1+6, 7+1, 7+8, 15+7, 22+15
>
> name: augene, tripletone
> wedgie: <<3, 0, -6, -7, -18, -14]]
> mapping: [<3, 5, 7, 8], <0, -1, 0, 2]>
> TOP period: 399.020013
> TOP generator: 90.593035
> MOS: 3+3, 3+6, 3+9
>
> name: beatles
> wedgie: <<2, -9, -4, -19, -12, 16]]
> mapping: [<1, 1, 5, 4], <0, 2, -9, -4]>
> TOP period: 1197.104145
> TOP generator: 354.720338
> MOS: 1+1, 1+2, 3+1, 3+4, 7+3
>
> name: liese, gawel
> wedgie: <<3, 12, 11, 12, 9, -8]]
> mapping: [<1, 3, 8, 8], <0, -3, -12, -11]>
> TOP period: 1202.624742
> TOP generator: 569.049147
> MOS: 1+1, 2+1, 2+3, 2+5, 2+7, 2+9, 2+11, 2+13, 2+15, 17+2
>
> name: flattone
> wedgie: <<1, 4, -9, 4, -17, -32
> mapping: [<1, 2, 4, -1], <0, -1, -4, 9]>
> TOP period: 1202.536419
> TOP generator: 507.137966
> MOS: 1+1, 2+1, 2+3, 5+2, 7+5, 7+12
>
> name: superpyth
> wedgie: <<1, 9, -2, 12, -6, -30]]
> mapping: [<1, 2, 6, 2], <0, -1, -9, 2]>
> TOP period: 1197.596121
> TOP generator: 489.427183
> MOS: 1+1, 2+1, 2+3, 5+2, 5+7, 5+12, 5+17
>
> name: meantone
> wedgie: <<1, 4, 10, 4, 13, 12]]
> mapping: [<1, 2, 4, 7], <0, -1, -4, -10]>
> TOP period: 1201.698520
> TOP generator: 504.13413
> MOS: 1+1, 2+1, 2+3, 5+2, 7+5, 12+7, 19+12
>
> name: cynder, mothra
> wedgie: <<3, 12, -1, 12, -10, -36]]
> mapping: [<1, 1, 0, 3], <0, 3, 12, -1]>
> TOP period: 1201.698520
> TOP generator: 232.521463
> MOS: 1+1, 1+2, 1+3, 1+4, 5+1, 5+6, 5+11, 5+16, 5+21
>
> name: sensi(sept), semisixths
> wedgie: <<7, 9, 13, -2, 1, 5]]
> mapping: [<1, -1, -1, -2], <0, 7, 9, 13]>
> TOP period: 1198.389531
> TOP generator: 443.160293
> MOS: 1+1, 2+1, 3+2, 3+5, 8+3, 8+11, 19+8, 27+19
>
> name: peppermint
> wedgie: <<1, 21, 15, 31, 21, -24]]
> mapping: [<1, 2, 11, 9], <0, -1, -21, -15]>
> TOP period: 1200.114945
> TOP generator: 495.775687
> MOS: 1+1, 2+1, 2+3, 5+2, 5+7, 12+5, 17+12, 29+17
>
> name: superkleismic
> wedgie: <<9, 10, -3, -5, -30, -35]]
> mapping: [<1, 4, 5, 2], <0, -9, -10, 3]>
> TOP period: 1201.371918
> TOP generator: 322.373137
> MOS: 1+1, 1+2, 3+1, 4+3, 4+7, 11+4, 15+11
>
> name: magic
> wedgie: <<5, 1, 12, -10, 5, 25]]
> mapping: [<1, 0, 2, -1], <0, 5, 1, 12]>
> TOP period: 1201.276744
> TOP generator: 380.795718
> MOS: 1+1, 1+2, 3+1, 3+4, 3+7, 3+10, 3+13, 3+16
>
> name: hemififths
> wedgie: <<18, -7, 1, -53, -49, 22]]
> mapping: [<1, 5, 1, 3], <0, -18, 7, -1]>
> TOP period: 1198.747107
> TOP generator: 227.210819
> MOS: 1+1, 1+2, 1+3, 1+4, 5+1, 5+6, 5+11, 16+5, 21+16, 37+21
>
> name: myna
> wedgie: <<10, 9, 7, -9, -17, -9]]
> mapping: [<1, -1, 0, 1], <0, 10, 9, 7]>
> TOP period: 1198.828458
> TOP generator: 309.892661
> MOS: 1+1, 1+2, 3+1, 4+3, 4+7, 4+11, 4+15, 4+19, 4+23, 27+4, 31+27
>
> name: valentine
> wedgie: <<9, 5, -3, -13, -30, -21]]
> mapping: [<1, 1, 2, 3], <0, 9, 5, -3]>
> TOP period: 1199.792743
> TOP generator: 77.833153
> MOS: 1+1, 1+2, ..., 1+14, 15+1, 15+16, 31+15, 31+46
>
> name: orwell
> wedgie: <<7, -3, 8, -21, -7, 27]]
> mapping: [<1, 0, 3, 1], <0, 7, -3, 8]>
> TOP period: 1199.532657
> TOP generator: 271.493647
> MOS: 1+1, 1+2, 1+3, 4+1, 4+5, 9+4, 9+13, 22+9, 31+22
>
> name: garibaldi
> wedgie: <<1, -8, -14, -15, -25, -10]]
> mapping: [<1, 2, -1, -3], <0, -1, 8, 14]>
> TOP period: 1200.760624
> TOP generator: 498.119330
> MOS: 1+1, 2+1, 2+3, 5+2, 5+7, 12+5, 12+17, 12+29, 41+12, 41+53
>
> name: rodan
> wedgie: <<3, 17, -1, 20, -10, -50]]
> mapping: [<1, 1, -1, 3], <0, 3, 17, -1]>
> TOP period: 1200.231587
> TOP generator: 234.380469
> MOS: 1+1, 1+2, 1+3, 1+4, 5+1, 5+6, 5+11, 5+16, 5+21, 5+26, 5+31, 5+36
>
> name: vulture
> wedgie: <<4, 21, -3, 24, -16, -66]]
> mapping: [<1, 0, -6, 4], <0, 4, 21, -3]>
> TOP period: 1199.274449
> TOP generator: 475.411671
> MOS: 1+1, 2+1, 3+2, 5+3, 5+8, 5+13, 5+18, 5+23, 5+28, 5+33, 5+38, 5+43,
> 5+48, 53+5
>
> name: miracle
> wedgie: <<6, -7, -2, -25, -20, 15]]
> mapping: [<1, 1, 3, 3], <0, 6, -7, -2]>
> TOP period: 1200.631014
> TOP generator: 116.720642
> MOS: 1+1, 1+2, ..., 1+9, 10+1, 10+11, 10+21, 31+10
>
> name: compton
> wedgie: <<0, 12, 24, 19, 38, 22]]
> mapping: [<12, 19, 28, 34], <0, 0, -1, -2]>
> TOP period: 100.051421
> TOP generator: 15.126072
> MOS: 12+12, 12+24, 12+36, 12+48, 12+60, 72+12
>
> name: hemikleismic
> wedgie: <<12, 10, -9, -12, -48, -49]]
> mapping: [<1, 0, 1, 4], <0, 12, 10, -9]>
> TOP period: 1199.411231
> TOP generator: 158.574015
> MOS: 1+1, 1+2, 1+3, ..., 1+6, 7+1, 8+7, 15+8, 15+23, 15+38
>
> name: catakleismic
> wedgie: <<6, 5, 22, -6, 18, 37]]
> mapping: [<1, 0, 1, -3], <0, 6, 5, 22]>
> TOP period: 1200.536355
> TOP generator: 316.906396
> MOS: 1+1, 1+2, 3+1, 4+3, 4+7, 4+11, 15+4, 19+15, 19+34, 53+19
>
> name: guiron
> wedgie: <<3, -24, -1, -45, -10, 65]]
> mapping: [<1, 1, 7, 3], <0, 3, -24, -1]>
> TOP period: 1200.486331
> TOP generator: 233.998391
> MOS: 1+1, 1+2, 1+3, 1+4, 5+1, 5+6, 5+11, 5+16, 5+21, 5+26, 5+31, 36+5
>
> name: misty
> wedgie: <<3, -12, -30, -26, -56, -36]]
> mapping: [<3, 5, 6, 6], <0, -1, 4, 10]>
> TOP period: 399.887155
> TOP generator: 96.944209
> MOS: 3+3, 3+6, 3+9, 12+3, 12+15, 12+27, 12+39, 12+51, 12+75
>
> name: kwai
> wedgie: <<1, 33, 27, 50, 40, -30]]
> mapping: [<1, 2, 16, 14], <0, -1, -33, -27]>
> TOP period: 1199.680495
> TOP generator: 497.252002
> MOS: 1+1, 2+1, 2+3, 5+2, 5+7, 12+5, 12+17, 29+12
>
> name: hemiw�rschmidt
> wedgie: <<16, 2, 5, -34, -37, 6]]
> mapping: [<1, -1, 2, 2], <0, 16, 2, 5]>
> TOP period: 1199.692003
> TOP generator: 193.822428
> MOS: 1+1, 1+2, 1+3, 1+4, 1+5, 6+1, 6+7, 6+13, 6+19, 6+25
>
> name: amity
> wedgie: <<5, 13, -17, 9, -41, -76]]
> mapping: [<1, 3, 6, -2], <0, -5, -13, 17]>
> TOP period: 1199.723894
> TOP generator: 339.355813
> MOS: 1+1, 1+2, 3+1, 4+3, 7+4, 7+11, 7+18, 7+25, 7+32, 7+39, 46+7, 53+46
>
> name: gamera
> wedgie: <<23, 40, 1, 10, -63, -110]]
> mapping: [<1, 6, 10, 3], <0, -23, -40, -1]>
> TOP period: 1199.851847
> TOP generator: 230.313719
> MOS: 1+1, 1+2, 1+3, 1+4, 5+1, 5+6, 5+11, 5+16, 21+5, 26+21, 26+47, 26+73
>
> name: ennealimmal
> wedgie: <<18, 27, 18, 1, -22, -34]]
> mapping: [<9, 15, 22, 26], <0, -2, -3, -2]>
> TOP period: 133.337375
> TOP generator: 49.023986
> MOS: 9+9, 18+9, 27+18, 27+45, 72+27
>
>
>
>
>
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Ozan Yarman wrote:
> Which one is 79/80 MOS 2deg159tET?

Not one of those that I've listed. Let's see ... if i've got it right, it would be this:

wedgie: <<33, 54, 95, 9, 58, 69]]
mapping: [<1, 2, 3, 4], <0, -33, -54, -95]>
TOP period: 1199.716050
TOP generator: 15.061426
MOS: 1+1, 1+2, 1+3, ..., 1+78, 79+1

Or you could take this to the 11-limit with exactly the same TOP tuning.

wedgie: <<33, 54, 95, 43, 9, 58, -46, 69, -87, -208]]
mapping: [<1, 2, 3, 4, 4], <0, -33, -54, -95, -43]>

monz wrote:

> Also, i've begun making separate Encyclopedia pages
> for each of the families which Herman tabulated in
> his posts. But i'd like to make them conform to the
> ones which are already in the Encyclopedia and which
> were mostly done by you. To do that, i need to know
> which 7-limit temperaments go with which 5-limit ones.

Compare the tuning maps. E.g.

5-limit meantone: [<1, 2, 4], <0, -1, -4]>
dominant: [<1, 2, 4, 2], <0, -1, -4, 2]>
flattone: [<1, 2, 4, -1], <0, -1, -4, 9]>
7-limit meantone: [<1, 2, 4, 7], <0, -1, -4, -10]>

In each of these cases, the first three elements of the 7-limit mapping for each generator match the mapping of 5-limit meantone.

Similarly:

srutal: [<2, 3, 5], <0, 1, -2]>
pajara: [<2, 3, 5, 6], <0, 1, -2, -2]>

augmented: [<3, 5, 7], <0, -1, 0]>
august: [<3, 5, 7, 9], <0, -1, 0, -2]>
augene: [<3, 5, 7, 8], <0, -1, 0, 2]>

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:

> First off, the Encyclopedia needs a page explaining
> "Hermite comma sequence", which i assume goes along
> with "Hermite reduction". Would you please write some
> definitions and illustrations for me?

If you've seen my web page on comma sequences, you know the
definition of a Hermite comma sequence is technical. Are you usre you
want it for your encyclopedia? You could just link.

> It looks like you're describing 7-limit temperaments
> here, given that you list 3 commas for each example.
> How about some family names?

Actually, they are 11-limit temperaments, and even the two 11-limit
versions of meantone have never had agreeed-on names, though I've
tried naming them.

> Also, i've begun making separate Encyclopedia pages
> for each of the families which Herman tabulated in
> his posts. But i'd like to make them conform to the
> ones which are already in the Encyclopedia and which
> were mostly done by you. To do that, i need to know
> which 7-limit temperaments go with which 5-limit ones.

Well, that is the sort of thing the Hermite comma sequences do for
you. Moreover, they work for all regular temperaments, though in the
case of equal temperaments the sort of information you get is that
12, 24, 72 and 84 are all in the same 3-limit family, and 12 and 24
in the same 5-limit family. Which you knew already.

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:

> Compare the tuning maps. E.g.
>
> 5-limit meantone: [<1, 2, 4], <0, -1, -4]>
> dominant: [<1, 2, 4, 2], <0, -1, -4, 2]>
> flattone: [<1, 2, 4, -1], <0, -1, -4, 9]>
> 7-limit meantone: [<1, 2, 4, 7], <0, -1, -4, -10]>
>
> In each of these cases, the first three elements of the 7-limit
mapping
> for each generator match the mapping of 5-limit meantone.

But then you also want to consider godzilla, for instance:

[<1, 2, 4, 3], <0, -2, -8, -1]]

Or mothra:

[<1, 1, 0, 3], <0, 3, 12, -1]]

Or squares:

[<1, 3, 8, 6], <0, -4, -16, -9]]

or semififths/murat:

[<1, 1, 0, 6], <0, 2, 8, -11]]

The comma sequence approach, I think correctly, counts them all in
the meantone family:

dominant: [81/80, 64/63]
flattone: [81/80, 137781/131072]
septimal meantone: [81/80, 59049/57344]
godzilla: [81/80, 49/48]
mothra: [81/80, 1029/1024]
squares: [81/80, 19683/19208]
murat: [81/80, 8680203/8388608]

Putting these in monzo form might be better, as you can read off more
information. For septimal meantone, for instance, we have

[|-4 4 -1 0>, |-13 10 0 -1>]

The "-1" exponent for 7 on the second comma shows it is not
contorted; we get the opposite result for godzilla, mothra, squares
and murat.

It lacks a name. What shall we name it? Ozmosis perhaps?

----- Original Message -----
From: "Herman Miller" <hmiller@IO.COM>
To: <tuning@yahoogroups.com>
Sent: 02 Haziran 2007 Cumartesi 4:52
Subject: Re: [tuning] Re: request for temperament family datasheets

> Ozan Yarman wrote:
> > Which one is 79/80 MOS 2deg159tET?
>
> Not one of those that I've listed. Let's see ... if i've got it right,
> it would be this:
>
> wedgie: <<33, 54, 95, 9, 58, 69]]
> mapping: [<1, 2, 3, 4], <0, -33, -54, -95]>
> TOP period: 1199.716050
> TOP generator: 15.061426
> MOS: 1+1, 1+2, 1+3, ..., 1+78, 79+1
>
> Or you could take this to the 11-limit with exactly the same TOP tuning.
>
> wedgie: <<33, 54, 95, 43, 9, 58, -46, 69, -87, -208]]
> mapping: [<1, 2, 3, 4, 4], <0, -33, -54, -95, -43]>
>
>

Ah, I've got it... Crafty Ozan's MOS = Cozmos

Oz.

----- Original Message -----
From: "Herman Miller" <hmiller@IO.COM>
To: <tuning@yahoogroups.com>
Sent: 02 Haziran 2007 Cumartesi 4:52
Subject: Re: [tuning] Re: request for temperament family datasheets

> Ozan Yarman wrote:
> > Which one is 79/80 MOS 2deg159tET?
>
> Not one of those that I've listed. Let's see ... if i've got it right,
> it would be this:
>
> wedgie: <<33, 54, 95, 9, 58, 69]]
> mapping: [<1, 2, 3, 4], <0, -33, -54, -95]>
> TOP period: 1199.716050
> TOP generator: 15.061426
> MOS: 1+1, 1+2, 1+3, ..., 1+78, 79+1
>
> Or you could take this to the 11-limit with exactly the same TOP tuning.
>
> wedgie: <<33, 54, 95, 43, 9, 58, -46, 69, -87, -208]]
> mapping: [<1, 2, 3, 4, 4], <0, -33, -54, -95, -43]>
>
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> It lacks a name. What shall we name it? Ozmosis perhaps?

Sounds good to me.

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@sbcglobal.net>
To: <tuning@yahoogroups.com>
Sent: 02 Haziran 2007 Cumartesi 23:00
Subject: [tuning] Re: request for temperament family datasheets

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > It lacks a name. What shall we name it? Ozmosis perhaps?
>
> Sounds good to me.
>
>

Didn't you like "Crafty Ozan's Moment of Symmetry" (Cozmos)?

Oz.

Some 11-limit temperaments

name: shrutar
wedgie: <<4, -8, 14, -2, -22, 11, -17, 55, 23, -54]]
mapping: [<2, 3, 5, 5, 7], <0, 2, -4, 7, -1]>
TOP period: 599.774873
TOP generator: 52.660207
MOS: 2+2, 2+4, 2+6, 2+8, 2+10, 2+12, 2+14, 2+16, 2+18, 2+10, 22+2,
22+24, 46+22

name: kwai
wedgie: <<1, 33, 27, -18, 50, 40, -32, -30, -156, -144]]
mapping: [<1, 2, 16, 14, -4], <0, -1, -33, -27, 18]>
TOP period: 1199.680495
TOP generator: 497.252002
MOS: 1+1, 2+1, 2+3, 5+2, 5+7, 12+5, 12+17, 29+12, 41+29

name: octoid
wedgie: <<24, 32, 40, 24, -5, -4, -45, 3, -55, -71
mapping: [<8, 13, 19, 23, 28], <0, -3, -4, -5, -3]>
TOP period: 150.033735
TOP generator: 16.238470
MOS: 8+8, 8+16, 8+24, 8+32, 8+40, 8+48, 8+56, 8+64

name: hemiennealimmal
wedgie: <<36, 54, 36, 18, 2, -44, -96, -68, -145, -74]]
mapping: [<18, 28, 41, 50, 62], <0, 2, 3, 2, 1]>
TOP period: 66.669400
TOP generator: 17.644891
MOS: 18+18, 18+36, 54+18, 72+54, 72+126, 72+198

Some 13-limit temperaments

name: cassandra 2
wedgie: <<1, -8, -14, -18, -21, -15, -25, -32, -37, -10, -14, -19, -2,
-7, -6]]
mapping: [<1, 2, -1, -3, -4, -5], <0, -1, 8, 14, 18, 21]>
TOP period: 1200.314568
TOP generator: 497.571038
MOS: 1+1, 2+1, 2+3, 5+2, 5+7, 12+5, 12+17, 29+12, 41+29

name: twothirdtonic
wedgie: <<13, -3, 11, 5, 12, -35, -19, -37, -29, 34, 22, 39, -24, -7, 23]]
mapping: [<1, 3, 2, 4, 4, 5], <0, -13, 3, -11, -5, -12]>
TOP period: 1199.635986
TOP generator: 130.327864
MOS: 1+1, 1+2, 1+3, ..., 1+8, 9+1, 9+10, 9+19, 9+28, 37+9

name: hitchcock
wedgie: <<5, 13, -17, 9, -6, 9, -41, -3, -28, -76, -24, -62, 84, 46, -54]]
mapping: [<1, 3, 6, -2, 6, 2], <0, -5, -13, 17, -9, 6]>
TOP period: 1200.623603
TOP generator: 339.610306
MOS: 1+1, 1+2, 3+1, 4+3, 7+4, 7+11, 7+18, 7+25, 7+32, 7+39, 46+7

name: cassandra 1
wedgie: <<1, -8, -14, 23, 20, -15, -25, 33, 28, -10, 81, 76, 113, 108,
-16]]
mapping: [<1, 2, -1, -3, 13, 12], <0, -1, 8, 14, -23, -20]>
TOP period: 1200.449663
TOP generator: 498.064040
MOS: 1+1, 2+1, 2+3, 5+2, 5+7, 12+5, 12+17, 12+29, 41+12, 53+41

name: unidec
wedgie: <<12, 22, -4, -6, 4, 7, -40, -51, -38, -71, -90, -72, -3, 26, 36
mapping: [<2, 5, 8, 5, 6, 8], <0, -6, -11, 2, 3, -2]>
TOP period: 600.449773
TOP generator: 183.199617
MOS: 2+2, 2+4, 6+2, 6+8, 6+14, 20+6, 26+20, 46+26

name: mystery
wedgie: <<0, 29, 29, 29, 29, 46, 46, 46, 46, -14, -33, -40, -19, -26, -7
mapping: [<29, 46, 67, 81, 100, 107], <0, 0, 1, 1, 1, 1]>
TOP period: 41.369298
TOP generator: 16.083636
MOS: 29+29, 58+29, 87+58, 145+87, 145+232

Some rank 3 temperaments:

name: starling
comma: [1, 2, -3, 1> 126/125
TOP tuning: <1199.010636, 1900.386896, 2788.610946, 3366.048410]

name: marvel
comma: [-5, 2, 2, -1> 225/224
TOP tuning: <1200.493660, 1901.172569, 2785.167472, 3370.211784]

name: tyr
comma: [-12, 0, -2, 1, 4> 102487/102400
TOP tuning: <1200.044166, 1901.955001, 2786.416265, 3368.701916,
4151.165152]

Ozan Yarman wrote:
> It lacks a name. What shall we name it? Ozmosis perhaps?
> Actually there are other possibilities. The one I originally mentioned, <<33, 54, 95, 9, 58, 69]], is the 80&159 temperament. I picked that one since 79 isn't a consistent ET in the 7-limit, but the mapping of 7 as [4, -95> is a problem if you only have a 79 or 80-note MOS to work with.

So I looked at some 79&80 temperaments. There are two that may be of interest:

wedgie: <<47, -54, -15, -195, -156, 117]]
mapping: [<1, 1, 3, 3], <0, 47, -54, -15]>
TOP: P = 1198.922568, G = 14.994471

wedgie: <<33, -26, 15, -118, -69, 108]]
mapping: [<1, 2, 2, 3], <0, -33, 26, -15]>
TOP: P = 1198.999997, G = 15.024448

Of these, the second one looks like the better choice.

There are more possibilities in the 11-limit.

wedgie: <<33, 54, 15, 43, 9, -69, -46, -117, -87, 69]]
mapping: [<1, 2, 3, 3, 4], <0, -33, -54, -15, -43]>
TOP: 0.916555 (P = 1199.083445, G = 15.056755)

wedgie: <<47, -54, -15, -43, -195, -156, -231, 117, 87, -69]]
mapping: [<1, 1, 3, 3, 4], <0, 47, -54, -15, -43]>
TOP: 1.077432 (P = 1198.922568, G = 14.994471)

wedgie: <<33, -26, 15, 43, -118, -69, -46, 108, 190, 69]]
mapping: [<1, 2, 2, 3, 4], <0, -33, 26, -15, -43]>
TOP: 1.000003 (P = 1198.999997, G = 15.024448)

wedgie: <<33, 54, 95, 43, 9, 58, -46, 69, -87, -208]]
mapping: [<1, 2, 3, 4, 4], <0, -33, -54, -95, -43]>
TOP: 0.283950 (P = 1199.716050, G = 15.061426)

wedgie: <<33, 54, 15, -37, 9, -69, -173, -117, -273, -156]]
mapping: [<1, 2, 3, 3, 3], <0, -33, -54, -15, 37]>
TOP: 0.916555 (P = 1199.083445, G = 15.056755)

It might be best to say that the 79- or 80-note MOS of 159-ET is a particular tuning that is consistent with each of these temperaments, in the same way that 12-ET is consistent with meantone, diminished, and augmented at the same time. But it would be interesting if one of these in particular is a better match for the way the scale is being used in practice.

> > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> > >
> > > It lacks a name. What shall we name it? Ozmosis perhaps?
> >
> > Sounds good to me.
> >
> >
>
> Didn't you like "Crafty Ozan's Moment of Symmetry" (Cozmos)?
>
> Oz.

I vote for Ozmosis!

-Carl

----- Original Message -----
From: "Herman Miller" <hmiller@IO.COM>
To: <tuning@yahoogroups.com>
Sent: 03 Haziran 2007 Pazar 4:05
Subject: Re: [tuning] Re: request for temperament family datasheets

> Ozan Yarman wrote:
> > It lacks a name. What shall we name it? Ozmosis perhaps?
> >
>
> Actually there are other possibilities. The one I originally mentioned,
> <<33, 54, 95, 9, 58, 69]], is the 80&159 temperament. I picked that one
> since 79 isn't a consistent ET in the 7-limit, but the mapping of 7 as
> [4, -95> is a problem if you only have a 79 or 80-note MOS to work with.
>
> So I looked at some 79&80 temperaments. There are two that may be of
> interest:
>
> wedgie: <<47, -54, -15, -195, -156, 117]]
> mapping: [<1, 1, 3, 3], <0, 47, -54, -15]>
> TOP: P = 1198.922568, G = 14.994471
>
> wedgie: <<33, -26, 15, -118, -69, 108]]
> mapping: [<1, 2, 2, 3], <0, -33, 26, -15]>
> TOP: P = 1198.999997, G = 15.024448
>
> Of these, the second one looks like the better choice.
>

Very interesting. However, all are practically the same, no?

> There are more possibilities in the 11-limit.
>
> wedgie: <<33, 54, 15, 43, 9, -69, -46, -117, -87, 69]]
> mapping: [<1, 2, 3, 3, 4], <0, -33, -54, -15, -43]>
> TOP: 0.916555 (P = 1199.083445, G = 15.056755)
>
> wedgie: <<47, -54, -15, -43, -195, -156, -231, 117, 87, -69]]
> mapping: [<1, 1, 3, 3, 4], <0, 47, -54, -15, -43]>
> TOP: 1.077432 (P = 1198.922568, G = 14.994471)
>
> wedgie: <<33, -26, 15, 43, -118, -69, -46, 108, 190, 69]]
> mapping: [<1, 2, 2, 3, 4], <0, -33, 26, -15, -43]>
> TOP: 1.000003 (P = 1198.999997, G = 15.024448)
>
> wedgie: <<33, 54, 95, 43, 9, 58, -46, 69, -87, -208]]
> mapping: [<1, 2, 3, 4, 4], <0, -33, -54, -95, -43]>
> TOP: 0.283950 (P = 1199.716050, G = 15.061426)
>
> wedgie: <<33, 54, 15, -37, 9, -69, -173, -117, -273, -156]]
> mapping: [<1, 2, 3, 3, 3], <0, -33, -54, -15, 37]>
> TOP: 0.916555 (P = 1199.083445, G = 15.056755)
>

And what of 13-limit?

> It might be best to say that the 79- or 80-note MOS of 159-ET is a
> particular tuning that is consistent with each of these temperaments, in
> the same way that 12-ET is consistent with meantone, diminished, and
> augmented at the same time.

But, surely it is more precise? I mean, pitch deviations are negligible.

I employ 79 for a closed 12-tone subset and transpositions of Rast... In
contrast, I use 80 for transposing the rest of the Maqamat.

But it would be interesting if one of these
> in particular is a better match for the way the scale is being used in
> practice.
>
>

I myself prefer the simple-frequencies version here:

262 C
264.5
266.75
269
271.25
273.75
276.25 C#
278.5 Db
281
283.5
286
288.5
291
293.5 D
296
298.75
301.25
304
306.5
309.25 D#
312 Eb
314.75
317.5
320.25
323
326
328.75 E
331.75 Fb
334.5
337.5
340.5
343.5
346.5 E#
349.333333333333 F
352.5
355.5
358.75
361.75
365
368.25 F#
371.25 Gb
374.75
378
381.25
384.75
388
393 G
396.5
400
403.5
407
410.5
414 G#
417.75 Ab
421.25
425
428.75
432.5
436.25
440 A
444
447.75
452
456
459.75
463.75 A#
467.777777777777 Bb
472
476
480.25
484.5
488.75
492.75 B
497.25 cb
501.5
506
510.25
514.75
519.25 B#
524 c

Ozmosis it is then!

----- Original Message -----
From: "Carl Lumma" <clumma@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 03 Haziran 2007 Pazar 9:31
Subject: [tuning] Re: request for temperament family datasheets

> > > --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> > > >
> > > > It lacks a name. What shall we name it? Ozmosis perhaps?
> > >
> > > Sounds good to me.
> > >
> > >
> >
> > Didn't you like "Crafty Ozan's Moment of Symmetry" (Cozmos)?
> >
> > Oz.
>
> I vote for Ozmosis!
>
> -Carl
>
>

Ozan Yarman wrote:

> Very interesting. However, all are practically the same, no?

They're all the same when tuned to 159-ET. The differences only become apparent if you use a different tuning (and even then, if you use the "wrong" mapping you're not likely to notice much difference).

> And what of 13-limit?

Here are a few possibilities.

wedgie: <<33, 54, 15, 43, 24, 9, -69, -46, -84, -117, -87, -144, 69, 12, -76]]
mapping: [<1, 2, 3, 3, 4, 4], <0, -33, -54, -15, -43, -24]>
TOP: 1.159565 (P = 1198.866480, G = 14.967882)

wedgie: <<47, -54, -15, -43, -24, -195, -156, -231, -212, 117, 87, 144, -69, -12, 76]]
mapping: [<1, 1, 3, 3, 4, 4], <0, 47, -54, -15, -43, -24]>
TOP: 1.157248 (P = 1198.842752, G = 14.963570)

wedgie: <<33, -26, 15, 43, 24, -118, -69, -46, -84, 108, 190, 152, 69, 12, -76]]
mapping: [<1, 2, 2, 3, 4, 4], <0, -33, 26, -15, -43, -24]>
TOP: 1.159565 (P = 1198.866480, G = 14.967882)

wedgie: <<33, 54, 95, 43, 24, 9, 58, -46, -84, 69, -87, -144, -208, -284, -76]]
mapping: [<1, 2, 3, 4, 4, 4], <0, -33, -54, -95, -43, -24]>
TOP: 0.418356 (P = 1200.279661, G = 15.089129)

wedgie: <<33, 54, 15, -37, 24, 9, -69, -173, -84, -117, -273, -144, -156, 12, 220]]
mapping: [<1, 2, 3, 3, 3, 4], <0, -33, -54, -15, 37, -24]>
TOP: 1.159565 (P = 1198.866480, G = 14.967882)

wedgie: <<33, 54, 15, 43, -56, 9, -69, -46, -211, -117, -87, -330, 69, -213, -353]]
mapping: [<1, 2, 3, 3, 4, 3], <0, -33, -54, -15, -43, 56]>
TOP: 0.916555 (P = 1199.083445, G = 15.056755)

Three of these have the same TOP tuning (P = 1198.866480, G = 14.967882) but different mappings. It's possible there could be an error in my algorithm, since I haven't done much with 13-limit temperaments, but it could simply be that the difference in the error for those mappings is less than the TOP error for the other primes.

But looking at your chart it appears you have G at -33 generators and E at +26, relative to C. The large step in the scale is between 388 Hz and 393 Hz (G). So that definitely suggests this 7-limit temperament:

wedgie: <<33, -26, 15, -118, -69, 108]]
mapping: [<1, 2, 2, 3], <0, -33, 26, -15]>
TOP: 1.000003 (P = 1198.999997, G = 15.024448)

To keep this within the range of -33 to +45 generators, you could end up with this as a 13-limit mapping:

wedgie: <<33, -26, 15, -37, 24, -118, -69, -173, -84, 108, 4, 152, -156, 12, 220]]
mapping: [<1, 2, 2, 3, 3, 4], <0, -33, 26, -15, 37, -24]>
TOP: 1.159565 (P = 1198.866480, G = 14.967882)

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:

> So I looked at some 79&80 temperaments. There are two that may be
of
> interest:
>
> wedgie: <<47, -54, -15, -195, -156, 117]]
> mapping: [<1, 1, 3, 3], <0, 47, -54, -15]>
> TOP: P = 1198.922568, G = 14.994471
>
> wedgie: <<33, -26, 15, -118, -69, 108]]
> mapping: [<1, 2, 2, 3], <0, -33, 26, -15]>
> TOP: P = 1198.999997, G = 15.024448

The trouble with these is that 159 is 17-limit consistent, making the
patent val the clear best choice through the 17-limit (I would say
through the 29-limit, really.) And these are not systems supported by
the best tuning, whereas ozmosis is.

> It might be best to say that the 79- or 80-note MOS of 159-ET is a
> particular tuning that is consistent with each of these
temperaments, in
> the same way that 12-ET is consistent with meantone, diminished,
and
> augmented at the same time.

Both 80 and 159 are 17-limit consistent, which suggests you should
stick to 80&159 at least through to 17-limit ozmosis.

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@sbcglobal.net>
To: <tuning@yahoogroups.com>
Sent: 04 Haziran 2007 Pazartesi 2:21
Subject: [tuning] Re: request for temperament family datasheets

> --- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> > So I looked at some 79&80 temperaments. There are two that may be
> of
> > interest:
> >
> > wedgie: <<47, -54, -15, -195, -156, 117]]
> > mapping: [<1, 1, 3, 3], <0, 47, -54, -15]>
> > TOP: P = 1198.922568, G = 14.994471
> >
> > wedgie: <<33, -26, 15, -118, -69, 108]]
> > mapping: [<1, 2, 2, 3], <0, -33, 26, -15]>
> > TOP: P = 1198.999997, G = 15.024448
>
> The trouble with these is that 159 is 17-limit consistent, making the
> patent val the clear best choice through the 17-limit (I would say
> through the 29-limit, really.) And these are not systems supported by
> the best tuning, whereas ozmosis is.
>

What is patent val and how is it 29-limit consistent?

> > It might be best to say that the 79- or 80-note MOS of 159-ET is a
> > particular tuning that is consistent with each of these
> temperaments, in
> > the same way that 12-ET is consistent with meantone, diminished,
> and
> > augmented at the same time.
>
> Both 80 and 159 are 17-limit consistent, which suggests you should
> stick to 80&159 at least through to 17-limit ozmosis.
>
>
>

I myself alterate between 79 and 80 when transposing. A 12-tone closed-cycle
subset does not work in 80, for example.

Oz.

Which one among these was deemed best by Gene and you lastly Herman?

Oz.

----- Original Message -----
From: "Herman Miller" <hmiller@IO.COM>
To: <tuning@yahoogroups.com>
Sent: 04 Haziran 2007 Pazartesi 0:47
Subject: Re: [tuning] Re: request for temperament family datasheets

> Ozan Yarman wrote:
>
> > Very interesting. However, all are practically the same, no?
>
> They're all the same when tuned to 159-ET. The differences only become
> apparent if you use a different tuning (and even then, if you use the
> "wrong" mapping you're not likely to notice much difference).
>
> > And what of 13-limit?
>
> Here are a few possibilities.
>
> wedgie: <<33, 54, 15, 43, 24, 9, -69, -46, -84, -117, -87, -144, 69, 12,
> -76]]
> mapping: [<1, 2, 3, 3, 4, 4], <0, -33, -54, -15, -43, -24]>
> TOP: 1.159565 (P = 1198.866480, G = 14.967882)
>
> wedgie: <<47, -54, -15, -43, -24, -195, -156, -231, -212, 117, 87, 144,
> -69, -12, 76]]
> mapping: [<1, 1, 3, 3, 4, 4], <0, 47, -54, -15, -43, -24]>
> TOP: 1.157248 (P = 1198.842752, G = 14.963570)
>
> wedgie: <<33, -26, 15, 43, 24, -118, -69, -46, -84, 108, 190, 152, 69,
> 12, -76]]
> mapping: [<1, 2, 2, 3, 4, 4], <0, -33, 26, -15, -43, -24]>
> TOP: 1.159565 (P = 1198.866480, G = 14.967882)
>
> wedgie: <<33, 54, 95, 43, 24, 9, 58, -46, -84, 69, -87, -144, -208,
> -284, -76]]
> mapping: [<1, 2, 3, 4, 4, 4], <0, -33, -54, -95, -43, -24]>
> TOP: 0.418356 (P = 1200.279661, G = 15.089129)
>
> wedgie: <<33, 54, 15, -37, 24, 9, -69, -173, -84, -117, -273, -144,
> -156, 12, 220]]
> mapping: [<1, 2, 3, 3, 3, 4], <0, -33, -54, -15, 37, -24]>
> TOP: 1.159565 (P = 1198.866480, G = 14.967882)
>
> wedgie: <<33, 54, 15, 43, -56, 9, -69, -46, -211, -117, -87, -330, 69,
> -213, -353]]
> mapping: [<1, 2, 3, 3, 4, 3], <0, -33, -54, -15, -43, 56]>
> TOP: 0.916555 (P = 1199.083445, G = 15.056755)
>
> Three of these have the same TOP tuning (P = 1198.866480, G = 14.967882)
> but different mappings. It's possible there could be an error in my
> algorithm, since I haven't done much with 13-limit temperaments, but it
> could simply be that the difference in the error for those mappings is
> less than the TOP error for the other primes.
>
> But looking at your chart it appears you have G at -33 generators and E
> at +26, relative to C. The large step in the scale is between 388 Hz and
> 393 Hz (G). So that definitely suggests this 7-limit temperament:
>
> wedgie: <<33, -26, 15, -118, -69, 108]]
> mapping: [<1, 2, 2, 3], <0, -33, 26, -15]>
> TOP: 1.000003 (P = 1198.999997, G = 15.024448)
>
> To keep this within the range of -33 to +45 generators, you could end up
> with this as a 13-limit mapping:
>
> wedgie: <<33, -26, 15, -37, 24, -118, -69, -173, -84, 108, 4, 152, -156,
> 12, 220]]
> mapping: [<1, 2, 2, 3, 3, 4], <0, -33, 26, -15, 37, -24]>
> TOP: 1.159565 (P = 1198.866480, G = 14.967882)
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> Which one among these was deemed best by Gene and you lastly Herman?

I didn't like Herman's proposals, and think ozmosis is the way to go.

You mean:

OZMOSIS
wedgie: <<33, 54, 95, 43, 9, 58, -46, 69, -87, -208]]
mapping: [<1, 2, 3, 4, 4], <0, -33, -54, -95, -43]>
TOP period: 1199.716050
TOP generator: 15.061426
MOS: 1+1, 1+2, 1+3, ..., 1+78, 79+1

----- Original Message -----
From: "Gene Ward Smith" <genewardsmith@sbcglobal.net>
To: <tuning@yahoogroups.com>
Sent: 08 Haziran 2007 Cuma 0:44
Subject: [tuning] Re: request for temperament family datasheets

> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
> >
> > Which one among these was deemed best by Gene and you lastly Herman?
>
> I didn't like Herman's proposals, and think ozmosis is the way to go.
>
>

Herman Miller wrote:
> Some 11-limit temperaments
> > name: shrutar
> wedgie: <<4, -8, 14, -2, -22, 11, -17, 55, 23, -54]]
> mapping: [<2, 3, 5, 5, 7], <0, 2, -4, 7, -1]>
> TOP period: 599.774873
> TOP generator: 52.660207
> MOS: 2+2, 2+4, 2+6, 2+8, 2+10, 2+12, 2+14, 2+16, 2+18, 2+10, 22+2,
> 22+24, 46+22

Manuel Op de Coul noticed that the numbers given for TOP period and generator are not the correct values. What seems to have happened is that I gave the TOP-RMS values by mistake. The correct TOP period and generator values are:

TOP period: 599.822848
TOP generator: 52.372763

> name: cassandra 2
> wedgie: <<1, -8, -14, -18, -21, -15, -25, -32, -37, -10, -14, -19, -2,
> -7, -6]]
> mapping: [<1, 2, -1, -3, -4, -5], <0, -1, 8, 14, 18, 21]>
> TOP period: 1200.314568
> TOP generator: 497.571038
> MOS: 1+1, 2+1, 2+3, 5+2, 5+7, 12+5, 12+17, 29+12, 41+29

And in this case the correct values are:
TOP period: 1201.533357
TOP generator: 497.891124

Sorry for the mix-up.