Names for forgotten or unclassified temperaments

Hi tuners.

I've found a couple of temperaments which don't seem to be documented on the commonly cited webpages like the Xenwiki entries, Graham's Temperament Finder etc. Therefore I find it appropriate to mention them here for the sake of extending the repertoire or for possible future inclusion elsewhere.

The symbol "*" means that the name has occured on mailing list archives or on other webpages.

The symbol "#" means that I have a personal suggestion for a name but I don't know of anyone else having mentioned the temperament.

The first one I'll maybe never use and I currently call it "useless" but I'm includeing it anyway.

----------

[-18 7 3] = 7 tritones in 10/1, probably not very meaningful.

Generator close to 25/18 but 25/18 is not mapped to 1 generator

[-9 -6 8] = doublewide *

[-2 13 -8] = unicorn *

[16 -13 2] = semephere # ("e" is the 5th letter and this is a 5-limit temperament)

[-5 -10 9] = shibboleth *

[13 5 -9] = valentine *

[6 -14 7] = sevond # (i.e. 7 seconds equated with an octave)

[-1 -14 10] = fifive # (5 generators to a fifth)

----------

Petr

--- In tuning@yahoogroups.com, Petr Pařízek <petrparizek2000@...> wrote:
> [-18 7 3] = 7 tritones in 10/1, probably not very meaningful.
>
> Generator close to 25/18 but 25/18 is not mapped to 1 generator
>
> [-9 -6 8] = doublewide *
>
> [-2 13 -8] = unicorn *
>
> [16 -13 2] = semephere # ("e" is the 5th letter and this is a 5-limit
> temperament)
>
> [-5 -10 9] = shibboleth *
>
> [13 5 -9] = valentine *
>
> [6 -14 7] = sevond # (i.e. 7 seconds equated with an octave)
>
> [-1 -14 10] = fifive # (5 generators to a fifth)

I'm sorry, what are these triples of numbers? I assumed at first they were 5-limit wedgies, but they must not be because that interpretation isn't making sense.

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:

> I'm sorry, what are these triples of numbers? I assumed at first they were 5-limit wedgies, but they must not be because that interpretation isn't making sense.
>

If you interpret them as monzos it makes sense, though the names don't always. But these might be good commas to list.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> If you interpret them as monzos it makes sense, though the names don't always. But these might be good commas to list.

Oh, the monzos of the *commas*. Got it.

Keenan

Gene wrote:

> If you interpret them as monzos it makes sense, though the names don't > always.

If you're referring to those marked with the number sign, I'm obviously not insisting that these should be used in every case. I've just used them for my personal purposes because I need to call them something. If others have better suggestions, I'm happy to discuss them. Actually, that's why I've listed the commas in the first place.

Petr

--- In tuning@yahoogroups.com, Petr PaÅo?=ízek <petrparizek2000@...> wrote:

>
> [6 -14 7] = sevond # (i.e. 7 seconds equated with an octave)

The difference between 7 seconds and the octave is the Pythagorean comma. Or did you mean something else?

On Sun, Jun 5, 2011 at 11:11 PM, lobawad <lobawad@...> wrote:

> --- In tuning@yahoogroups.com, Petr PaÅo?=ízek <petrparizek2000@...>
> wrote:
>
> >
> > [6 -14 7] = sevond # (i.e. 7 seconds equated with an octave)
>
> The difference between 7 seconds and the octave is the Pythagorean comma.
> Or did you mean something else?
>

I think that would be the difference between 6 seconds and the octave is the
P.C.

[ (3/2)^2 / 2 ]^7 / 2 = 3^14 / 2^22 = ( (3/2)^2 / 2 ) ( 3^12 / 2^19 ) =
Second + P.C.

Yes, of course, sorry- seven seconds is the Pythagorean double augmented prime, and the temperament Petr has here would I assume be intended to access the 7th partial via 16:7, by tempering out the septimal schisma between 9:8^7 and 16:7.

--- In tuning@yahoogroups.com, Daniel Nielsen <nielsed@...> wrote:
>
> On Sun, Jun 5, 2011 at 11:11 PM, lobawad <lobawad@...> wrote:
>
> > --- In tuning@yahoogroups.com, Petr PaÅo?=ízek <petrparizek2000@>
> > wrote:
> >
> > >
> > > [6 -14 7] = sevond # (i.e. 7 seconds equated with an octave)
> >
> > The difference between 7 seconds and the octave is the Pythagorean comma.
> > Or did you mean something else?
> >
>
>
> I think that would be the difference between 6 seconds and the octave is the
> P.C.
>
> [ (3/2)^2 / 2 ]^7 / 2 = 3^14 / 2^22 = ( (3/2)^2 / 2 ) ( 3^12 / 2^19 ) =
> Second + P.C.
>

Oh- "sevond". :-) That's a good fanciful name, goofy but catchy and appropriate.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> Yes, of course, sorry- seven seconds is the Pythagorean double augmented prime, and the temperament Petr has here would I assume be intended to access the 7th partial via 16:7, by tempering out the septimal schisma between 9:8^7 and 16:7.
>
> --- In tuning@yahoogroups.com, Daniel Nielsen <nielsed@> wrote:
> >
> > On Sun, Jun 5, 2011 at 11:11 PM, lobawad <lobawad@> wrote:
> >
> > > --- In tuning@yahoogroups.com, Petr PaÅo?=ízek <petrparizek2000@>
> > > wrote:
> > >
> > > >
> > > > [6 -14 7] = sevond # (i.e. 7 seconds equated with an octave)
> > >
> > > The difference between 7 seconds and the octave is the Pythagorean comma.
> > > Or did you mean something else?
> > >
> >
> >
> > I think that would be the difference between 6 seconds and the octave is the
> > P.C.
> >
> > [ (3/2)^2 / 2 ]^7 / 2 = 3^14 / 2^22 = ( (3/2)^2 / 2 ) ( 3^12 / 2^19 ) =
> > Second + P.C.
> >
>

Lobawad wrote:

> The difference between 7 seconds and the octave is the Pythagorean comma. > Or did you mean something else?

I meant (10/9)^7.

Petr

I wrote:

> I meant (10/9)^7.

After all, you can dig it from the prime exponents:
If you widen the interval by an octave, you get [7 -14 7]. This clearly shows that there's something to the power of 7 there. And [1 -2 1] is nothing else than, voila, 10/9.

Petr

--- In tuning@yahoogroups.com, Petr Parízek <petrparizek2000@...> wrote:
>
> Lobawad wrote:
>
> > The difference between 7 seconds and the octave is the Pythagorean comma.
> > Or did you mean something else?
>
> I meant (10/9)^7.
>
> Petr
>

Oh- seven minor whole tones. "Second" by itself implies the whole tone.

Lobawad wrote:

> Oh- seven minor whole tones. "Second" by itself implies the whole tone.

Whatever we call it in the end, I was primarily listing the temperament just "to say it's there", although it exploits quite a lot of "mistuning". What I'm much more interested in are those like the one I called "fifive" in the first message of this thread. If a temperament like "kwazy" (or what the strange name is) is included in some listings, then this one would deserve the same. Both have a half-octave period and kwazy requires much more generators for a full triad (13 compared to 7).

Petr

Semephere is the one that I called Immunity here:

/tuning/topicId_99315.html#99323

This one is great. To hell with Amity! It turns (81/80)^3 into 16/15,
whereas Amity turns (81/80)^3 into 25/24. It lends itself to
slightly-sharp fifths, and is supported by 34-equal, one of my EDO's
for the 5-limit.

The sevond one is cool, I stumbled on this but opted not to post it to
keep the post focused more on the (81/80)^n = 25/24 or 16/15 theme. It
tempers out 5000000/4782969 and makes for a pretty obvious comma pump
too. There's a similar 1/5-oct microtemperament here eliminating
838860800000/847288609443 as well, any ideas for naming? I think Gene
came up with it first.

Fifive looks really cool too, what's the period and generator mapping for it?

Other than the ones you mentioned, there's also Gravity, so named
because the generator is a "grave" fifth, and Absurdity, so named
because Graham thought it was too complex to be really usable (it
equates (81/80)^5 with 25/24, if you want to give it a shot). See this
thread for those:

/tuning/topicId_99315.html#99315

There were a few weird ones here that explore (25/24)^n = 16/15

/tuning/topicId_99315.html#99335

And some interesting ones that explore (128/125)^n = 25/24

/tuning/topicId_99315.html#99324

The "double schismatic" one is theoretically interesting, although
pretty far out there.

-Mike

There's also (10/9)^3 = 3/2, which is one of the crappiest commas
ever, but as it's supported by 16-equal is probably worth mentioning.

-Mike

On Tue, Jun 7, 2011 at 6:23 AM, Mike Battaglia <battaglia01@...> wrote:
> Semephere is the one that I called Immunity here:
>
> /tuning/topicId_99315.html#99323
>
> This one is great. To hell with Amity! It turns (81/80)^3 into 16/15,
> whereas Amity turns (81/80)^3 into 25/24. It lends itself to
> slightly-sharp fifths, and is supported by 34-equal, one of my EDO's
> for the 5-limit.
>
> The sevond one is cool, I stumbled on this but opted not to post it to
> keep the post focused more on the (81/80)^n = 25/24 or 16/15 theme. It
> tempers out 5000000/4782969 and makes for a pretty obvious comma pump
> too. There's a similar 1/5-oct microtemperament here eliminating
> 838860800000/847288609443 as well, any ideas for naming? I think Gene
> came up with it first.
>
> Fifive looks really cool too, what's the period and generator mapping for it?
>
>
> Other than the ones you mentioned, there's also Gravity, so named
> because the generator is a "grave" fifth, and Absurdity, so named
> because Graham thought it was too complex to be really usable (it
> equates (81/80)^5 with 25/24, if you want to give it a shot). See this
> thread for those:
>
> /tuning/topicId_99315.html#99315
>
> There were a few weird ones here that explore (25/24)^n = 16/15
>
> /tuning/topicId_99315.html#99335
>
> And some interesting ones that explore (128/125)^n = 25/24
>
> /tuning/topicId_99315.html#99324
>
> The "double schismatic" one is theoretically interesting, although
> pretty far out there.
>
> -Mike
>

Mike Battaglia <battaglia01@...> wrote:

> Fifive looks really cool too, what's the period and
> generator mapping for it?

http://x31eq.com/cgi-bin/rt.cgi?ets=60+34&limit=5

2 3 5
[< 2 2 3 ]
< 0 5 7 ]>

Generator Tunings (cents)
[600.017, 140.628>

Graham

On Tue, Jun 7, 2011 at 7:04 AM, Graham Breed <gbreed@...> wrote:
>
> Mike Battaglia <battaglia01@...> wrote:
>
> > Fifive looks really cool too, what's the period and
> > generator mapping for it?
>
> http://x31eq.com/cgi-bin/rt.cgi?ets=60+34&limit=5
>
> 2 3 5
> [< 2 2 3 ]
> < 0 5 7 ]>
>
> Generator Tunings (cents)
> [600.017, 140.628>

I meant what interval gets mapped to one period, and what interval
gets mapped to one generator? I'm away from my MATLAB rig at the
moment and don't have the tools to work it out.

-Mike

Mike Battaglia <battaglia01@...> wrote:

> > 2 3 5
> > [< 2 2 3 ]
> > < 0 5 7 ]>

> I meant what interval gets mapped to one period, and what
> interval gets mapped to one generator? I'm away from my
> MATLAB rig at the moment and don't have the tools to work
> it out.

Lordy -- well, a period would have something to do with
3^7/5^5. Maybe 6250:2187.

A generator would be 3^3/5^2 or 27:25.

Graham