Some unnamed 7-limit temperaments

Hi there,

I was experimenting with Graham's updated scripts for listing temperaments and I found quite a lot of interesting 3D 7-limit temperaments that way. I'm thinking of the question whether some of the unnamed ones could be "significant enough to deserve a name".

The list describes them in terms of complexity, "adjusted error in cents", and constituent ETs. I'll let you see what I've got:

7-prime limit

complexity error (cents)
Marvel 0.097 1.348 19 & 31 & 41
breed 0.160 0.076 27 & 31 & 41
Starling 0.099 2.358 27 & 31 & 19
Gamelan 0.159 0.899 46 & 31 & 41
Ragismic 0.179 0.038 27 & 19 & 53
31 & 46 & 53 0.173 0.528 46 & 31 & 53
19 & 27 & 41 0.121 1.995 27 & 41 & 19
Hemifamity 0.173 0.566 46 & 41 & 53
19 & 31 & 99 0.172 0.600 99 & 31 & 19
Orwellian 0.141 1.580 27 & 31 & 53
19 & 41 & 99 0.181 0.607 99 & 41 & 19
27 & 41 & 53 0.146 1.569 27 & 41 & 53
19 & 53 & 58 0.200 0.622 58 & 19 & 53
19 & 53 & 68 0.207 0.665 68 & 19 & 53
31 & 41 & 80 0.212 0.561 80 & 31 & 41
5 & 19 & 31 0.095 3.847 5 & 31 & 19
Landscape 0.233 0.024 27 & 72 & 12
41 & 53 & 77 0.239 0.139 77 & 41 & 53
15 & 19 & 41 0.123 3.014 15 & 41 & 19
12 & 46 & 72 0.229 0.595 46 & 72 & 12
12 & 22 & 72 0.194 1.348 22 & 72 & 12
19 & 41 & 84 0.194 1.348 84 & 41 & 19
41 & 50 & 53 0.194 1.348 50 & 41 & 53
31 & 53 & 60 0.194 1.348 60 & 31 & 53
19 & 31 & 94 0.194 1.348 94 & 31 & 19
10 & 19 & 53 0.194 1.348 10 & 19 & 53
31 & 34 & 41 0.194 1.348 34 & 31 & 41
31 & 53 & 87 0.242 0.165 87 & 31 & 53
12 & 22 & 46 0.164 2.030 22 & 12 & 46
22 & 27 & 72 0.247 0.077 22 & 72 & 27

Petr

--- In tuning@yahoogroups.com, Petr Paøízek <p.parizek@...> wrote:

> The list describes them in terms of complexity, "adjusted error in cents",
> and constituent ETs. I'll let you see what I've got:

Some of these I've proposed names for, and floated the suggestions on the tuning-math list, but for the ones I've never composed in that may not be much of a claim if you have a better idea. It should be noted that simply giving the comma provides a practical naming system. The same cannot be said for three val names, which I don't think should be taken as any kind of standard.

> 31 & 46 & 53 0.173 0.528 46 & 31 & 53

6144/6125, "hewuermity"

> 19 & 27 & 41 0.121 1.995 27 & 41 & 19

245/243, "octarod"

3136/3125 "parahemwuer"

> 19 & 41 & 99 0.181 0.607 99 & 41 & 19

10976/10935, "parahemfi"

> 27 & 41 & 53 0.146 1.569 27 & 41 & 53

4000/3969, "octagari"

> 19 & 53 & 58 0.200 0.622 58 & 19 & 53

19683/19600, "cataharry"

> 19 & 53 & 68 0.207 0.665 68 & 19 & 53

15625/15552, hanson+7

> 31 & 41 & 80 0.212 0.561 80 & 31 & 41

16875/16807, "mirkwai"

> 5 & 19 & 31 0.095 3.847 5 & 31 & 19

81/80, meantone+7

> 41 & 53 & 77 0.239 0.139 77 & 41 & 53

32805/32768, schismatic+7

> 15 & 19 & 41 0.123 3.014 15 & 41 & 19

875/864, "supermagic"

> 12 & 46 & 72 0.229 0.595 46 & 72 & 12

320000/321489, no known name

> 12 & 22 & 72 0.194 1.348 22 & 72 & 12

225/224, "contorted" marvel, discard

> 19 & 41 & 84 0.194 1.348 84 & 41 & 19

225/224, contorted marvel, discard

> 41 & 50 & 53 0.194 1.348 50 & 41 & 53

225/224, contorted marvel, discard

> 31 & 53 & 60 0.194 1.348 60 & 31 & 53

225/224, contorted marvel, discard

> 19 & 31 & 94 0.194 1.348 94 & 31 & 19

225/224, contorted marvel, discard

I'm getting tired of this so I think I'll quit. Besides, who can tell without close examination what Graham means by "34"?

Hi Gene.

Thanks for such a lot of work, that's exactly the kind of thing I was thinking about.

I've now found your list of commas, which gives me a much better idea on how I might go on with the remaining temperaments from "my" list. Trying to preserve the system, then "31&53&87" would be "tertiapent", "12&22&46" is diaschismatic with 7 added, and "22&27&72" is "ennprod" -- although I'm not sure where things like "tertiadec" and "tertiapent" come from.

You wrote:

> 6144/6125 hewuermity

Origin? -- I wanted to suggest "norwell"; anyway, you've probably found the temperament much sooner than me, so .. Maybe I should let it go. :-D

Petr

I wrote:

> although I'm not sure where things like "tertiadec" and "tertiapent" come > from.

Except that it's actually "tertiapont" ... Well, I'll have to be more careful when reading unfamiliar words next time.

Petr

--- In tuning@yahoogroups.com, Petr Pa��zek <p.parizek@...> wrote:
>
> sure where things like "tertiadec" and "tertiapent" come from.

The naming system, which I am not particularly in love with, involves combining two rank two temperaments which share the given comma. Tertiaseptal (140&171) and enneadecal (152&171) can meld names so as to form tertiaendec or tertiadec. Tertiaseptal and pontiac (118&171) can meld into tertiapont.

> You wrote:
>
> > 6144/6125 hewuermity
>
> Origin? -- I wanted to suggest "norwell"; anyway, you've probably found the
> temperament much sooner than me, so .. Maybe I should let it go. :-D

It comes from hemiwuerschmidt and amity. Orwell and amity instead would certainly make sense, and probably a better name. Where did you get "norwell" from?

Gene wrote:

> It comes from hemiwuerschmidt and amity. Orwell and amity instead would > certainly make sense, and probably > a better name. Where did you get > "norwell" from?

I'm not good at combining 2D temperaments into a 3D one. When I first found the interval of 6144/6125, what I knew was that it was the distance comparing two 35/32 seconds to a 6/5 minor third. At that time, I wasn't thinking of amity at all because its high complexity made me almost forget about it (13 generators for a single triad, compared to 10 generators in orwell). Since the 6144/6125 seemed to me to be one of the characteristic properties of orwell, I first called the 3D version "anti-orwell" to distinguish it from the 2D version. Later, as I thought that name was too long, I changed it to "non-orwell", which later became "norwell".

Anyway, a question now remains if my idea of picking particularly orwell as "a familiar temperament with a characteristic unison vector of 6144/6125" couldn't be possibly replaced by something else, provided there would be a more familiar or less complex 2D tuning which also tempers it out.

Another possibility might be something like "ormity" (if I stick to the idea of combining two 2D tunings) but there's still "too little of orwell" there for me.

Petr

On 6 May 2010 23:13, genewardsmith <genewardsmith@...> wrote:

> Some of these I've proposed names for, and floated the suggestions on the tuning-math list, but for the ones I've never composed in that may not be much of a claim if you have a better idea. It should be noted that simply giving the comma provides a practical naming system. The same cannot be said for three val names, which I don't think should be taken as any kind of standard.
<snip>

I'll look at these next week.

I could integrate Manuel's list of interval names, but not now.

> I'm getting tired of this so I think I'll quit. Besides, who can tell without close examination what Graham means by "34"?

On the right hand side, hover over the link and you'll see the mapping
in the status bar. Or click the link.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> > I'm getting tired of this so I think I'll quit. Besides, who
> > can tell without close examination what Graham means by "34"?
>
> On the right hand side, hover over the link and you'll see the
> mapping in the status bar. Or click the link.

Where?

-Carl

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:

> I'm not good at combining 2D temperaments into a 3D one. When I first found
> the interval of 6144/6125, what I knew was that it was the distance
> comparing two 35/32 seconds to a 6/5 minor third. At that time, I wasn't
> thinking of amity at all because its high complexity made me almost forget
> about it (13 generators for a single triad, compared to 10 generators in
> orwell).

I'm afraid my naming system favored complex rank two temperaments because I wanted the optimal tunings to be reasonably close and have the comma in question be highly characteristic of the temperament. But having better-known temperaments as sources for the name is a strong argument for changing this to porcupine and orwell, in which case you would call it porwell, not so different from norwell.

> But having better-known temperaments as sources for the name is a strong > argument
> for changing this to porcupine and orwell, in which case you would call it > porwell, not so different from norwell.

Sure, and even better than that. :-) ... I'll probably put it into my temperament notes, it sounds nice.

Petr

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> > But having better-known temperaments as sources for the name is a strong
> > argument
> > for changing this to porcupine and orwell, in which case you would call it
> > porwell, not so different from norwell.
>
> Sure, and even better than that. :-) ... I'll probably put it into my
> temperament notes, it sounds nice.

Porwell it is, then, I guess. What about 245/243? Magic and sensi together might give sensamagic. Bohlen-Pierce and magic together might give magebop. Godzilla and rodan together might give monster.

Gene wrote:

> What about 245/243? Magic and sensi together might give sensamagic.
> Bohlen-Pierce and magic together might give magebop. Godzilla and rodan > together might give monster.

At first, I wanted to somehow mention superpyth and BP (since superpyth can easily demonstrate the 245/243 tempering even on a conventional keyboard) but I didn't find a "satisfactory" way to do that. Personally, I've been sometimes referring to superpyth as "spyth", which would allow "bospy" or "spybo". The only problem is that I don't know about anyone else abbreviating superpyth, so the question is what might be some alternatives -- maybe something like "bosup" could do it.

Then, if I'm right that semaphore is the "double-meantone" which maps 7/4 to [3, -1], another possibility may be "bosem", which could serve both for "BP & semaphore" and "BP & semisixths".
Or, if we want to stress that "sensi" and "semisixths" are the same, then it could be "sebo".

Another characteristic temperament is octacot, which would make it "boct" or "octabo".

As to monster, I thought there already was another temperament called monster.

Petr

I wrote:

> Then, if I'm right that semaphore is the "double-meantone" which maps 7/4 > to
> [3, -1]

I meant 7/1, of course.

Petr

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:

> At first, I wanted to somehow mention superpyth and BP (since superpyth can
> easily demonstrate the 245/243 tempering even on a conventional keyboard)
> but I didn't find a "satisfactory" way to do that.

What about "supermage"? It's kind of neat in a gameboy sort of way.

Gene wrote:

> What about "supermage"? It's kind of neat in a gameboy sort of way.

That would probably call for renaming supermagic, which I was not intending to do.
The fact is that the two 3D temperaments seem to have little in common and that I find supermagic like a 3D version of keemun while the 245/243 temperament is essentially something very different because the "prime of equivalence" is not even contained in the comma (I mean, assuming the approximants are 3, 5 and 7).

Petr

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> Gene wrote:
>
> > What about "supermage"? It's kind of neat in a gameboy sort of way.
>
> That would probably call for renaming supermagic, which I was not intending
> to do.

I don't think I have supermagic on any of my lists. Which is it?

Gene wrote:

> I don't think I have supermagic on any of my lists. Which is it?

You probably do since you've yourself referred to it in your first reply to me three days ago. It's the one where 875/864 vanishes -- that's why I was calling it 3D keemun.

Petr

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> Gene wrote:
>
> > I don't think I have supermagic on any of my lists. Which is it?
>
> You probably do since you've yourself referred to it in your first reply to
> me three days ago. It's the one where 875/864 vanishes -- that's why I was
> calling it 3D keemun.

Ah. I still like magebop for the 245/243 temperament, even though I obviously can't remember these names myself. It has both magic and Bohlen-Pierce in it.

Gene wrote:

> Ah. I still like magebop for the 245/243 temperament, even though
> I obviously can't remember these names myself. It has both magic and > Bohlen-Pierce in it.

Hmmm, ... I'm still not sure; it looks like we would never agree on this. 7-limit magic is significantly more complex than 5-limit magic and therefore it's not very obvious (for someone like me) that a temperament like that may exploit the 245/243 tempering for such and such reasons.
If I should make a 3D temperament by combining a 2D one with, let's say, miracle, I would probably have no problem with that since 5-limit and 7-limit miracle are essentially equally complex. But in this case, it's more than twice as many generators needed to approximate a single 4:6:7:8 compared to 4:5:6:8. This makes me think, similarly to meantone, that magic is "primarily" a 5-limit temperament and that the 7s are simply "something extra" which happens to be close enough to be applicable.

Petr

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
This makes me think, similarly to meantone, that magic
> is "primarily" a 5-limit temperament and that the 7s are simply "something
> extra" which happens to be close enough to be applicable.

Hmmm...I wonder how Graham thinks of it? I think of magic as primarily an 11-limit temperament, actually, tempering out 100/99, 225/224, and 245/243.

On 10 May 2010 10:59, genewardsmith <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>  This makes me think, similarly to meantone, that magic
>> is "primarily" a 5-limit temperament and that the 7s are simply "something
>> extra" which happens to be close enough to be applicable.
>
> Hmmm...I wonder how Graham thinks of it? I think of magic as primarily an 11-limit temperament, actually, tempering out 100/99, 225/224, and 245/243.

I think of magic as primarily a 9-limit temperament with both 11 and
13 tagged on as "something extra". The second simplest interval is
9:7.* It's a standout 9-limit temperament, best in its field, with
the possible exception of meantone. It doesn't stand out in the
11-limit, but it makes the list. Also the 2.3.5.7.13-limit.

By Petr's logic, isn't meantone primarily a twisting of Pythagorean
intonation? The 5-limit's four times as complex as the 3-limit, after
all.

* This is not counting 1:1. If you really want to, you can say 1:1 is
the simplest interval, being no generators, and 9:7 is third.

Graham

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:

> Hmmm, ... I'm still not sure; it looks like we would never agree on this.
> 7-limit magic is significantly more complex than 5-limit magic and therefore
> it's not very obvious (for someone like me) that a temperament like that may
> exploit the 245/243 tempering for such and such reasons.

Here's a thought: 245/243 tells us that two 9/7s make up a 5/3. Hence, the temperaments which most exploit this and for which the comma is most characteristic are the ones where 9/7 has a low complexity. And this means sensi (complexity 1) and magic (complexity 2). So my proposal "sensamagic" is the way to go by this reasoning, which strikes me as pretty strong.

By way of comparison, we have godzilla (complexity 3), superpyth (complexity 4), octacot (complexity 5), shrutar (complexity 6) and rodan (complexity 7).

On 10 May 2010 13:43, genewardsmith <genewardsmith@...> wrote:

> Here's a thought: 245/243 tells us that two 9/7s make up a 5/3.
> Hence, the temperaments which most exploit this and for which
> the comma is most characteristic are the ones where 9/7 has a
> low complexity. And this means sensi (complexity 1) and magic
> (complexity 2). So my proposal "sensamagic" is the way to go
> by this reasoning, which strikes me as pretty strong.

I have a way of searching by unison vectors you know. Go to
http://x31eq.com/temper/uv.html and stick your comma in the box.
Press the button and you get an objective ordering of temperaments
that remove it. Objective for those of you pressing the button,
anyway. I get to choose one subjective parameter, whose value happens
to be 2. What it gives in this case is: magic, sensisept, semaphore,
superpyth, octacot, ...

> By way of comparison, we have godzilla (complexity 3),
> superpyth (complexity 4), octacot (complexity 5),
> shrutar (complexity 6) and rodan (complexity 7).

I don't have godzilla. Put that on the list with anything else you
decide on in this thread.

Graham

Graham wrote:

> By Petr's logic, isn't meantone primarily a twisting of
> Pythagorean intonation? The 5-limit's four times as complex as the > 3-limit,
> after all.

I don't think so since Pythagorean has dissonant thirds and the promoters of meantone were aiming for consonant thirds. I view most 2D temperaments as some sort of reduction of a 3D system. If I decide to temper out 81/80 within the 1:2:3:5 system, that means I'm giving a different meaning to thirds and sixths than they have in Pythagorean.
It's similar as if I tempered out 64/63 within the 1:2:3:7 system. This way, I'm also giving a totally different meaning to thirds and sixths than they have in Pythagorean. And if I want to stress the fact that I've got this from a "fiveless" system, I probably won't use the 5-limit approximations that superpyth offers.
... Now I'm realizing how terribly difficult it is to describe my way of treating 2D temperaments.

Petr

Gene wrote:

> Here's a thought: 245/243 tells us that two 9/7s make up a 5/3.

Agreed.

> Hence, the temperaments which most exploit this and for which the comma is > most characteristic
> are the ones where 9/7 has a low complexity.

Agreed.

> And this means sensi (complexity 1) and magic (complexity 2). So my > proposal "sensamagic"
> is the way to go by this reasoning, which strikes me as pretty strong.

To be honest, I was thinking similarly a few hours ago when I was coming home from school today. I knew about semisixths for a long time but only today I realized the new fact about magic -- i.e. after viewing semisixths as "semitenths" and learning that magic is essentially semisixths split into halves.

Well, I'll think about it for another while yet ... I'm still not decided.

Petr