So what about cents?

Should cents be depreciated on the grounds that they are pro-twelve? If so, what else should we use? What about, for instance, millioctaves?

I'm not in favor, but other people seem to be.

On Mon, Jun 13, 2011 at 6:41 PM, genewardsmith
<genewardsmith@...> wrote:
>
> Should cents be depreciated on the grounds that they are pro-twelve? If so, what else should we use? What about, for instance, millioctaves?
>
> I'm not in favor, but other people seem to be.

I'm absolutely not in favor of this, and not just because of convention:

1) The point of a "cent" is to function as a fine subdivision
underneath a coarser template.
2) This coarse template should serve the purpose of enabling you to
roughly specify where, in interval space, you want to go, with the
fine subdivision helping you to narrow things down further.
3) 12-equal is a great coarse template, and not just because it's the
existing convention. It's a good coarse template because it's very low
in badness, and hence gets you very close to a lot of just intervals.
4) This leads to a handy encapsulating of information where,
heirarchically speaking, the coarse grid (hundreds-place) is enough to
get you decently close to where you want to go, and the tens-place is
enough to really dial it in, and then the ones-place is there to
perfect the intonation and so on.
5) Through the 17-limit, the simplest intervals are the ones that
conform more and more to the coarse grid, meaning that 700 cents is
almost a perfect 3/2, 400 cents is more out of tune for 5/4, 1000
cents even more for 7/4, 600 cents even more for 11/8, and although
13/8 is marginally better than 11/8 it's still pretty bad.
6) Hence in 12-equal, conformity to the coarse grid is roughly
inversely proportional to complexity, which is likely a very desirable
property if we're treating more complex intervals as less important
than less complex ones.
7) You can imagine what would happen to the above properties if we
were all using 13-equal as a template instead of 12-equal, for
example. None of the above properties would apply, and the coarse grid
would be pretty useless, thus leading to a relatively inefficient
heirarchical encapsulation of information.
8) The use of millioctaves is effectively a vote for 10-equal as a
coarse grid, so I'll let you decide how you feel about how well
10-equal serves this purpose.

The reason that people are advocating millioctaves is, in my opinion,
a mistaken attempt to "get away from the cultural underpinnings of
12-equal." If we're going to really get away from cultural biases
towards it, we should objectively look at it on the basis of how well
and how economically it approximates just intonation.

Now that we're all looking at 13-limit JI and beyond, it may be a
worthwhile goal is to come up with a reference coarse grid that
requires less delving into the fine grid - i.e. use a more accurate
EDO. The zeta integral sequence gives a killer list for these, which
inherently obeys property #6 above, so you might consider 19-equal a
good choice for this. Alternatively, it might also be worthwhile to
take a look at 22-equal. If we relax the restriction on #6 a bit,
15-equal might be a good choice as well for 11-limit JI.

-Mike

> What about, for instance, millioctaves?

Terrible idea. Too biased toward 10-EDO.

Regards,
Jake

Brilliantly put, Mike. This about sums up the issues as well as possible. I'll add that 26-EDO is the lowest EDO consistent in the 13-limit, perhaps that enters it in the running. 31 and 41 are also good contenders, though they lead to a pretty fine "coarse" grid. Of course I agree that cents are probably here to stay, and for all the good reasons you listed.

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, Jun 13, 2011 at 6:41 PM, genewardsmith
> <genewardsmith@...> wrote:
> >
> > Should cents be depreciated on the grounds that they are pro-twelve? If so, what else should we use? What about, for instance, millioctaves?
> >
> > I'm not in favor, but other people seem to be.
>
> I'm absolutely not in favor of this, and not just because of convention:
>
> 1) The point of a "cent" is to function as a fine subdivision
> underneath a coarser template.
> 2) This coarse template should serve the purpose of enabling you to
> roughly specify where, in interval space, you want to go, with the
> fine subdivision helping you to narrow things down further.
> 3) 12-equal is a great coarse template, and not just because it's the
> existing convention. It's a good coarse template because it's very low
> in badness, and hence gets you very close to a lot of just intervals.
> 4) This leads to a handy encapsulating of information where,
> heirarchically speaking, the coarse grid (hundreds-place) is enough to
> get you decently close to where you want to go, and the tens-place is
> enough to really dial it in, and then the ones-place is there to
> perfect the intonation and so on.
> 5) Through the 17-limit, the simplest intervals are the ones that
> conform more and more to the coarse grid, meaning that 700 cents is
> almost a perfect 3/2, 400 cents is more out of tune for 5/4, 1000
> cents even more for 7/4, 600 cents even more for 11/8, and although
> 13/8 is marginally better than 11/8 it's still pretty bad.
> 6) Hence in 12-equal, conformity to the coarse grid is roughly
> inversely proportional to complexity, which is likely a very desirable
> property if we're treating more complex intervals as less important
> than less complex ones.
> 7) You can imagine what would happen to the above properties if we
> were all using 13-equal as a template instead of 12-equal, for
> example. None of the above properties would apply, and the coarse grid
> would be pretty useless, thus leading to a relatively inefficient
> heirarchical encapsulation of information.
> 8) The use of millioctaves is effectively a vote for 10-equal as a
> coarse grid, so I'll let you decide how you feel about how well
> 10-equal serves this purpose.
>
> The reason that people are advocating millioctaves is, in my opinion,
> a mistaken attempt to "get away from the cultural underpinnings of
> 12-equal." If we're going to really get away from cultural biases
> towards it, we should objectively look at it on the basis of how well
> and how economically it approximates just intonation.
>
> Now that we're all looking at 13-limit JI and beyond, it may be a
> worthwhile goal is to come up with a reference coarse grid that
> requires less delving into the fine grid - i.e. use a more accurate
> EDO. The zeta integral sequence gives a killer list for these, which
> inherently obeys property #6 above, so you might consider 19-equal a
> good choice for this. Alternatively, it might also be worthwhile to
> take a look at 22-equal. If we relax the restriction on #6 a bit,
> 15-equal might be a good choice as well for 11-limit JI.
>
> -Mike
>

I couldn't agree more Jake.

The purpose of using measurements biased towards 12-equal is to facilitate the learning curve required to understand microtonal music.

--- In tuning@yahoogroups.com, Jake Freivald <jdfreivald@...> wrote:
>
> > What about, for instance, millioctaves?
>
> Terrible idea. Too biased toward 10-EDO.
>
> Regards,
> Jake
>

Hello Alternate Tuning list,
at last I've managed to join this group :) A big hello in the round!

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> I'm not in favor, but other people seem to be.
>
It was my suggestion to add millioctaves to cents in the xenharmonic wiki. ;)
Millioctaves are log2 values only scaled by 1:1000, that's the advantage. [1]

I would not want to replace cents with millioctaves. But there are cases, in which Cents are not better than millioctaves: for example when evaluating tonal systems in terms of their approximations to pure intervals.

Best regards,
Wolf [2]

[1] Yes, also log2 values may be considered as "somewhat xenophobe" ;)
[2] ps. In the wiki, I contribute as Peu.

On Mon, Jun 13, 2011 at 9:08 PM, cityoftheasleep
<igliashon@...> wrote:
>
> Brilliantly put, Mike. This about sums up the issues as well as possible. I'll add that 26-EDO is the lowest EDO consistent in the 13-limit, perhaps that enters it in the running. 31 and 41 are also good contenders, though they lead to a pretty fine "coarse" grid. Of course I agree that cents are probably here to stay, and for all the good reasons you listed.
>
> -Igs

That's not a bad idea. It's definitely very true that whatever we find
should be an EDO that has low ambiguity, at least one where the val
with the least TOP-RMS error is also the patent val, which is a
slightly relaxed version of the consistency requirement.

26-equal implies relaxing criteria #6, where we want simpler primes to
be more accurate than more complex ones. If we're going to go that
route, then another option that isn't as bad as it looks is 21-equal,
as an equal-tempered version of blackjack, meaning that it might just
destroy all other competitors in terms of being a coarse grid for the
11-limit. (For the record, I firmly believe that miracle is going to
become one of the Best Temperaments Ever, once we work out the
MODMOS's and figure out the generalities of chromatic harmony in it).

A last thing to think about - most existing musicians actually don't
find it very easy to think in cents at all, so there's plenty of time
to indoctrinate them. Yes, they get the idea (once you tell them) that
a cent is 1/100th of a semitone, but quiz the average musician on what
interval class 900 cents is and they'll have to think a second for
sure. Instead, people tend to think more diatonically, with there
being "fourths" and "thirds" and all that, so it might very well,
paradoxically, become more intuitive for the coarse grid to correspond
to something like 7-equal, and just have people make more use of the
fine grid. If this actually did turn out to be more intuitive, then
that would actually be a good reason to use millicents, as 10-EDO is
both miracle and pajara in one.

-Mike

--- In tuning@yahoogroups.com, "wolfpeuker" <wolfpeuker@...> wrote:
>
> Hello Alternate Tuning list,
> at last I've managed to join this group :) A big hello in the round!

Hi! Didn't know there was a problem with joining.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> Hi! Didn't know there was a problem with joining.
>
I was just hard, to make this personal decision. (to register at yahoo)