5-limit comma names

Since the monzisma (450359962737049600/450283905890997363) is named and appears on Manuel's list, there is a prima facie case for naming at least the significant 5-limit commas of lesser height which don't yet have names. Here's a proposal:

16875/16384 "Negrisma"

The comma of Negri's temperament.

78732/78125 "hemisixths comma"

1600000/1594323, "amitisma"

Or "amt comma", but because of the complaints about amt I'm wondering
if we could call it "amity" instead.

2109375/2097152 "Georgema"

After George Orwell (sorry, George. :))

4294967296/4271484375 "septathirds comma"

1224440064/1220703125 "parakleisma"

6115295232/6103515625 "semisuper comma"

19073486328125/19042491875328 "enneadecima"

Manuel called this the "19-tone comma", but that sounds like it should be3^19/2^30. If the temperament is enneadecimal, this seems like a good name for the comma ((5/3)^19 2^(-14))

274877906944/274658203125 "hemithirds comma",

50031545098999707/50000000000000000 "heptidecatonma"

This comma is 6 (9/10)^17; I propose "minortone" for the corresponding temperament, with generator almost exactly 10/9.

9010162353515625/9007199254740992 "quasiseptima"

I propose "quasiseptimal" for the corresponding temperament, since it's generator is an excellent approximation to 9/7.

--- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:

> 19073486328125/19042491875328 "enneadecima"
>
> Manuel called this the "19-tone comma", but that sounds like it
>should be3^19/2^30.

from one point of view, the most notable feature of 19-tone are its
pure minor thirds, so constructing a chain of 19 6:5s comes to mind
rather readily.

--- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:
> --- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
>
> > 19073486328125/19042491875328 "enneadecima"
> >
> > Manuel called this the "19-tone comma", but that sounds like it
> >should be3^19/2^30.
>
> from one point of view, the most notable feature of 19-tone are its
> pure minor thirds, so constructing a chain of 19 6:5s comes to mind
> rather readily.

I was thinking of the context of his list, where we also have the
41-tone comma and Mercator's comma.

--- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> --- In tuning-math@y..., "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> > --- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...>
wrote:
> >
> > > 19073486328125/19042491875328 "enneadecima"
> > >
> > > Manuel called this the "19-tone comma", but that sounds like it
> > >should be3^19/2^30.
> >
> > from one point of view, the most notable feature of 19-tone are
its
> > pure minor thirds, so constructing a chain of 19 6:5s comes to
mind
> > rather readily.
>
> I was thinking of the context of his list, where we also have the
> 41-tone comma

isn't the most notable feature of 41-tone its pure perfect fifth?

> and Mercator's comma.

same for 53-tone, of course.

--- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:

> isn't the most notable feature of 41-tone its pure perfect fifth?
>
> > and Mercator's comma.
>
> same for 53-tone, of course.

We could say the term "n-tone comma" is reserved for the case where
m/n is a convergent to the log base two of a consonant interval. The comma you were asking about, (7/6)^9 / 4, would then be the "9-tone comma". This does not disambiguate the term completely, but it's probably good enough.

Other commas would be:

11-tone comma (7/9)^11 * 16
26-tone comma (8/7)^26 / 32
28-tone comma (5/4)^28 * 2^(-9)
33-tone comma (7/5)^33 * 2^(-16)
35-tone comma (5/7)^35 * 2^17
59-tone comma (4/5)^59 * 2^19
68-tone comma (7/5)^68 * 2^(-33)
80-tone comma (9/7)^80 * 2^(-29)
171-tone comma (7/9)^171 * 2^62

--- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> --- In tuning-math@y..., "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
>
> > isn't the most notable feature of 41-tone its pure perfect fifth?
> >
> > > and Mercator's comma.
> >
> > same for 53-tone, of course.
>
> We could say the term "n-tone comma" is reserved for the case where
> m/n is a convergent to the log base two of a consonant interval.

is there no n for which this would be ambiguous?

--- In tuning-math@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:

> is there no n for which this would be ambiguous?

Certainly there are--80 is a convergent for 9/7 and 11/10, for instance. If you go out far enough any n will be ambiguous.

--- In tuning-math@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:

> 2109375/2097152 "Georgema"
>
> After George Orwell (sorry, George. :))

Somehow I missed the fact that this already has two different names on the Fokker list, one being Fokker's comma (the other is semicomma.)