For people who love 5-limit JI: what are the most important "accidentals?"

For 5-limit JI lovers: if you had to list the most important commas
that turn up as "accidentals" in a tuning system, what would they be?
I'm not talking about commas that you temper out, but commas that
you're deliberately using as "chromas."

Some obvious suggestions:
1) 25/24
2) 81/80
3) 128/125
4) 648/625
5) 250/243
6) 27/25
7) 135/128
8) 2048/2025

This is for a hypothetical notation system. What are the commas and
accidentals that are really important to be able to notate simply?

Keep in mind that this doesn't assume anything about the underlying
scale that we're using for nominals, so don't assume it's the 5-limit
major scale or the Pythagorean major scale or anything like that. I'm
just trying to find the "most important 5-limit chromas" in general,
as a starting point, which would hypothetically turn up regardless of
what 5-limit scale you're playing, even if you're playing in a
tempered scale or something.

-Mike

I'm certainly not the most mathematically adventurous person on here, but with whatever 5-limit music I end up playing with, the overwhelmingly important comma is 25/24. To me, 5-limit really is about playing with 5/4 and 6/5. 81/80 can be important if I want to make like I'm modulating, but that only really applies if it's the kind of modulation where I change key center while retaining most or all of the intervallic relationships between the pitches of whatever scale and the old versus new key centers. This doesn't necessarily happen. But those thirds always happen.

Andrew

--- In tuning@yahoogroups.com, "bigAndrewM" <bigandrewm@...> wrote:
>
> I'm certainly not the most mathematically adventurous person on here, but with whatever 5-limit music I end up playing with, the overwhelmingly important comma is 25/24. To me, 5-limit really is about playing with 5/4 and 6/5. 81/80 can be important if I want to make like I'm modulating, but that only really applies if it's the kind of modulation where I change key center while retaining most or all of the intervallic relationships between the pitches of whatever scale and the old versus new key centers. This doesn't necessarily happen. But those thirds always happen.
>
> Andrew
>

I wonder how you could even have "5-limit" music with 25:24 tempered out? It's odd to see it listed as a "comma", rather than as a chromatic semitone.

Am 22.03.2012 07:21, schrieb lobawad:
>
>
> --- In tuning@yahoogroups.com, "bigAndrewM" <bigandrewm@...> wrote:
>>
>> I'm certainly not the most mathematically adventurous person on here, but with whatever 5-limit music I end up playing with, the overwhelmingly important comma is 25/24. To me, 5-limit really is about playing with 5/4 and 6/5. 81/80 can be important if I want to make like I'm modulating, but that only really applies if it's the kind of modulation where I change key center while retaining most or all of the intervallic relationships between the pitches of whatever scale and the old versus new key centers. This doesn't necessarily happen. But those thirds always happen.
>>
>> Andrew
>>
>
> I wonder how you could even have "5-limit" music with 25:24 tempered out? It's odd to see it listed as a "comma", rather than as a chromatic semitone.
>
I think using the word "comma" was just a mistake - what Andrew really
wanted to point out, that 81/80 is not important for his music.

Wolf

--- In tuning@yahoogroups.com, Wolf Peuker <wolfpeuker@...> wrote:
>
> Am 22.03.2012 07:21, schrieb lobawad:
> >
> >
> > --- In tuning@yahoogroups.com, "bigAndrewM" <bigandrewm@> wrote:
> >>
> >> I'm certainly not the most mathematically adventurous person on here, but with whatever 5-limit music I end up playing with, the overwhelmingly important comma is 25/24. To me, 5-limit really is about playing with 5/4 and 6/5. 81/80 can be important if I want to make like I'm modulating, but that only really applies if it's the kind of modulation where I change key center while retaining most or all of the intervallic relationships between the pitches of whatever scale and the old versus new key centers. This doesn't necessarily happen. But those thirds always happen.
> >>
> >> Andrew
> >>
> >
> > I wonder how you could even have "5-limit" music with 25:24 tempered out? It's odd to see it listed as a "comma", rather than as a chromatic semitone.
> >
> I think using the word "comma" was just a mistake - what Andrew really
> wanted to point out, that 81/80 is not important for his music.
>
> Wolf
>

Mike introduced it as comma, that is what I was referring to.

I do not think that I understand what Big Andrew is saying, for surely we do not need to modulate in 5-limit to raise the question of 81:80.

Hi lobawad,

Am 22.03.2012 10:17, schrieb lobawad:
>>> I wonder how you could even have "5-limit" music with 25:24 tempered out? It's odd to see it listed as a "comma", rather than as a chromatic semitone.
>>>
>> I think using the word "comma" was just a mistake - what Andrew really
>> wanted to point out, that 81/80 is not important for his music.
>>
>> Wolf
>>
>
> Mike introduced it as comma, that is what I was referring to.
Ok, I see.
>
> I do not think that I understand what Big Andrew is saying, for surely we do not need to modulate in 5-limit to raise the question of 81:80.
Here I was not precise enough: I got that Big Andrew was using 25/24 as
an interval in contrast to 81/80 (which is clearly not very surprising).

Best regards,
Wolf

--- In tuning@yahoogroups.com, Wolf Peuker <wolfpeuker@...> wrote:
>
> Hi lobawad,
>
> Am 22.03.2012 10:17, schrieb lobawad:
> >>> I wonder how you could even have "5-limit" music with 25:24 tempered out? It's odd to see it listed as a "comma", rather than as a chromatic semitone.
> >>>
> >> I think using the word "comma" was just a mistake - what Andrew really
> >> wanted to point out, that 81/80 is not important for his music.
> >>
> >> Wolf
> >>
> >
> > Mike introduced it as comma, that is what I was referring to.
> Ok, I see.
> >
> > I do not think that I understand what Big Andrew is saying, for surely we do not need to modulate in 5-limit to raise the question of 81:80.
> Here I was not precise enough: I got that Big Andrew was using 25/24 as
> an interval in contrast to 81/80 (which is clearly not very surprising).
>
> Best regards,
> Wolf
>

I see, yes that makes sense.

Yes, modulation isn't required to end up using 81/80. And I do end up using it often. I just use 25/24 more often.

Andrew

--- In tuning@yahoogroups.com, Wolf Peuker <wolfpeuker@...> wrote:
>
> Hi lobawad,
>
> Am 22.03.2012 10:17, schrieb lobawad:
> >>> I wonder how you could even have "5-limit" music with 25:24 tempered out? It's odd to see it listed as a "comma", rather than as a chromatic semitone.
> >>>
> >> I think using the word "comma" was just a mistake - what Andrew really
> >> wanted to point out, that 81/80 is not important for his music.
> >>
> >> Wolf
> >>
> >
> > Mike introduced it as comma, that is what I was referring to.
> Ok, I see.
> >
> > I do not think that I understand what Big Andrew is saying, for surely we do not need to modulate in 5-limit to raise the question of 81:80.
> Here I was not precise enough: I got that Big Andrew was using 25/24 as
> an interval in contrast to 81/80 (which is clearly not very surprising).
>
> Best regards,
> Wolf
>

Hi all,
a closer look into the world after 81/80 might be worth it. There are
some larger intervals (i.e. 27/25) - I added sizes (in cents).

--Wolf

Am 21.03.2012 16:50, schrieb Mike Battaglia:
> For 5-limit JI lovers: if you had to list the most important commas
> that turn up as "accidentals" in a tuning system, what would they be?
> I'm not talking about commas that you temper out, but commas that
> you're deliberately using as "chromas."
>
> Some obvious suggestions:
> 1) 25/24
70.7 cents

> 2) 81/80
21.5 cents

> 3) 128/125
41.1 cents

> 4) 648/625
62.6 cents

> 5) 250/243
49.2 cents

> 6) 27/25
133.2 cents

> 7) 135/128
92.2 cents

> 8) 2048/2025
19.6 cents