Re: Earth Tones: The Schumann Resonance Tuning

Hello, there, Jacky Ligon, and thank you for your "Earth resonance"
tuning.

Whatever view one might take about the role of integer rounding and
the like in producing the ratios you describe, a first-blush reaction
for me was that very close approximations of some of these intervals
may be found in 29-tET (or 29-EDO as the Monz would say, if I have it
right), one of my favorite neo-Gothic tunings.

For example, 33:26 and 13:11 are within a cent or so of the regular
major and minor third, while the 41-cent step you mention is very
close to the 29-tET diesis or fifthtone, half of a usual diatonic
semitone in a neo-Gothic style. Likewise the 13:10 and 15:13 -- or
here 11/29 octave and 6/29 octave -- are favorite 29-tET cadential
intervals respectively expanding to a fifth or contracting to a
unison.

As for a 3:2 fifth, here 29-tET is only about 1.49 cents wide.

Of course, your scale based on precise integer ratios has its own
character: I was just pleasantly amused to see some of the ratios
whose close approximations I'm accustomed to in 24-out-of-29-tET.

Most appreciatively,

Margo Schulter
mschulter@value.net

--- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:
> Hello, there, Jacky Ligon, and thank you for your "Earth resonance"
> tuning.
>
> Whatever view one might take about the role of integer rounding and
> the like in producing the ratios you describe, a first-blush
reaction
> for me was that very close approximations of some of these intervals
> may be found in 29-tET (or 29-EDO as the Monz would say, if I have
it
> right), one of my favorite neo-Gothic tunings.
>
> For example, 33:26 and 13:11 are within a cent or so of the regular
> major and minor third, while the 41-cent step you mention is very
> close to the 29-tET diesis or fifthtone, half of a usual diatonic
> semitone in a neo-Gothic style. Likewise the 13:10 and 15:13 -- or
> here 11/29 octave and 6/29 octave -- are favorite 29-tET cadential
> intervals respectively expanding to a fifth or contracting to a
> unison.
>
> As for a 3:2 fifth, here 29-tET is only about 1.49 cents wide.
>
> Of course, your scale based on precise integer ratios has its own
> character: I was just pleasantly amused to see some of the ratios
> whose close approximations I'm accustomed to in 24-out-of-29-tET.

Margo,

Hello! Been missing you!!!

Thanks so much for pointing this out. I took a look at my n-tET
spreadsheet, and there are indeed similarities. This is why I love to
share here - other perspectives and valuable insights are revealed
that I'm sure would never occur to me. With all the beautiful spirits
circumambulating around the topic, like planets in orbit around
tuning theory, our different views of the facets always enrich and
bless me from my participation.

What would I do without all you gentlefolk?

In Infinite Gratitude,

Jacky Ligon

--- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:
> Hello, there, Jacky Ligon, and thank you for your "Earth resonance"
> tuning.
>
> Whatever view one might take about the role of integer rounding and
> the like in producing the ratios you describe, a first-blush
reaction
> for me was that very close approximations of some of these intervals
> may be found in 29-tET (or 29-EDO as the Monz would say, if I have
it
> right), one of my favorite neo-Gothic tunings.
>
> For example, 33:26 and 13:11 are within a cent or so of the regular
> major and minor third, while the 41-cent step you mention is very
> close to the 29-tET diesis or fifthtone, half of a usual diatonic
> semitone in a neo-Gothic style. Likewise the 13:10 and 15:13 -- or
> here 11/29 octave and 6/29 octave -- are favorite 29-tET cadential
> intervals respectively expanding to a fifth or contracting to a
> unison.
>
> As for a 3:2 fifth, here 29-tET is only about 1.49 cents wide.
>
> Of course, your scale based on precise integer ratios has its own
> character: I was just pleasantly amused to see some of the ratios
> whose close approximations I'm accustomed to in 24-out-of-29-tET.

Margo,

Hello! Been missing you!!!

Thanks so much for pointing this out. I took a look at my n-tET
spreadsheet, and there are indeed similarities. This is why I love to
share here - other perspectives and valuable insights are revealed
that I'm sure would never occur to me. With all the beautiful spirits
circumambulating around the topic, like planets in orbit around
tuning theory, our different views of the facets always enrich and
bless me from my participation.

What would I do without all you gentlefolk?

In Infinite Gratitude,

Jacky Ligon

--- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:
> Hello, there, Jacky Ligon, and thank you for your "Earth resonance"
> tuning.
>
> Whatever view one might take about the role of integer rounding and
> the like in producing the ratios you describe, a first-blush
reaction
> for me was that very close approximations of some of these intervals
> may be found in 29-tET (or 29-EDO as the Monz would say, if I have
it
> right), one of my favorite neo-Gothic tunings.
>
> For example, 33:26 and 13:11 are within a cent or so of the regular
> major and minor third, while the 41-cent step you mention is very
> close to the 29-tET diesis or fifthtone, half of a usual diatonic
> semitone in a neo-Gothic style. Likewise the 13:10 and 15:13 -- or
> here 11/29 octave and 6/29 octave -- are favorite 29-tET cadential
> intervals respectively expanding to a fifth or contracting to a
> unison.
>
> As for a 3:2 fifth, here 29-tET is only about 1.49 cents wide.
>
> Of course, your scale based on precise integer ratios has its own
> character: I was just pleasantly amused to see some of the ratios
> whose close approximations I'm accustomed to in 24-out-of-29-tET.

Margo,

Hello! Been missing you!!!

Thanks so much for pointing this out. I took a look at my n-tET
spreadsheet, and there are indeed similarities. This is why I love to
share here - other perspectives and valuable insights are revealed
that I'm sure would never occur to me. With all the beautiful spirits
circumambulating around the topic, like planets in orbit around
tuning theory, our different views of the facets always enrich and
bless me from my participation.

What would I do without all you gentlefolk?

In Infinite Gratitude,

Jacky Ligon

--- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:
> Hello, there, Jacky Ligon, and thank you for your "Earth resonance"
> tuning.
>
> Whatever view one might take about the role of integer rounding and
> the like in producing the ratios you describe, a first-blush reaction
> for me was that very close approximations of some of these intervals
> may be found in 29-tET (or 29-EDO as the Monz would say, if I have it
> right), one of my favorite neo-Gothic tunings.
>
> For example, 33:26 and 13:11 are within a cent or so of the regular
> major and minor third, while the 41-cent step you mention is very
> close to the 29-tET diesis or fifthtone, half of a usual diatonic
> semitone in a neo-Gothic style. Likewise the 13:10 and 15:13 -- or
> here 11/29 octave and 6/29 octave -- are favorite 29-tET cadential
> intervals respectively expanding to a fifth or contracting to a
> unison.
>
> As for a 3:2 fifth, here 29-tET is only about 1.49 cents wide.
>
> Of course, your scale based on precise integer ratios has its own
> character: I was just pleasantly amused to see some of the ratios
> whose close approximations I'm accustomed to in 24-out-of-29-tET.
>
> Most appreciatively,
>
> Margo Schulter
> mschulter@v...

It's not a coincidence; 29-tET is the simplest ET consistent through the 13-limit.

I wrote:
>
> It's not a coincidence; 29-tET is the simplest ET consistent through the 13-limit.

Sorry . . . 26-tET is also consistent through the 13-limit -- but 29-tET is the simplest ET
consistent through the 15-limit.