Reply to Joseph Pehrson (from MakeMicroMusic)

>> 12 harmonics (on C, they're C C G C Ev G Bb< C D E F#< G, a hexad)
>
>> Within this chord, we can find 29 intervals per octave.
>
>> They are all shown, with their ratios, compared with 72-equal,
>here:
>
>> http://www.72note.com/erlich/intervalliccontinuum.html
>
>> The color shows "octave-equivalent harmonic entropy", colored
>> according to George Secor's system.

>***Hi Paul,

>Of course, I know this chart well; it's on my wall! :)

>I'd forgotten, though, that there were 29 intervals per octave. And
>how do you get a "hexad??" That would be six pitches, yes??

>Thanks!

>JP

Yup -- there are only six different note-names among those 12
harmonics. Thus, in the usual octave-equivalent way of thinking about
things, it's a 'hexad'. In fact, it's Partch's "otonal hexad" built
on C.

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

/tuning/topicId_53252.html#53252

> >> 12 harmonics (on C, they're C C G C Ev G Bb< C D E F#< G, a
hexad)
> >
> >> Within this chord, we can find 29 intervals per octave.
> >
> >> They are all shown, with their ratios, compared with 72-equal,
> >here:
> >
> >> http://www.72note.com/erlich/intervalliccontinuum.html
> >
> >> The color shows "octave-equivalent harmonic entropy", colored
> >> according to George Secor's system.
>
>
> >***Hi Paul,
>
> >Of course, I know this chart well; it's on my wall! :)
>
> >I'd forgotten, though, that there were 29 intervals per octave. And
> >how do you get a "hexad??" That would be six pitches, yes??
>
> >Thanks!
>
> >JP
>
> Yup -- there are only six different note-names among those 12
> harmonics. Thus, in the usual octave-equivalent way of thinking
about
> things, it's a 'hexad'. In fact, it's Partch's "otonal hexad" built
> on C.

***Oh... sure, I see it now... E and Ev are, of course, considered
identical in this system...

JP

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> /tuning/topicId_53252.html#53252
>
> > >> 12 harmonics (on C, they're C C G C Ev G Bb< C D E F#< G, a
> hexad)
> > >
> > >> Within this chord, we can find 29 intervals per octave.
> > >
> > >> They are all shown, with their ratios, compared with 72-equal,
> > >here:
> > >
> > >> http://www.72note.com/erlich/intervalliccontinuum.html
> > >
> > >> The color shows "octave-equivalent harmonic entropy", colored
> > >> according to George Secor's system.
> >
> >
> > >***Hi Paul,
> >
> > >Of course, I know this chart well; it's on my wall! :)
> >
> > >I'd forgotten, though, that there were 29 intervals per octave.
And
> > >how do you get a "hexad??" That would be six pitches, yes??
> >
> > >Thanks!
> >
> > >JP
> >
> > Yup -- there are only six different note-names among those 12
> > harmonics. Thus, in the usual octave-equivalent way of thinking
> about
> > things, it's a 'hexad'. In fact, it's Partch's "otonal hexad"
built
> > on C.
>
>
> ***Oh... sure, I see it now... E and Ev are, of course, considered
> identical in this system...
>
> JP

D'oh! Silly me! They *both* should have been Ev.