Re: Magic triples for 72

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
This is a complete list of everything where the first two
> intervals are under 600 cents.

It was supposed to be, anyway. I'd better try again.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> >
> This is a complete list of everything where the first two
> > intervals are under 600 cents.
>
> It was supposed to be, anyway. I'd better try again.

Here's the corrected list, this time only up to the 13-limit; the
three intervals together form an octave if we assume the comma which
follows, or stick to 72-et. Joseph is invited to ponder this list of
chords.

[11/9, 11/9, 4/3] 243/242
[10/9, 16/13, 16/11] 1287/1280
[12/11, 9/8, 18/11] 243/242
[13/12, 13/12, 12/7] 169/168
[13/12, 14/11, 16/11] 364/363
[11/10, 9/8, 13/8] 1287/1280
[11/10, 13/10, 7/5] 1001/1000
[13/12, 13/11, 11/7] 169/168
[13/11, 13/11, 13/9] 2197/2178
[14/13, 6/5, 20/13] 169/168
[7/6, 11/9, 7/5] 540/539
[10/9, 10/9, 13/8] 325/324
[10/9, 5/4, 13/9] 325/324
[9/8, 14/11, 7/5] 441/440
[5/4, 5/4, 9/7] 225/224
[8/7, 11/9, 10/7] 441/440
[6/5, 9/7, 13/10] 351/350
[12/11, 14/11, 13/9] 364/363
[14/13, 14/13, 12/7] 169/168
[16/13, 14/11, 14/11] 1573/1568
[11/10, 7/6, 14/9] 540/539
[12/11, 9/7, 10/7] 540/539
[13/12, 10/9, 5/3] 325/324
[12/11, 13/11, 14/9] 364/363
[14/13, 12/11, 22/13] 169/168
[14/13, 16/13, 3/2] 169/168
[12/11, 8/7, 8/5] 385/384
[13/12, 8/7, 13/8] 169/168
[13/12, 13/10, 10/7] 169/168
[7/6, 16/13, 18/13] 169/168
[14/13, 4/3, 18/13] 169/168
[9/8, 9/7, 18/13] 729/728
[13/11, 14/11, 4/3] 364/363
[10/9, 8/7, 11/7] 441/440
[8/7, 6/5, 16/11] 385/384
[13/12, 9/7, 13/9] 169/168
[14/13, 10/9, 5/3] 351/350
[6/5, 6/5, 18/13] 325/324
[9/8, 5/4, 10/7] 225/224
[14/13, 14/11, 16/11] 1573/1568
[7/6, 13/11, 16/11] 364/363
[9/8, 13/10, 11/8] 1287/1280
[10/9, 7/6, 20/13] 351/350
[7/6, 5/4, 11/8] 385/384

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> Here's the corrected list, this time only up to the 13-limit; the
> three intervals together form an octave if we assume the comma which
> follows, or stick to 72-et. Joseph is invited to ponder this list of
> chords.

Here is the same list, pruned of intervals less than 8/7, and ordered
according to the size of the comma:

[7/6, 16/13, 18/13] 169/168

[5/4, 5/4, 9/7] 225/224

[11/9, 11/9, 4/3] 243/242

[16/13, 14/11, 14/11] 1573/1568

[6/5, 6/5, 18/13] 325/324

[6/5, 9/7, 13/10] 351/350

[13/11, 14/11, 4/3] 364/363

[7/6, 13/11, 16/11] 364/363

[8/7, 6/5, 16/11] 385/384

[7/6, 5/4, 11/8] 385/384

[8/7, 11/9, 10/7] 441/440

[7/6, 11/9, 7/5] 540/539

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

/tuning/topicId_49180.html#49184

> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > >
> > This is a complete list of everything where the first two
> > > intervals are under 600 cents.
> >
> > It was supposed to be, anyway. I'd better try again.
>
> Here's the corrected list, this time only up to the 13-limit; the
> three intervals together form an octave if we assume the comma which
> follows, or stick to 72-et. Joseph is invited to ponder this list of
> chords.
>

***Thanks, Gene... I'm looking this over...

JP

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

/tuning/topicId_49180.html#49184

> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > >
> > This is a complete list of everything where the first two
> > > intervals are under 600 cents.
> >
> > It was supposed to be, anyway. I'd better try again.
>
> Here's the corrected list, this time only up to the 13-limit; the
> three intervals together form an octave if we assume the comma which
> follows, or stick to 72-et. Joseph is invited to ponder this list of
> chords.
>

***Thanks, Gene... I'm looking this over...

JP