Michael Harrison Tuning

Hello, all. Does anyone know the pitch ratios for the 24-note
tuning that Michael Harrison uses on his "Harmonic Piano"? I
believe it is 7-limit but I've only come across Harrison's 12-
note "Revelation" tuning. Dave Benson mentions Harrison's 24-note
tuning in his "Mathematics and Music" lecture notes but shows it
comprised of 34 notes vice 24 (I think Dr. Benson made an error.)
Thanks for your time and comment.

--- In tuning@yahoogroups.com, "ham_45242" <arl_123@h...> wrote:

> Hello, all. Does anyone know the pitch ratios for the 24-note
> tuning that Michael Harrison uses on his "Harmonic Piano"?

Harrison mentions his scale in the liner notes, but does not actually
give it. It presumably is a subset of a 7-limit scale of 34 notes
which he does give:

! harisev.scl
Seven-limit scale of Michael Harrison
34
!
28/27
135/128
16/15
243/224
9/8
8/7
7/6
32/27
6/5
135/112
5/4
81/64
9/7
21/16
4/3
112/81
45/32
64/45
81/56
3/2
32/21
14/9
128/81
8/5
224/135
5/3
27/16
12/7
7/4
16/9
15/8
243/128
27/14
2

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "ham_45242" <arl_123@h...> wrote:
>
> > Hello, all. Does anyone know the pitch ratios for the 24-note
> > tuning that Michael Harrison uses on his "Harmonic Piano"?
>
> Harrison mentions his scale in the liner notes, but does not actually
> give it.

A few days back I mentioned Harrison's unknown scale and asked what
7-limit microtempering made the best 24 note scale. I concluded
probably hemiwuerschmidt, which is true but not at all suited to
Harrison's music. Harrison places a strong emphasis on 3, with 7
secondary and 5 even more in background (or gone altogether, as in the
revelation scale.) Hemiwuerschmidt places the most emphasis on 5, then
7, and last 3.

If you look at the 34 note scale I gave, you find approximations based
on the schisma and the comma which rejoices in the dubious name of
"beta 5", namely 5120/5103. Putting these together gives septimal
schismic; if that isn't accurate enough, there is 7-limit planar
schismic. A piano which gave 11 consecutive fifths of any hunk of 53
or 94 equal that one asked for would be an interesting thing to see in
action, though 12 notes is really not enough at a time for septimal
schismic. One that gave 24 or even just 17 notes at a time would be
much better--split all the keys and you have 24.

Hello, everyone. I may have asked this before but does anyone know
the pitch ratios that Michael Harrison used on his "Harmonic Piano"
that provides 24 notes per octave? Harrison details the 12-note
"Revelation" tuning on his website but not the 24-note tuning. Any
insight would be greatly appreciated. Sincerely,

He must have rediscovered the Rauf Yekta's 24-tone Pythagorean system, or
its 5-limit schismatic simplification.

Oz.

----- Original Message -----
From: "ham_45242" <arl_123@hotmail.com>
To: <tuning@yahoogroups.com>
Sent: 28 Temmuz 2006 Cuma 15:27
Subject: [tuning] Michael Harrison Tuning

> Hello, everyone. I may have asked this before but does anyone know
> the pitch ratios that Michael Harrison used on his "Harmonic Piano"
> that provides 24 notes per octave? Harrison details the 12-note
> "Revelation" tuning on his website but not the 24-note tuning. Any
> insight would be greatly appreciated. Sincerely,
>
>
>

> Hello, everyone. I may have asked this before but does anyone know
> the pitch ratios that Michael Harrison used on his "Harmonic Piano"
> that provides 24 notes per octave? Harrison details the 12-note
> "Revelation" tuning on his website but not the 24-note tuning. Any
> insight would be greatly appreciated. Sincerely,

He gives them in the liner notes for

http://www.amazon.com/gp/product/B000000R32/

-Carl

> He must have rediscovered the Rauf Yekta's 24-tone Pythagorean
> system, or its 5-limit schismatic simplification.
>
> Oz.

Nope, his tuning is 7-limit.

-Carl

So, what are the ratios?

----- Original Message -----
From: "Carl Lumma" <clumma@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 28 Temmuz 2006 Cuma 19:18
Subject: [tuning] Re: Michael Harrison Tuning

> > He must have rediscovered the Rauf Yekta's 24-tone Pythagorean
> > system, or its 5-limit schismatic simplification.
> >
> > Oz.
>
> Nope, his tuning is 7-limit.
>
> -Carl
>

> > > He must have rediscovered the Rauf Yekta's 24-tone Pythagorean
> > > system, or its 5-limit schismatic simplification.
> >
> > Nope, his tuning is 7-limit.
>
> So, what are the ratios?

Please refer to the liner notes.

-Carl

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> > --- In tuning@yahoogroups.com, "ham_45242" <arl_123@h...> wrote:
> >
> > > Hello, all. Does anyone know the pitch ratios for the 24-note
> > > tuning that Michael Harrison uses on his "Harmonic Piano"?
> >
> > Harrison mentions his scale in the liner notes, but does not actually
> > give it.
>
> A few days back I mentioned Harrison's unknown scale and asked what
> 7-limit microtempering made the best 24 note scale. I concluded
> probably hemiwuerschmidt, which is true but not at all suited to
> Harrison's music. Harrison places a strong emphasis on 3, with 7
> secondary and 5 even more in background (or gone altogether, as in the
> revelation scale.) Hemiwuerschmidt places the most emphasis on 5, then
> 7, and last 3.
>
> If you look at the 34 note scale I gave, you find approximations based
> on the schisma and the comma which rejoices in the dubious name of
> "beta 5", namely 5120/5103. Putting these together gives septimal
> schismic; if that isn't accurate enough, there is 7-limit planar
> schismic. A piano which gave 11 consecutive fifths of any hunk of 53
> or 94 equal that one asked for would be an interesting thing to see in
> action, though 12 notes is really not enough at a time for septimal
> schismic. One that gave 24 or even just 17 notes at a time would be
> much better--split all the keys and you have 24.

I would have thought a slightly more pressing question is how to get
24 notes per octave out of a piano... and where to put your fingers.

~~~T~~~

He tunes the third strings a `comma` apart and uses seperate dampers for
them. Then, using the soft pedal, he achieves, through 12 keys per octave, a
24-tone tuning the 7-limit ratios of which still elude me, since I could not
find the complete list of pitches in the address given by Carl.

Oz.

> One that gave 24 or even just 17 notes at a time would be
> > much better--split all the keys and you have 24.
>
>
> I would have thought a slightly more pressing question is how to get
> 24 notes per octave out of a piano... and where to put your fingers.
>
> ~~~T~~~
>
>

> I would have thought a slightly more pressing question is how to get
> 24 notes per octave out of a piano... and where to put your fingers.

By repurposing the una corda pedal (24, 12-at-a-time).

-Carl