Myna[7] as an alternative to the diatonic scale

Having mentioned that Myna[7] has no tetrads, I thought I'd better point out that it has other things going for it, and could be used as a septimal alternative to Meantone[7].

(1) Four 1-6/5-7/5 otonal triads
(2) Four 1-7/6-7/5 utonal triads

Compare the three each of 5-limit triads in meantone.

(3) Five 1-6/5-10/7 classic diminished triads
(4) Four 1-6/5-10/7-12/7 classic diminished seventh chords (ie, same as in meantone.)

That thar is a powerful lot of harmony packed into just seven notes, I reckon. I don't recall anyone taking advantage of the fact. Modulating Myna[7] within the scope of Myna[11] could be compared to modulating Meantone[7] within the scope of Meantone[12], which sufficed to make people happy for quite some time. Time to break out your 11 or 15 note myna guitars!

On Sun, Jan 23, 2011 at 8:56 PM, genewardsmith
<genewardsmith@...> wrote:
>
> Having mentioned that Myna[7] has no tetrads, I thought I'd better point out that it has other things going for it, and could be used as a septimal alternative to Meantone[7].
>
> (1) Four 1-6/5-7/5 otonal triads
> (2) Four 1-7/6-7/5 utonal triads
>
> Compare the three each of 5-limit triads in meantone.
>
> (3) Five 1-6/5-10/7 classic diminished triads
> (4) Four 1-6/5-10/7-12/7 classic diminished seventh chords (ie, same as in meantone.)
>
> That thar is a powerful lot of harmony packed into just seven notes, I reckon. I don't recall anyone taking advantage of the fact. Modulating Myna[7] within the scope of Myna[11] could be compared to modulating Meantone[7] within the scope of Meantone[12], which sufficed to make people happy for quite some time. Time to break out your 11 or 15 note myna guitars!

This might make sense in a sort of nonoctave approach, or where you
use different scale in the bass than in the treble. This approach
wasn't explored much in western music because the root for the major
chord is also the same thing as the bottom note doubled down an
octave. The same applies to the minor chord, which is generally heard
as 3/2 with some weakly tonal inharmonic note in the middle. But when
you're dealing with 5:6:7 as a tonal chord, to double the 5 down an
octave makes the whole thing sound a lot more dissonant.

This is sort of an expansion on a technique I've been using in
12-equal harmony some time, which stems from Stravinsky's "modal
fields" approach. Some day, when I have enough time to think like a
normal person, I'll have to try to work some of this out.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> This might make sense in a sort of nonoctave approach, or where you
> use different scale in the bass than in the treble. This approach
> wasn't explored much in western music because the root for the major
> chord is also the same thing as the bottom note doubled down an
> octave.

It seems to me it wasn't explored much because people were using chains of fifths, not minor thirds. And what definition of "root" are you using? It doesn't make a hell of a lot of sense to me.

The same applies to the minor chord, which is generally heard
> as 3/2 with some weakly tonal inharmonic note in the middle. But when
> you're dealing with 5:6:7 as a tonal chord, to double the 5 down an
> octave makes the whole thing sound a lot more dissonant.

This scale no doubt works better in close harmony.

On Sun, Jan 23, 2011 at 10:32 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > This might make sense in a sort of nonoctave approach, or where you
> > use different scale in the bass than in the treble. This approach
> > wasn't explored much in western music because the root for the major
> > chord is also the same thing as the bottom note doubled down an
> > octave.
>
> It seems to me it wasn't explored much because people were using chains of fifths, not minor thirds. And what definition of "root" are you using? It doesn't make a hell of a lot of sense to me.

I meant VF, sorry. I don't see what you mean about the fifth vs third
generator. I don't think you got my point about the 5:6:7 and the
nonoctave scale.

If we're using 4:5:6, and if you naively double the bottom note down
an octave, it makes sense because 4:5:6 is a rooted triad. Doubling
the bottom note down an octave for 10:12:15 works as well because we
hear the VF pop out for 10:12:15 as though it were a 3/2 with an extra
note in there.

There's also that a minor chord, if you double the root down a bunch
of times, might be more perceptually related to 16:19:24, because I'd
expect that 1:2:4:8:16:19:24 has a stronger field of attraction than
5:10:20:40:80:96:120. This is just a conjecture, something to think
about, something you've no doubt heard a million times before on this
list, and I'm not going to argue it.

Either way, if you do that with 5:6:7, you end up with a much more
dissonant chord than 5:6:7 alone. If, instead of doubling the bottom
note an octave, your approach to the bass is to play the note
corresponding to the VF of each chord, and so treat the "root" of
5:6:7 as 1, 2, and 4 instead of as 5, it ends up sounding more
consonant.

-Mike

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> Having mentioned that Myna[7] has no tetrads, I thought I'd better point out that it has other things going for it, and could be used as a septimal alternative to Meantone[7].

In case anyone wants to play with it:

! myna7opt.scl
Lesfip version of 7-limit Myna[7]
7
!
267.31590
310.96887
579.17475
620.82525
889.03113
932.68410
1200.0000

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

I was playing with it on Scala, and note it has perfectly good traditional note names which Scala doesn't default to, but set the notation scheme to P31 and you are in business: C D# Eb F# Gb A Bbb C.

On 24 January 2011 05:56, genewardsmith <genewardsmith@...> wrote:

> That thar is a powerful lot of harmony packed into just seven notes, I reckon. I don't recall anyone taking advantage of the fact. Modulating Myna[7] within the scope of Myna[11] could be compared to modulating Meantone[7] within the scope of Meantone[12], which sufficed to make people happy for quite some time. Time to break out your 11 or 15 note myna guitars!

Myna gets more competitive in the 13-limit, like here:

http://x31eq.com/cgi-bin/pregular.cgi?limit=13&error=3

I don't care about "complete whateverads" at this point, but there are
going to be a lot of chords with 13-limit rationalizations. 13:11
needs 31 steps, but 7:10:13 only 15 notes and 5:6:7 will be very
common. Caveat: this isn't a system I've looked at in detail or tuned
up.

Graham

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
> In case anyone wants to play with it:
>
> ! myna7opt.scl
> Lesfip version of 7-limit Myna[7]
> 7
> !
> 267.31590
> 310.96887
> 579.17475
> 620.82525
> 889.03113
> 932.68410
> 1200.0000
>

Do you think the error in the 19-EDO version is too high in the 7-limit to approximate the desired harmonies? I'd encountered this scale in 19-EDO before but never worked out the harmonic basis for it. Though now that I think about it, I could see the 19-EDO as sort of a 13-limit version, supplanting 5:6:7 triads with 13:15:18 triads. Not as smooth, but perhaps still usable. I'll have to try it out. It's a bit improper for my tastes, but not totally unacceptable.

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> Do you think the error in the 19-EDO version is too high in the 7-limit to approximate the desired harmonies?

19 simply doesn't do it justice; it's quite an accurate 7-limit temperament, and 19 isn't. Why not a 19-note MOS instead, in 58 or 89? As Graham pointed out, it's very interesting as a 13-limit temperament as well as 7-limit; 89 is better for the 7-limit, 58 for 13.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> 19 simply doesn't do it justice; it's quite an accurate 7-limit temperament, and 19 isn't. Why > not a 19-note MOS instead, in 58 or 89? As Graham pointed out, it's very interesting as a
> 13-limit temperament as well as 7-limit; 89 is better for the 7-limit, 58 for 13.

What about 23-EDO? If you're just looking at the subgroup harmonies that the 7-note MOS does, it looks to me like 23-EDO should do it justice.

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > 19 simply doesn't do it justice; it's quite an accurate 7-limit temperament, and 19 isn't. Why > not a 19-note MOS instead, in 58 or 89? As Graham pointed out, it's very interesting as a
> > 13-limit temperament as well as 7-limit; 89 is better for the 7-limit, 58 for 13.
>
> What about 23-EDO? If you're just looking at the subgroup harmonies that the 7-note MOS does, it looks to me like 23-EDO should do it justice.

It's pretty flat, and anyway is only good for a subgroup. But it's definately an interesting plan for anyone using 23 or interested in doing so. Either the 2.5/3.7/3 subgroup or the 2.5/3.7/3.13 subgroup would work.