19-EDO as an Alternate BP Temperament

Okay folks, I've done a little exploring, and discovered that YES, 19-EDO can be used as a slightly-compressed 30-ED3 to be fully compatible with Bohlen-Pierce music. First, 19-EDO produces 1:3:5:7:9 chords with similar accuracy to 13-ED3. Second, the Moment of Symmetry scales suggested as a basis for tonality in BP are based on an approximate 7:9, and 19-EDO's approximation of this interval works equally well as a generator for these scales, when 30 degrees of 19-EDO is used as a repeat-period. The step sizes will be 2 degrees for the small size and 5 degrees for the large size, basically the 19-EDO diatonic semitone and minor third.

I don't know about you guys, but I think this is kind of a big deal! The fact that you can have meantone AND BP on one instrument WITHOUT needing step-sizes smaller than a quarter-tone, who knew?

-Igs

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

> I don't know about you guys, but I think this is kind of a big deal! The fact that you can have meantone AND BP on one instrument WITHOUT needing step-sizes smaller than a quarter-tone, who knew?

Subdividing 3 into 30 parts has been discussed, and of course stretching octaves for 19, which is a related notion. But what makes it BP?

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

> Subdividing 3 into 30 parts has been discussed, and of course stretching octaves for 19, which is a related notion. But what makes it BP?
>
Well, the good 1:3:5:7:9 harmonies, for one; the approximate-7:9-generator MOS scales for two. In other words, anything written for BP as 13-ED3 could be played in 30-ED3, so it could also be played in 19-EDO (if 19-EDO is treated as 30-ED3). Yes, in 19-EDO the tritave is tempered, but it's still certainly close enough to get the job done. And on a 19-EDO guitar it wouldn't take much adjustment to stretch the intonation to make the tritave pure and the octave impure.

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

> Well, the good 1:3:5:7:9 harmonies, for one; the approximate-7:9-generator MOS scales for two.

If that's all it takes to be Bohlen-Pierce, then squares temperament, which has a 9/7 generator and like 19 tempers out 81/80, is also Bohlen-Pierce. An 11/31 of an octave generator works for that, but once again you could stretch. As for 19 and 9/7 generators, that suggests sensi temperament; tune the generator to 17/46 and you are good to go for a sensi MOS of 19 notes.

If you want 9/7 generators with extreme accuracy, there's always supermajor, a microtemperament. Tune 80 notes to 62/171 and give Ozan's 80 note MOS some competition. Not sure how that works with your guitar, though.:)

Igs wrote:

> Well, the good 1:3:5:7:9 harmonies, for one;
> the approximate-7:9-generator MOS scales for two.

I think the latter is even more important than the former since the 245/243 tempering is one of the characteristic properties of BP and the only way to get a 9-tone MOS. It's similar to mapping meantone to 7-equal on one side (which sounds "super-dark") and 12-equal on the other (which sounds "super-bright").

Petr

I want to throw this into the mix.

The BP tuning I used on my piece came from Fractal Tune Smithy.
And it looks like a JI version of BP and not real BP or am I totally confused?

! C:\Cakewalk\scales\BP13.scl
!

 13
!
27/25
25/21
9/7
7/5
75/49
5/3
9/5
49/25
15/7
7/3
63/25
25/9
3/1

Chris

On Fri, Jun 11, 2010 at 5:22 PM, cityoftheasleep
<igliashon@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> > Subdividing 3 into 30 parts has been discussed, and of course stretching octaves for 19, which is a related notion. But what makes it BP?
> >
> Well, the good 1:3:5:7:9 harmonies, for one; the approximate-7:9-generator MOS scales for two. In other words, anything written for BP as 13-ED3 could be played in 30-ED3, so it could also be played in 19-EDO (if 19-EDO is treated as 30-ED3). Yes, in 19-EDO the tritave is tempered, but it's still certainly close enough to get the job done. And on a 19-EDO guitar it wouldn't take much adjustment to stretch the intonation to make the tritave pure and the octave impure.
>

Chris wrote:

> The BP tuning I used on my piece came from Fractal Tune Smithy.
> And it looks like a JI version of BP and not real BP or am I totally > confused?

That's an "untempered" version that Bohlen himself suggested. It's similar to replacing a meantone chain with the "Euler's monochord" scale.

Petr

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> Igs wrote:
>
> > Well, the good 1:3:5:7:9 harmonies, for one;
> > the approximate-7:9-generator MOS scales for two.
>
> I think the latter is even more important than the former since the 245/243
> tempering is one of the characteristic properties of BP and the only way to
> get a 9-tone MOS. It's similar to mapping meantone to 7-equal on one side
> (which sounds "super-dark") and 12-equal on the other (which sounds
> "super-bright").

They are both equally important. The MOS without the harmonies violates the harmonic principal of BP, which is why a generator flat of 7:9 doesn't do the job very well--you won't get approximate 1:3:5:7:9 harmonies. It'd be like playing meantone music in extreme superpyth (like a 712¢ generator): right melodic structure, wrong harmonies.

OTOH, The odd-harmonic harmonies without the MOS makes "diatonic" BP impossible (it'd be like trying to play meantone music in porcupine temperament).

Igs wrote:

> They are both equally important. The MOS without the harmonies violates > the harmonic principal of BP,
> which is why a generator flat of 7:9 doesn't do the job very well--you > won't get
> approximate 1:3:5:7:9 harmonies. It'd be like playing meantone music in > extreme superpyth
> (like a 712� generator): right melodic structure, wrong harmonies.
>
OTOH, The odd-harmonic harmonies without the MOS makes "diatonic" BP impossible
> (it'd be like trying to play meantone music in porcupine temperament).

Agreed. And this entire thing (i.e. the 9-tone MOS and the 1:3:5:7 chords) can be "cleverly" translated into two intervals -- one which works as the period and another which works as the "comma" to temper out. These are 3/1 and 245/243, respectively. For meantone, OTOH, they are 2/1 and 81/80.

BTW: If you choose a period of 2/1 and a comma of 245/243, you get an interesting 3D temperament which we still can't agree what to call. :-) Anyway, it offers quite nice harmonies -- I've first tried it out last year and it works nicely. If you want to listen, I've stored it here (sorry for a few mistakes there, I haven't used any sequencer this time, it's just the way my thoughts were flowing and I was playing in real-time):
http://www.box.net/shared/y5h2g71r5u

Petr

I like it - especially towards the end where the improvisation becomes
more lyrical.

Chris

If you want to listen, I've stored it here (sorry for a
> few mistakes there, I haven't used any sequencer this time, it's just the
> way my thoughts were flowing and I was playing in real-time):
> http://www.box.net/shared/y5h2g71r5u
>
> Petr

Here's another improv by Petr that completely impresses me.

I'd love to see the Scala file. This sounds great.

(The sheer volume of stuff here, plus my natural thick-headedness, means I can't absorb a lot of stuff, and I have no idea how you came up with this tuning.)

Baby steps for me.

I'd love to try this one out--to my ear it stands out as particularly euphonious.

Caleb

On Jun 12, 2010, at 2:24 AM, Petr Parízek wrote:

> Igs wrote:
>
> > They are both equally important. The MOS without the harmonies violates
> > the harmonic principal of BP,
> > which is why a generator flat of 7:9 doesn't do the job very well--you
> > won't get
> > approximate 1:3:5:7:9 harmonies. It'd be like playing meantone music in
> > extreme superpyth
> > (like a 712¢ generator): right melodic structure, wrong harmonies.
> >
> OTOH, The odd-harmonic harmonies without the MOS makes "diatonic" BP
> impossible
> > (it'd be like trying to play meantone music in porcupine temperament).
>
> Agreed. And this entire thing (i.e. the 9-tone MOS and the 1:3:5:7 chords)
> can be "cleverly" translated into two intervals -- one which works as the
> period and another which works as the "comma" to temper out. These are 3/1
> and 245/243, respectively. For meantone, OTOH, they are 2/1 and 81/80.
>
> BTW: If you choose a period of 2/1 and a comma of 245/243, you get an
> interesting 3D temperament which we still can't agree what to call. :-)
> Anyway, it offers quite nice harmonies -- I've first tried it out last year
> and it works nicely. If you want to listen, I've stored it here (sorry for a
> few mistakes there, I haven't used any sequencer this time, it's just the
> way my thoughts were flowing and I was playing in real-time):
> http://www.box.net/shared/y5h2g71r5u
>
> Petr
>
>