Full thread (11 messages)
From: cityoftheasleep (2010-06-11)
Subject: 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
From: genewardsmith (2010-06-11)
Subject: Re: 19-EDO as an Alternate BP Temperament
--- In [email protected], "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?
From: cityoftheasleep (2010-06-11)
Subject: Re: 19-EDO as an Alternate BP Temperament
--- In [email protected], "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.
From: genewardsmith (2010-06-11)
Subject: Re: 19-EDO as an Alternate BP Temperament
--- In [email protected], "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.:)
From: Petr Parízek (2010-06-11)
Subject: Re: [tuning] Re: 19-EDO as an Alternate BP Temperament
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
From: Chris Vaisvil (2010-06-11)
Subject: Re: [tuning] Re: 19-EDO as an Alternate BP Temperament
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 [email protected], "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.
>
From: Petr Parízek (2010-06-11)
Subject: Re: [tuning] Re: 19-EDO as an Alternate BP Temperament
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
From: cityoftheasleep (2010-06-11)
Subject: Re: 19-EDO as an Alternate BP Temperament
--- In [email protected], Petr Parízek 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).
From: Petr Parízek (2010-06-12)
Subject: Re: [tuning] Re: 19-EDO as an Alternate BP 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\ufffd 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
From: Chris Vaisvil (2010-06-12)
Subject: Re: [tuning] Re: 19-EDO as an Alternate BP Temperament
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
From: caleb morgan (2010-06-12)
Subject: Re: [tuning] Re: 19-EDO as an Alternate BP Temperament
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
>
>