Yahoo Tuning Groups Ultimate Backup tuning Warping 5-limit harmonies -- mavila and others

Petr Paďż˝ďż˝zek wrote:
> Hi again,
> > In message 52723, Paul Erlich mentions the idea of using mavila (i.e. > "pelogic") to warp 5-limit harmonies. Then he goes on:
> > "Gene's method is more "warped" and alters the order of the notes, but major
> > triads get mapped to (rough) second-inversion major triads,
> > etc. . . . I asked Gene to elaborate but he has yet to respond."
> > Any idea of what he means by "Gene's method"?
> > Petr

It looks like he's referring to Gene's "Mysterious Mush", which was a warped version of Couperin's "Les Barricades Mystďż˝rieuses". I googled "Mysterious Mush" and found this scale in the Scala archive:

! smithgw_mush.scl
Mysterious mush scale. Gene Smith's meantone to TOP pelogic transformation
12
!
-1175.551080
-163.507699
848.535681
-327.015398
685.027982
-490.523090
521.520283
-654.030800
358.012584
1370.055964
194.504885
1206.548265

So in addition to being retuned to TOP mavila, the scale is inverted, and some notes are displaced up or down an octave.

🔗Carl Lumma <carl@...>

> > In message 52723, Paul Erlich mentions the idea of using
> > mavila (i.e. "pelogic") to warp 5-limit harmonies. Then
> > he goes on:
> >
> > "Gene's method is more "warped" and alters the order of
> > the notes, but major triads get mapped to (rough)
> > second-inversion major triads, etc. . . . I asked Gene
> > to elaborate but he has yet to respond."
> >
> > Any idea of what he means by "Gene's method"?
> >
> > Petr
>
> It looks like he's referring to Gene's "Mysterious Mush",
> which was a warped version of Couperin's "Les Barricades
> Mystérieuses".

Paul was referring to Gene's Scala transforms, which were
used for Mush but first presented here in 2003. Gene
realized that because Scala doesn't care if scales are in
pitch-height order, it can be used not only to change the
*tuning* of a MIDI file or keyboard but also the *mapping*.
I mentioned this recently in connection with one of
Robert Martin's "algorithms", which apparently was of the
same ilk. I believe Gene's approach was something like:

1. Infer a generator/period mapping for the scale used in
the original MIDI file. If you only want to change the
generator you can just do the generator mapping, e.g.
+0 -5 +2 -3 +4 -1 +6 +1 -4 -2 +5 for 12-ET.

2. Change the generator, e.g. from 3/2 to 7/4. If the
scale in step 1 is based chord like 0 +4 +1, it helps if
it's still consonant under the new generator.

3. Use the new generator and the mapping in step 1 to
create a scale.

4. Retune the MIDI file with the scale from step 3.

-Carl

🔗Petr Parízek <p.parizek@...>

Carl wrote:

> Paul was referring to Gene's Scala transforms, which were
> used for Mush but first presented here in 2003. Gene
> realized that because Scala doesn't care if scales are in
> pitch-height order, it can be used not only to change the
> *tuning* of a MIDI file or keyboard but also the *mapping*.

Interesting. It seems everything I've tried has already been done earlier. I
was doing something similar in 2006 but that was on a 3d basis instead of
2d. What I did then was make some music specifically for the 5-limit 12-tone
scale which is called "Euler.scl" in Manuel's archive. If you take 1/1 as C,
then you can think of this scale as a rank 3 tuning starting on F whose
period is 2/1 and whose generators are 3/2 (used three times) and 5/4 (used
twice). My first variation was that I replaced the other generator of 5/4
with 6/5, which changed all major triads to minor and vice versa. In another
version, I replaced 2/1 with 4/1, 3/2 with 5/2 and 5/4 with 3/2. In another
one, I left 2/1 alone and replaced 3/2 with 5/3 and 5/4 with 4/3. In another
one, I used 3/1 instead of 2/1, 9/5 instead of 3/2, and 7/5 instead of 5/4.
And in the last retuning, I used 3/1 in place of 2/1, 7/3 instead of 3/2,
and 5/3 instead of 5/4.
It was very interesting to hear how many different possibilities it offered,
even though all versions except the last two still used 5-limit intervals.
I think you were also following the TL very actively at that time, so maybe
you recall that. I'm still keeping the files on my hard drive anyway.

Petr

🔗Carl Lumma <carl@...>

Petr wrote:
> > Paul was referring to Gene's Scala transforms, which were
> > used for Mush but first presented here in 2003. Gene
> > realized that because Scala doesn't care if scales are in
> > pitch-height order, it can be used not only to change the
> > *tuning* of a MIDI file or keyboard but also the *mapping*.
>
> Interesting. It seems everything I've tried has already been
> done earlier. I was doing something similar in 2006 but that
> was on a 3d basis instead of 2d. What I did then was make som
> music specifically for the 5-limit 12-tone scale which is
> called "Euler.scl" in Manuel's archive. If you take 1/1 as C,
> then you can think of this scale as a rank 3 tuning starting
> on F whose period is 2/1 and whose generators are 3/2 (used
> three times) and 5/4 (used twice).

Sounds like a 5-limit Euler genus. It's a convex structure
in the 5-limit lattice and therefore rank-3 in a sense, even
though the mapping is simply an identity.

> My first variation was that I replaced the other generator of
> 5/4 with 6/5, which changed all major triads to minor and
> vice versa.

That's kindof like what happens with meantone->mavila, except
the 5ths are changed.

> In another version, I replaced 2/1 with 4/1, 3/2 with 5/2
> and 5/4 with 3/2. In another one, I left 2/1 alone and
> replaced 3/2 with 5/3 and 5/4 with 4/3. In another one, I
> used 3/1 instead of 2/1, 9/5 instead of 3/2, and 7/5 instead
> of 5/4. And in the last retuning, I used 3/1 in place of
> 2/1, 7/3 instead of 3/2, and 5/3 instead of 5/4.
> It was very interesting to hear how many different possibilities
> it offered, even though all versions except the last two still
> used 5-limit intervals.
> I think you were also following the TL very actively at that
> time, so maybe you recall that. I'm still keeping the files
> on my hard drive anyway.

I don't! Would you re-release them?

-Carl

🔗Petr Pařízek <p.parizek@...>

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Petr Paøízek <p.parizek@...> wrote:
>
> For Carl:
>
> I've made a Rar archive with the retuned music and the scales
> as you asked.
> The MIDI file called "m-12" is in 12-EDO. The others use the
> following respective scales:
> m-ji.mid -- euler.scl
> m-jimin.mid -- mmswap.scl
> m-jiwh.mid -- wh.scl
> m-jiti.mid -- trinv.scl
> m-jiti2.mid -- trinv2.scl
> m-odd.mid -- odd12.scl
> m-odd2.mid -- odd12a.scl
>
> Here is the link: https://download.yousendit.com/758ED95204F20AFE
>
> Petr

Fabulous. I like the original and minor swap versions
very much. Next I would say trinv2 worked pretty well.

I never realized how good a patch the GM Rhodes is (at
least with my synth) for this kind of thing. Usually
with Scala I use Reed Organ, Clarinet, Percussive Organ,
stuff like that.

You may also like to try some of Gene's transforms,
as seen here:
/tuning/topicId_43689.html#43703
and here:
/tuning/topicId_43689.html#43704

-Carl

🔗Carl Lumma <carl@...>

🔗Petr Parízek <p.parizek@...>

Carl wrote:

> Fabulous. I like the original and minor swap versions
> very much.

When I was making the "mmswap" scale that day, the only thing I was sure about was that the 25/24 steps would go in opposite directions compared to the original version. But when I heard it a while later, my first conclusion was that syntonic comma shifts could be nicely explained by comparing to accidentals. At that moment, I found it clearly "audible" that a step of 81/80 became 135/128 after swapping major and minor and that a 135/128 step became 81/80. So you have, for example, two pitches for Ab, the lower of which is the replacement for A, the higher one being the replacement for A#.

> Next I would say trinv2 worked pretty well.

Maybe it's because fifths are replaced by, in fact, octave-inverted fifths. It sounds a bit like if the music was inverted in general with the exception that major chords don't become minor ones and that there are some octave transpositions because 5/4 is replaced with 5/3 instead of 5/6. Anyway, general inversion seems to work nicely as well -- though I didn't include this version in the archive, I also used "Invert" and "Reverse" with the "Euler.scl" loaded in Scala, which turned all the ratios into their reciprocals. The only disadvantage was that this made flutes play lower than the other instruments (and therefore difficult to hear in some moments) but the harmonic progressions were nicely mirrored and easy to follow.

> I never realized how good a patch the GM Rhodes is (at
> least with my synth) for this kind of thing. Usually
> with Scala I use Reed Organ, Clarinet, Percussive Organ,
> stuff like that.

I would be particularly interested to hear what the "odd2" version sounds like with your equipment -- do you think you could made an audio recording for me somehow?

> You may also like to try some of Gene's transforms,
> as seen here:
> /tuning/topicId_43689.html#43703
> and here:
> /tuning/topicId_43689.html#43704

Gene's transforms offer the advantage of all fifths being playable, which is, as he sais himself, the same as in meantone. That includes, as I can see, also the case where meantone turns into superpelog. And that is also why he used mavila when he changed a major third up to a minor third down and so on. Interestingly, when I first thought of the idea of swapping minor and major two years ago like in the case of "mmswap", it didn't occur to me at all that I could also do something similar by heavily tempering the fifths -- for one thing, I was not thinking about temperaments as I was doing all of that in terms of 5-limit JI; for another thing, I considered such fifths "too mistuned" at that time so I probably wouldn't have done it even if I had knownthat something like mavila existed; and then, I considered "euler.scl" a rank 3 tuning so I thought it was appropriate to use the same approach for remapping the intervals. Rethinking all of this two years later, I'm realizing that this allowed me to use mappings you could never "audibly" approximate with rank 2 temperaments, which is a great advantage in favor of this method. The only disadvantage I'm finding here, at least for the time being, is that you can't view the original D-A and F#-C# as fifths because they are a comma narrower and have different meaning than a 3/2. But anyway, I don't think it's any difficult not to play them.

> Oh, and did you retune these with Scala? They seem
> remarkably clean considering they're polytimbral and
> have fast-moving sections.

I did. :-)

Petr

🔗Carl Lumma <carl@...>

🔗Petr Parízek <p.parizek@...>

Carl wrote:

> The synth I used to listen was just the built-in
> "Microsoft GS Wavetable SW Synth". Still want me to record
> it for you?

I don't think it matters. If you find some time to make the recording, I'll be glad anyway.

> Does the original piece of music have a name?

It doesn't because I didn't consider it finished. I just needed some music which went through the keys of C major, E major, E minor, and possibly G# minor (and since I didn't seem to have any piece which could meet my requirement, I made one). In the end, the first version (where some parts were played by different instruments and where the G# minor really was used) didn't sound so nice to my ear so I made a second version (the one I've sent you) with a different ending, which eventually resulted in stripping the G# minor modulation. I'm still hoping to make another "semi-improv" one day where a modulation into G# minor will find its way.

Petr

Warping 5-limit harmonies -- mavila and others

🔗Petr Pařízek <p.parizek@...>

🔗Herman Miller <hmiller@...>

🔗Carl Lumma <carl@...>

🔗Petr Parízek <p.parizek@...>

🔗Carl Lumma <carl@...>

🔗Petr Pařízek <p.parizek@...>

🔗Carl Lumma <carl@...>

🔗Carl Lumma <carl@...>

🔗Carl Lumma <carl@...>

🔗Petr Parízek <p.parizek@...>

🔗Carl Lumma <carl@...>

🔗Petr Parízek <p.parizek@...>