New music again, after a long period of silence

Hi again,

well, I have to tell you something ... This is what I've just finished about half an hour ago. :-D Although the "style" may be changing during the piece, the temperament used is still the same overall the composition. I even don't think I have to tell you what the temperament is; towards the end, there are lots of "model" comma pumps played, which can spell it out quite nicely.
Here's the link:
www.sendspace.com/file/frygkc

Petr

--- In tuning@yahoogroups.com, Petr Pařízek <p.parizek@...> wrote:

> Here's the link:
> www.sendspace.com/file/frygkc

A lot of great moments in there, as usual. Love the choice
of ending chord.

Sounds like 15-ET in some ways, but with much greater accuracy.
Is this porcupine or magic?

-Carl

    I know I don't say this very often.
But, I agree...this is fantastic music.

    There's enough energy and rhythmic layering to make you want to move and just enough difference in the chord structure vs. 12TET to really make you wonder and feel amazed but, at the same time, it contains nothing so unpredictable that you have to strain your mind to interpret it.
   So it sneaks past most of the problems/"traps" I find with most micro-tonal music and even with neo-classical music in general.

   I am also very interested in learning what tuning and scales you used for this.

-Michael

--- On Fri, 2/20/09, Carl Lumma <carl@...> wrote:

From: Carl Lumma <carl@...>
Subject: [tuning] Re: New music again, after a long period of silence
To: tuning@yahoogroups.com
Date: Friday, February 20, 2009, 9:24 AM

--- In tuning@yahoogroups. com, Petr Pařízek <p.parizek@. ..> wrote:

> Here's the link:

> www.sendspace. com/file/ frygkc

A lot of great moments in there, as usual. Love the choice

of ending chord.

Sounds like 15-ET in some ways, but with much greater accuracy.

Is this porcupine or magic?

-Carl

Carl wrote:

> Sounds like 15-ET in some ways, but with much greater accuracy.
> Is this porcupine or magic?

My original idea was 5-limit porcupine. There are pure octaves and the generator is the 8th root of 32/15, which is, IIRC, about 164 cents. I had also some ideas of stretched octaves but the Yamaha XG retuning command format doesn't allow any other octaves than 2/1. Anyway, I should probably say that this is the first time ever that I was able to tune porcupine in XG. I already wanted to try it sooner but I was always getting locked on the problem that I could only use maximum deviations of +/-63 cents from 12-equal. But today I made one clever change; i took a chain of 12 generators, not 11, and removed one of the tones, which eventually gave me a 12-tone scale. After having improvised in it for a while, I realized how well I could approximate not only 5-limit intervals but 11-limit ones as well. So, later, I decided to deliberately use these approximations in the chord progressions. They are sounding only rather soft but they are there.

Petr

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> Carl wrote:
>
> > Sounds like 15-ET in some ways, but with much greater accuracy.
> > Is this porcupine or magic?
>
> My original idea was 5-limit porcupine. There are pure octaves
> and the generator is the 8th root of 32/15, which is, IIRC, about
> 164 cents. I had also some ideas of stretched octaves but the
> Yamaha XG retuning command format doesn't allow any other octaves
> than 2/1. Anyway, I should probably say that this is the first
> time ever that I was able to tune porcupine in XG. I already
> wanted to try it sooner but I was always getting locked on the
> problem that I could only use maximum deviations of +/-63 cents
> from 12-equal. But today I made one clever change; i took a chain
> of 12 generators, not 11, and removed one of the tones, which
> eventually gave me a 12-tone scale. After having improvised in
> it for a while, I realized how well I could approximate not only
> 5-limit intervals but 11-limit ones as well. So, later, I decided
> to deliberately use these approximations in the chord progressions.
> They are sounding only rather soft but they are there.
>
> Petr

Thanks; glad to know my ears are working. One of the open areas
in regular temperament research is the classification of
rank 2 temperaments above the 7-limit. We've never done a deep
dive on it, partly because the relationships between temperaments
gets tricky (e.g. which of the 8 meantone-like mappings should be
called the 11-limit extension of meantone). Anyway, music like
this is good reason to continue the search. I heard the 11-limit
intervals and really thought they added to the piece, but could
tell it was something like porcupine due to the 3rds-based
movements.

-Carl

Carl wrote:

> (e.g. which of the 8 meantone-like mappings should be
> called the 11-limit extension of meantone)

I never knew about 8 possibilities, I only knew of four. When I first began investigating 11-limit meantones back in 2002, I very quickly took preference for mapping 11/8 as a double-diminished fifth. A few months later, I found someone telling me that he preferred mapping 11/8 as a double-augmented third. The reason for my preference for the double-diminished fifth is the fact that this makes major sixths/minor thirds better "in tune" and also three minor seconds then get acceptably close to 16/13.

Petr

My previous message doesn't want to get through, so I'll try to send it once again.

Carl wrote:

> (e.g. which of the 8 meantone-like mappings should be
> called the 11-limit extension of meantone)

I never knew about 8 possibilities, I only knew of four. When I first began investigating 11-limit meantones back in 2002, I very quickly took preference for mapping 11/8 as a double-diminished fifth. A few months later, I found someone telling me that he preferred mapping 11/8 as a double-augmented third. The reason for my preference for the double-diminished fifth is the fact that this makes major sixths/minor thirds better "in tune" and also three minor seconds then get acceptably close to 16/13.

Petr

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> Carl wrote:
>
> > (e.g. which of the 8 meantone-like mappings should be
> > called the 11-limit extension of meantone)
>
> I never knew about 8 possibilities, I only knew of four.

Sorry, I made that number up! I see I should have
been more clear about that.

> When I first began investigating 11-limit meantones back in
> 2002, I very quickly took preference for mapping 11/8 as a
> double-diminished fifth. A few months later, I found someone
> telling me that he preferred mapping 11/8 as a double-augmented
> third. The reason for my preference for the double-diminished
> fifth is the fact that this makes major sixths/minor thirds
> better "in tune" and also three minor seconds then get
> acceptably close to 16/13.

Interesting.

-Carl

Petr Par�zek wrote:
> Carl wrote:
> >> Sounds like 15-ET in some ways, but with much greater accuracy.
>> Is this porcupine or magic?
> > My original idea was 5-limit porcupine. There are pure octaves and the > generator is the 8th root of 32/15, which is, IIRC, about 164 cents. I > had also some ideas of stretched octaves but the Yamaha XG retuning > command format doesn�t allow any other octaves than 2/1. Anyway, I > should probably say that this is the first time ever that I was able to > tune porcupine in XG. I already wanted to try it sooner but I was always > getting locked on the problem that I could only use maximum deviations > of +/-63 cents from 12-equal. But today I made one clever change; i took > a chain of 12 generators, not 11, and removed one of the tones, which > eventually gave me a 12-tone scale. After having improvised in it for a > while, I realized how well I could approximate not only 5-limit > intervals but 11-limit ones as well. So, later, I decided to > deliberately use these approximations in the chord progressions. They > are sounding only rather soft but they are there.
> > Petr

It's interesting how limitations in the system can lead to creative solutions. I'd like to see some of these chord progressions written out. I can play along in porcupine tuning and figure out how it works, but it could be useful for future reference. There's the question of notating it, though.

Herman wrote:

> I'd like to see some of these chord progressions written out.
> I can play along in porcupine tuning and figure out how it works, but it
> could be useful for future reference. There's the question of notating
> it, though.

Well, I was just thinking about some �model versions� of comma pumps and this is the result. Similarly as a major triad in meantone can be viewed as generator numbers of �0 1 4� (i.e. 1 generator maps the prime 3 and 4 generators map the prime 5), a major triad in porcupine can be viewed as generator numbers of �0 3 5�. So in meantone I can happily make a comma pump by keeping adding or subtracting 1 from the generator numbers and modifiing one of them to use as few generators as possible in the entire chord progression (as long as at least one of them is preserved in consecutive chords). For example: I can do �0_1_4, 1_2_5, -1_2_3, -1_0_3, 0_1_4� (C G d F C, like in Abba�s �s.o.s.�) or �0_1_4, 0_3_4, -1_2_3, 1_2_5, 0_1_4� (C a d G C). Similarly, in porcupine, I can make a comma pump by adding or subtracting 2 (not 1 because none of the generator numbers in the triad are 1 step apart there). So for example, I can do it like �0_3_5, 0_2_5, -1_2_4, -1_1_4, -2_1_3, 0_3_5� (which is one of the progressions I�ve used there) or I can do �0_3_5, 1_3_6, 1_4_6, -1_2_4, 0_2_5, 0_3_5� (hey, I�m realizing I haven�t used this one, I�ll probably have to make another version some day :-D).

Petr