Yahoo Tuning Groups Ultimate Backup makemicromusic Re: [MMM] 13-ET pentatonic ukulele

Moments of symmetry covers many of these ideas as far as scales but also goes into the bi-level scales which often are the most interesting.
Page 7-9. the latter (9) covers the 13 tone pentatonics.
http://anaphoria.com/mos.PDF

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

dasdasdva wrote:
>
> Ben and Louisa------------------->
>
> should anybody else be interested, here's a WAV version with sans
> encoding problems (i took the ZeBox version to pasture) :
>
> https://download.yousendit.com/Q01IeW4zcHZUWUR2Wmc9PQ > <https://download.yousendit.com/Q01IeW4zcHZUWUR2Wmc9PQ>
>
> And for whatever it's worth, the peculiar layout of this instrument
> is a specific and somewhat experimental adaptation of the basic idea
> of a liberated "white key" music---->which in my opinion Slonimsky
> generally refered to as "pandiatonicism".
>
> The basic idea is that the 7-tone diatonic scale can be somewhat
> rudimentally generalized as a maximally even, 7-out-of-12. If you're
> not familiar with this concept, try checking the work of Clough where
> the mathematical conception is given a very useful music theory
> application:
>
> http://en.wikipedia.org/wiki/Maximally_even > <http://en.wikipedia.org/wiki/Maximally_even>
>
> Understanding the ideas of Myhill--the so-called Myhill's property--
> really helps to make the musical application of maximal evenness
> clear:
>
> http://en.wikipedia.org/wiki/Myhill%27s_property > <http://en.wikipedia.org/wiki/Myhill%27s_property>
>
> Going one step further, or rather simplifying and generalizing, i
> would say that both Clough's conception of maximal evenness and
> Myhill's "Myhill property" reflect something that i'd call
> palindromic symmetry. And that this property is an extremely useful
> way to begin traversing non-standard equal temperaments.
>
> Applying these ideas to the ukulele, i took the 13-tone equal
> temperament as a way to test the idea; especially because this
> temperament was so often referred to in the music theory literature
> as something of an apex of discordance (it's often been written that
> had Schoenberg really wanted to liberate dissonance and manifestly
> bypass tonality, he should have discarded 12-tone equal temperament
> and applied his organizational schemes in the direction of 13-tone
> equal temperament). While this view is obviously seductive on a
> number of levels, i also found it incompatible with my own empirical
> experiences.
>
> To try to prove this point, i decided that i would apply all these
> ideas on a simple ,acoustic folk instrument which turned out to be
> this tenor ukulele. The choice of an 8-tone "pandiatonic" subset was
> not entirely arbitrary. Basically I took the basic idea that the
> standard diatonic scale was built from a circle of 12-TET's nearest
> approximation to a harmonic fifth, and extrapolated that to 13-TET
> where :
>
> (LOG(3/2))*(13/LOG(2)) = ~8
>
> The resulting scale would be represented in scale-steps as a 21221212
> maximally even 8-out-of-13 where 2 is a pandiatonic whole-step at
> ~185 cents and 1 is a pandiatonic half-step at ~92 cents. As Regards
> Myhill's property, it gives the following arrangement (in cents):
>
> 0, 185, 277, 462, 646, 738, 923, 1015, 1200
> 0, 92, 277, 462, 554, 738, 831, 1015, 1200
> 0, 185, 369, 462, 646, 738, 923, 1108, 1200
> 0, 185, 277, 462, 554, 738, 923, 1015, 1200
> 0, 92, 277, 369, 554, 738, 831, 1015, 1200
> 0, 185, 277, 462, 646, 738, 923, 1108, 1200
> 0, 92, 277, 462, 554, 738, 923, 1015, 1200
> 0, 185, 369, 462, 646, 831, 923, 1108, 1200
>
> This type of palindromic symmetry necessitates an extrapolation of
> Myhill's property where you'd have shared intervals of an augmented
> 3rds and a diminished 4th as well as an augmented 6ths and a
> diminished 7ths. This in turn implicates the existence of a perfect
> 3rd and 4th/6th and 7th. Interestingly, these realignments of basic
> diatonic thinking and terminology would interestingly enough seem to
> place the 13-TET "perfect" intervals at the seventh limit as 7/6
> 21/16 and 32/21 12/7, and their "augmented" and "diminished"
> counterparts at the thirteen limit as 16/13 and 13/8 respectively.
>
> daniel
>
> --- In MakeMicroMusic@yahoogroups.com > <mailto:MakeMicroMusic%40yahoogroups.com>, "dasdasdva" <dasdasdva@...>
> wrote:
> >
> >
> > thanks guys. No percussion on this Carl, it's just solo Uke, and
> > mostly an improv---maybe it's the nylon strings though (my son
> plays
> > them quite roughly with a pick, and as they're soft, they scratch,
> > divot and pock, and when you're finger-picking these abrasions
> > scratch on the fleshy fingertip part of your fingers and make and
> odd
> > scrapping "swoooshh".
> > daniel
> >
> >
> > --- In MakeMicroMusic@yahoogroups.com > <mailto:MakeMicroMusic%40yahoogroups.com>, "Dante Rosati"
> > <danterosati@> wrote:
> > >
> > > beautiful piece Dan!
> > >
> > > Dante
> > >
> > > On Sat, Nov 22, 2008 at 12:39 PM, dasdasdva <dasdasdva@> wrote:
> > > > For anyone who might be interested, here's very simple bit of a
> > 13-tone
> > > > equal temperament pentatonic---probably a little sweeter
> sounding
> > than
> > > > you might think
> > > >
> > > > http://zebox.com/daniel_anthony_stearns/ > <http://zebox.com/daniel_anthony_stearns/>
> > > >
> > > > Ben and Louisa
> > > > (1st piece, top of page
> > > >
> > > >
> > >
> >
>
>

dasdasdva originally wrote:
The resulting scale would be represented in scale-steps as a
21221212

This is what he places on the white notes. Both forms though are "symmetrical" depending on where you start just like dorian is on the white notes in 12.
The sequence with 2 2 1 2 2 2 1 2 2 comes out if you use the generator 7 instead of 8( or 6 instead of 5). but this is harder to see if you right it out this way as opposed to 2 2 2 2 1 2 2 2 1 but one can use any mode one wishes.
Paul Erlich was like you in that he preferred to place his scales in this order which can be seen in his papers when he diagrams horograms.
For me it is easier to keep track of the generator the other way but to each his own. I don't know of any advantage to a scale to be an inversion of itself. Dorian is great and was hooked on it for quite some time

if you look at the horograms there are some other 13 tone scales including a 7 and a six
http://anaphoria.com/hrgm.PDF
interestingly the 6)13 doesn't come up in the first 32 horograms which is a bit surprising

I can't help but thinking of the Bunuel film when the person sees the spider on the wall and crushes it and exclaims
" I hate Symmetry!"

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

dasdasdva wrote:
>
> hi there kraig.interestingly, Erv gives the 13-tet diatonic 8-tone
> white notes as 0 1 3 5 6 8 9 11 13 whereas i have them as 0 2 3 5 7 8
> 10 12 and the 5-tone black keys at 1 4 6 9 11. My rationale is that
> there are major, minor, augmented, and diminished intervals, and that
> this arrangement best corresponds to what i call (lacking a better
> more imaginative term) palindromic symmetry .
>
> --- In MakeMicroMusic@yahoogroups.com > <mailto:MakeMicroMusic%40yahoogroups.com>, Kraig Grady <kraiggrady@...>
> wrote:
> >
> > Moments of symmetry covers many of these ideas as far as scales but
> also
> > goes into the bi-level scales which often are the most interesting.
> > Page 7-9. the latter (9) covers the 13 tone pentatonics.
> > http://anaphoria.com/mos.PDF <http://anaphoria.com/mos.PDF>
> >
> >
> >
> > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > Mesotonal Music from:
> > _'''''''_ ^North/Western Hemisphere:
> > North American Embassy of Anaphoria Island <http://anaphoria.com/ > <http://anaphoria.com/>>
> >
> > _'''''''_ ^South/Eastern Hemisphere:
> > Austronesian Outpost of Anaphoria
> <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> >
> >
> >
> > dasdasdva wrote:
> > >
> > > Ben and Louisa------------------->
> > >
> > > should anybody else be interested, here's a WAV version with sans
> > > encoding problems (i took the ZeBox version to pasture) :
> > >
> > > https://download.yousendit.com/Q01IeW4zcHZUWUR2Wmc9PQ > <https://download.yousendit.com/Q01IeW4zcHZUWUR2Wmc9PQ>
> > > <https://download.yousendit.com/Q01IeW4zcHZUWUR2Wmc9PQ > <https://download.yousendit.com/Q01IeW4zcHZUWUR2Wmc9PQ>>
> > >
> > > And for whatever it's worth, the peculiar layout of this
> instrument
> > > is a specific and somewhat experimental adaptation of the basic
> idea
> > > of a liberated "white key" music---->which in my opinion Slonimsky
> > > generally refered to as "pandiatonicism".
> > >
> > > The basic idea is that the 7-tone diatonic scale can be somewhat
> > > rudimentally generalized as a maximally even, 7-out-of-12. If
> you're
> > > not familiar with this concept, try checking the work of Clough
> where
> > > the mathematical conception is given a very useful music theory
> > > application:
> > >
> > > http://en.wikipedia.org/wiki/Maximally_even > <http://en.wikipedia.org/wiki/Maximally_even>
> > > <http://en.wikipedia.org/wiki/Maximally_even > <http://en.wikipedia.org/wiki/Maximally_even>>
> > >
> > > Understanding the ideas of Myhill--the so-called Myhill's
> property--
> > > really helps to make the musical application of maximal evenness
> > > clear:
> > >
> > > http://en.wikipedia.org/wiki/Myhill%27s_property > <http://en.wikipedia.org/wiki/Myhill%27s_property>
> > > <http://en.wikipedia.org/wiki/Myhill%27s_property > <http://en.wikipedia.org/wiki/Myhill%27s_property>>
> > >
> > > Going one step further, or rather simplifying and generalizing, i
> > > would say that both Clough's conception of maximal evenness and
> > > Myhill's "Myhill property" reflect something that i'd call
> > > palindromic symmetry. And that this property is an extremely
> useful
> > > way to begin traversing non-standard equal temperaments.
> > >
> > > Applying these ideas to the ukulele, i took the 13-tone equal
> > > temperament as a way to test the idea; especially because this
> > > temperament was so often referred to in the music theory
> literature
> > > as something of an apex of discordance (it's often been written
> that
> > > had Schoenberg really wanted to liberate dissonance and manifestly
> > > bypass tonality, he should have discarded 12-tone equal
> temperament
> > > and applied his organizational schemes in the direction of 13-tone
> > > equal temperament). While this view is obviously seductive on a
> > > number of levels, i also found it incompatible with my own
> empirical
> > > experiences.
> > >
> > > To try to prove this point, i decided that i would apply all these
> > > ideas on a simple ,acoustic folk instrument which turned out to be
> > > this tenor ukulele. The choice of an 8-tone "pandiatonic" subset
> was
> > > not entirely arbitrary. Basically I took the basic idea that the
> > > standard diatonic scale was built from a circle of 12-TET's
> nearest
> > > approximation to a harmonic fifth, and extrapolated that to 13-TET
> > > where :
> > >
> > > (LOG(3/2))*(13/LOG(2)) = ~8
> > >
> > > The resulting scale would be represented in scale-steps as a
> 21221212
> > > maximally even 8-out-of-13 where 2 is a pandiatonic whole-step at
> > > ~185 cents and 1 is a pandiatonic half-step at ~92 cents. As
> Regards
> > > Myhill's property, it gives the following arrangement (in cents):
> > >
> > > 0, 185, 277, 462, 646, 738, 923, 1015, 1200
> > > 0, 92, 277, 462, 554, 738, 831, 1015, 1200
> > > 0, 185, 369, 462, 646, 738, 923, 1108, 1200
> > > 0, 185, 277, 462, 554, 738, 923, 1015, 1200
> > > 0, 92, 277, 369, 554, 738, 831, 1015, 1200
> > > 0, 185, 277, 462, 646, 738, 923, 1108, 1200
> > > 0, 92, 277, 462, 554, 738, 923, 1015, 1200
> > > 0, 185, 369, 462, 646, 831, 923, 1108, 1200
> > >
> > > This type of palindromic symmetry necessitates an extrapolation of
> > > Myhill's property where you'd have shared intervals of an
> augmented
> > > 3rds and a diminished 4th as well as an augmented 6ths and a
> > > diminished 7ths. This in turn implicates the existence of a
> perfect
> > > 3rd and 4th/6th and 7th. Interestingly, these realignments of
> basic
> > > diatonic thinking and terminology would interestingly enough seem
> to
> > > place the 13-TET "perfect" intervals at the seventh limit as 7/6
> > > 21/16 and 32/21 12/7, and their "augmented" and "diminished"
> > > counterparts at the thirteen limit as 16/13 and 13/8 respectively.
> > >
> > > daniel
> > >
> > > --- In MakeMicroMusic@yahoogroups.com > <mailto:MakeMicroMusic%40yahoogroups.com>
> > > <mailto:MakeMicroMusic%40yahoogroups.com>, "dasdasdva"
> <dasdasdva@>
> > > wrote:
> > > >
> > > >
> > > > thanks guys. No percussion on this Carl, it's just solo Uke, and
> > > > mostly an improv---maybe it's the nylon strings though (my son
> > > plays
> > > > them quite roughly with a pick, and as they're soft, they
> scratch,
> > > > divot and pock, and when you're finger-picking these abrasions
> > > > scratch on the fleshy fingertip part of your fingers and make
> and
> > > odd
> > > > scrapping "swoooshh".
> > > > daniel
> > > >
> > > >
> > > > --- In MakeMicroMusic@yahoogroups.com > <mailto:MakeMicroMusic%40yahoogroups.com>
> > > <mailto:MakeMicroMusic%40yahoogroups.com>, "Dante Rosati"
> > > > <danterosati@> wrote:
> > > > >
> > > > > beautiful piece Dan!
> > > > >
> > > > > Dante
> > > > >
> > > > > On Sat, Nov 22, 2008 at 12:39 PM, dasdasdva <dasdasdva@>
> wrote:
> > > > > > For anyone who might be interested, here's very simple bit
> of a
> > > > 13-tone
> > > > > > equal temperament pentatonic---probably a little sweeter
> > > sounding
> > > > than
> > > > > > you might think
> > > > > >
> > > > > > http://zebox.com/daniel_anthony_stearns/ > <http://zebox.com/daniel_anthony_stearns/>
> > > <http://zebox.com/daniel_anthony_stearns/ > <http://zebox.com/daniel_anthony_stearns/>>
> > > > > >
> > > > > > Ben and Louisa
> > > > > > (1st piece, top of page
> > > > > >
> > > > > >
> > > > >
> > > >
> > >
> > >
> >
>
>

Re: [MMM] 13-ET pentatonic ukulele

🔗Carl Lumma <carl@...>

🔗Dante Rosati <danterosati@...>

🔗Carl Lumma <carl@...>

🔗Kraig Grady <kraiggrady@...>

🔗Herman Miller <hmiller@...>

🔗Kraig Grady <kraiggrady@...>

🔗Aaron Krister Johnson <aaron@...>