Ben and Louisa

For anyone who might be interested, here's very simple piece based on
a 13-tone equal temperament pentatonic---probably a little sweeter
sounding thanyou might think given the tuning's reputation:

http://zebox.com/daniel_anthony_stearns/

Ben and Louisa
(1st piece, top of page-----------------------------/

FWiW, the peculiar layout of this instrument is a specific and
somewhat experimental adaptation of the basic idea of a
liberated "white key" music---->what 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

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

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
deviation/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 seem to
place the 13-TET perfect intervals at the seventh limit as 7/6 21/16
and 32/21 12/7, and their aug and dim counterparts at the thirteen
limit as 16/13 and 13/8 respectively.

daniel

caleb sez: ok, I read that you are playing a ukulele.

Some kind of adjustable fretting, or something?

On Nov 24, 2008, at 2:51 PM, daniel_anthony_stearns wrote:

> For anyone who might be interested, here's very simple piece based on
> a 13-tone equal temperament pentatonic---probably a little sweeter
> sounding thanyou might think given the tuning's reputation:
>
> http://zebox.com/daniel_anthony_stearns/
>
> Ben and Louisa
> (1st piece, top of page-----------------------------/
>
> FWiW, the peculiar layout of this instrument is a specific and
> somewhat experimental adaptation of the basic idea of a
> liberated "white key" music---->what 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
>
> 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
>
> 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
> deviation/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 seem to
> place the 13-TET perfect intervals at the seventh limit as 7/6 21/16
> and 32/21 12/7, and their aug and dim counterparts at the thirteen
> limit as 16/13 and 13/8 respectively.
>
> daniel
>
>
>

And, lest my first reaction got lost in the mail:

I enjoyed this very much. I would have been proud to write/make this.

On Nov 24, 2008, at 2:51 PM, daniel_anthony_stearns wrote:

> For anyone who might be interested, here's very simple piece based on
> a 13-tone equal temperament pentatonic---probably a little sweeter
> sounding thanyou might think given the tuning's reputation:
>
> http://zebox.com/daniel_anthony_stearns/
>
> Ben and Louisa
> (1st piece, top of page-----------------------------/
>
> FWiW, the peculiar layout of this instrument is a specific and
> somewhat experimental adaptation of the basic idea of a
> liberated "white key" music---->what 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
>
> 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
>
> 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
> deviation/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 seem to
> place the 13-TET perfect intervals at the seventh limit as 7/6 21/16
> and 32/21 12/7, and their aug and dim counterparts at the thirteen
> limit as 16/13 and 13/8 respectively.
>
> daniel
>
>
>

caleb sez: I wanted to give my shoot-from-the-hip impression:

That's lovely. I would be proud to have made that.

Both in the vaguely africanish pentatonicish sound, and the back-and-forth of the harmony, and the tune/figuration.

I'm not sure if it doesn't just sound a little out of tune--which sounds great.

(I know, I know, that's probably not a hip thing to say here)

Boy, one thing I'm learning here--the varieties of tuning!

Is that you playing a real guitar?

caleb

On Nov 24, 2008, at 2:51 PM, daniel_anthony_stearns wrote:

> For anyone who might be interested, here's very simple piece based on
> a 13-tone equal temperament pentatonic---probably a little sweeter
> sounding thanyou might think given the tuning's reputation:
>
> http://zebox.com/daniel_anthony_stearns/
>
> Ben and Louisa
> (1st piece, top of page-----------------------------/
>
> FWiW, the peculiar layout of this instrument is a specific and
> somewhat experimental adaptation of the basic idea of a
> liberated "white key" music---->what 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
>
> 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
>
> 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
> deviation/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 seem to
> place the 13-TET perfect intervals at the seventh limit as 7/6 21/16
> and 32/21 12/7, and their aug and dim counterparts at the thirteen
> limit as 16/13 and 13/8 respectively.
>
> daniel
>
>
>

Any mistake in hearing it was mine, not the tech's fault.

I simply don't know from tenor ukuleles.

It sounded good either way--but you really hear that the octaves aren't in tune--which sounds fine to me.

On Nov 24, 2008, at 4:52 PM, daniel_anthony_stearns wrote:

> Thanks Caleb, i never really listen to uploads ever(just assumiong
> they're right), but as someone kindly pointed out in another forum,
> there's obviously an unidendified problem with this one's encoding
> (fu*k and grrrrrrrr and hooooovnooooo!).................okay, yanked
> it and try here (as a WAV) should anybody else be interested :
>
> https://download.yousendit.com/Q01IeW4zcHZUWUR2Wmc9PQ
>
> --- In tuning@yahoogroups.com, caleb morgan <calebmrgn@...> wrote:
> >
> >
> > caleb sez: I wanted to give my shoot-from-the-hip impression:
> >
> > That's lovely. I would be proud to have made that.
> >
> > Both in the vaguely africanish pentatonicish sound, and the back-
> and-
> > forth of the harmony, and the tune/figuration.
> >
> > I'm not sure if it doesn't just sound a little out of tune--which
> > sounds great.
> >
> > (I know, I know, that's probably not a hip thing to say here)
> >
> > Boy, one thing I'm learning here--the varieties of tuning!
> >
> > Is that you playing a real guitar?
> >
> > caleb
> >
> >
> >
> >
> >
> >
> >
> >
> >
> > On Nov 24, 2008, at 2:51 PM, daniel_anthony_stearns wrote:
> >
> > > For anyone who might be interested, here's very simple piece
> based on
> > > a 13-tone equal temperament pentatonic---probably a little sweeter
> > > sounding thanyou might think given the tuning's reputation:
> > >
> > > http://zebox.com/daniel_anthony_stearns/
> > >
> > > Ben and Louisa
> > > (1st piece, top of page-----------------------------/
> > >
> > > FWiW, the peculiar layout of this instrument is a specific and
> > > somewhat experimental adaptation of the basic idea of a
> > > liberated "white key" music---->what 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
> > >
> > > 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
> > >
> > > 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
> > > deviation/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
> seem to
> > > place the 13-TET perfect intervals at the seventh limit as 7/6
> 21/16
> > > and 32/21 12/7, and their aug and dim counterparts at the thirteen
> > > limit as 16/13 and 13/8 respectively.
> > >
> > > daniel
> > >
> > >
> > >
> >
>
>
>

Hi Dan.

For one thing, that's a nice piece ... The only problem I have when listening to this sort of music is that the melodic and/or harmonic "phrases" remind me so much of regular tonal harmonic progressions that it's difficult for me to think of it as a completely new tonal "terrain" rather than badly tuned 12-EDO. But since this hasn't happened to me with all the microtonal pieces I've heard, there must be something in those pieces, not in the tunings, which makes me think like that more in some cases and less in others.

For another thing, I didn't realize you could speak Czech. :-D

Petr

I'm a Boston-area boy, bred, born & raised.

I speak a mixture of egghead, wonk, hipster, and the Queen's English, with possibly traces of Aspergerese thrown in--I jest.

why do you ask?

something about Czech? The mists are clearing.....I'm getting....that I have missed the point....

caleb

On Nov 24, 2008, at 5:12 PM, daniel_anthony_stearns wrote:

> ullo there Caleb---->BtW,what's your nationality/native language?
>
>
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