bimodal, 10-tone I-IV-V scales

Has anyone considered (or used) 10-tone scales extrapolated from a - a
la Enrique Ubieta, bimodal I-IV-V?

Both a 5-limit:

4/3 8/5 5/3 2/1
1/1 6/5 5/4 3/2
3/2 9/5 15/8 9/8

5/3-----5/4----15/8
/|\ /|\ /|\
/ | \ / | \ / | \
/ | \ / | \ / | \
4/3--+--1/1--+--3/2--+--9/8
\ | / \ | / \ | /
\ | / \ | / \ | /
\|/ \|/ \|/
8/5-----6/5-----9/5

and a 7-limit:

4/3 14/9 5/3 2/1
1/1 7/6 5/4 3/2
3/2 7/4 15/8 9/8

5/3-------5/4------15/8
/ \ / \ / \
/ \ / \ / \
/ \ / \ / \
14/9.---/-,7/6.-\-/-,7/4. \ / \
`4/3'-----`1/1'-----`3/2-------9/8

interpretation would be represented by the same 2L & 8s, 2 1 1 1 2 1 1
1 1 1 (two step size) step structure in 12-tET, but 19 and 31-tET
(both of which would use three step sizes to render the two step size
cardinality) could also be used to interesting effect I would think...

Ubieta himself suggests a C D E F# G A Bb B, 8-tone overtone scale,
i.e., a 12-tET, 8-16 harmonic series scale: "While we are on the
subject of invented scales, I would like to propose a scale that I
have dubbed the overtone scale (C-D-F#-G-A-Bb-B) because it
encompasses the eight distinct sounds of the harmonic series in an
octave." But if you wanted this to actually be consistent through the
whole 15-odd limit you would have to go up to 29-tET:

9---------------------26
/ \ /\
/ \ / \
/ \ / \
/ \ / \
/ \ / \
/ 13 / \
/ \ / \
/ ,23. \ / \
/ ,' `. \ / \
/ ,' 20 \ / \
/ ,' `. \/ \
0'--------------------`17---------------------5

Though I would think that these types of concerns would hardly seem to
apply as a far as the "Bimodalism -- A New Dimension and Ethos in
Harmony" paper of Ubieta's that I saw goes, it did get my imagination
going, and was an enjoyable read as far as it goes... Here's a fairly
typical, and provocative, excerpt for anyone who might be interested:

"...we must recall that:

four centuries ago, Luca Marenzio (1553-1599) wrote madrigals
that could have been written by a Richard Strauss; Hans Neusiedler
(1508-1563) in The Jew's Dance and Mozart in A Musical Joke-as
both composers wrote with satirical purpose in mind-gave two clear
signals in their respective centuries so as to be literally
considered the forerunners of bitonality; both Chopin and Lizst,
each intending to expand tonality, wrote ostensible passages
in a frank atonality; Giovanni Battista Vitali (1644-1692)
fully constructed the cyclical form of the sonata, two
centuries before C�sar Franck accomplished it in his Sonata in A
for piano and violin; it is Ernest Fanelli (1860-1919), not
Debussy, who some acknowledged as the father of musical
Impressionism; the unfairly forgotten Pietro Raimondi
(1786-1853) deliberately and systematically wrote an ingenious
collection of fugues in four and six simultaneous tonalities,
apart from his Three Oratorios In One, juxtaposing contrary
tempos and meters, long before Milhaud (or even Bart�k or Ives)
began to experiment with polytonality and Stravinsky, Carter,
and Blacher, with polymeter, metric modulation and variable
meters, respectively; the virtuoso pianist Charles Kunkel
(1840-1923) used a tone cluster effect in his work, Alpine Storm
(1888), before Charles Ives used this effect in 1911 in the
second movement of his Concord Sonata, and before Henry
Cowell-its principal user-coined the term in 1915; a Clavecin
Oculaire, invented in 1734 by Louis- Bertrand Castell (1688-1757),
preceded by almost two centuries the synaesthetic inventions of
sound and color that Scriabin exhibited in his Prometheus
(1910); microtonality, since its extinction in Greek antiquity,
reemerged systematized by the astronomer Christiaan Huygens
(1629-1695) in his Tricesimorprimal Temperament, many times before
Jacques Hal�vy practiced microtonality in his cantata,
Prom�thee Encha�n� (1847), and before Richard Stein
(1882-1942), Alois H�ba (1893-1973), and Juli�n Carrillo (1875-
1965) with his Sonido 13, made their first experiments
fractionalizing the octave into several microtones of different
values; as trustworthy sources indicate, it was Charles Ives who
originally conceived of the twelve-tone technique before
Schoenberg (or even Josef Matthias Hauer); in 1914, Erik Satie
instructed that sheets of paper be inserted between piano strings
in Le pi�ge de M�duse, and Rued Langgaard (1893-1952)
instructed that a glissando be played on the piano strings in
Sfaerernes musik (1918), before John Cage (following Cowell's
experiments, respectively) could have embodied all these ideas in
his Prepared Piano or Klaviergamelan (1940), whose
industrialization and universality were owing to the
inventions by its performer and promoter, Richard Burger
(q.v.: Burgerack, Pianotation, and so forth); Ravel's
Bol�ro should be considered the true forerunner of
minimalism, a work that features all the components of this style;
and that Mozart, again, amusing himself, threw the dice to vary
the order of a group of numbered measures, long before
John Cage, Karlheinz Stockhausen, and many other composers were to
write aleatoric music in our day.

The challenging character of these historic events, however, should
not alter our wise evaluation of the matter at hand: In art, the
paternity of an aesthetic idea is not consequently attributed to who,
by hazard or intent, originates the essence of the idea, but to
who-regardless of claims to origination-develops the idea to its
consecration."

<http://www.ubieta.com/bio.htm>

Dan

Has anyone considered (or used) 10-tone scales extrapolated from a - a
la Enrique Ubieta, bimodal I-IV-V?

Both a 5-limit:

4/3 8/5 5/3 2/1
1/1 6/5 5/4 3/2
3/2 9/5 15/8 9/8

5/3-----5/4----15/8
/|\ /|\ /|\
/ | \ / | \ / | \
/ | \ / | \ / | \
4/3--+--1/1--+--3/2--+--9/8
\ | / \ | / \ | /
\ | / \ | / \ | /
\|/ \|/ \|/
8/5-----6/5-----9/5

and a 7-limit:

4/3 14/9 5/3 2/1
1/1 7/6 5/4 3/2
3/2 7/4 15/8 9/8

5/3-------5/4------15/8
/ \ / \ / \
/ \ / \ / \
/ \ / \ / \
14/9.---/-,7/6.-\-/-,7/4. \ / \
`4/3'-----`1/1'-----`3/2-------9/8

interpretation would be represented by the same 2L & 8s, 2 1 1 1 2 1 1
1 1 1 (two step size) step structure in 12-tET, but 19 and 31-tET
(both of which would use three step sizes to render the two step size
cardinality) could also be used to interesting effect I would think...

Ubieta himself suggests a C D E F# G A Bb B, 8-tone overtone scale,
i.e., a 12-tET, 8-16 harmonic series scale: "While we are on the
subject of invented scales, I would like to propose a scale that I
have dubbed the overtone scale (C-D-F#-G-A-Bb-B) because it
encompasses the eight distinct sounds of the harmonic series in an
octave." But if you wanted this to actually be consistent through the
whole 15-odd limit you would have to go up to 29-tET:

9---------------------26
/ \ /\
/ \ / \
/ \ / \
/ \ / \
/ \ / \
/ 13 / \
/ \ / \
/ ,23. \ / \
/ ,' `. \ / \
/ ,' 20 \ / \
/ ,' `. \/ \
0'--------------------`17---------------------5

Though I would think that these types of concerns would hardly seem to
apply as a far as the "Bimodalism -- A New Dimension and Ethos in
Harmony" paper of Ubieta's that I saw goes, it did get my imagination
going, and was an enjoyable read as far as it goes... Here's a fairly
typical, and provocative, (and slightly edited) excerpt for anyone who
might be interested:

"...we must recall that:

four centuries ago, Luca Marenzio (1553-1599) wrote madrigals that
could have been written by a Richard Strauss;

Hans Neusiedler (1508-1563) in The Jew's Dance and Mozart in A Musical
Joke-as both composers wrote with satirical purpose in mind-gave two
clear signals in their respective centuries so as to be literally
considered the forerunners of bitonality;

both Chopin and Lizst, each intending to expand tonality, wrote
ostensible passages in a frank atonality;

Giovanni Battista Vitali (1644-1692) fully constructed the cyclical
form of the sonata, two centuries before C�sar Franck accomplished it
in his Sonata in A for piano and violin;

it is Ernest Fanelli (1860-1919), not Debussy, who some acknowledged
as the father of musical Impressionism;
the unfairly forgotten Pietro Raimondi (1786-1853) deliberately and
systematically wrote an ingenious collection of fugues in four and six
simultaneous tonalities, apart from his Three Oratorios In One,
juxtaposing contrary tempos and meters, long before Milhaud (or even
Bart�k or Ives) began to experiment with polytonality and Stravinsky,
Carter, and Blacher, with polymeter, metric modulation and variable
meters, respectively;

the virtuoso pianist Charles Kunkel (1840-1923) used a tone cluster
effect in his work, Alpine Storm (1888), before Charles Ives used this
effect in 1911 in the second movement of his Concord Sonata, and
before Henry Cowell-its principal user-coined the term in 1915;

a Clavecin Oculaire, invented in 1734 by Louis-Bertrand Castell
(1688-1757), preceded by almost two centuries the synaesthetic
inventions of sound and color that Scriabin exhibited in his
Prometheus (1910);

microtonality, since its extinction in Greek antiquity, reemerged
systematized by the astronomer Christiaan Huygens (1629-1695) in his
Tricesimorprimal Temperament, many times before Jacques Hal�vy
practiced microtonality in his cantata, Prom�thee Encha�n� (1847), and
before Richard Stein (1882-1942), Alois H�ba (1893-1973), and Juli�n
Carrillo (1875-1965) with his Sonido 13, made their first experiments
fractionalizing the octave into several microtones of different
values;

as trustworthy sources indicate, it was Charles Ives who originally
conceived of the twelve-tone technique before Schoenberg (or even
Josef Matthias Hauer);

in 1914, Erik Satie instructed that sheets of paper be inserted
between piano strings in Le pi�ge de M�duse, and Rued Langgaard
(1893-1952) instructed that a glissando be played on the piano strings
in Sfaerernes musik (1918), before John Cage (following Cowell's
experiments, respectively) could have embodied all these ideas in his
Prepared Piano or Klaviergamelan (1940), whose industrialization and
universality were owing to the inventions by its performer and
promoter, Richard Burger (q.v.: Burgerack, Pianotation, and so forth);

Ravel's Bol�ro should be considered the true forerunner of minimalism,
a work that features all the components of this style;

and that Mozart, again, amusing himself, threw the dice to vary the
order of a group of numbered measures, long before John Cage,
Karlheinz Stockhausen, and many other composers were to write
aleatoric music in our day...

The challenging character of these historic events, however, should
not alter our wise evaluation of the matter at hand: In art, the
paternity of an aesthetic idea is not consequently attributed to who,
by hazard or intent, originates the essence of the idea, but to
who-regardless of claims to origination-develops the idea to its
consecration."

<http://www.ubieta.com/bio.htm>

Dan

5/3-------5/4------15/8
/ \ / \ / \
/ \ / \ / \
/ \ / \ / \
14/9.---/-,7/6.-\-/-,7/4. \ / \
`4/3'-----`1/1'-----`3/2-------9/8

Heya Dan,

This is a subset of Kraig Grady's "Centaur" scale, which I used for _Wolves_.

-Carl

>
> 5/3-------5/4------15/8
> / \ / \ / \
> / \ / \ / \
> / \ / \ / \
> 14/9.---/-,7/6.-\-/-,7/4. \ / \
> `4/3'-----`1/1'-----`3/2-------9/8
>
>This is a subset of Kraig Grady's "Centaur" scale, which I used for
>_Wolves_.

Actually, to be fair to Kraig, the scale used on Wolves is not _exactly_ the same as the Centaur. I had independently discovered the Centaur in 1997, but the the version used for Wolves has its 15/8 tempered flat by half a 225/224.

-Carl