Scale of the Day: A Pythagorean Octotonic-1 - Lydian Mode

The A Pythagorean Octotonic-1 - Lydian Mode - Scale. It's a Pythagorean tuning because the largest prime factor for these frequency ratios is 3. It's an Octotonic-1 scale because it's an 8-note scale of alternating whole/half steps. And it's in "Lydian Mode" because the largest prime factor (3) is always found in the numerator - making each note either the tonic or an otonal interval relative to the tonic. This otonality leads to the odd spellings such as the C double-sharp augmented third - as the D-natural perfect fourth would be the utonal 4/3 - or the B-Sharp augmented second - instead of the also utonal C-natural minor third (32/27). Which highlights the fact that the Pythagorean augmented third does not equal the Pythagorean perfect fourth - something that is lost in equal temperament.

Scale of the Day: A Octotonic-2 mapped to the Square-root-of-2

The A Octotonic-2 mapped to the Square-root-of-2 Scale. Compressed to fit within the confines of the 600-cent "tritone," the alternating sequence of minor seconds/major seconds becomes an alternating sequence of quarter-tones/half-steps.

HurdAudio Rotation: The Tri-Centric Edition

Beck: Guero. 2004. Interscope Records: B0003481-02.

There's been a noticeable dearth of beats in the HurdAudio rotation, or at least anything one could conceivably use to get their freak on. I'm still not a big fan of the Dust Brothers production sound - in many ways they seem like a step backward from Beck's more adventurously over produced outings. Ultimately it's the song writing that holds this one together and elevates it well beyond the average "alternative" rock outing. And it certainly provides some much need balance and perspective to a listening diet that runs heavy on the heady side.

Anthony Braxton: Piano Quartet, Yoshi's 1994 [disc 3]. 1994. Music & Arts: CD 849.

Anthony Braxton: piano
Marty Ehrlich: alto saxophone, soprano saxophone, clarinet
Joe Fonda: bass
Arthur Fuller: drums

After finally sinking my ears into the first disc of this collection I move my attention to the third disc... and it's back to struggling to hear through Braxton's plodding piano solos. It's hard to fault Braxton for pushing these jazz standards toward a more open tradition, but I'm struggling mightily with the narrow dynamic range whenever the piano shifts into the focal point and the difficulty of hearing within this music when confronted with that sound. Ehrlich, Fonda and Fuller are outstanding throughout this set. Repeated listening might reveal new layers to this performance, but my initial impression is disappointment. And that's a reflection of the high expectations I have for Anthony Braxton's music. Perhaps the shackles of the jazz standards will always pale compared to the exuberant brilliance of his original compositions.

Anthony Braxton: 9 Compositions (Iridium) 2006[disc 2] . 2006. Firehouse 12 Records: FH12-04-03-001.

Recorded live: March 16, 2006 at Iridium Jazz Club, New York City.

The Anthony Braxton 12+1tet
Anthony Braxton: composer, alto saxophone, soprano saxophone, sopranino saxophone, clarinet and Eb contalto clarinet
Taylor Ho Bynum: cornet, flugelhorn, trumpbone, piccolo trumpet, bass trumpet, shell
Andrew Raffo Dewar: soprano saxophone, c-melody saxophone, clarinet
James Fei: alto saxophone, soprano saxophone, clarinet, bass clarinet
Mary Halvorson: electric guitar
Stephen H. Lehman: alto saxophone, sopranino saxophone
Nicole Mitchell: flute, alto flute, bass flute, piccolo, voice
Jessica Pavone: viola, violin
Reut Regev: trombone, flugelbone
Jay Rozen: tuba, euphonium
Sara Schoenbeck: bassoon, suona
Aaron Siegel: percussion, vibraphone
Carl Testa: acoustic bass, bass clarinet

Disc 2 = Composition 351 - dedicated to the composer/scholar Harvey Sollberger

Thick, wildly varied group improvisation guided by the unifying force of Braxtonian logic. This music is a high achievement in large ensemble improvised sound. I'm particularly impressed by Nicole Mitchell's flute work in this set as well as the sparse vocalizations of the swinging melodic lines that spring into this texture. This is a music of sonic clouds and pulse, a pulse that is often obscured by the density of this sound but never lost. It's original large ensemble music like this that holds these ears in complete awe of Anthony Braxton.

Scale of the Day: B Octotonic-2

The intervallic content of the B Octotonic-2 Scale. This is the straight, no-frills equal temperament scale of alternating minor/major seconds just as Messiaen or Metallica have used it.

Scale of the Day: A Octotonic-2 (1+1)

The A Octotonic-2 (1+1) Scale as one would find it on any conventionally tuned, equal tempered instrument. One of the advantages of an equal tempered octotonic scale is the number of major and minor triads available for vaguely tonal allusions between "unrelated" keys. In this altered octotonic scale one has the ingredients for A minor, A major, B major, C minor, C major, E minor, and F-sharp minor. This makes for a collection of triadic harmonies not often found within more diatonic contexts. And that's in addition to the augmented and diminished triads one expects from Octotonic scales.

HurdAudio Rotation: The Piano-centric Edition

Udo Kasemets: Pythagoras Tree: Works for Piano. 1996. Hat Hut Recordings: hat[now]ART 113.

Stephen Clarke: piano
Timepiece (1964) version 1
Tangovariables on the word TANGO (1986)
Timepiece (1964) version 2
3/7 D'un Morceau en Forme de Poire (1995)
Feigenbaum Cascades (1995)
Pythagoras Tree (1994)
Music of the First Eleven Primes (1995)

The Estonian composer Udo Kasemets has long been a curiosity for me. When I lived in Toronto he was an eccentric presence on the new music scene with his austere, mathematically inclined and John Cage inspired compositions. Pythagoras Tree is a quiet manifestation of the active mind of Kasemets. Clarke gives these piano pieces a steady, accurate presentation with many of the qualities that make Kasemets' music (and personality) so unique and rewarding to focus on. The brief glimpses of his music - and this disc is but one of those glimpses - suggest a larger body of subtle works offering similarly understated rewards.

NOW Orchestra & Marilyn Crispell: Pola. 2005. Victo: cd 097.

Marilyn Crispell: piano
Kate Hammett-Vaughn: voice
Bruce Freedman: alto saxophone
Graham Ord: tenor saxophone, soprano saxophone, flute
Saul Berson: alto saxophone, clarinet, flute
John Korsrud: trumpet, bugle
Kevin Elaschuk: trumpet, bugle
Rod Murray: trombone
Brad Muirhead: bass trombone
Ron Samworth: guitar
Paul Blaney: bass
Clyde Reed: bass
Dylan van der Schyff: drums
Coat Cooke: tenor saxophone, baritone saxophone, flute

A collaboration between the NOW Orchestra and Marilyn Crispell has enormous appeal in the HurdAudio pantheon. Though I can't help being a little disappointed that NOW's regular pianist wasn't included on this project as the creative heat generated between Marilyn Crispell and Paul Plimley would be something to hear. But the sonic shades found on Pola are far from disappointing as Coat Cooke's compositions provide a tremendous impetus for this heady, large ensemble experience. Crispell's "Yin Yang" is a fantastic translation of Crispell's sensibilities channeled through the NOW Orchestra. While Crispell's presence is clearly felt, the focal point of much of this music shifts freely throughout the ensemble in a sound that is more collaborative than concerto.

Dane Rudhyar: Works for Piano. 2004. Hat Hut Records: hat[now]ART 140.

Steffen Schleiermacher: piano
Granites (1929)
Three Paeans (1927)
Tetragrams 1st Serie (1920-27)
-Quest
-Crucifixion
-Rebirth
Third Pentagram (1926)

Exquisitely dissonant and deeply mystical piano pieces from the pioneer of transpersonal astrology. There's something majestic about the harmonic density of these short works that sets them apart and suggests a path yet to be fully explored. Schleiermacher does enormous justice to these difficult works (I used to play Third Pentagram - a fiendishly difficult piece). Dane Rudhyar's music is painfully overdue for some kind of revival as we re-asses the music of the early twentieth century.

Scale of the Day: B Chromatic

The B Chromatic Scale as one would find it on any conventionally tuned, equal tempered instrument. The sequence of exponents: 1/12, 1/6, 1/4, 1/3, etc. could also be represented as 1/12, 2/12, 3/12, 4/12, 5/12, 6/12, etc. as the 12 equal divisions of the octave that is equal temperament.