Checking out various harmonies from the natural harmonic series. The first two chords go from 8:10:13 to 30:35:39 (1:1, 5:4, 13:8 to 1:1, 7:6, 13:8). Those are the harmonies I decided to concentrate on for a longer piece. Homemade shakuhachi and clarinet (and yes I used a guide track on this one- I can do these pretty close out of thin air but I want them to be exaxt. You don't want to see the cross-fingerings and embouchure funk necessary to pull them off). 

DarkCastle TarkanGrood

For clarinet trio. The heart harmony of the piece is tuned to the natural harmonic partials 8:10:13 (a pure "major third" of 5:4 within the naturally-occuring "neutral sixth" of 13:8 almost exactly halfway between the minor and major sixth of contemporary Western music). 

Clarinets performed by three of Tarkan Grood, thanks to the magic of multitrack recording. Written on 12 January 2013 and performed the next day.

This piece is best notated in 37 equal divisions of an octave, and extended pieces highlighting the harmonies presented here would be best generally conceived of in 37 tones. In practice acoustic instruments will vary the pitches from the mathematically exact pitches of 37 equal, because there is a palpable acoustic effect created by such harmonies as 8:10:13, but these variations are only a few cents and just add life to the piece, not presenting a problem of the whole piece wandering about in pitch due to shifting of commas.

A Valley Of Gold Unfolding Tarkan Grood

Another tune for the "Xenharmonic Alliance" Facebook group. This tune uses all nine tones of the near-rational (that is, using intervals derived directly from the harmonic series) structure generated by dividing the harmonic ratio of 3:1 into seven equal parts and using that interval (very close to a 7:6) as a generator, (in the way one would traditionally used a tempered 3:2.) 

This structure is called "orwell 9" by the tuning theorists here:

http://xenharmonic.wikispaces.com

This tune presents a melody- the scale we would derive from this melody would be a simple scale of only six tones. The accompaniment uses the six tones of the melody and introduces the other three tones of the nine tones we have in our near-Just structure as well. When the melody comes about again, it brings in these three other tones, at first in the way we would call chromatic, then the tones are steadily more incorporated so that if we were to derive a scale from the melody, we'd have all nine tones.

So, throughout the piece we have the whole near-Just sctructure being used, and by the end of the piece, the melodic "scale" uses all nine tones as well. 

The way these nine tones all work together is not the same as how nine tones of the usual 12-tET tuning work, or how other tunings work. 



Mountain Village Tarkan Grood

Ancient and Medieval Tetrachords in Polyphony

description to follow

Flowering Trees Tarkan Grood

Ancient and Medieval Tetrachords in Polyphony

Willows Tarkan Grood

Ancient and Medieval Tetrachords in Polyphony 
Tetrachords of Avicenna (Ibn Sin) for Baglama and 3 Clarinets

Blossoms Tarkan Grood

Ancient and Medieval Tetrachords in Polyphony
Cura Saz, 2 clarinets, 2 jinashi shakuhachi flutes

PetalsOnWater Tarkan Grood

Diatonic tetrachord of Ibn Sin (Avicenna) in a chain of conjuct tetrachords. Clarinet and anbaric klavir written and performed by Takan Grood.

This piece cannot be performed in the 12-tone equal temperament which is the standard tuning in the Western world, and increasingly around the world. We could play the melody, but four of the seven notes in the octave would be different by almost a quartertone, and the keyboard part is literally impossible in 12-tET, because three minor thirds don't make a major sixth as they do in 12-tET- they make a minor seventh (two stacked fourths)! 

The harmonic change from two stacked fourths to three stacked minor thirds while retaining the same outer intervals (that is, the same minor seventh is played split precisely in two, then precisely in three) happens throughout the piece and is the heart of the harmonic structure.

I call this tuning "Avicenna Diatonic Temperament", because it is a built on a diatonic tetrachord of Avicenna, and the whole tuning is a long chain of these tetrachords.  Fifteen tones makes a symmetrical "complete" system, you can go to 29 tones to fill the octave completely. 

Though my goals were different, the scale that is the end result is for all practical purposes the same as "porcupine temperament in 29-edo" as described here: 

http://xenharmonic.wikispaces.com/Porcupine

I split the 4:3 precisely in three for the generator, which is a bit different, and the approximations of rational intervals as  described on that page do not apply to the way I'm using the scale, which is to have near-perfect 14:13, 9:8 and 11:10 making a perfect 4:3 (which was  Avicenna's goal for this particular tetrachord) in a rich practical arrangement. 


Something About Pineapples Tarkan Grood

Ancient and Medieval Tetrachords in Polyphony, for New Music

For three clarinets and cura saz, written and performed by Tarkan Grood.

This piece uses only the enharmonic tetrachord, in the tuning of Archytus. 

Pomegranate TarkanGrood

Another little example of stuff for the Xenharmonic Facebook group. This one is in nineteen equal tones to the octave and is based on the sonority 5:6:7:9 alternating with its inversion against the octave, or put another way the octave is divided into chunks large and small, and LsLs alternates with sLsL. 

Multitrack clarinets and shot glass performed written and performed by Tarkan Grood, 3 March 2013

Tarkan Grood

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