Armodue harmony: Difference between revisions

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In Armodue the tenth of sixteen eka can be divided into 2, 4, or 8 parts.

* * * * * //(begins rough translation)* * * * *//

But apart from these subdivisions of the tenth, the modal system of Messiaen can be extended to all intervals with sizes between 3 and 8 eka.

If example we assume as limit interval the 6 eka one (two tomes plus a quarter tome in the 12edo System) we obtain the following sequence of notes:

1, 4, 7#, 2, 5#, 8#, 3, 6#, 1

As we can ascertain, in the range os three tenths (equivalent to three 12-edo octave) the circle closes and from the starting note 1 we arrive againto the note 1 three tenths up, by 6 eka successive carrying.

In strictly mathematic terms, the least common multiple of 16 eka (the tenth wide) and 6 eka (the carried interval) is 48 eka (corrisponding to the size of three tenths).

Every interval of six eka - carried eight times in the three tenths range - can organizing in several manner at his inside; if example in modules of: 3 + 2 + 1 eka, in that case we obtain the following 24 notes scalar system:

1, 2#, 3#, 4; (4), 6, 7, 7#; (7#), 9, 1#, 2; (2), 3#, 5, 5#; (5#), 7, 8, 8#; (8#), 1#, 2#, 3; (3), 5, 6, 6#; (6#), 8, 9, 1.

[note: the repeated parenthetical notes wants to highlight how the first and the last note of every group coincides]

All of sixteen notes appears at least one time inside the illustrated scale.

So, it's essenzial to remember the sphere of membership of the note in respect to the three tenths.

Supposing - for semplicity - to play in a three tenths register, we'll have eight notes for tenth in disposition for create the chord and melody and counterpoints texture.

Precisely, the notes:

1, 2#, 3#, 4, 6, 7, 7#, 9 in the first tenth, the lowest;

1#, 2, 3#, 5, 5#, 7, 8, 8# in the second tenth, the central;

1#, 2#, 3, 5, 6, 6#, 8, 9 in the third tenth, the highest.

Note that if we carry the originary defining intervals of 6 eka starting from note 1# instead 1, we obtain the eight pivot notes missing in the note 1 sequence:

1#, 5, 8, 2#, 6, 9, 3#, 7, 1#

At the so finded notes we can apply the same division according to the 3-2-1 eka module, obtaining the same 24 notes scale, but raised of 1 eka.

~~XXX~~

* * * * *

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In Armodue the tenth of sixteen eka can be divided into 2, 4, or 8 parts.

<ul><li>* * * * (begins rough translation)* * * * *</li></ul>