Expanding tonal space/planar extensions: Difference between revisions
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==== Extending tonal space to the right ==== | ==== Extending tonal space to the right ==== | ||
As we know, interval spacing actually gets narrower in the next higher octave of an overtone scale. For a more natural appearance of adjacent octaves, we can shift the two corresponding frames (e.g. orange and blue) vertically by one octave. This even leaves room for the more dense intervals of the 6th octave in the upper right corner. | As we know, interval spacing actually gets narrower in the next higher octave of an overtone scale. For a more natural appearance of adjacent octaves, we can shift the two corresponding frames (e.g. orange and blue) vertically by one octave (Fig.4). This even leaves room for the more dense intervals of the 6th octave in the upper right corner. | ||
[[File:Fig-4_Extending_450_1-32_2oct.png|640px|center]] | [[File:Fig-4_Extending_450_1-32_2oct.png|640px|center]] | ||
::<center><small><u>Fig.4</u>: Two octaves view of tonal space</small></center> | ::<center><small><u>Fig.4</u>: Two octaves view of tonal space</small></center> | ||
The ''slanted'' fine blue lines connect intervals that share a common numerator, since Harry Partch also known as ''[[Otonality and utonality|utonalities]]'' | The ''slanted'' fine blue lines connect intervals that share a common numerator, since Harry Partch also known as ''[[Otonality and utonality|utonalities]]'' (for example starting at harmonic ''h6'': <math>( | ||
\frac{6}{6}, \frac{6}{5}, \frac{6}{4}, \frac{6}{3}, \frac{6}{2})</math> ). | \frac{6}{6}, \frac{6}{5}, \frac{6}{4}, \frac{6}{3}, \frac{6}{2})</math> ). | ||