Expanding tonal space/planar extensions: Difference between revisions
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So we extend the plane of tonal space downward by ''fractional modes'' < 1 and | So we extend the plane of tonal space downward by ''fractional modes'' < 1 and | ||
enter the field of tritaves, pentaves and doubled octaves (also known as tetraves). | enter the field of tritaves, pentaves and doubled octaves (also known as tetraves). | ||
[[File:Fig-6_Extending_LE-1_4562.png|thumb|520px|center|<u>Fig.6</u>: Extending tonal space downward]] | |||
==== Tritave ==== | |||
In a Mode '''2<sup>-1'''</sup> (=0.5) overtone scale the first interval above the fundamental is the [[Tritave|tritave]] (3/1, Fig.6), which substitutes the [[Octave|octave]] (2/1), the first interval in the Mode 1 overtone scale. Incrementing ''m'' in steps of 1, we find only odd harmonics (e.g. 3, 5, 7, 9, 11) and no octaves in this fractional mode of the overtone scale. | |||
::::<math> | |||
r=\frac{0.5+1}{0.5}=\frac{3}{1}</math> | |||
::::<math> | |||
r_{cents}= ln(r)\cdot\frac{1200}{ln(2)} \approx 1902</math> ¢ | |||