Expanding tonal space/planar extensions: Difference between revisions

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==== 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]]

::<center>Fig.4: Two octaves view of tonal space</center>

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>(

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> ).

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== Find out more about tonal space… ==

====[[Expanding tonal space|Part I: Expanding tonal space]]====

==== [[Expanding tonal space|Part I: Expanding tonal space]] ====

==== [[Expanding tonal space/projections|Part III: Projections]] ====

==== [[Expanding tonal space/third dimension|Part IV: Third dimension]] ====

== See also... ==

@@ Line 28: / Line 28: @@
 ==== 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]]
 ::<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]]'' <br>(for example starting at harmonic  ''h6'': <math>(
+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> ).
@@ Line 94: / Line 94: @@
 == Find out more about tonal space… ==
-====[[Expanding tonal space|Part I: Expanding tonal space]]====
+==== [[Expanding tonal space|Part I: <span style="font-weight:normal">Expanding tonal space</span>]] ====
+==== [[Expanding tonal space/projections|Part III: <span style="font-weight:normal">Projections</span>]] ====
+==== [[Expanding tonal space/third dimension|Part IV: <span style="font-weight:normal">Third dimension</span>]] ====
 == See also... ==