3-5-7-15 hexany: Difference between revisions

Line 1:

[[File:3-5-7-15_Hexany.png|thumb|Circle diagram.]] A 7-limit [[Hexany]]. This creates a scale of 1 7/6 5/4 7/5 3/2 7/4 2/1, with steps of 7/6 15/14 28/25 15/14 7/6 8/7. This is highly notable because it contains both the harmonic sequence 4:5:6:7 and the subharmonic sequence 7/7 7/6 7/5 7/4 above the root, and at least one copy of every interval in the [[7-odd-limit]] [[tonality diamond]] somewhere in the scale. This means it is <i>the</i> optimal configuration for maximising the number and variety of simple harmonies available in a hexatonic scale. Melodically it is fairly strong as well, with every step larger than a 12edo semitone and a ratio of approximately 2.2 between the largest and smallest step. However, expanding it out to a bihexany without including any repeated notes or intervals too small to be melodically useful is significantly more challenging than many seemingly more complex hexanies.

[[File:3-5-7-15_Hexany.png|thumb|Circle diagram.]] A 7-limit [[Hexany]]. This creates a scale of 1 7/6 5/4 7/5 3/2 7/4 2/1, with steps of 7/6 15/14 28/25 15/14 7/6 8/7. This is highly notable because it contains both the harmonic sequence 4:5:6:7 and the subharmonic sequence 7/7 7/6 7/5 7/4 above the root, and at least one copy of every interval in the [[7-odd-limit]] [[tonality diamond]] somewhere in the scale. This means it is <i>the</i> optimal configuration for maximising the number and variety of simple harmonies available in a hexatonic scale. Melodically it is fairly strong as well, with every step larger than a 12edo semitone and a ratio of approximately 2.2 between the largest and smallest step. However, expanding it out to a bihexany without including any repeated notes or intervals too small to be melodically useful is significantly more challenging than many seemingly more complex hexanies, as is demonstrated in the following examples.

*[[3-5-7-15 by 9/8 bihexany]]

*[[3-5-7-15 by 9/5 bihexany]]

*[[3-5-7-15 by 45/28 bihexany]]

*[[3-5-7-15 by 27/14 bihexany]]

*[[3-5-7-15 by 11/7 bihexany]]

*[[3-5-7-15 by 17/14 bihexany]]

*[[3-5-7-15 by 19/14 bihexany]]

*[[3-5-7-15 by 23/14 bihexany]]

<pre>

! 3-5-7-15_Hexany.scl

@@ Line 1: / Line 1: @@
-[[File:3-5-7-15_Hexany.png|thumb|Circle diagram.]] A 7-limit [[Hexany]]. This creates a scale of 1 7/6 5/4 7/5 3/2 7/4 2/1, with steps of 7/6 15/14 28/25 15/14 7/6 8/7. This is highly notable because it contains both the harmonic sequence 4:5:6:7 and the subharmonic sequence 7/7 7/6 7/5 7/4 above the root, and at least one copy of every interval in the [[7-odd-limit]] [[tonality diamond]] somewhere in the scale. This means it is <i>the</i> optimal configuration for maximising the number and variety of simple harmonies available in a hexatonic scale. Melodically it is fairly strong as well, with every step larger than a 12edo semitone and a ratio of approximately 2.2 between the largest and smallest step. However, expanding it out to a bihexany without including any repeated notes or intervals too small to be melodically useful is significantly more challenging than many seemingly more complex hexanies.
+[[File:3-5-7-15_Hexany.png|thumb|Circle diagram.]] A 7-limit [[Hexany]]. This creates a scale of 1 7/6 5/4 7/5 3/2 7/4 2/1, with steps of 7/6 15/14 28/25 15/14 7/6 8/7. This is highly notable because it contains both the harmonic sequence 4:5:6:7 and the subharmonic sequence 7/7 7/6 7/5 7/4 above the root, and at least one copy of every interval in the [[7-odd-limit]] [[tonality diamond]] somewhere in the scale. This means it is <i>the</i> optimal configuration for maximising the number and variety of simple harmonies available in a hexatonic scale. Melodically it is fairly strong as well, with every step larger than a 12edo semitone and a ratio of approximately 2.2 between the largest and smallest step. However, expanding it out to a bihexany without including any repeated notes or intervals too small to be melodically useful is significantly more challenging than many seemingly more complex hexanies, as is demonstrated in the following examples.
+*[[3-5-7-15 by 9/8 bihexany]]
+*[[3-5-7-15 by 9/5 bihexany]]
+*[[3-5-7-15 by 45/28 bihexany]]
+*[[3-5-7-15 by 27/14 bihexany]]
+*[[3-5-7-15 by 11/7 bihexany]]
+*[[3-5-7-15 by 17/14 bihexany]]
+*[[3-5-7-15 by 19/14 bihexany]]
+*[[3-5-7-15 by 23/14 bihexany]]
 <pre>
 ! 3-5-7-15_Hexany.scl