Phoenix: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2015-11-~~26 10~~:05:48 UTC</tt>.

: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2015-11-27 01:39:19 UTC</tt>.

: The original revision id was <tt>~~567860713~~</tt>.

: The original revision id was <tt>567924407</tt>.

: The revision comment was: <tt></tt>

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12edo can be smoothly deformed into phoenix by gradually moving all pitches toward their nearest neighbors, and finally adding the new "interstitial" pitches at the end.

In phoenix, the pentad 4:5:6:7:8 (represented by scale degrees 0, 6, 11, 15, 19) could be considered the basic chord, along with its utonal counterpart with triads considered incomplete. Unlike tetrads (which sound rather unstable since the top note is a seventh), but like triads, pentads have a great deal of stability and finality due to its highest note being a (tempered) octave, which is even more consonant than the perfect fifth of triads.

The otonal 4:5:6:7:8 has a happy sound, akin to a major triad (which it contains) but richer, whereas the utonal version sounds melancholy, like the minor triad (which it also contains). These are therefore the minor and major chords of phoenix. (Similar pentads can of course be voiced in 19edo as well, but do not sound as good because the sum of squared errors is higher, the 7 in particular is way out of tune in 19edo).

Phoenix scales are best used over only a finite range of around five octaves; harmonics larger than this range are once again matched poorly. A phoenix piano could be built and would have around 97 keys on it (which is only slightly more than an ordinary piano); pianos are especially good instruments for phoenix because they have built-in octave stretching already. Another option though is to end at 87 keys (one fewer than an ordinary piano) since there the largest interval here is the 24th harmonic. Pianos are good instruments for phoenix because they have stretched octaves already.

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12edo can be smoothly deformed into phoenix by gradually moving all pitches toward their nearest neighbors, and finally adding the new &quot;interstitial&quot; pitches at the end.

In phoenix, the pentad 4:5:6:7:8 (represented by scale degrees 0, 6, 11, 15, 19) could be considered the basic chord, along with its utonal counterpart with triads considered incomplete. Unlike tetrads (which sound rather unstable since the top note is a seventh), but like triads, pentads have a great deal of stability and finality due to its highest note being a (tempered) octave, which is even more consonant than the perfect fifth of triads.

The otonal 4:5:6:7:8 has a happy sound, akin to a major triad (which it contains) but richer, whereas the utonal version sounds melancholy, like the minor triad (which it also contains). These are therefore the minor and major chords of phoenix. (Similar pentads can of course be voiced in 19edo as well, but do not sound as good because the sum of squared errors is higher, the 7 in particular is way out of tune in 19edo).

Phoenix scales are best used over only a finite range of around five octaves; harmonics larger than this range are once again matched poorly. A phoenix piano could be built and would have around 97 keys on it (which is only slightly more than an ordinary piano); pianos are especially good instruments for phoenix because they have built-in octave stretching already. Another option though is to end at 87 keys (one fewer than an ordinary piano) since there the largest interval here is the 24th harmonic. Pianos are good instruments for phoenix because they have stretched octaves already.

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2015-11-26 10:05:48 UTC</tt>.<br>
+: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2015-11-27 01:39:19 UTC</tt>.<br>
-: The original revision id was <tt>567860713</tt>.<br>
+: The original revision id was <tt>567924407</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 25: / Line 25: @@
 edo can be smoothly deformed into phoenix by gradually moving all pitches toward their nearest neighbors, and finally adding the new "interstitial" pitches at the end.
+In phoenix, the pentad 4:5:6:7:8 (represented by scale degrees 0, 6, 11, 15, 19) could be considered the basic chord, along with its utonal counterpart with triads considered incomplete. Unlike tetrads (which sound rather unstable since the top note is a seventh), but like triads, pentads have a great deal of stability and finality due to its highest note being a (tempered) octave, which is even more consonant than the perfect fifth of triads.
+The otonal 4:5:6:7:8 has a happy sound, akin to a major triad (which it contains) but richer, whereas the utonal version sounds melancholy, like the minor triad (which it also contains). These are therefore the minor and major chords of phoenix. (Similar pentads can of course be voiced in 19edo as well, but do not sound as good because the sum of squared errors is higher, the 7 in particular is way out of tune in 19edo).
 Phoenix scales are best used over only a finite range of around five octaves; harmonics larger than this range are once again matched poorly. A phoenix piano could be built and would have around 97 keys on it (which is only slightly more than an ordinary piano); pianos are especially good instruments for phoenix because they have built-in octave stretching already. Another option though is to end at 87 keys (one fewer than an ordinary piano) since there the largest interval here is the 24th harmonic. Pianos are good instruments for phoenix because they have stretched octaves already.
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 &lt;br /&gt;
 edo can be smoothly deformed into phoenix by gradually moving all pitches toward their nearest neighbors, and finally adding the new &amp;quot;interstitial&amp;quot; pitches at the end.&lt;br /&gt;
+&lt;br /&gt;
+In phoenix, the pentad 4:5:6:7:8 (represented by scale degrees 0, 6, 11, 15, 19) could be considered the basic chord, along with its utonal counterpart with triads considered incomplete. Unlike tetrads (which sound rather unstable since the top note is a seventh), but like triads, pentads have a great deal of stability and finality due to its highest note being a (tempered) octave, which is even more consonant than the perfect fifth of triads. &lt;br /&gt;
+&lt;br /&gt;
+The otonal 4:5:6:7:8 has a happy sound, akin to a major triad (which it contains) but richer, whereas the utonal version sounds melancholy, like the minor triad (which it also contains). These are therefore the minor and major chords of phoenix. (Similar pentads can of course be voiced in 19edo as well, but do not sound as good because the sum of squared errors is higher, the 7 in particular is way out of tune in 19edo). &lt;br /&gt;
 &lt;br /&gt;
 Phoenix scales are best used over only a finite range of around five octaves; harmonics larger than this range are once again matched poorly. A phoenix piano could be built and would have around 97 keys on it (which is only slightly more than an ordinary piano); pianos are especially good instruments for phoenix because they have built-in octave stretching already. Another option though is to end at 87 keys (one fewer than an ordinary piano) since there the largest interval here is the 24th harmonic. Pianos are good instruments for phoenix because they have stretched octaves already.&lt;br /&gt;