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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
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| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-09-21 11:06:54 UTC</tt>.<br>
| | | en = Nonoctave |
| : The original revision id was <tt>256579346</tt>.<br>
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| : The revision comment was: <tt></tt><br>
| | | ja = ノンオクターブ |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
| | A '''nonoctave''' scale is a scale whose [[equivalence interval]] is not the [[octave]] (2/1). |
| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">//Nonoctave scales// come in many varieties, but what unites them is a lack of octaves. A common approach to building a sensible scale without octaves is to divide some nonoctave interval into logarithmically equal parts, as one would divide the octave to arrive at an [[EDO]]. Such a scale is sometimes called an [[EDONOI]], short for "equal divisions of a nonoctave interval". One can also build rational scales with nonoctave repeats or no repeat (e.g. [[Superparticular-Nonoctave-MOS]]). Nonoctave scales may contain a "near octave" or "tempered octave" which would be an interval near a [[2_1|2/1]] but not measuring 1200¢. In this category, there are stretched octaves and compressed octaves, each having their own character.
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| ==Why choose a Nonoctave Scale?==
| | Nonoctave scales come in many varieties, but what unites them is an aversion of [[octave]]s. A common approach to building a sensible scale without octaves is to divide some nonoctave interval into logarithmically [[equal]] parts, as one would divide the octave to arrive at an [[EDO]]. Such a scale is sometimes called an [[edonoi|EDONOI]], short for "equal divisions of a nonoctave interval". One can also build rational scales with nonoctave repeats or no repeat (e.g. [[Superparticular-Nonoctave-MOS|Superparticular-Nonoctave-MOS]]). |
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| | Nonoctave scales may contain a [[pseudo-octave]] (aka “near octave" or "tempered octave") which would be an interval near but not exactly 1200¢. In this category, there are [[Octave stretch|stretched octaves]] and compressed octaves, each having their own character. |
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| | Composers and theorists known for their work in nonoctave scales include [[X. J. Scott]]; [[Wendy Carlos]]; [[Gary Morrison]]; [[Carlo Serafini]]; and [[Heinz Bohlen]], [[John Pierce]], and [[Kees van Prooijen]], the latter trio being associated with the [[Bohlen–Pierce scale]]. |
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| | == Why choose a Nonoctave Scale? == |
| Here are only a few reasons. Add your own! | | Here are only a few reasons. Add your own! |
| # The 2/1 octave is distractingly consonant, and gets in the way when exploring xenharmonic resources. If your music is seeking to explore new consonances, then why would you keep the oldest, simplest consonance in the system? It is too easy to fall back on the octave and resolve everything unfamiliar to a plain old characterless octave.
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| # The 2/1 octave is boring; it doesn't even sound like a distinct interval!
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| # Octave-repetition is too [[redundancy|redundant]]. In a nonoctave scale, each part of the range offers new intervals. Thus, with only a few tones, a great variety is possible. In an octave-repeating scale, once the octave is reached, there is nothing new to be had.
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| # Octave stretching and compressing turns boring vanilla octaves into exciting, vibrant, active near-octaves. Near-octaves may provide that function of octave-redundancy, while not introducing the distracting consonance of a 2/1.
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| # Instruments in different ranges have different pitches available to them. This allows for more interesting polyphony.
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| Composers and theorists known for their work in nonoctave scales include [[X. J. Scott]] (see: [[http://www.nonoctave.com]]); [[Wendy Carlos]]; [[Gary Morrison]]; [[Carlo Serafini]]; and [[Heinz Bohlen]], [[John Pierce]], and [[Kees van Prooijen]], the latter trio being associated with the [[Bohlen-Pierce]] scale.</pre></div>
| | <ol><li>The 2/1 octave is distractingly [[consonant]], and gets in the way when exploring xenharmonic resources. If your music is seeking to explore new consonances, then why would you keep the oldest, simplest consonance in the system? It is too easy to fall back on the octave and resolve everything unfamiliar to a plain old characterless octave.</li> |
| <h4>Original HTML content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>nonoctave</title></head><body><em>Nonoctave scales</em> come in many varieties, but what unites them is a lack of octaves. A common approach to building a sensible scale without octaves is to divide some nonoctave interval into logarithmically equal parts, as one would divide the octave to arrive at an <a class="wiki_link" href="/EDO">EDO</a>. Such a scale is sometimes called an <a class="wiki_link" href="/EDONOI">EDONOI</a>, short for &quot;equal divisions of a nonoctave interval&quot;. One can also build rational scales with nonoctave repeats or no repeat (e.g. <a class="wiki_link" href="/Superparticular-Nonoctave-MOS">Superparticular-Nonoctave-MOS</a>). Nonoctave scales may contain a &quot;near octave&quot; or &quot;tempered octave&quot; which would be an interval near a <a class="wiki_link" href="/2_1">2/1</a> but not measuring 1200¢. In this category, there are stretched octaves and compressed octaves, each having their own character.<br />
| | <li>The 2/1 octave is boring; it doesn't even sound like a distinct interval!</li> |
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Why choose a Nonoctave Scale?"></a><!-- ws:end:WikiTextHeadingRule:0 -->Why choose a Nonoctave Scale?</h2>
| | <li>Octave-repetition is too [[redundancy|redundant]]. In a nonoctave scale, each part of the range offers new intervals. Thus, with only a few tones, a great variety is possible. In an octave-repeating scale, once the octave is reached, there is nothing new to be had.</li> |
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| Here are only a few reasons. Add your own!<br />
| | <li>Octave stretching and compressing turns boring vanilla octaves into exciting, vibrant, active near-octaves. Near-octaves may provide that function of octave-redundancy, while not introducing the distracting consonance of a 2/1.</li> |
| <ol><li>The 2/1 octave is distractingly consonant, and gets in the way when exploring xenharmonic resources. If your music is seeking to explore new consonances, then why would you keep the oldest, simplest consonance in the system? It is too easy to fall back on the octave and resolve everything unfamiliar to a plain old characterless octave.</li><li>The 2/1 octave is boring; it doesn't even sound like a distinct interval!</li><li>Octave-repetition is too <a class="wiki_link" href="/redundancy">redundant</a>. In a nonoctave scale, each part of the range offers new intervals. Thus, with only a few tones, a great variety is possible. In an octave-repeating scale, once the octave is reached, there is nothing new to be had.</li><li>Octave stretching and compressing turns boring vanilla octaves into exciting, vibrant, active near-octaves. Near-octaves may provide that function of octave-redundancy, while not introducing the distracting consonance of a 2/1.</li><li>Instruments in different ranges have different pitches available to them. This allows for more interesting polyphony.</li></ol><br />
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| Composers and theorists known for their work in nonoctave scales include <a class="wiki_link" href="/X.%20J.%20Scott">X. J. Scott</a> (see: <a class="wiki_link_ext" href="http://www.nonoctave.com" rel="nofollow">http://www.nonoctave.com</a>); <a class="wiki_link" href="/Wendy%20Carlos">Wendy Carlos</a>; <a class="wiki_link" href="/Gary%20Morrison">Gary Morrison</a>; <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a>; and <a class="wiki_link" href="/Heinz%20Bohlen">Heinz Bohlen</a>, <a class="wiki_link" href="/John%20Pierce">John Pierce</a>, and <a class="wiki_link" href="/Kees%20van%20Prooijen">Kees van Prooijen</a>, the latter trio being associated with the <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> scale.</body></html></pre></div>
| | <li>Instruments in different ranges have different pitches available to them. This allows for more interesting polyphony.</li> |
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| | <li>You can play musical scales without repeating at any intervals and it has infinite notes too!</li></ol> |
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| | Consider exploring a scale from the [[Gallery_of_nonoctave_scales|Gallery of nonoctave scales]]. |
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| | [[Category:Nonoctave| ]] <!-- Main article --> |
| | [[Category:Tuning]] |