17ed5: Difference between revisions
Wikispaces>Kosmorsky **Imported revision 262469926 - Original comment: ** |
Wikispaces>Kosmorsky **Imported revision 262471362 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2011-10-07 02: | : This revision was by author [[User:Kosmorsky|Kosmorsky]] and made on <tt>2011-10-07 02:54:36 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>262471362</tt>.<br> | ||
: The revision comment was: <tt></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> | 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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<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">=Division of the 5/1 into 17 tones= | <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">=Division of the 5/1 into 17 tones= | ||
Suppose you go hunting for alternate tonalities | Suppose you go hunting for alternate tonalities. The octave has been pretty well explored, not that there isn't a lot to be done. The tritave beckons - but Bohlen, Pierce and friends have kind of found what you'd be looking for. While there's tremendous ground to cover there, you have the pioneering instinct, so you examine the 5th harmonic as an equivalence. | ||
The first place to look is isoharmonic chords. In diatonic music we take 4:5:6:(7):8 and get the sublime meantone, and assorted other possibilities. In the tritave one finds that 1:2:3 looks back to the octave - although [[11edt]] does it very prettily. But when you crack open that 2/1 shell, you get to the meat of the tritave - [[Bohlen-Pierce]]- based on 3:5:7:9 isoharmony. In the pentave (5/1 and I am perpetuating the technically incorrect terminology, because it works) the first thing you find is 1:2:3:4:5 which is a good lock combination, but not the best pentave-specific chord. But if you pry it open like a clam you'll find a pearl - 5:9:13:17:21:25 a stunning consonance. The full pentad is a little complex, so you might expect to leave out the 21st, just like one does the 7th in diatonicism. | The first place to look is isoharmonic chords. In diatonic music we take 4:5:6:(7):8 and get the sublime meantone, and assorted other possibilities. In the tritave one finds that 1:2:3 looks back to the octave - although [[11edt]] does it very prettily. But when you crack open that 2/1 shell, you get to the meat of the tritave - [[Bohlen-Pierce]]- based on 3:5:7:9 isoharmony. In the pentave (5/1 and I am perpetuating the technically incorrect terminology, because it works) the first thing you find is 1:2:3:4:5 which is a good lock combination, but not the best pentave-specific chord. But if you pry it open like a clam you'll find a pearl - 5:9:13:17:21:25 a stunning consonance. The full pentad is a little complex, so you might expect to leave out the 21st, just like one does the 7th in diatonicism. | ||
So what does one do with this? Well it took me long enough to stumble on the answer... a year... Anything worth hearing is worth taking the 17th root of. Because bizarrely enough, the pattern known as "superpyth" in an octave context, is the key to tempering together these cosmic harmonies in the pentave! So I dub it "hyperpyth" but if you want to call it "kosmorsky" that's fine by me too. Musical examples forthcoming. | So what does one do with this? Well it took me long enough to stumble on the answer... a year... But the rule is now: Anything worth hearing is worth taking the 17th root of. Because bizarrely enough, the pattern known as "superpyth" in an octave context, is the key to tempering together these cosmic harmonies in the pentave! So I dub it "hyperpyth" but if you want to call it "kosmorsky" that's fine by me too. Musical examples forthcoming. | ||
17ed5 offers a good compromise between 13/5 and 17/5, but the 9/5 of 983 cents is a little bit flat. Nevertheless it's the simplest equal hyperpyth, and quite consonant, like rolling clouds of colorful interstellar dust. However, in hyperpyth, 21/5 isn't necessarily represented, at least not well - which is the case in 17ed5. Luckily, 27, 29, and 39 do a fair job of it. I wonder if there is an alternate pentave system involving 11 and 7 to correspond to octaves' "[[26edo|Orgone]]"? I bet there is and I'll look for it soon. | 17ed5 offers a good compromise between 13/5 and 17/5, but the 9/5 of 983 cents is a little bit flat. Nevertheless it's the simplest equal hyperpyth, and quite consonant, like rolling clouds of colorful interstellar dust. However, in hyperpyth, 21/5 isn't necessarily represented, at least not well - which is the case in 17ed5. Luckily, 27, 29, and 39 do a fair job of it. I wonder if there is an alternate pentave system involving 11 and 7 to correspond to octaves' "[[26edo|Orgone]]"? I bet there is and I'll look for it soon. | ||
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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>17ed5</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Division of the 5/1 into 17 tones"></a><!-- ws:end:WikiTextHeadingRule:0 -->Division of the 5/1 into 17 tones</h1> | <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>17ed5</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Division of the 5/1 into 17 tones"></a><!-- ws:end:WikiTextHeadingRule:0 -->Division of the 5/1 into 17 tones</h1> | ||
<br /> | <br /> | ||
Suppose you go hunting for alternate tonalities | Suppose you go hunting for alternate tonalities. The octave has been pretty well explored, not that there isn't a lot to be done. The tritave beckons - but Bohlen, Pierce and friends have kind of found what you'd be looking for. While there's tremendous ground to cover there, you have the pioneering instinct, so you examine the 5th harmonic as an equivalence.<br /> | ||
<br /> | <br /> | ||
The first place to look is isoharmonic chords. In diatonic music we take 4:5:6:(7):8 and get the sublime meantone, and assorted other possibilities. In the tritave one finds that 1:2:3 looks back to the octave - although <a class="wiki_link" href="/11edt">11edt</a> does it very prettily. But when you crack open that 2/1 shell, you get to the meat of the tritave - <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a>- based on 3:5:7:9 isoharmony. In the pentave (5/1 and I am perpetuating the technically incorrect terminology, because it works) the first thing you find is 1:2:3:4:5 which is a good lock combination, but not the best pentave-specific chord. But if you pry it open like a clam you'll find a pearl - 5:9:13:17:21:25 a stunning consonance. The full pentad is a little complex, so you might expect to leave out the 21st, just like one does the 7th in diatonicism.<br /> | The first place to look is isoharmonic chords. In diatonic music we take 4:5:6:(7):8 and get the sublime meantone, and assorted other possibilities. In the tritave one finds that 1:2:3 looks back to the octave - although <a class="wiki_link" href="/11edt">11edt</a> does it very prettily. But when you crack open that 2/1 shell, you get to the meat of the tritave - <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a>- based on 3:5:7:9 isoharmony. In the pentave (5/1 and I am perpetuating the technically incorrect terminology, because it works) the first thing you find is 1:2:3:4:5 which is a good lock combination, but not the best pentave-specific chord. But if you pry it open like a clam you'll find a pearl - 5:9:13:17:21:25 a stunning consonance. The full pentad is a little complex, so you might expect to leave out the 21st, just like one does the 7th in diatonicism.<br /> | ||
<br /> | <br /> | ||
So what does one do with this? Well it took me long enough to stumble on the answer... a year... Anything worth hearing is worth taking the 17th root of. Because bizarrely enough, the pattern known as &quot;superpyth&quot; in an octave context, is the key to tempering together these cosmic harmonies in the pentave! So I dub it &quot;hyperpyth&quot; but if you want to call it &quot;kosmorsky&quot; that's fine by me too. Musical examples forthcoming.<br /> | So what does one do with this? Well it took me long enough to stumble on the answer... a year... But the rule is now: Anything worth hearing is worth taking the 17th root of. Because bizarrely enough, the pattern known as &quot;superpyth&quot; in an octave context, is the key to tempering together these cosmic harmonies in the pentave! So I dub it &quot;hyperpyth&quot; but if you want to call it &quot;kosmorsky&quot; that's fine by me too. Musical examples forthcoming.<br /> | ||
<br /> | <br /> | ||
17ed5 offers a good compromise between 13/5 and 17/5, but the 9/5 of 983 cents is a little bit flat. Nevertheless it's the simplest equal hyperpyth, and quite consonant, like rolling clouds of colorful interstellar dust. However, in hyperpyth, 21/5 isn't necessarily represented, at least not well - which is the case in 17ed5. Luckily, 27, 29, and 39 do a fair job of it. I wonder if there is an alternate pentave system involving 11 and 7 to correspond to octaves' &quot;<a class="wiki_link" href="/26edo">Orgone</a>&quot;? I bet there is and I'll look for it soon.<br /> | 17ed5 offers a good compromise between 13/5 and 17/5, but the 9/5 of 983 cents is a little bit flat. Nevertheless it's the simplest equal hyperpyth, and quite consonant, like rolling clouds of colorful interstellar dust. However, in hyperpyth, 21/5 isn't necessarily represented, at least not well - which is the case in 17ed5. Luckily, 27, 29, and 39 do a fair job of it. I wonder if there is an alternate pentave system involving 11 and 7 to correspond to octaves' &quot;<a class="wiki_link" href="/26edo">Orgone</a>&quot;? I bet there is and I'll look for it soon.<br /> | ||