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Wikispaces>MasonGreen1 **Imported revision 584997851 - Original comment: ** |
Wikispaces>MasonGreen1 **Imported revision 584997871 - 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:MasonGreen1|MasonGreen1]] and made on <tt>2016-06-07 22:55: | : This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-06-07 22:55:59 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>584997871</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
<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">**Angel** is a name proposed by Mason Green for the temperament that tempers out 81:80 (thus, it is a meantone system), and has a period that is a flattened 3:2, four of which make a pentave (5:1), while its generator is an octave. This temperament is very closely related to quarter-comma meantone (which was the standard for most Western classical music); the key difference is that meantone has a period of an octave and a fifth as a generator, whereas the roles of the fifth and octave are reversed in angel. (Due to the period being a fifth, setting the generator to an octave is equivalent to using a perfect fourth or whole tone as the generator instead). | <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">**Angel** is a name* proposed by Mason Green for the temperament that tempers out 81:80 (thus, it is a meantone system), and has a period that is a flattened 3:2, four of which make a pentave (5:1), while its generator is an octave. This temperament is very closely related to quarter-comma meantone (which was the standard for most Western classical music); the key difference is that meantone has a period of an octave and a fifth as a generator, whereas the roles of the fifth and octave are reversed in angel. (Due to the period being a fifth, setting the generator to an octave is equivalent to using a perfect fourth or whole tone as the generator instead). | ||
If the pentaves are required to be exactly 5:1, then the fifths will be exactly the same size as the fifths of quarter-comma meantone (namely, the fourth root of five), but the octaves will be slightly flat (by less than half a cent). On the other hand, if the octaves are made perfect (making this a [[31edo]] temperament), the pentaves will be slightly sharp. Both options are perceptually very close to one another. | If the pentaves are required to be exactly 5:1, then the fifths will be exactly the same size as the fifths of quarter-comma meantone (namely, the fourth root of five), but the octaves will be slightly flat (by less than half a cent). On the other hand, if the octaves are made perfect (making this a [[31edo]] temperament), the pentaves will be slightly sharp. Both options are perceptually very close to one another. | ||
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In particular, the angel MOS with 11 notes per period has long chains of ten octaves, which spans nearly the entire range of human hearing. Many if not most common-practice pieces can be easily translated into this scale, since the deviation from a purely octave-repeating system only becomes apparent for melodies and harmonies spanning several octaves. Compound intervals (spanning more than an octave) are sometimes perceived as more or less consonant than their simple counterparts; this is especially true for high-limit intervals like 11:8 (which is more consonant in compound form). Thus it may actually be beneficial to use a system that doesn't exactly repeat at the octave. | In particular, the angel MOS with 11 notes per period has long chains of ten octaves, which spans nearly the entire range of human hearing. Many if not most common-practice pieces can be easily translated into this scale, since the deviation from a purely octave-repeating system only becomes apparent for melodies and harmonies spanning several octaves. Compound intervals (spanning more than an octave) are sometimes perceived as more or less consonant than their simple counterparts; this is especially true for high-limit intervals like 11:8 (which is more consonant in compound form). Thus it may actually be beneficial to use a system that doesn't exactly repeat at the octave. | ||
The complexity of the complete 12-limit otonality (1:2:3:4:5:6:7:8:9:10:11:12) is nine, and those of the 10-limit and 8-limit otonalities are both four. The angel-chromatic scale thus contains three (up to period equivalence) complete otonalities and three complete utonalities in the 10-limit, while the angel-enharmonic scale contains two of each 12-limit complete chord.</pre></div> | The complexity of the complete 12-limit otonality (1:2:3:4:5:6:7:8:9:10:11:12) is nine, and those of the 10-limit and 8-limit otonalities are both four. The angel-chromatic scale thus contains three (up to period equivalence) complete otonalities and three complete utonalities in the 10-limit, while the angel-enharmonic scale contains two of each 12-limit complete chord. | ||
*Because this temperament almost seems too good to be true.</pre></div> | |||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<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>Angel</title></head><body><strong>Angel</strong> is a name proposed by Mason Green for the temperament that tempers out 81:80 (thus, it is a meantone system), and has a period that is a flattened 3:2, four of which make a pentave (5:1), while its generator is an octave. This temperament is very closely related to quarter-comma meantone (which was the standard for most Western classical music); the key difference is that meantone has a period of an octave and a fifth as a generator, whereas the roles of the fifth and octave are reversed in angel. (Due to the period being a fifth, setting the generator to an octave is equivalent to using a perfect fourth or whole tone as the generator instead).<br /> | <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>Angel</title></head><body><strong>Angel</strong> is a name* proposed by Mason Green for the temperament that tempers out 81:80 (thus, it is a meantone system), and has a period that is a flattened 3:2, four of which make a pentave (5:1), while its generator is an octave. This temperament is very closely related to quarter-comma meantone (which was the standard for most Western classical music); the key difference is that meantone has a period of an octave and a fifth as a generator, whereas the roles of the fifth and octave are reversed in angel. (Due to the period being a fifth, setting the generator to an octave is equivalent to using a perfect fourth or whole tone as the generator instead).<br /> | ||
<br /> | <br /> | ||
If the pentaves are required to be exactly 5:1, then the fifths will be exactly the same size as the fifths of quarter-comma meantone (namely, the fourth root of five), but the octaves will be slightly flat (by less than half a cent). On the other hand, if the octaves are made perfect (making this a <a class="wiki_link" href="/31edo">31edo</a> temperament), the pentaves will be slightly sharp. Both options are perceptually very close to one another.<br /> | If the pentaves are required to be exactly 5:1, then the fifths will be exactly the same size as the fifths of quarter-comma meantone (namely, the fourth root of five), but the octaves will be slightly flat (by less than half a cent). On the other hand, if the octaves are made perfect (making this a <a class="wiki_link" href="/31edo">31edo</a> temperament), the pentaves will be slightly sharp. Both options are perceptually very close to one another.<br /> | ||
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In particular, the angel MOS with 11 notes per period has long chains of ten octaves, which spans nearly the entire range of human hearing. Many if not most common-practice pieces can be easily translated into this scale, since the deviation from a purely octave-repeating system only becomes apparent for melodies and harmonies spanning several octaves. Compound intervals (spanning more than an octave) are sometimes perceived as more or less consonant than their simple counterparts; this is especially true for high-limit intervals like 11:8 (which is more consonant in compound form). Thus it may actually be beneficial to use a system that doesn't exactly repeat at the octave.<br /> | In particular, the angel MOS with 11 notes per period has long chains of ten octaves, which spans nearly the entire range of human hearing. Many if not most common-practice pieces can be easily translated into this scale, since the deviation from a purely octave-repeating system only becomes apparent for melodies and harmonies spanning several octaves. Compound intervals (spanning more than an octave) are sometimes perceived as more or less consonant than their simple counterparts; this is especially true for high-limit intervals like 11:8 (which is more consonant in compound form). Thus it may actually be beneficial to use a system that doesn't exactly repeat at the octave.<br /> | ||
<br /> | <br /> | ||
The complexity of the complete 12-limit otonality (1:2:3:4:5:6:7:8:9:10:11:12) is nine, and those of the 10-limit and 8-limit otonalities are both four. The angel-chromatic scale thus contains three (up to period equivalence) complete otonalities and three complete utonalities in the 10-limit, while the angel-enharmonic scale contains two of each 12-limit complete chord.</body></html></pre></div> | The complexity of the complete 12-limit otonality (1:2:3:4:5:6:7:8:9:10:11:12) is nine, and those of the 10-limit and 8-limit otonalities are both four. The angel-chromatic scale thus contains three (up to period equivalence) complete otonalities and three complete utonalities in the 10-limit, while the angel-enharmonic scale contains two of each 12-limit complete chord.<br /> | ||
<br /> | |||
*Because this temperament almost seems too good to be true.</body></html></pre></div> | |||
Revision as of 22:55, 7 June 2016
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author MasonGreen1 and made on 2016-06-07 22:55:59 UTC.
- The original revision id was 584997871.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
**Angel** is a name* proposed by Mason Green for the temperament that tempers out 81:80 (thus, it is a meantone system), and has a period that is a flattened 3:2, four of which make a pentave (5:1), while its generator is an octave. This temperament is very closely related to quarter-comma meantone (which was the standard for most Western classical music); the key difference is that meantone has a period of an octave and a fifth as a generator, whereas the roles of the fifth and octave are reversed in angel. (Due to the period being a fifth, setting the generator to an octave is equivalent to using a perfect fourth or whole tone as the generator instead). If the pentaves are required to be exactly 5:1, then the fifths will be exactly the same size as the fifths of quarter-comma meantone (namely, the fourth root of five), but the octaves will be slightly flat (by less than half a cent). On the other hand, if the octaves are made perfect (making this a [[31edo]] temperament), the pentaves will be slightly sharp. Both options are perceptually very close to one another. More specifically, the term angel may refer to various MOSes and MODMOSes that are derived from this temperament. There are MOSes with 3, 4, 7, and 11 notes per period; these have 5, 7, 12, and 19 notes per octave and so may be considered the angel equivalents of the pentatonic, diatonic, chromatic, and enharmonic scales respectively. Although angel scales are not octave-repeating, the fact that the generator is an octave makes them far less xenharmonic than one might think. You don't even have to train yourself to hear pentaves as equivalent, since the octave can still be thought of as a "pseudo-equivalency" due to its being the generator. In particular, the angel MOS with 11 notes per period has long chains of ten octaves, which spans nearly the entire range of human hearing. Many if not most common-practice pieces can be easily translated into this scale, since the deviation from a purely octave-repeating system only becomes apparent for melodies and harmonies spanning several octaves. Compound intervals (spanning more than an octave) are sometimes perceived as more or less consonant than their simple counterparts; this is especially true for high-limit intervals like 11:8 (which is more consonant in compound form). Thus it may actually be beneficial to use a system that doesn't exactly repeat at the octave. The complexity of the complete 12-limit otonality (1:2:3:4:5:6:7:8:9:10:11:12) is nine, and those of the 10-limit and 8-limit otonalities are both four. The angel-chromatic scale thus contains three (up to period equivalence) complete otonalities and three complete utonalities in the 10-limit, while the angel-enharmonic scale contains two of each 12-limit complete chord. *Because this temperament almost seems too good to be true.
Original HTML content:
<html><head><title>Angel</title></head><body><strong>Angel</strong> is a name* proposed by Mason Green for the temperament that tempers out 81:80 (thus, it is a meantone system), and has a period that is a flattened 3:2, four of which make a pentave (5:1), while its generator is an octave. This temperament is very closely related to quarter-comma meantone (which was the standard for most Western classical music); the key difference is that meantone has a period of an octave and a fifth as a generator, whereas the roles of the fifth and octave are reversed in angel. (Due to the period being a fifth, setting the generator to an octave is equivalent to using a perfect fourth or whole tone as the generator instead).<br /> <br /> If the pentaves are required to be exactly 5:1, then the fifths will be exactly the same size as the fifths of quarter-comma meantone (namely, the fourth root of five), but the octaves will be slightly flat (by less than half a cent). On the other hand, if the octaves are made perfect (making this a <a class="wiki_link" href="/31edo">31edo</a> temperament), the pentaves will be slightly sharp. Both options are perceptually very close to one another.<br /> <br /> More specifically, the term angel may refer to various MOSes and MODMOSes that are derived from this temperament. There are MOSes with 3, 4, 7, and 11 notes per period; these have 5, 7, 12, and 19 notes per octave and so may be considered the angel equivalents of the pentatonic, diatonic, chromatic, and enharmonic scales respectively.<br /> <br /> Although angel scales are not octave-repeating, the fact that the generator is an octave makes them far less xenharmonic than one might think. You don't even have to train yourself to hear pentaves as equivalent, since the octave can still be thought of as a "pseudo-equivalency" due to its being the generator.<br /> <br /> In particular, the angel MOS with 11 notes per period has long chains of ten octaves, which spans nearly the entire range of human hearing. Many if not most common-practice pieces can be easily translated into this scale, since the deviation from a purely octave-repeating system only becomes apparent for melodies and harmonies spanning several octaves. Compound intervals (spanning more than an octave) are sometimes perceived as more or less consonant than their simple counterparts; this is especially true for high-limit intervals like 11:8 (which is more consonant in compound form). Thus it may actually be beneficial to use a system that doesn't exactly repeat at the octave.<br /> <br /> The complexity of the complete 12-limit otonality (1:2:3:4:5:6:7:8:9:10:11:12) is nine, and those of the 10-limit and 8-limit otonalities are both four. The angel-chromatic scale thus contains three (up to period equivalence) complete otonalities and three complete utonalities in the 10-limit, while the angel-enharmonic scale contains two of each 12-limit complete chord.<br /> <br /> *Because this temperament almost seems too good to be true.</body></html>