Magic: Difference between revisions
Wikispaces>genewardsmith **Imported revision 519400250 - Original comment: ** |
Wikispaces>x31eq **Imported revision 520238678 - Original comment: ** |
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**Magic** is a linear temperament in which the ~380 cent generator represents 5/4, and five of those make a 3/1. This implies that the [[magic comma]] 3125/3072 is tempered out, making it a member of the [[Magic family]]. This article also assumes the default mapping for the prime 7, which tempers out 225/224 and makes two generators equivalent to 14/9. 7/4 can be reached by 12 generators in this mapping. (There is an alternative mapping for 7 known as [[Magic family#Muggles|muggles]], but there's basically no reason to use it unless you're using [[19edo]], in which case it's identical to magic anyway.) | **Magic** is a linear temperament in which the ~380 cent generator represents 5/4, and five of those make a 3/1. This implies that the [[magic comma]] 3125/3072 is tempered out, making it a member of the [[Magic family]]. This article also assumes the default mapping for the prime 7, which tempers out 225/224 and makes two generators equivalent to 14/9. 7/4 can be reached by 12 generators in this mapping. (There is an alternative mapping for 7 known as [[Magic family#Muggles|muggles]], but there's basically no reason to use it unless you're using [[19edo]], in which case it's identical to magic anyway.) | ||
EDOs that contain good magic scales include [[19edo]], [[22edo]], [[41edo]] and [[104edo]]. | EDOs that contain good magic scales include [[19edo]], [[22edo]], [[41edo]], [[60edo]] and [[104edo]]. | ||
Because the generator is so close to 1\3 of an octave, and the interval left over (which represents both 128/125 and 25/24) is accordingly so small, all small magic MOSes consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following MOSes, where s always represents the characteristic small interval of 128/125~25/24. | Because the generator is so close to 1\3 of an octave, and the interval left over (which represents both 128/125 and 25/24) is accordingly so small, all small magic MOSes consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following MOSes, where s always represents the characteristic small interval of 128/125~25/24. | ||
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<strong>Magic</strong> is a linear temperament in which the ~380 cent generator represents 5/4, and five of those make a 3/1. This implies that the <a class="wiki_link" href="/magic%20comma">magic comma</a> 3125/3072 is tempered out, making it a member of the <a class="wiki_link" href="/Magic%20family">Magic family</a>. This article also assumes the default mapping for the prime 7, which tempers out 225/224 and makes two generators equivalent to 14/9. 7/4 can be reached by 12 generators in this mapping. (There is an alternative mapping for 7 known as <a class="wiki_link" href="/Magic%20family#Muggles">muggles</a>, but there's basically no reason to use it unless you're using <a class="wiki_link" href="/19edo">19edo</a>, in which case it's identical to magic anyway.)<br /> | <strong>Magic</strong> is a linear temperament in which the ~380 cent generator represents 5/4, and five of those make a 3/1. This implies that the <a class="wiki_link" href="/magic%20comma">magic comma</a> 3125/3072 is tempered out, making it a member of the <a class="wiki_link" href="/Magic%20family">Magic family</a>. This article also assumes the default mapping for the prime 7, which tempers out 225/224 and makes two generators equivalent to 14/9. 7/4 can be reached by 12 generators in this mapping. (There is an alternative mapping for 7 known as <a class="wiki_link" href="/Magic%20family#Muggles">muggles</a>, but there's basically no reason to use it unless you're using <a class="wiki_link" href="/19edo">19edo</a>, in which case it's identical to magic anyway.)<br /> | ||
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EDOs that contain good magic scales include <a class="wiki_link" href="/19edo">19edo</a>, <a class="wiki_link" href="/22edo">22edo</a>, <a class="wiki_link" href="/41edo">41edo</a> and <a class="wiki_link" href="/104edo">104edo</a>.<br /> | EDOs that contain good magic scales include <a class="wiki_link" href="/19edo">19edo</a>, <a class="wiki_link" href="/22edo">22edo</a>, <a class="wiki_link" href="/41edo">41edo</a>, <a class="wiki_link" href="/60edo">60edo</a> and <a class="wiki_link" href="/104edo">104edo</a>.<br /> | ||
<br /> | <br /> | ||
Because the generator is so close to 1\3 of an octave, and the interval left over (which represents both 128/125 and 25/24) is accordingly so small, all small magic MOSes consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following MOSes, where s always represents the characteristic small interval of 128/125~25/24.<br /> | Because the generator is so close to 1\3 of an octave, and the interval left over (which represents both 128/125 and 25/24) is accordingly so small, all small magic MOSes consist of three large intervals alternating with three groups of this small interval. Specifically, there are the following MOSes, where s always represents the characteristic small interval of 128/125~25/24.<br /> | ||