MOS scale: Difference between revisions
Wikispaces>Osmiorisbendi **Imported revision 221058430 - Original comment: ** |
Wikispaces>keenanpepper **Imported revision 227404888 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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: | : This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-05-11 04:01:22 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>227404888</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> | ||
| Line 19: | Line 19: | ||
5. The unison or starting point of the scale is then allowed to be transferred to any scale degree--all the modes of a MOS are legal. | 5. The unison or starting point of the scale is then allowed to be transferred to any scale degree--all the modes of a MOS are legal. | ||
Condition Four is [[http://en.wikipedia.org/wiki/Myhill | Condition Four is [[http://en.wikipedia.org/wiki/Myhill%27s_property|Myhill's propery]] where, as a [[periodic scale]], the scale has every generic interval aside from the initial unison interval and intervals some number of periods from it having exactly two specific intervals. Another characterization of when a generated scale is a MOS is that the number of scale steps is the denominator of a [[http://en.wikipedia.org/wiki/Continued_fraction|convergent or semiconvergent]] of the ratio g/P of the generator and the period. | ||
These conditions entail that the generated scale has exactly two sizes of steps when sorted into ascending order of size, and usually that latter condition suffices to define a MOS. However, when the generator is a rational fraction of the period and the number of steps is more than half of the total possible, a generated scale can have only two sizes of steps and the pseudo-Myhill property, meaning that not all non-unison classes have only two specific intervals. | These conditions entail that the generated scale has exactly two sizes of steps when sorted into ascending order of size, and usually that latter condition suffices to define a MOS. However, when the generator is a rational fraction of the period and the number of steps is more than half of the total possible, a generated scale can have only two sizes of steps and the pseudo-Myhill property, meaning that not all non-unison classes have only two specific intervals. | ||
| Line 75: | Line 75: | ||
Keemun[11] [[[4L 7s]]] | Keemun[11] [[[4L 7s]]] | ||
Sensi[11] [[[8L 3s]]] | Sensi[11] [[[8L 3s]]] | ||
Slendric[11] [[[5L 6s]]] | |||
Meantone[12] [[[7L 5s]]] | Meantone[12] [[[7L 5s]]] | ||
| Line 316: | Line 317: | ||
5. The unison or starting point of the scale is then allowed to be transferred to any scale degree--all the modes of a MOS are legal.<br /> | 5. The unison or starting point of the scale is then allowed to be transferred to any scale degree--all the modes of a MOS are legal.<br /> | ||
<br /> | <br /> | ||
Condition Four is <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Myhill | Condition Four is <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Myhill%27s_property" rel="nofollow">Myhill's propery</a> where, as a <a class="wiki_link" href="/periodic%20scale">periodic scale</a>, the scale has every generic interval aside from the initial unison interval and intervals some number of periods from it having exactly two specific intervals. Another characterization of when a generated scale is a MOS is that the number of scale steps is the denominator of a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Continued_fraction" rel="nofollow">convergent or semiconvergent</a> of the ratio g/P of the generator and the period. <br /> | ||
<br /> | <br /> | ||
These conditions entail that the generated scale has exactly two sizes of steps when sorted into ascending order of size, and usually that latter condition suffices to define a MOS. However, when the generator is a rational fraction of the period and the number of steps is more than half of the total possible, a generated scale can have only two sizes of steps and the pseudo-Myhill property, meaning that not all non-unison classes have only two specific intervals.<br /> | These conditions entail that the generated scale has exactly two sizes of steps when sorted into ascending order of size, and usually that latter condition suffices to define a MOS. However, when the generator is a rational fraction of the period and the number of steps is more than half of the total possible, a generated scale can have only two sizes of steps and the pseudo-Myhill property, meaning that not all non-unison classes have only two specific intervals.<br /> | ||
| Line 599: | Line 600: | ||
Keemun[11] [<a class="wiki_link" href="/4L%207s">4L 7s</a>]<br /> | Keemun[11] [<a class="wiki_link" href="/4L%207s">4L 7s</a>]<br /> | ||
Sensi[11] [<a class="wiki_link" href="/8L%203s">8L 3s</a>]<br /> | Sensi[11] [<a class="wiki_link" href="/8L%203s">8L 3s</a>]<br /> | ||
Slendric[11] [<a class="wiki_link" href="/5L%206s">5L 6s</a>]<br /> | |||
<br /> | <br /> | ||
Meantone[12] [<a class="wiki_link" href="/7L%205s">7L 5s</a>]<br /> | Meantone[12] [<a class="wiki_link" href="/7L%205s">7L 5s</a>]<br /> | ||