Fokker block: Difference between revisions
Wikispaces>genewardsmith **Imported revision 497223258 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 497223384 - 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:genewardsmith|genewardsmith]] and made on <tt>2014-03-20 18: | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-03-20 18:10:24 UTC</tt>.<br> | ||
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Returning to our pajmagorpor22 example, we have that pajmagorpor22 = Fokblock([385/384, 176/175, 100/99, 225/224], [14, 9, 4, 13]). It is also equal to Fokblock([385/384, 176/175, 100/99, 225/224], [15, 9, 4, 13]), reflecting the fact that pajara has a period of half on octave, ie that P1 = 2. Hence the pajara MOS mode is 7|3(2) in UDP notation. Finding the others by the fact thatfor them Pk=1 and ak=U, we have that the mode, in product word form, is (pajara 7|3(2))*(magic 9|12)*(orwell 4|17)*(porcupine 13|8). We can easily reverse this process, finding the chroma basis from the Fokker group basis, and the offset ai from the corresponding U and Pi as Pi*U, and so display S in terms of Fokblock. | Returning to our pajmagorpor22 example, we have that pajmagorpor22 = Fokblock([385/384, 176/175, 100/99, 225/224], [14, 9, 4, 13]). It is also equal to Fokblock([385/384, 176/175, 100/99, 225/224], [15, 9, 4, 13]), reflecting the fact that pajara has a period of half on octave, ie that P1 = 2. Hence the pajara MOS mode is 7|3(2) in UDP notation. Finding the others by the fact thatfor them Pk=1 and ak=U, we have that the mode, in product word form, is (pajara 7|3(2))*(magic 9|12)*(orwell 4|17)*(porcupine 13|8). We can easily reverse this process, finding the chroma basis from the Fokker group basis, and the offset ai from the corresponding U and Pi as Pi*U, and so display S in terms of Fokblock. | ||
If we want to compute Fokker blocks in subgroups resulting from excluding one or more odd primes, we can do so by adding the primes to the list of chromas. For instance [[nofives]] is Fokblock([64/63, 729/686, 5], [3, 4, 0]). | If we want to compute Fokker blocks in subgroups resulting from excluding one or more odd primes, we can do so by adding the primes to the list of chromas. For instance [[nofives]] is Fokblock([64/63, 729/686, 5], [3, 4, 0]). We may also use this method on other subgroups. For instance, the11^3 modes Fokblock([225/224, 1728/1715, 7/5], [a1, a2, a3]) define an arena of the 2.5.7/3 subgroup. | ||
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Returning to our pajmagorpor22 example, we have that pajmagorpor22 = Fokblock([385/384, 176/175, 100/99, 225/224], [14, 9, 4, 13]). It is also equal to Fokblock([385/384, 176/175, 100/99, 225/224], [15, 9, 4, 13]), reflecting the fact that pajara has a period of half on octave, ie that P1 = 2. Hence the pajara MOS mode is 7|3(2) in UDP notation. Finding the others by the fact thatfor them Pk=1 and ak=U, we have that the mode, in product word form, is (pajara 7|3(2))*(magic 9|12)*(orwell 4|17)*(porcupine 13|8). We can easily reverse this process, finding the chroma basis from the Fokker group basis, and the offset ai from the corresponding U and Pi as Pi*U, and so display S in terms of Fokblock.<br /> | Returning to our pajmagorpor22 example, we have that pajmagorpor22 = Fokblock([385/384, 176/175, 100/99, 225/224], [14, 9, 4, 13]). It is also equal to Fokblock([385/384, 176/175, 100/99, 225/224], [15, 9, 4, 13]), reflecting the fact that pajara has a period of half on octave, ie that P1 = 2. Hence the pajara MOS mode is 7|3(2) in UDP notation. Finding the others by the fact thatfor them Pk=1 and ak=U, we have that the mode, in product word form, is (pajara 7|3(2))*(magic 9|12)*(orwell 4|17)*(porcupine 13|8). We can easily reverse this process, finding the chroma basis from the Fokker group basis, and the offset ai from the corresponding U and Pi as Pi*U, and so display S in terms of Fokblock.<br /> | ||
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If we want to compute Fokker blocks in subgroups resulting from excluding one or more odd primes, we can do so by adding the primes to the list of chromas. For instance <a class="wiki_link" href="/nofives">nofives</a> is Fokblock([64/63, 729/686, 5], [3, 4, 0]). | If we want to compute Fokker blocks in subgroups resulting from excluding one or more odd primes, we can do so by adding the primes to the list of chromas. For instance <a class="wiki_link" href="/nofives">nofives</a> is Fokblock([64/63, 729/686, 5], [3, 4, 0]). We may also use this method on other subgroups. For instance, the11^3 modes Fokblock([225/224, 1728/1715, 7/5], [a1, a2, a3]) define an arena of the 2.5.7/3 subgroup.</body></html></pre></div> | ||