Phi as a generator: Difference between revisions
Wikispaces>genewardsmith **Imported revision 288919029 - Original comment: ** |
Wikispaces>guest **Imported revision 330710882 - 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:guest|guest]] and made on <tt>2012-05-06 13:42:51 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>330710882</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 14: | Line 14: | ||
Alas there is! Ratios of 2 are the most common, and these are what the octave reduces, from the altissima 144th harmonic to the solid terrestrial 9/8 major second. So while the octave makes good sense as the equivalence, things do still occur, by and by, which may advantageously be reduced by tritaves, etc., so lets not dismiss the option entirely, and to lesser degrees up the number line. | Alas there is! Ratios of 2 are the most common, and these are what the octave reduces, from the altissima 144th harmonic to the solid terrestrial 9/8 major second. So while the octave makes good sense as the equivalence, things do still occur, by and by, which may advantageously be reduced by tritaves, etc., so lets not dismiss the option entirely, and to lesser degrees up the number line. | ||
While this is but a rank-2 temperament, suppose more generators could be added, apply phi temperament to arbitrarily higher ranks? For the price of a 3/1 you get a 7/1 and so on. That's an interesting idea on its own but it gets even much better, when one considers periods. The period, as I imagine it and maybe I'm way off the mark mathematically, can be seen as an abstract, degenerate rank. It might not be immediately so, 600 cents hardly fills in for 701.955, but eventually it gets there, at very least with phi tunings. For the price of complexity one gets a different kind of simplicity. | While this is but a rank-2 temperament, suppose more generators could be added, apply phi temperament to arbitrarily higher ranks? For the price of a 3/1 you get a 7/1 and so on. That's an interesting idea on its own but it gets even much better, when one considers periods. The period, as I imagine it and maybe I'm way off the mark mathematically, can be seen as an abstract, degenerate rank. It might not be immediately so, 600 cents hardly fills in for 701.955, but eventually it gets there, at very least with phi tunings. For the price of complexity one gets a different kind of simplicity. | ||
(Heck maybe this is mathematical gibberish for you REAL mathematicians but it works for and makes intuitive sense to me.) | (Heck maybe this is mathematical gibberish for you REAL mathematicians but it works for and makes intuitive sense to me.) | ||
| Line 36: | Line 36: | ||
ET: [[23edo|23]] (30:69) | ET: [[23edo|23]] (30:69) | ||
ET: [[36edo|36]] (30:39) best value! | ET: [[36edo|36]] (30:39) best value! | ||
ET: [[ | ET: [[121edo|121]] (8.749 : 12.675) | ||
--- | --- | ||
| Line 140: | Line 140: | ||
Alas there is! Ratios of 2 are the most common, and these are what the octave reduces, from the altissima 144th harmonic to the solid terrestrial 9/8 major second. So while the octave makes good sense as the equivalence, things do still occur, by and by, which may advantageously be reduced by tritaves, etc., so lets not dismiss the option entirely, and to lesser degrees up the number line.<br /> | Alas there is! Ratios of 2 are the most common, and these are what the octave reduces, from the altissima 144th harmonic to the solid terrestrial 9/8 major second. So while the octave makes good sense as the equivalence, things do still occur, by and by, which may advantageously be reduced by tritaves, etc., so lets not dismiss the option entirely, and to lesser degrees up the number line.<br /> | ||
<br /> | <br /> | ||
While this is but a rank-2 temperament, suppose more generators could be added, apply phi temperament to arbitrarily higher ranks? For the price of a 3/1 you get a 7/1 and so on. That's an interesting idea on its own but it gets even much better, when one considers periods. The period, as I imagine it and maybe I'm way off the mark mathematically, can be seen as an abstract, degenerate rank. It might not be immediately so, 600 cents hardly fills in for 701.955, but eventually it gets there, at very least with phi tunings. For the price of complexity one gets a different kind of simplicity. <br /> | While this is but a rank-2 temperament, suppose more generators could be added, apply phi temperament to arbitrarily higher ranks? For the price of a 3/1 you get a 7/1 and so on. That's an interesting idea on its own but it gets even much better, when one considers periods. The period, as I imagine it and maybe I'm way off the mark mathematically, can be seen as an abstract, degenerate rank. It might not be immediately so, 600 cents hardly fills in for 701.955, but eventually it gets there, at very least with phi tunings. For the price of complexity one gets a different kind of simplicity.<br /> | ||
<br /> | <br /> | ||
(Heck maybe this is mathematical gibberish for you REAL mathematicians but it works for and makes intuitive sense to me.)<br /> | (Heck maybe this is mathematical gibberish for you REAL mathematicians but it works for and makes intuitive sense to me.)<br /> | ||
| Line 162: | Line 162: | ||
ET: <a class="wiki_link" href="/23edo">23</a> (30:69)<br /> | ET: <a class="wiki_link" href="/23edo">23</a> (30:69)<br /> | ||
ET: <a class="wiki_link" href="/36edo">36</a> (30:39) best value!<br /> | ET: <a class="wiki_link" href="/36edo">36</a> (30:39) best value!<br /> | ||
ET: <a class="wiki_link" href="/ | ET: <a class="wiki_link" href="/121edo">121</a> (8.749 : 12.675)<br /> | ||
<br /> | <br /> | ||
---<br /> | ---<br /> | ||