Titanium: Difference between revisions
Wikispaces>MasonGreen1 **Imported revision 586854029 - Original comment: ** |
Wikispaces>MasonGreen1 **Imported revision 586854051 - 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>2016-07-13 00: | : This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-07-13 00:13:34 UTC</tt>.<br> | ||
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Enneatonic scales of this form can be extended to 13-note MOSes, while those where the generator is smaller than 2\9 extend to 14 notes. Either the 13 or 14 note scale could be considered the "chromatic" scale of titanium (in much the same way the enneatonic scale is analogous to the diatonic). When the generator is smaller than 2\9, the temperament and scales generated from it could be called "brittle", while if it is larger than 2\9 (as in the scale above), this variant of titanium temperament and its scales could be referred to as "ductile". (A reference to the fact that titanium metal undergoes a brittle-to-ductile transition at high temperatures). "Brittle" titanium gives a slightly closer approximation of 3:2, but "ductile" titanium gives a better 5:4 and 7:5. | Enneatonic scales of this form can be extended to 13-note MOSes, while those where the generator is smaller than 2\9 extend to 14 notes. Either the 13 or 14 note scale could be considered the "chromatic" scale of titanium (in much the same way the enneatonic scale is analogous to the diatonic). When the generator is smaller than 2\9, the temperament and scales generated from it could be called "brittle", while if it is larger than 2\9 (as in the scale above), this variant of titanium temperament and its scales could be referred to as "ductile". (A reference to the fact that titanium metal undergoes a brittle-to-ductile transition at high temperatures). "Brittle" titanium gives a slightly closer approximation of 3:2, but "ductile" titanium gives a better 5:4 and 7:5. | ||
While pajara temperament and Paul Erlich's scales are closely related to Indian music theory (pajara temperament can be used to construct a 22-note MODMOS that easily represents the sruti system), titanium temperament and its enneatonic scales have a natural kinship with Indonesian music, being related to both slendro (via tempering out 49:48, and in fact the enneatonic scale can be considered a sort of extended slendro), and pelog scales (via the presence of the flat fifths | While pajara temperament and Paul Erlich's scales are closely related to Indian music theory (pajara temperament can be used to construct a 22-note MODMOS that easily represents the sruti system), titanium temperament and its enneatonic scales have a natural kinship with Indonesian music, being related to both slendro (via tempering out 49:48, and in fact the enneatonic scale can be considered a sort of extended slendro), and pelog scales (via the presence of the flat fifths. Also, the complete pelog scale does not however occur as a subset of the enneatonic, but does occur as a subset of the 13- and 14-note "chromatic" titanium scales. Moreover, pelog scales are sometimes described as approximating a 7-note subset of 9edo, and 9edo falls within the titanium temperament's tuning range). | ||
Titanium does not extend well to the 9-odd-limit since the 3:2 is already extremely flat. However, beyond the 9th harmonic it performs better, with the 11th and 13th harmonics having passable mappings (tempering out 33:32 and 65:64, respectively). While pure octaves are possible, titanium (especially the ductile version) also benefits greatly from octave stretching, since the 3rd, 7th, 11th, and 13th harmonics are all flat, while the 5th is near-just in the above example. An octave of around 1205-1207 cents is worth trying.</pre></div> | Titanium does not extend well to the 9-odd-limit since the 3:2 is already extremely flat. However, beyond the 9th harmonic it performs better, with the 11th and 13th harmonics having passable mappings (tempering out 33:32 and 65:64, respectively). While pure octaves are possible, titanium (especially the ductile version) also benefits greatly from octave stretching, since the 3rd, 7th, 11th, and 13th harmonics are all flat, while the 5th is near-just in the above example. An octave of around 1205-1207 cents is worth trying.</pre></div> | ||
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Enneatonic scales of this form can be extended to 13-note MOSes, while those where the generator is smaller than 2\9 extend to 14 notes. Either the 13 or 14 note scale could be considered the &quot;chromatic&quot; scale of titanium (in much the same way the enneatonic scale is analogous to the diatonic). When the generator is smaller than 2\9, the temperament and scales generated from it could be called &quot;brittle&quot;, while if it is larger than 2\9 (as in the scale above), this variant of titanium temperament and its scales could be referred to as &quot;ductile&quot;. (A reference to the fact that titanium metal undergoes a brittle-to-ductile transition at high temperatures). &quot;Brittle&quot; titanium gives a slightly closer approximation of 3:2, but &quot;ductile&quot; titanium gives a better 5:4 and 7:5.<br /> | Enneatonic scales of this form can be extended to 13-note MOSes, while those where the generator is smaller than 2\9 extend to 14 notes. Either the 13 or 14 note scale could be considered the &quot;chromatic&quot; scale of titanium (in much the same way the enneatonic scale is analogous to the diatonic). When the generator is smaller than 2\9, the temperament and scales generated from it could be called &quot;brittle&quot;, while if it is larger than 2\9 (as in the scale above), this variant of titanium temperament and its scales could be referred to as &quot;ductile&quot;. (A reference to the fact that titanium metal undergoes a brittle-to-ductile transition at high temperatures). &quot;Brittle&quot; titanium gives a slightly closer approximation of 3:2, but &quot;ductile&quot; titanium gives a better 5:4 and 7:5.<br /> | ||
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While pajara temperament and Paul Erlich's scales are closely related to Indian music theory (pajara temperament can be used to construct a 22-note MODMOS that easily represents the sruti system), titanium temperament and its enneatonic scales have a natural kinship with Indonesian music, being related to both slendro (via tempering out 49:48, and in fact the enneatonic scale can be considered a sort of extended slendro), and pelog scales (via the presence of the flat fifths | While pajara temperament and Paul Erlich's scales are closely related to Indian music theory (pajara temperament can be used to construct a 22-note MODMOS that easily represents the sruti system), titanium temperament and its enneatonic scales have a natural kinship with Indonesian music, being related to both slendro (via tempering out 49:48, and in fact the enneatonic scale can be considered a sort of extended slendro), and pelog scales (via the presence of the flat fifths. Also, the complete pelog scale does not however occur as a subset of the enneatonic, but does occur as a subset of the 13- and 14-note &quot;chromatic&quot; titanium scales. Moreover, pelog scales are sometimes described as approximating a 7-note subset of 9edo, and 9edo falls within the titanium temperament's tuning range).<br /> | ||
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Titanium does not extend well to the 9-odd-limit since the 3:2 is already extremely flat. However, beyond the 9th harmonic it performs better, with the 11th and 13th harmonics having passable mappings (tempering out 33:32 and 65:64, respectively). While pure octaves are possible, titanium (especially the ductile version) also benefits greatly from octave stretching, since the 3rd, 7th, 11th, and 13th harmonics are all flat, while the 5th is near-just in the above example. An octave of around 1205-1207 cents is worth trying.</body></html></pre></div> | Titanium does not extend well to the 9-odd-limit since the 3:2 is already extremely flat. However, beyond the 9th harmonic it performs better, with the 11th and 13th harmonics having passable mappings (tempering out 33:32 and 65:64, respectively). While pure octaves are possible, titanium (especially the ductile version) also benefits greatly from octave stretching, since the 3rd, 7th, 11th, and 13th harmonics are all flat, while the 5th is near-just in the above example. An octave of around 1205-1207 cents is worth trying.</body></html></pre></div> | ||