49ed6: Difference between revisions
Wikispaces>MasonGreen1 **Imported revision 580357767 - Original comment: ** |
Wikispaces>MasonGreen1 **Imported revision 580364841 - 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>2016-04- | : This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-04-18 02:30:10 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>580364841</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> | ||
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Usable prime harmonics include the 3:1 (about 3 cents flat), the 5:1 (about a cent flat), and the 7:1 and 13:1 (around 12 and 9 cents flat, respectively). The 7:1 and 13:1 in particular are much improved; with pure octaves they are too far out of tune to be usable for most, but the situation changes with the stretched version. | Usable prime harmonics include the 3:1 (about 3 cents flat), the 5:1 (about a cent flat), and the 7:1 and 13:1 (around 12 and 9 cents flat, respectively). The 7:1 and 13:1 in particular are much improved; with pure octaves they are too far out of tune to be usable for most, but the situation changes with the stretched version. | ||
Other variants (which stretch the octave slightly more, but the differences are probably imperceptible) are | Other variants (which stretch the octave slightly more, but the differences are probably imperceptible) are 44ed5 and 93ed30. The latter of the two optimizes the accuracy of the 1:5:6 triad, since the 5 is as flat as the 6 is sharp. | ||
Tunings in this range are a promising option for stiff-stringed instruments since they have stretched partials, and the most noticeable partial is the 2nd; thus, a piano tuned to have beatless octaves will actually have them around 1203 cents or so (depending on string length), which coincidentally is very close to what the zeta-optimal stretched version of 19edo has.</pre></div> | Tunings in this range are a promising option for stiff-stringed instruments since they have stretched partials, and the most noticeable partial is the 2nd; thus, a piano tuned to have beatless octaves will actually have them around 1203 cents or so (depending on string length), which coincidentally is very close to what the zeta-optimal stretched version of 19edo has.</pre></div> | ||
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Usable prime harmonics include the 3:1 (about 3 cents flat), the 5:1 (about a cent flat), and the 7:1 and 13:1 (around 12 and 9 cents flat, respectively). The 7:1 and 13:1 in particular are much improved; with pure octaves they are too far out of tune to be usable for most, but the situation changes with the stretched version.<br /> | Usable prime harmonics include the 3:1 (about 3 cents flat), the 5:1 (about a cent flat), and the 7:1 and 13:1 (around 12 and 9 cents flat, respectively). The 7:1 and 13:1 in particular are much improved; with pure octaves they are too far out of tune to be usable for most, but the situation changes with the stretched version.<br /> | ||
<br /> | <br /> | ||
Other variants (which stretch the octave slightly more, but the differences are probably imperceptible) are | Other variants (which stretch the octave slightly more, but the differences are probably imperceptible) are 44ed5 and 93ed30. The latter of the two optimizes the accuracy of the 1:5:6 triad, since the 5 is as flat as the 6 is sharp.<br /> | ||
<br /> | <br /> | ||
Tunings in this range are a promising option for stiff-stringed instruments since they have stretched partials, and the most noticeable partial is the 2nd; thus, a piano tuned to have beatless octaves will actually have them around 1203 cents or so (depending on string length), which coincidentally is very close to what the zeta-optimal stretched version of 19edo has.</body></html></pre></div> | Tunings in this range are a promising option for stiff-stringed instruments since they have stretched partials, and the most noticeable partial is the 2nd; thus, a piano tuned to have beatless octaves will actually have them around 1203 cents or so (depending on string length), which coincidentally is very close to what the zeta-optimal stretched version of 19edo has.</body></html></pre></div> | ||