Kite's thoughts on pergens: Difference between revisions
Wikispaces>TallKite **Imported revision 625559027 - Original comment: ** |
Wikispaces>TallKite **Imported revision 625617753 - Original comment: last one with tipping point / sweet spot math** |
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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:TallKite|TallKite]] and made on <tt>2018-01- | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2018-01-30 16:08:58 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>625617753</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>last one with tipping point / sweet spot math</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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As noted above, in the chord names section, the 5th of pajara (half-8ve) tends to be sharp, thus it has E = ^^d2. But injera, also half-8ve, has a flat 5th, and thus E = vvd2. The tipping point for half-octave with a d2 enharmonic is 700¢, 12-edo's 5th. It is fine for two temperaments with the same pergen to be on opposite sides of the tipping point. But it isn't acceptable for a single temperament to "tip over". That would lead to the up symbol sometimes meaning down in pitch. Or even worse, the direction of ups and downs for a piece would reverse if the tuning is adjusted slightly. | As noted above, in the chord names section, the 5th of pajara (half-8ve) tends to be sharp, thus it has E = ^^d2. But injera, also half-8ve, has a flat 5th, and thus E = vvd2. The tipping point for half-octave with a d2 enharmonic is 700¢, 12-edo's 5th. It is fine for two temperaments with the same pergen to be on opposite sides of the tipping point. But it isn't acceptable for a single temperament to "tip over". That would lead to the up symbol sometimes meaning down in pitch. Or even worse, the direction of ups and downs for a piece would reverse if the tuning is adjusted slightly. | ||
Does the temperament's "sweet spot", where the damage to those JI ratios likely to occur in chords is minimized, ever contain the tipping point? | Does the temperament's "sweet spot", where the damage to those JI ratios likely to occur in chords is minimized, ever contain the tipping point? Negri does. | ||
The tipping point is affected by the choice of enharmonic. Half-8ve can be notated with E = vvM2. The tipping point becomes 600¢, a __very__ unlikely 5th, and tipping is impossible. For single-comma temperaments, the choice of E is usually dictated by the 3-limit mapping of the comma. Thus for 5-limit and 7-imit temperaments, the choice of E is a given. However, the mapping of primes 11 and 13 is not agreed on. | The tipping point is affected by the choice of enharmonic. Half-8ve can be notated with E = vvM2. The tipping point becomes 600¢, a __very__ unlikely 5th, and tipping is impossible. For single-comma temperaments, the choice of E is usually dictated by the 3-limit mapping of the comma. Thus for 5-limit and 7-imit temperaments, the choice of E is a given. However, the mapping of primes 11 and 13 is not agreed on. | ||
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As noted above, in the chord names section, the 5th of pajara (half-8ve) tends to be sharp, thus it has E = ^^d2. But injera, also half-8ve, has a flat 5th, and thus E = vvd2. The tipping point for half-octave with a d2 enharmonic is 700¢, 12-edo's 5th. It is fine for two temperaments with the same pergen to be on opposite sides of the tipping point. But it isn't acceptable for a single temperament to &quot;tip over&quot;. That would lead to the up symbol sometimes meaning down in pitch. Or even worse, the direction of ups and downs for a piece would reverse if the tuning is adjusted slightly.<br /> | As noted above, in the chord names section, the 5th of pajara (half-8ve) tends to be sharp, thus it has E = ^^d2. But injera, also half-8ve, has a flat 5th, and thus E = vvd2. The tipping point for half-octave with a d2 enharmonic is 700¢, 12-edo's 5th. It is fine for two temperaments with the same pergen to be on opposite sides of the tipping point. But it isn't acceptable for a single temperament to &quot;tip over&quot;. That would lead to the up symbol sometimes meaning down in pitch. Or even worse, the direction of ups and downs for a piece would reverse if the tuning is adjusted slightly.<br /> | ||
<br /> | <br /> | ||
Does the temperament's &quot;sweet spot&quot;, where the damage to those JI ratios likely to occur in chords is minimized, ever contain the tipping point? | Does the temperament's &quot;sweet spot&quot;, where the damage to those JI ratios likely to occur in chords is minimized, ever contain the tipping point? Negri does.<br /> | ||
<br /> | <br /> | ||
The tipping point is affected by the choice of enharmonic. Half-8ve can be notated with E = vvM2. The tipping point becomes 600¢, a <u>very</u> unlikely 5th, and tipping is impossible. For single-comma temperaments, the choice of E is usually dictated by the 3-limit mapping of the comma. Thus for 5-limit and 7-imit temperaments, the choice of E is a given. However, the mapping of primes 11 and 13 is not agreed on.<br /> | The tipping point is affected by the choice of enharmonic. Half-8ve can be notated with E = vvM2. The tipping point becomes 600¢, a <u>very</u> unlikely 5th, and tipping is impossible. For single-comma temperaments, the choice of E is usually dictated by the 3-limit mapping of the comma. Thus for 5-limit and 7-imit temperaments, the choice of E is a given. However, the mapping of primes 11 and 13 is not agreed on.<br /> | ||