Porcupine family: Difference between revisions

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<span style="display: block; text-align: right;">[[de:Porcupine]]</span>

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The 5-limit parent comma for the porcupine family is 250/243, the maximal [[~~diesis|~~diesis]] or porcupine comma. Its [[~~monzo|~~monzo]] is |1 -5 3>, and flipping that yields <<3 5 1|| for the [[~~wedgie|~~wedgie]]. This tells us the [[~~generator|~~generator]] is a minor whole tone, the [[~~10/9|~~10/9]] interval, and that three of these add up to a fourth, with two more giving the minor sixth. In fact, (10/9)^3 = 4/3 * 250/243, and (10/9)^5 = 8/5 * (250/243)^2. 3\22 is a very recommendable generator, and MOS of 7, 8 and 15 notes make for some nice scale possibilities.

The 5-limit parent comma for the porcupine family is 250/243, the maximal [[diesis]] or porcupine comma. Its [[monzo]] is |1 -5 3>, and flipping that yields <<3 5 1|| for the [[wedgie]]. This tells us the [[generator]] is a minor whole tone, the [[10/9]] interval, and that three of these add up to a fourth, with two more giving the minor sixth. In fact, (10/9)^3 = 4/3 * 250/243, and (10/9)^5 = 8/5 * (250/243)^2. 3\22 is a very recommendable generator, and MOS of 7, 8 and 15 notes make for some nice scale possibilities.

valid range: [150.000, 171.429] (8 to 7)

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strict range: [157.821, 166.015]

[[POTE_tuning|POTE generator]]: 163.950

[[POTE_tuning|POTE generator]]: ~27/25 = 163.950

Map: [<1 2 3|, <0 -3 -5|]

EDOs: [[7edo|7]], [[15edo|15]], [[22edo|22]], [[95edo|95c]], [[117edo|117bc]], [[139edo|139bc]], [[161edo|161bc]], [[183edo|183bc]]

Badness: 0.0308

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 <span style="display: block; text-align: right;">[[de:Porcupine]]</span>
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-The 5-limit parent comma for the porcupine family is 250/243, the maximal [[diesis|diesis]] or porcupine comma. Its [[monzo|monzo]] is |1 -5 3&gt;, and flipping that yields &lt;&lt;3 5 1|| for the [[wedgie|wedgie]]. This tells us the [[generator|generator]] is a minor whole tone, the [[10/9|10/9]] interval, and that three of these add up to a fourth, with two more giving the minor sixth. In fact, (10/9)^3 = 4/3 * 250/243, and (10/9)^5 = 8/5 * (250/243)^2. 3\22 is a very recommendable generator, and MOS of 7, 8 and 15 notes make for some nice scale possibilities.
+The 5-limit parent comma for the porcupine family is 250/243, the maximal [[diesis]] or porcupine comma. Its [[monzo]] is |1 -5 3&gt;, and flipping that yields &lt;&lt;3 5 1|| for the [[wedgie]]. This tells us the [[generator]] is a minor whole tone, the [[10/9]] interval, and that three of these add up to a fourth, with two more giving the minor sixth. In fact, (10/9)^3 = 4/3 * 250/243, and (10/9)^5 = 8/5 * (250/243)^2. 3\22 is a very recommendable generator, and MOS of 7, 8 and 15 notes make for some nice scale possibilities.
 valid range: [150.000, 171.429] (8 to 7)
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 strict range: [157.821, 166.015]
-[[POTE_tuning|POTE generator]]: 163.950
+[[POTE_tuning|POTE generator]]: ~27/25 = 163.950
 Map: [&lt;1 2 3|, &lt;0 -3 -5|]
-EDOs: [[15edo|15]], [[22edo|22]], [[95edo|95c]], [[117edo|117bc]], [[139edo|139bc]], [[161edo|161bc]], [[183edo|183bc]]
+EDOs: [[7edo|7]], [[15edo|15]], [[22edo|22]], [[95edo|95c]], [[117edo|117bc]], [[139edo|139bc]], [[161edo|161bc]], [[183edo|183bc]]
 Badness: 0.0308