239edo: Difference between revisions

Line 9:

Another notable feature of 239edo is that many of its [[5-limit]] intervals are mapped to composite numbers of steps: [[3/2]] to 140, [[4/3]] to 99, [[5/3]] to 176, [[5/4]] to 77, [[6/5]] to 63, and [[8/5]] to 162. Not only that, but plenty of these form relatively simple logarithmic ratios with each other, as described by [[Don Page comma]]s. In particular: [[gammic]], where 9 units form 6/5, 11 form 5/4, and 20 form 3/2; [[quartonic]], where 7 units form 6/5, 11 form 4/3, and 18 form 8/5; and [[escapade]], where 7 units form 5/4, 9 form 4/3, and 16 form 5/3, are all supported by 239edo with generators 7\239, 9\239, and 11\239 respectively. 239edo is describable as the unique intersection of any two of these.

As a result, 239edo possesses many of the structures associated with temperaments such as [[tetracot]], [[porcupine]], [[bleu]], [[orwell]], and [[sensamagic]], but with interpretations of their generators that are generally much more precise than those temperaments provide (and are thus distinguished from the intervals that those temperaments' simplest generators are mapped to in 239edo). This proves advantageous in terms of adeptness at representing different "flavors" of categories of interval: for example, 239edo distinguishes [[11/10]] (the "pine" generator, 1/3 of a perfect fourth) at 33\239, from [[32/29]] (the diminished third on the chain of fifths) at 34\239, from [[31/28]] (the "tetracot" generator, 1/4 of a perfect fifth) at 35\239, from [[10/9]] (the sesquiaugmented unison) at 36\239.

As a result, 239edo possesses many of the structures associated with temperaments such as [[tetracot]], [[porcupine]], [[bleu]], [[orwell]], and [[sensamagic]], but with interpretations of their generators that are generally much more precise than those temperaments provide (and are thus distinguished from the intervals that those temperaments' simplest generators are mapped to in 239edo). This proves advantageous in terms of adeptness at representing different "flavors" of categories of interval: for example, in the category of submajor or [[equable heptatonic]] seconds, 239edo distinguishes [[11/10]] (the "pine" generator, 1/3 of a perfect fourth) at 33\239, from [[32/29]] (the diminished third on the chain of fifths) at 34\239, from [[31/28]] (the "tetracot" generator, 1/4 of a perfect fifth) at 35\239, from [[10/9]] (the sesquiaugmented unison) at 36\239.

In addition to its 11-limit, 239edo also encompasses a large variety of higher primes, and is specifically commendable in the 2.3.5.7.11.17.29.31.37.43.53.59 subgroup. Primes 23, 67, and 71 are for the most part usable as well, though one should be cautious about pitting 23 against sharp odds (like 9 or 33).

@@ Line 9: / Line 9: @@
 Another notable feature of 239edo is that many of its [[5-limit]] intervals are mapped to composite numbers of steps: [[3/2]] to 140, [[4/3]] to 99, [[5/3]] to 176, [[5/4]] to 77, [[6/5]] to 63, and [[8/5]] to 162. Not only that, but plenty of these form relatively simple logarithmic ratios with each other, as described by [[Don Page comma]]s. In particular: [[gammic]], where 9 units form 6/5, 11 form 5/4, and 20 form 3/2; [[quartonic]], where 7 units form 6/5, 11 form 4/3, and 18 form 8/5; and [[escapade]], where 7 units form 5/4, 9 form 4/3, and 16 form 5/3, are all supported by 239edo with generators 7\239, 9\239, and 11\239 respectively. 239edo is describable as the unique intersection of any two of these.
-As a result, 239edo possesses many of the structures associated with temperaments such as [[tetracot]], [[porcupine]], [[bleu]], [[orwell]], and [[sensamagic]], but with interpretations of their generators that are generally much more precise than those temperaments provide (and are thus distinguished from the intervals that those temperaments' simplest generators are mapped to in 239edo). This proves advantageous in terms of adeptness at representing different "flavors" of categories of interval: for example, 239edo distinguishes [[11/10]] (the "pine" generator, 1/3 of a perfect fourth) at 33\239, from [[32/29]] (the diminished third on the chain of fifths) at 34\239, from [[31/28]] (the "tetracot" generator, 1/4 of a perfect fifth) at 35\239, from [[10/9]] (the sesquiaugmented unison) at 36\239.
+As a result, 239edo possesses many of the structures associated with temperaments such as [[tetracot]], [[porcupine]], [[bleu]], [[orwell]], and [[sensamagic]], but with interpretations of their generators that are generally much more precise than those temperaments provide (and are thus distinguished from the intervals that those temperaments' simplest generators are mapped to in 239edo). This proves advantageous in terms of adeptness at representing different "flavors" of categories of interval: for example, in the category of submajor or [[equable heptatonic]] seconds, 239edo distinguishes [[11/10]] (the "pine" generator, 1/3 of a perfect fourth) at 33\239, from [[32/29]] (the diminished third on the chain of fifths) at 34\239, from [[31/28]] (the "tetracot" generator, 1/4 of a perfect fifth) at 35\239, from [[10/9]] (the sesquiaugmented unison) at 36\239.
 In addition to its 11-limit, 239edo also encompasses a large variety of higher primes, and is specifically commendable in the 2.3.5.7.11.17.29.31.37.43.53.59 subgroup. Primes 23, 67, and 71 are for the most part usable as well, though one should be cautious about pitting 23 against sharp odds (like 9 or 33).