Syntonic–chromatic equivalence continuum: Difference between revisions
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* [[Sevond]] (''n'' = 3.5) | * [[Sevond]] (''n'' = 3.5) | ||
* [[Brahmagupta]] (''n'' = 21/4 = 5.25) | * [[Brahmagupta]] (''n'' = 21/4 = 5.25) | ||
* [[Geb]] (''n'' = 16/3 = 5.{{overline|3}}) | |||
* [[Raider]] (''n'' = 37/7 = 5.{{overline|285714}}) | * [[Raider]] (''n'' = 37/7 = 5.{{overline|285714}}) | ||
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The 5-limit 6b&7 temperament. Its name is "porcupine" spelled backwards, because that's what this temperament is - it's porcupine, with the generator sharp of 2\7 such that the major and minor thirds switch places. The fifths are very flat, meaning that this is more of a melodic temperament than a harmonic one. | The 5-limit 6b&7 temperament. Its name is "porcupine" spelled backwards, because that's what this temperament is - it's porcupine, with the generator sharp of 2\7 such that the major and minor thirds switch places. The fifths are very flat, meaning that this is more of a melodic temperament than a harmonic one. | ||
Subgroup: 2.3.5 | |||
[[Comma list]]: 1125/1024 | |||
[[Mapping]]: [{{val| 1 2 2 }}, {{val| 0 -3 2 }}] | |||
[[POTE generator]]: ~16/15 = 173.101 | |||
{{Val list|legend=1| 6b, 7 }} | |||
[ | [[Badness]]: 0.1439 | ||
== Absurdity == | == Absurdity == | ||
The 5-limit 7&84 temperament, so named because it truly is an absurd temperament. The generator is 81/80 and the period is 800/729, which is (10/9) / (81/80). This is also part of the syntonic-chromatic equivalence continuum, in this case where (81/80)<sup>5</sup> = 25/24. | The 5-limit 7&84 temperament, so named because it truly is an absurd temperament. The generator is 81/80 and the period is 800/729, which is (10/9) / (81/80). This is also part of the syntonic-chromatic equivalence continuum, in this case where (81/80)<sup>5</sup> = 25/24. | ||
Subgroup: 2.3.5 | |||
[[Comma list]]: 10460353203/10240000000 | |||
[[Mapping]]: [{{val| 7 0 -17 }}, {{val| 0 1 3 }}] | |||
[[POTE generator]]: ~10/9 = 185.901 cents | |||
{{Val list|legend=1| 7, 70, 77, 84, 329 }} | |||
[ | [[Badness]]: 0.3412 | ||
== Sevond == | == Sevond == | ||
This is a fairly obvious temperament; it just equates 7 10/9's with a 2/1, hence the period is 10/9. One generator from 5\7 puts you at 3/2, two generators from 2\7 puts you at 5/4. | This is a fairly obvious temperament; it just equates 7 10/9's with a 2/1, hence the period is 10/9. One generator from 5\7 puts you at 3/2, two generators from 2\7 puts you at 5/4. | ||
Subgroup: 2.3.5 | |||
[[Comma list]]: 5000000/4782969 | |||
[[Mapping]]: [{{val| 7 0 -6 }}, {{val| 0 1 2 }}] | |||
[[POTE generator]]: ~3/2 = 706.288 cents | |||
Badness: 0.3393 | {{Val list|legend=1| 7, 42, 49, 56, 119 }} | ||
[[Badness]]: 0.3393 | |||
=== 7-limit === | === 7-limit === | ||
Adding 875/864 to the commas extends this to the 7-limit: | Adding 875/864 to the commas extends this to the 7-limit: | ||
Subgroup: 2.3.5.7 | |||
[[Comma list]]: 875/864, 327680/321489 | |||
[[Mapping]]: [{{val| 7 0 -6 53 }}, {{val| 0 1 2 -3 }}] | |||
[[POTE generator]]: ~3/2 = 705.613 | |||
{{Val list|legend=1| 7, 56, 63, 119 }} | |||
== Seville == | == Seville == | ||
This is similar to the above, but provides a less complex avenue to 5, but this time at the cost of accuracy. One generator from 5\7 puts you at 3/2, and one generator from 2\7 puts you at 5/4. | This is similar to the above, but provides a less complex avenue to 5, but this time at the cost of accuracy. One generator from 5\7 puts you at 3/2, and one generator from 2\7 puts you at 5/4. | ||
Subgroup: 2.3.5 | |||
[[Comma list]]: 78125/69984 | |||
[[Mapping]]: [{{val| 7 0 5 }}, {{val| 0 1 1 }}] | |||
[[POTE generator]]: ~3/2 = 706.410 | |||
{{Val list|legend=1| 7, 35b, 42c, 49c, 56cc, 119cccc }} | |||
[ | [[Badness]]: 0.4377 | ||
[[Category:7edo]] | [[Category:7edo]] | ||