29edo: Difference between revisions

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=== Interval Flavors ===

29edo has inframinor, neogothic minor, supraminor, submajor, neogothic major, and ultramajor thirds and sevenths. This is in contrast to systems like [[31edo]], where there are ~~only~~ subminor, minor, neutral, major, and supermajor thirds and sevenths. This is due to 29edo representing 2.3.7/5.11/5.13/5 well, and ratios between two primes greater than 3 tend to land between interval categories of intervals in a 2.3.p subgroup. For example, 2.3.5 intervals are major/minor, 2.3.7 intervals are supermajor/subminor, and 2.3.11 and 2.3.13 intervals are ~~neutral~~. 31edo, on the other hand, represents 2.3.5.7.11 well, and thus has interval categories represented in 2.3.5, 2.3.7, and 2.3.11. It can also be seen from the fact that the 29&31 temperament, [[tritonic]], maps seconds and thirds to large numbers of generators, so they differ more in tuning between the systems.

29edo has [[Ultramajor and inframinor|inframinor (arto)]], [[Neogothic major and minor|neogothic minor]], supraminor, submajor, neogothic major, and ultramajor (tendo) thirds and sevenths. This is in contrast to systems like [[31edo]], where there are subminor, minor, neutral, major, and supermajor thirds and sevenths. This is due to 29edo representing 2.3.7/5.11/5.13/5 well, and ratios between two primes greater than 3 tend to land between interval categories of intervals in a 2.3.p subgroup. For example, 2.3.5 intervals are major/minor, 2.3.7 intervals are [[Supermajor and subminor|supermajor/subminor]], and 2.3.11 and 2.3.13 intervals are [[Neutral|artoneutral/tendoneutral]]. 31edo, on the other hand, represents 2.3.5.7.11 well, and thus has interval categories represented in 2.3.5, 2.3.7, and 2.3.11. It can also be seen from the fact that the 29&31 temperament, [[tritonic]], maps seconds and thirds to large numbers of generators, so they differ more in tuning between the systems.

=== Subsets and Supersets ===

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 === Interval Flavors ===
-edo has inframinor, neogothic minor, supraminor, submajor, neogothic major, and ultramajor thirds and sevenths. This is in contrast to systems like [[31edo]], where there are only subminor, minor, neutral, major, and supermajor thirds and sevenths. This is due to 29edo representing 2.3.7/5.11/5.13/5 well, and ratios between two primes greater than 3 tend to land between interval categories of intervals in a 2.3.p subgroup. For example, 2.3.5 intervals are major/minor, 2.3.7 intervals are supermajor/subminor, and 2.3.11 and 2.3.13 intervals are neutral. 31edo, on the other hand, represents 2.3.5.7.11 well, and thus has interval categories represented in 2.3.5, 2.3.7, and 2.3.11. It can also be seen from the fact that the 29&31 temperament, [[tritonic]], maps seconds and thirds to large numbers of generators, so they differ more in tuning between the systems.
+edo has [[Ultramajor and inframinor|inframinor (arto)]], [[Neogothic major and minor|neogothic minor]], supraminor, submajor, neogothic major, and ultramajor (tendo) thirds and sevenths. This is in contrast to systems like [[31edo]], where there are subminor, minor, neutral, major, and supermajor thirds and sevenths. This is due to 29edo representing 2.3.7/5.11/5.13/5 well, and ratios between two primes greater than 3 tend to land between interval categories of intervals in a 2.3.p subgroup. For example, 2.3.5 intervals are major/minor, 2.3.7 intervals are [[Supermajor and subminor|supermajor/subminor]], and 2.3.11 and 2.3.13 intervals are [[Neutral|artoneutral/tendoneutral]]. 31edo, on the other hand, represents 2.3.5.7.11 well, and thus has interval categories represented in 2.3.5, 2.3.7, and 2.3.11. It can also be seen from the fact that the 29&31 temperament, [[tritonic]], maps seconds and thirds to large numbers of generators, so they differ more in tuning between the systems.
 === Subsets and Supersets ===

29edo: Difference between revisions

Fitzgerald Lee (talk | contribs)