Tour of regular temperaments: Difference between revisions
Changed the headings, a family is not itself of a certain prime limit, rather it is defined by a comma of a certain prime limit. |
→Families defined by a 2.3.5 (ya) comma: added the Suprapyth or Sayo family |
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===[[Schismatic family|Schismatic or Layo family]] (P8, P5)=== | ===[[Schismatic family|Schismatic or Layo family]] (P8, P5)=== | ||
The schismatic family tempers out the schisma of [-15 8 1> = [[32805/32768]], which is the amount by which the Pythagorean comma exceeds the syntonic comma. The 5-limit version of the temperament is a [[Microtempering|microtemperament]] which flattens the fifth by a fraction of a schisma, but other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity; whereas meantone equates four 3/2's with 5/1, schismatic equates eight 4/3's with 10/1, so that the Pythagorean diminished fourth of 8192/6561 is equated with 5/4. Tunings include [[12edo]], [[29edo]], [[41edo]], [[53edo]], and [[118edo]]. | The schismatic family tempers out the schisma of [-15 8 1> = [[32805/32768]], which is the amount by which the Pythagorean comma exceeds the syntonic comma. The 5-limit version of the temperament is a [[Microtempering|microtemperament]] which flattens the fifth by a fraction of a schisma, but other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity; whereas meantone equates four 3/2's with 5/1, schismatic equates eight 4/3's with 10/1, so that the Pythagorean diminished fourth of 8192/6561 is equated with 5/4. Tunings include [[12edo]], [[29edo]], [[41edo]], [[53edo]], and [[118edo]]. | ||
=== [[Suprapyth|Suprapyth or Sayo family]] (P8, P5) === | |||
The Sup'''<u>ra</u>'''pyth or Sayo family tempers out [12 -9 1> = 20480/19683, which equates 5/4 to a Pythagorean augmented 2nd. Being a fourthward comma, it tends to sharpen the 5th, hence it's "super-pythagorean". The best 7-limit extension adds the Archy or Ru comma to make the [[Superpyth|Sup'''<u>e</u>'''rpyth]] temperament. | |||
===[[Pelogic family|Pelogic or Layobi family]] (P8, P5)=== | ===[[Pelogic family|Pelogic or Layobi family]] (P8, P5)=== | ||