Ennealimmal: Difference between revisions

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'''Ennealimmal''' (from "ennea-" = 9 and "large limma" = 27/25), 27 & 45, is a 7-limit rank-2 microtemperament that tempers out the two smallest 7-limit [[superparticular]] ratios:
'''Ennealimmal''' (from "ennea-" = 9 and "large limma" = 27/25), [[72edo|72]] & [[99edo|99]], is a 7-limit rank-2 microtemperament that tempers out the two smallest 7-limit [[superparticular]] ratios:
* 2401/2400 = [[Square-superparticular|S49]], the difference between the 49/40 neutral third and its 3/2-complement 60/49
* 2401/2400 = [[Square-superparticular|S49]], the difference between the 49/40 neutral third and its 3/2-complement 60/49
* 4375/4374, the difference between (27/25)<sup>2</sup> and 7/6
* 4375/4374, the difference between (27/25)<sup>2</sup> and 7/6

Revision as of 17:02, 7 April 2026

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Ennealimmal (from "ennea-" = 9 and "large limma" = 27/25), 72 & 99, is a 7-limit rank-2 microtemperament that tempers out the two smallest 7-limit superparticular ratios:

  • 2401/2400 = S49, the difference between the 49/40 neutral third and its 3/2-complement 60/49
  • 4375/4374, the difference between (27/25)2 and 7/6

This implies a period of 1\9 (representing 27/25) and a generator of 49/40. The generator can also be taken to be 5/3.

Theory

Intervals

Derivation of 1\9 period


View • Talk • EditRegular temperaments
Rank-2
Acot Blackwood (1/5-octave) • Whitewood (1/7-octave) • Compton (1/12-octave)
Monocot Meantone • Schismic • Gentle-fifth temperaments • Archy
Complexity 2 Diaschismic (diploid monocot) • Pajara (diploid monocot) • Injera (diploid monocot) • Rastmatic (dicot) • Mohajira (dicot) • Intertridecimal (dicot) • Interseptimal (alpha-dicot)
Complexity 3 Augmented (triploid) • Misty (triploid) • Slendric (tricot) • Porcupine (omega-tricot)
Complexity 4 Diminished (tetraploid) • Tetracot (tetracot) • Buzzard (alpha-tetracot) • Squares (beta-tetracot) • Negri (omega-tetracot)
Complexity 5-6 Magic (alpha-pentacot) • Amity (gamma-pentacot) • Kleismic (alpha-hexacot) • Miracle (hexacot)
Higher complexity Orwell (alpha-heptacot) • Sensi (beta-heptacot) • Octacot (octacot) • Wurschmidt (beta-octacot) • Valentine (enneacot) • Ammonite (epsilon-enneacot) • Myna (beta-decacot) • Ennealimmal (enneaploid dicot)
Straddle-3 A-Team (alter-tricot) • Machine (alter-monocot)
No-3 Mabilic (alpha-triseph) • Orgone (trimech) • Didacus (diseph)
No-octaves Sensamagic (monogem)
Exotemperaments Dicot • Mavila • Father
Higher-rank
Rank-3 Hemifamity • Marvel • Parapyth
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