Ennealimmal: Difference between revisions
From Xenharmonic Reference
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* 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 | ||
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. | 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 === | |||
{{Navbox regtemp}} | {{Navbox regtemp}} | ||
{{Cat|Temperaments}} | {{Cat|Temperaments}} | ||
Revision as of 16:57, 7 April 2026
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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:
- 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 | Trismegistus (alpha-triseph) • Orgone (trimech) • Didacus (diseph) |
| No-octaves | Sensamagic (monogem) |
| Exotemperaments | Dicot • Mavila • Father |
| Higher-rank | |
| Rank-3 | Hemifamity • Marvel • Parapyth |
