User:BudjarnLambeth/Sandbox

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Between 0.0239167 and 0.0239833

List of Octave-Based Fine Measures (Logarithmic)
Unit Name (Symbol): Divisions of Octave Prime Factors Origin / Significance
Eka 16 24 From Sanskrit eka: one, unit; chromatic unit of Armodue 16edo Theory[1].
Normal diesis 31 31 (prime) See the dedicated page.
Méride 43 43 (prime) Proposed by Joseph Sauveur, as 7 heptaméride units[2][3].
Holdrian comma 53 53 (prime) See the dedicated page.
Mercator’s old comma 55 5 x 11 Not to be confused with Mercator's comma.
Decitone 60 22 × 3 × 5
Morion 72 23 × 32 See the dedicated page.
Farab 144 24 × 32 1/12 of 12edo semitone; Proposed by al-Farabi in 10th century[2][4].
Mem 205 5 × 41 Unit used by H-Pi Instruments[2][5][6].
Tredek 270 2 × 33 × 5 Proposed by Joseph Monzo (2013)[7].
Savart* 300 22 × 3 × 52 Alexander Wood's definition of the Savart[8], containing 12edo.
Heptaméride / eptaméride / savart* 301 7 × 43 301 ≃ 1,000 × log102; 1/7 of Méride unit; proposed by Joseph Sauveur (1701), advocated by Félix Savart[2][9].
Gene 311 311 (prime) Proposed by Joseph Monzo (2007)[10].
Dröbisch Angle 360 23 × 32 × 5 Proposed as angle by Moritz Dröbisch in the 19th century, later by Andrew Pikler as the current name in Logarithmic Frequency Systems (1966)[2].
Squb 494 2 × 13 × 19 [citation needed]
Great iring / centitone 500 22 × 53 [citation needed]
Dexl 540 22 × 33 × 5 Proposed by Joseph Monzo (2023)[11].
Iring / centitone 600 23 × 3 × 52 Relative cent of 6edo (12edo tone); Proposed by Widogast Iring (1898), later by Joseph Yasser as a "centitone" (1932)[2][12].
Skisma (Sk) 612 22 × 32 × 17 Edo representation of Sagittal's Ultra (Herculean) precision level JI notation (58eda), where it is known as an "ultrina"[2][13].
Delfi 665 5 × 7 × 19 [2]
Small iring / centitone 700 22 × 52 x 7 [citation needed]
Woolhouse 730 2 × 5 × 73 Proposed by Wesley S.B. Woolhouse (1835)[14].
Millioctave (moct) 1000 23 × 53 See the dedicated page.
Cent (¢) 1200 24 × 3 × 52 See the dedicated page.
Greater muon 1224 23 × 32 × 17 [citation needed]
Triangular cent 1260 22 × 32 × 5 × 7 [citation needed]
Pion 1272 23 × 3 × 53 [citation needed]
Pound 1344 26 × 3 × 7 [citation needed]
Neutron 1392 24 × 3 × 29 [citation needed]
Lesser muon 1428 22 × 3 × 7 × 17 [citation needed]
Decifarab 1440 25 × 32 × 5 1/10 of Farab unit[2].
Quadratic cent 1452 22 × 3 × 112 [citation needed]
Ksion 1476 22 × 32 × 41 [citation needed]
Cubic cent 1500 22 × 3 × 53 [citation needed]
Heptamu (7mu) 1536 29 × 3 Seventh MIDI-resolution unit, 1/128 (1/(27)) of 12edo semitone[15]
Rhoon 1560 23 × 3 × 5 × 13 [citation needed]
śata 1600 26 × 52 From Sanskrit śatam: hundred; Relative cent of Armodue 16edo Theory[citation needed]
Tile 1632 25 × 3 × 17 [citation needed]
Iota 1700 22 × 52 × 17 Relative cent of 17edo; proposed by Margo Schulter (2002) and George Secor[2].
Harmos 1728 26 × 33 1728 = 123; 1/144 of 12edo semitone; Proposed by Paul Beaver[2][16].
Hind śat / Indian cent 2200 23 × 11 × 52 [citation needed]
Mina 2460 22 × 3 × 5 × 41 Abbreviation of "schismina", edo representation of Sagittal's Extreme (Olympian) precision level JI notation (233eda)[2][17].
Centidiesis 3100 22 × 52 x 31 [citation needed]
Centiméride 4300 22 × 52 x 43 [citation needed]
Major tina 8269 8269 (prime) Proposed by Flora Canou (2021)[18].
Tina 8539 8539 (prime) Provides good approximations for 41-limit primes except 37; named by Dave Keenan and George Secor; edo representation of Sagittal's Insane (Magrathean) precision level JI notation (809eda)[2][19].
Purdal 9900 22 × 32 × 52 × 11 Relative cent of 99edo; Suggested by Osmiorisbendi, advocated by Tútim Dennsuul Wafiil. See the dedicated page.
Türk sent / Turkish cent 10600 23 × 52 × 53 Relative cent of 106edo, 1/200 of 53edo; invented by M. Ekrem Karadeniz (1965), influenced by Abdülkadir Töre[2][20][21].
Prima 12276 22 × 32 × 11 × 31 Proposed by Erv Wilson, Gene Ward Smith and Gavin Putland[2].
Jinn 16808 23 × 11 × 191 See the dedicated page.
Jot 30103 30103 (prime) 30103 ≃ 100,000 × log102; Proposed by Augustus de Morgan (1864)[2][22][16].
Imp 31920 24 × 3 × 5 × 7 × 19 [2]
Flu 46032 24 × 3 × 7 × 137 Proposed by Gene Ward Smith (2005)[2][23].
Normal atom 78005 5 × 15601 Name proposed by Tristan Bay in 2023; 78005edo consistently maps Kirnberger's atom to 1 edostep and is a very strong 5-limit system. [citation needed]
MIDI Tuning Standard unit (14mu) 196608 216 × 3 Fourteenth MIDI-resolution unit, 1/16384 (1/(214)) of 12edo semitone[2].

Between 0.0239167 and 0.0239833

  1. ↑ Armodue: le risorse di un nuovo sistema musicale
  2. ↑ 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 Stichting Huygens-Fokker: Logarithmic Interval Measures
  3. ↑ Tonalsoft | Méride / 43-ed2 / 43-edo / 43-ET / 43-tone equal-temperament
  4. ↑ Tonalsoft | Farab.
  5. ↑ H-Pi Instruments | Hunt Theoretical System
  6. ↑ Tonalsoft | Mem, 205-edo
  7. ↑ Tonalsoft | Tredek, 270-edo
  8. ↑ The Physics of Music, Alexander Wood, 1944.
  9. ↑ Tonalsoft | Heptaméride
  10. ↑ Tonalsoft | Gene, 311-edo
  11. ↑ Tonalsoft | Dexl, 540-edo
  12. ↑ Tonalsoft | Centitone, iring
  13. ↑ Tonalsoft | Sk, 612-edo
  14. ↑ Essay on musical intervals, harmonics, and the temperament of the musical scale, &c, Wesley S.B. Woolhouse.
  15. ↑ Tonalsoft | 7mu / heptamu
  16. ↑ 16.0 16.1 Tonalsoft | Equal temperaments
  17. ↑ Tonalsoft | Mina
  18. ↑ The Sagittal Forum | Definition of the tina reviewed
  19. ↑ Tonalsoft | Tina
  20. ↑ Tonalsoft | Türk-sent
  21. ↑ 79-Tone Tuning & Theory for Turkish Maqam Music, Ozan Yarman.
  22. ↑ Tonalsoft | Jot
  23. ↑ Tonalsoft | Flu
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