Parapyth: Difference between revisions
m →Theory |
|||
| Line 2: | Line 2: | ||
== Theory == | == Theory == | ||
Parapyth has two non-period generators: the fifth (which is tuned in the [[gentle region]], i.e. somewhat sharp of just but flatter than 17edo) and the "spacer" 28/27, which is equated to 33/32. This is equivalent to taking the spacer 64/63, which may be equated with 81/80 (as in [[46edo]] and [[87edo]]) or | Parapyth has two non-period generators: the fifth (which is tuned in the [[gentle region]], i.e. somewhat sharp of just but flatter than 17edo) and the "spacer" 28/27, which is equated to 33/32. This is equivalent to taking the spacer 64/63, which may be equated with 81/80 (as in [[46edo]] and [[87edo]]) or tempered smaller than 81/80 (as in [[63edo]] and [[80edo]]) assuming prime 5 is added. | ||
=== Intervals === | === Intervals === | ||
{| class="wikitable" | {| class="wikitable" | ||
Revision as of 08:31, 5 April 2026
Parapyth is generally viewed as a no-5 2.3.7.11.13 rank-3 regular temperament 17 & 41 & 46, sometimes called Parapythic. (In the strict sense, parapyth is Margo Schulter's rank-3 tuning construct inspired by medieval European and Middle Eastern music theory, where Schulter imposes commas that are to be observed as well as commas that are to be tempered out.[citation needed])
Theory
Parapyth has two non-period generators: the fifth (which is tuned in the gentle region, i.e. somewhat sharp of just but flatter than 17edo) and the "spacer" 28/27, which is equated to 33/32. This is equivalent to taking the spacer 64/63, which may be equated with 81/80 (as in 46edo and 87edo) or tempered smaller than 81/80 (as in 63edo and 80edo) assuming prime 5 is added.
Intervals
| # spacers | -1 | 0 | +1 | |||
|---|---|---|---|---|---|---|
| # fifths | Cents* | JI | Cents* | JI | Cents* | JI |
| -7 | 1015.9 | 1072.1 | 13/7 | 1128.4 | 52/27 | |
| -6 | 519.9 | 576.1 | 39/28 | 632.3 | 13/9 | |
| -5 | 23.9 | 64/63 | 80.1 | 22/21 | 136.3 | 13/12 |
| -4 | 727.9 | 32/21 | 784.1 | 11/7 | 840.3 | 13/8 |
| -3 | 231.9 | 8/7 | 288.1 | 13/11 | 344.3 | 11/9 |
| -2 | 935.8 | 12/7 | 992.0 | 16/9, 39/22 | 1048.3 | 11/6 |
| -1 | 439.8 | 9/7 | 496.0 | 4/3 | 552.2 | 11/8 |
| 0 | 1143.8 | 27/14, 64/33 | 0 | 1/1 | 56.2 | 28/27, 33/32 |
| 1 | 647.8 | 16/11 | 704.0 | 3/2 | 760.2 | 14/9, 99/64 |
| 2 | 151.7 | 12/11 | 208.0 | 9/8, 44/39 | 264.2 | 7/6 |
| 3 | 855.7 | 18/11 | 911.9 | 22/13 | 968.1 | 7/4 |
| 4 | 359.7 | 16/13 | 415.9 | 14/11 | 472.1 | 21/16 |
| 5 | 1063.7 | 24/13 | 1119.9 | 21/11 | 1176.1 | 63/32 |
| 6 | 567.7 | 18/13 | 623.9 | 56/39 | 680.1 | |
| 7 | 71.6 | 27/26 | 127.9 | 14/13 | 184.1 | |
(* Cent values in 2.3.7.11.13 CE tuning. The 104edo tuning (~3/2 = 703.846c, ~28/27 = 57.692c) is close.)
Supporting temperaments
Rodan (Parapyth + Slendric) is arguably the most important rank-2 temperament that supports Parapyth (besides the gentle-fifth-generated 2.3.7.11.13 temperament Leapfrog, which see Gentle tuning).
Extensions
If prime 5 is added to 2.3.7.11.13 Parapyth via Aberschismic tempering equating 64/63 to 81/80, the resulting 2.3.5.7.11.13 temperament is called Pele (41 & 46 & 58).
If the diatonic augmented fourth is equated to 23/16, the resulting 2.3.7.11.13.23 temperament is called Skidoo (17 & 24 & 46). 63edo is a particularly good Skidoo tuning.
Prime 31 can be easily be added by equating 28/27~33/32 with 32/31.
| 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) |
| Exotemperament | Dicot • Mavila • Father |
| Higher-rank | |
| Rank-3 | Hemifamity • Marvel • Parapyth |
