Sensamagic: Difference between revisions
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'''Sensamagic''', sometimes known in a tritave-equivalent context as '''Bohlen-Pierce-Stearns''', is the temperament in the 3.5.7 subgroup equating a stack of two [[9/7]]<nowiki/>s with [[5/3]]; this means that the comma [[245/243]] is tempered out. 9/7 is tuned sharp (about 440 cents) and 5/3 is flattened (about 880 cents). It functions as a tritave analog of [[ | '''Sensamagic''' (b13 & b17), sometimes known in a tritave-equivalent context as '''Bohlen-Pierce-Stearns''' (BPS), is the temperament in the 3.5.7 subgroup equating a stack of two [[9/7]]<nowiki/>s with [[5/3]]; this means that the comma [[245/243]] is tempered out. 9/7 is tuned sharp (about 440 cents) and 5/3 is flattened (about 880 cents). It functions as a tritave analog of [[Meantone]], relating the two simplest prime harmonics after the equave with a medium accuracy. | ||
Sensamagic can be used as a temperament with octaves by one of several approaches: | Sensamagic can be used as a temperament with octaves by one of several approaches: | ||
* simply taking the octave as the period instead of the tritave, resulting in a 2.9/7.5/3 subgroup temperament known as | * simply taking the octave as the period instead of the tritave, resulting in a 2.9/7.5/3 subgroup temperament known as Sentry (11 & 19) | ||
* equating the octave to a false octave found on the | * equating the octave to a false octave found on the Sensamagic generator chain, such as 125/63 (resulting in [[Sensi]] (19 & 27)) or 49/25 (resulting in an obscure [[Porcupine]] extension called "Hedgehog" that splits the octave into two 7/5~10/7 tritones) | ||
* adding the octave as an additional generator, resulting in rank-3 | * adding the octave as an additional generator, resulting in rank-3 Sensamagic (41 & 19 & 27, or b65 & b30 & b43) | ||
This page will focus on tritave and rank-3 | This page will focus on tritave and rank-3 Sensamagic. | ||
''TODO: complete page'' | ''TODO: complete page'' | ||
== Interval chain == | |||
{| class="wikitable right-1 right-2" | |||
|- | |||
! # | |||
! Cents* | |||
! Approximate ratios | |||
|- | |||
| 0 | |||
| 0.0 | |||
| '''1/1''' | |||
|- | |||
| 1 | |||
| 440.7 | |||
| '''9/7''' | |||
|- | |||
| 2 | |||
| 881.3 | |||
| '''5/3''' | |||
|- | |||
| 3 | |||
| 1322.0 | |||
| 15/7 | |||
|- | |||
| 4 | |||
| 1762.7 | |||
| '''25/9''' | |||
|- | |||
| 5 | |||
| 301.4 | |||
| 25/21 | |||
|- | |||
| 6 | |||
| 742.0 | |||
| 75/49, 125/81 | |||
|- | |||
| 7 | |||
| 1182.7 | |||
| | |||
|- | |||
| 8 | |||
| 1623.4 | |||
| | |||
|- | |||
| 9 | |||
| 162.1 | |||
| | |||
|- | |||
| 10 | |||
| 602.7 | |||
| | |||
|- | |||
| 11 | |||
| 1043.4 | |||
| | |||
|- | |||
| 12 | |||
| 1484.1 | |||
| | |||
|} | |||
<nowiki>*</nowiki> in 3.5.7-subgroup [[CWE]] tuning, tritave reduced. Intervals may be additionally octave-reduced in rank-3 sensamagic. | |||
{{Navbox regtemp}} | {{Navbox regtemp}} | ||
Latest revision as of 04:29, 9 March 2026
Sensamagic (b13 & b17), sometimes known in a tritave-equivalent context as Bohlen-Pierce-Stearns (BPS), is the temperament in the 3.5.7 subgroup equating a stack of two 9/7s with 5/3; this means that the comma 245/243 is tempered out. 9/7 is tuned sharp (about 440 cents) and 5/3 is flattened (about 880 cents). It functions as a tritave analog of Meantone, relating the two simplest prime harmonics after the equave with a medium accuracy.
Sensamagic can be used as a temperament with octaves by one of several approaches:
- simply taking the octave as the period instead of the tritave, resulting in a 2.9/7.5/3 subgroup temperament known as Sentry (11 & 19)
- equating the octave to a false octave found on the Sensamagic generator chain, such as 125/63 (resulting in Sensi (19 & 27)) or 49/25 (resulting in an obscure Porcupine extension called "Hedgehog" that splits the octave into two 7/5~10/7 tritones)
- adding the octave as an additional generator, resulting in rank-3 Sensamagic (41 & 19 & 27, or b65 & b30 & b43)
This page will focus on tritave and rank-3 Sensamagic.
TODO: complete page
Interval chain
| # | Cents* | Approximate ratios |
|---|---|---|
| 0 | 0.0 | 1/1 |
| 1 | 440.7 | 9/7 |
| 2 | 881.3 | 5/3 |
| 3 | 1322.0 | 15/7 |
| 4 | 1762.7 | 25/9 |
| 5 | 301.4 | 25/21 |
| 6 | 742.0 | 75/49, 125/81 |
| 7 | 1182.7 | |
| 8 | 1623.4 | |
| 9 | 162.1 | |
| 10 | 602.7 | |
| 11 | 1043.4 | |
| 12 | 1484.1 |
* in 3.5.7-subgroup CWE tuning, tritave reduced. Intervals may be additionally octave-reduced in rank-3 sensamagic.
| 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 |
