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Created page with "'''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 meantone, relating the two simplest prime harmonics after the equave with a medium accuracy. Sensamagic ca..."
 
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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 [[meantone]], relating the two simplest prime harmonics after the equave with a medium accuracy.  
'''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 "sentry"
* 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]]) or 49/25 (resulting in an obscure porcupine extension called "hedgehog")
* 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
* 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.
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}}

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
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