Xenharmonic Wiki

User:UnbihexiumFan/Temperaments: Difference between revisions

← Older edit
VisualWikitext
No edit summary
 
(5 intermediate revisions by 2 users not shown)
Line 1: Line 1:
A collection of temperaments that I have found that may or may not have yet been discovered. A lot of these are the same as already-known temperaments but with non-octave periods. I am not very good with technical details so even though they are included as info on most temperaments I will not be putting it here.
A collection of temperaments that I have found that may or may not have yet been discovered. If you find any inaccuracies feel free to point them out on the [[User talk:UnbihexiumFan/Temperaments|talk page]].


== Stearnsmic 7/4-period temperaments ==
== Stearnsmic 7/4-period temperaments ==
Line 373: Line 373:
== 243/242+2079/2048-based temperaments ==
== 243/242+2079/2048-based temperaments ==


These temperaments temper out the rastma, [[243/242]], and an unnamed comma [[2079/2048]]. They are similar to [[mohajira]], but they can be tuned sharper to provide a better perfect fifth. In fact, mohajira is one possible fukk 7-limit extension, though this will focus on tunings sharper than mohajira.
These temperaments temper out the rastma, [[243/242]], and an unnamed comma [[2079/2048]]. They are similar to [[mohajira]], but they can be tuned sharper to provide a better perfect fifth. In fact, mohajira is one possible full 11-limit extension, though this will focus on tunings sharper than mohajira.


Interval chain in the 2.3.7.11-limit:
Interval chain in the 2.3.7.11-limit:
Line 396: Line 396:
| [[2/1]]
| [[2/1]]
|-
|-
| Ed
| E{{demiflat}}
| +1
| +1
| 349.08
| 349.08
| [[11/9]]~[[27/22]]
| [[11/9]]~[[27/22]]
| -1
| -1
| Ad
| A{{demiflat}}
| 850.92
| 850.92
| [[18/11]]~[[44/27]]
| [[18/11]]~[[44/27]]
Line 414: Line 414:
| [[4/3]]
| [[4/3]]
|-
|-
| Bd
| B{{demiflat}}
| +3
| +3
| 1047.23
| 1047.23
| [[11/6]]
| [[11/6]]
| -3
| -3
| Dd
| D{{demiflat}}
| 152.77
| 152.77
| [[12/11]]
| [[12/11]]
Line 428: Line 428:
| '''[[9/8]]'''
| '''[[9/8]]'''
| -4
| -4
| Bb
| B{{flat}}
| 1003.7
| 1003.7
| [[16/9]]
| [[16/9]]
|-
|-
| Ft
| F{{demisharp}}
| +5
| +5
| 545.38
| 545.38
| '''[[11/8]]'''
| '''[[11/8]]'''
| -5
| -5
| Gd
| G{{demiflat}}
| 654.62
| 654.62
| [[16/11]]
| [[16/11]]
Line 446: Line 446:
| [[27/16]]
| [[27/16]]
| -6
| -6
| Eb
| E{{flat}}
| 305.54
| 305.54
| [[32/27]]
| [[32/27]]
|-
|-
| Ct
| C{{demisharp}}
| +7
| +7
| 43.53
| 43.53
| [[33/32]]~[[64/63]]
| [[33/32]]~[[64/63]]
| -7
| -7
| Cd
| C{{demiflat}}
| 1156.47
| 1156.47
|
|
Line 464: Line 464:
| [[81/64]]
| [[81/64]]
| -8
| -8
| Ab
| A{{flat}}
| 807.39
| 807.39
|
|
|-
|-
| Gt
| G{{demisharp}}
| +9
| +9
| 741.68
| 741.68
| [[32/21]]
| [[32/21]]
| -9
| -9
| Fd
| F{{demiflat}}
| 458.32
| 458.32
| '''[[21/16]]'''
| '''[[21/16]]'''
Line 482: Line 482:
|
|
| -10
| -10
| Db
| D{{flat}}
| 109.24
| 109.24
|
|
|-
|-
| Dt
| D{{demisharp}}
| +11
| +11
| 239.84
| 239.84
| [[8/7]]
| [[8/7]]
| -11
| -11
| Bbd
| B{{sesquiflat}}
| 960.16
| 960.16
| '''[[7/4]]'''
| '''[[7/4]]'''
|-
|-
| F#
| F{{sharp}}
| +12
| +12
| 588.91
| 588.91
|
|
| -12
| -12
| Gb
| G{{flat}}
| 611.09
| 611.09
|
|
|-
|-
| At
| A{{demisharp}}
| +13
| +13
| 937.99
| 937.99
| [[12/7]]
| [[12/7]]
| -13
| -13
| Ebd
| E{{sesquiflat}}
| 262.01
| 262.01
| [[7/6]]
| [[7/6]]
|-
|-
| C#
| C{{sharp}}
| +14
| +14
| 87.06
| 87.06
| [[22/21]]
| [[22/21]]
| -14
| -14
| Cb
| C{{flat}}
| 1112.94
| 1112.94
| [[21/11]]
| [[21/11]]
|-
|-
| Et
| E{{demisharp}}
| +15
| +15
| 436.14
| 436.14
| [[9/7]]
| [[9/7]]
| -15
| -15
| Abd
| A{{sesquiflat}}
| 763.86
| 763.86
| [[14/9]]
| [[14/9]]
|-
|-
| G#
| G{{sharp}}
| +16
| +16
| 785.22
| 785.22
| [[11/7]]
| [[11/7]]
| -16
| -16
| Fb
| F{{flat}}
| 414.78
| 414.78
| [[14/11]]
| [[14/11]]
|-
|-
| Bt
| B{{demisharp}}
| +17
| +17
| 1134.29
| 1134.29
| [[27/14]]
| [[27/14]]
| -17
| -17
| Dbd
| D{{sesquiflat}}
| 65.71
| 65.71
| [[28/27]]
| [[28/27]]
|-
|-
| D#
| D{{sharp}}
| +18
| +18
| 283.37
| 283.37
| [[33/28]]
| [[33/28]]
| -18
| -18
| Bbb
| B{{flat2}}
| 916.63
| 916.63
|
|
Line 561: Line 561:
'''Bolded''' ratios are octave-reduced harmonics up to 21.
'''Bolded''' ratios are octave-reduced harmonics up to 21.


=== 2.3.7.11.13 extension ===
=== No-5's 19-limit extension ===


One extension to the 2.3.7.11.13 subgroup is to temper [[28/27]] to be equal to [[27/26]], tempering out [[729/728]]. This maps the 13th harmonic, [[13/8]], to the sesqui-augmented second, D{{sesquisharp}}.
While the major third is too sharp to be seen as [[5/4]], it can be seen as [[24/19]] or [[64/51]]. Treating it equal to both tempers out [[513/512]] and [[4131/4096]], providing a comma basis of [[2057/2052]], [[513/512]], [[154/153]], and [[243/242]]. The 17th harmonic is mapped to the minor second (-10 generators, D{{flat}} on C) and the 19th harmonic is mapped to the minor third (-6 generators, E{{flat}} on C). The 13th harmonic can be added by setting [[28/27]] equal to [[27/26]], tempering out [[729/728]]. This maps the 13th harmonic, [[13/8]], to the sesqui-augmented fifth (+23 generators, G{{sesquisharp}} on C).
 
2.3.7.11.17.19 extension: [[2057/2052]], [[513/512]], [[154/153]], [[243/242]]
Retrieved from "https://en.xen.wiki/w/User:UnbihexiumFan/Temperaments"