Xenharmonic Wiki

3L 7s (5/2-equivalent): Difference between revisions

← Older edit
VisualWikitext
m Moremajorthanmajor moved page User:Moremajorthanmajor/Greater sephiroid to 3L 7s (5/2-equivalent): In order to fix infobox
ArrowHead294 (talk | contribs)
14,512 edits
mNo edit summary
 
(3 intermediate revisions by 3 users not shown)
Line 1: Line 1:
{{Infobox MOS
{{Infobox MOS}}
| Name =
{{MOS intro}}
| Periods = 1
== Scale properties ==
| nLargeSteps = 3
{{TAMNAMS use}}
| nSmallSteps = 7
| Equalized = 3
| Collapsed = 1
| Pattern = LssLssLsss
| Equave = 5/2}}


'''3L 7s(<5/2>)''' occupies the spectrum from 10edo (L = s) to 3edo (s = 0).
=== Intervals ===
{{MOS intervals}}


[[TAMNAMS]] calls this MOS pattern '''sephiroid''' (named after the abstract temperament [[sephiroth]]).
=== Generator chain ===
{{MOS genchain}}


This MOS can represent tempered-flat chains of the 13th harmonic, which approximates phi (~833 cents). In the region of the spectrum around [[23edo]] (L = 3, s = 2) , the 17th and 21st harmonics are tempered toward most accurately, which together are a stable harmony. This is the major chord of the modi sephiratorum. Temperament using phi directly approximates the higher Fibonacci harmonics best.
=== Modes ===
{{MOS mode degrees}}


If L = s, i.e. multiples of 10edo, the 13th harmonic becomes nearly perfect. [[121edo]] seems to be the first to 'accurately' represent the comma (which might as well be represented accurately as it is quite small). Towards the other end, where the large and small steps are more contrasted, the comma [[65/64]] is liable to be tempered out, equating [[8/5]] and [[13/8]]. In this category fall [[13edo]], [[16edo]], [[19edo]], [[22edo]], [[29edo]], and so on. This ends at s = 0 which gives multiples of [[3edo]].
== Scale tree ==
{{MOS tuning spectrum}}


Harmonically, the arrangement forming a chord (degrees 0, 1, 4, 7, 10) is symmetrical – not ascending but rather descending, and so reminiscent of ancient Greek practice. These scales, and their truncated heptatonic forms referenced below, are strikingly linear in several ways and so seem suited to a similar outlook as traditional western music (modality, baroque tonality, classical tonality, etc. progressing to today) but with higher harmonics. For more details see Kosmorsky's [https://ia600706.us.archive.org/23/items/TractatumDeModiSephiratorum/ModiSephiratorum.pdf ''Tractatum de Modi Sephiratorum''] (Kosmorsky knows it should be "tractatus", but considers changing it is nothing but a bother.)
{{stub}}
 
There are MODMOS as well, but Kosmorsky has not explored them yet. There's enough undiscovered harmonic resources already in these to last me a while! Taking this approach to the 13th harmonic also yields heptatonic MOS with similar properties: [[3L 4s|4s+3L "mish"]] in the form of modes of ssLsLsL "led".
 
==Modes==
 
s s s L s s L s s L - Keter
 
s s L s s L s s L s - Chesed
 
s L s s L s s L s s - Netzach
 
L s s L s s L s s s - Malkuth
 
s s L s s L s s s L - Binah
 
s L s s L s s s L s - Tiferet
 
L s s L s s s L s s - Yesod
 
s s L s s s L s s L - Chokmah
 
s L s s s L s s L s - Gevurah
 
L s s s L s s L s s - Hod
 
==Scale tree==
{| class="wikitable center-all"
! colspan="7" |Generator
!Cents
!Normalized Cents
!''ed13\12''
!L
!s
!L/s
!Comments
|-
|3\10|| || || || ||
| ||360.000
|360.000
|''390.000''||1||1||1.000||
|-
|
|
|
|
|
|
|19\63
|361.905
|367.742
|''392.0635''
|7
|6
|1.167
|
|-
|  ||  ||  ||  ||  ||16\53
| ||362.264
|369.231
|''392.453''||6||5||1.200||Submajor
|-
|
|
|
|
|
|
|29\96
|362.500
|370.213
|''392.708''
|11
|9
|1.222
|
|-
|  ||  ||  ||  ||13\43||
| ||362.791
|371.429
|''393.023''||5||4||1.250||
|-
|  ||  ||  ||  ||  ||23\76
| ||363.158
|372.973
|''393.421''||9||7||1.286||
|-
|
|
|
|
|
|
|33\109
|363.303
|373.585
|''393.578''
|13
|10
|1.300
|
|-
|  ||  ||  ||10\33||  ||
| ||363.636
|375.000
|''393.939''||4||3||1.333||
|-
|  ||  ||  ||  ||  ||27\89
| ||364.045
|376.744
|''394.382''||11||8||1.375||
|-
|  ||  ||  ||  ||17\56||
| ||364.286
|377.778
|''394.643''||7||5||1.400||
|-
|  ||  ||  ||  ||  ||24\79
| ||364.557
|378.947
|''394.937''||10||7||1.428||
|-
|
|
|
|
|
|
|31\102
|364.706
|379.592
|''395.098''
|13
|9
|1.444
|
|-
|  ||  ||7\23||  ||  ||
| ||365.217
|381.818
|''395.652''||3||2||1.500||L/s = 3/2
|-
|
|
|
|
|
|
|32\105
|365.714
|384.000
|''396.1905''
|14
|9
|1.556
|
|-
|  ||  ||  ||  ||  ||25\82
| ||365.854
|384.615
|''396.3415''||11||7||1.571||
|-
|  ||  ||  ||  ||18\59||
| ||366.102
|385.714
|''396.610''||8||5||1.600||
|-
|  ||  ||  ||  ||  ||29\95
| ||366.316
|386.667
|''396.842''||13||8||1.625||Unnamed golden tuning
|-
|
|
|
|
|
|
|40\131
|366.412
|387.097
|''396.947''
|18
|11
|1.636
|
|-
|  ||  ||  ||11\36||  ||
| ||366.667
|388.235
|''397.222''||5||3||1.667||
|-
|
|
|
|
|
|
|37\121
|366.942
|389.474
|''397.521''
|17
|10
|1.700
|
|-
|  ||  ||  ||  ||  ||26\85
| ||367.059
|390.000
|''397.647''||12||7||1.714||
|-
|  ||  ||  ||  ||15\49||
| ||367.347
|391.304
|''397.959''||7||4||1.750||
|-
|  ||  ||  ||  ||  ||19\62
| ||367.742
|393.103
|''398.387''||9||5||1.800||
|-
|
|
|
|
|
|
|23\75
|368.000
|394.286
|''398.667''
|11
|6
|1.833
|
|-
|  ||4\13||  ||  ||  ||
| ||369.231
|400.000
|''400.000''||2||1||2.000||Basic sephiroid<br>(Generators smaller than this are proper)
|-
|
|
|
|
|
|
|21\68
|370.588
|406.452
|''401.471''
|11
|5
|2.200
|
|-
|  ||  ||  ||  ||  ||17\55
| ||370.909
|408.000
|''401.818''||9||4||2.250||
|-
|
|
|
|
|
|
|30\97
|371.134
|409.091
|''402.062''
|16
|7
|2.286
|
|-
|  ||  ||  ||  ||13\42||
| ||371.429
|410.526
|''402.381''||7||3||2.333||
|-
|
|
|
|
|
|
|35\113
|371.681
|411.765
|''402.655''
|19
|8
|2.375
|
|-
|  ||  ||  ||  ||  ||22\71
| ||371.831
|412.500
|''402.817''||12||5||2.400||
|-
|
|
|
|
|
|
|31\100
|372.000
|413.333
|''403.000''
|17
|7
|2.429
|
|-
|  ||  ||  ||9\29||  ||
| ||372.414
|415.385
|''403.448''||5||2||2.500||Sephiroth
|-
|
|
|
|
|
|
|32\103
|372.8155
|417.391
|''403.8835''
|18
|7
|2.571
|
|-
|  ||  ||  ||  ||  ||23\74
| ||372.973
|418.182
|''404.054''||13||5||2.600||
|-
|
|
|
|
|
|
|37\119
|373.109
|418.868
|''404.202''
|21
|8
|2.625
|Golden sephiroth
|-
|  ||  ||  ||  ||14\45||
| ||373.333
|420.000
|''404.444''||8||3||2.667||
|-
|
|
|
|
|
|
|33\106
|373.585
|421.277
|''404.717''
|19
|7
|2.714
|
|-
|  ||  ||  ||  ||  ||19\61
| ||373.770
|422.222
|''404.981''||11||4||2.750||
|-
|
|
|
|
|
|
|24\77
|374.000
|423.529
|''405.195''
|14
|5
|2.800
|
|-
|  ||  ||5\16||  ||  ||
| ||375.000
|428.571
|''406.250''||3||1||3.000||L/s = 3/1
|-
|
|
|
|
|
|
|21\67
|376.119
|434.483
|''407.463''
|13
|4
|3.250
|
|-
|  ||  ||  ||  ||  ||16\51
| ||376.471
|436.364
|''407.843''||10||3||3.333||
|-
|
|
|
|
|
|
|27\86
|376.744
|437.838
|''408.1395''
|17
|5
|3.400
|
|-
|  ||  ||  ||  ||11\35||
| ||377.143
|440.000
|''408.571''||7||2||3.500||
|-
|
|
|
|
|
|
|28\89
|377.528
|442.105
|''408.989''
|18
|5
|3.600
|
|-
|  ||  ||  ||  ||  ||17\54
| ||377.778
|443.478
|''409.259''||11||3||3.667||Muggles
|-
|
|
|
|
|
|
|23\73
|378.082
|445.161
|''409.589''
|15
|4
|3.750
|
|-
|  ||  ||  ||6\19||  ||
| ||378.947
|450.000
|''410.526''||4||1||4.000||Magic/horcrux
|-
|
|
|
|
|
|
|19\60
|380.000
|456.000
|''411.667''
|13
|3
|4.333
|
|-
|  ||  ||  ||  ||  ||13\41
| ||380.488
|458.8235
|''412.195''||9||2||4.500||Magic/witchcraft
|-
|
|
|
|
|
|
|20\63
|380.952
|461.5385
|''412.698''
|14
|3
|4.667
|
|-
|  ||  ||  ||  ||7\22||
| ||381.818
|466.667
|''413.636''||5||1||5.000||Magic/telepathy
|-
|
|
|
|
|
|
|15\47
|382.979
|473.684
|''414.894''
|11
|2
|5.500
|
|-
|  ||  ||  ||  ||  ||8\25
| ||384.000
|480.000
|''416.000''||6||1||6.000||Würschmidt↓
|-
|
|
|
|
|
|
|9\28
|385.714
|490.909
|''417.857''
|7
|1
|7.000
|
|-
|1\3||  ||  ||  ||  ||
| ||400.000
|600.000
|''433.333''||1||0||→ inf||
|}
Retrieved from "https://en.xen.wiki/w/3L_7s_(5/2-equivalent)"