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| Pattern = LssLssLsss
| Pattern = LssLssLsss
}}
}}
{{MOS intro}}
== Name ==
[[TAMNAMS]] suggests the temperament-agnostic name '''sephiroid''' for this scale, in reference to Kosmorsky's ''Tracatum de Modi Sephiratorum.''


{{MOS intro}}
== Scale properties ==
{{TAMNAMS use}}
 
=== Intervals ===
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}


==Name==
=== Proposed Names ===
[[TAMNAMS]] suggests the temperament-agnostic name '''sephiroid''' for this scale, in reference to Kosmorsky's ''Tracatum de Modi Sephiratorum.''
Mode names are described by Kosmorsky, which use names from the [[wikipedia:Sefirot|Sefirot]] (or sephiroth). Kosmorsky describes the mode Keter to be akin to the lydian mode of 5L 2s, and the mode Malkuth like the locrian mode.
{{MOS modes
| Mode Names=
Malkuth $
Yesod $
Hod $
Netzach $
Tiferet $
Gevurah $
Chesed $
Binah $
Chokmah $
Keter $
}}


==Intervals==
== Theory ==
:''This article assumes [[TAMNAMS]] for naming step ratios, mossteps, and mosdegrees.''
{{MOS intervals|MOS Prefix=seph}}
==Theory==
=== The ''modi sephiratorum'' ===
=== The ''modi sephiratorum'' ===
This MOS can represent tempered-flat chains of the 13th harmonic, which approximates phi (~833 cents).
This MOS can represent tempered-flat chains of the 13th harmonic, which approximates phi (~833 cents).


With sephiroid scales with a soft-of-basic step ratio (around L:s = 3:2, or 23edo), 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.
With sephiroid scales with a soft-of-basic step ratio (around {nowrap|L:s {{=}} 3:2}}, or 23edo), 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.


Scales approaching an equalized step ratio (L:s = 1:1, or [[10edo]]) contain a 13th harmonic that's nearly perfect. [[121edo]] seems to be the first to 'accurately' represent the comma{{Clarify}}. Scales approaching a collapsed step ratio (L:s = 1:0, or [[3edo]]) have the comma [[65/64]] liable to be tempered out, thus equating [[8/5]] and [[13/8]]. Edos include [[13edo]], [[16edo]], [[19edo]], [[22edo]], [[29edo]], and others.
Scales approaching an equalized step ratio ({{nowrap|L:s {{=}} 1:1}}, or [[10edo]]) contain a 13th harmonic that's nearly perfect. [[121edo]] seems to be the first to 'accurately' represent the comma{{Clarify}}. Scales approaching a collapsed step ratio ({{nowrap|L:s {{=}} 1:0}}, or [[3edo]]) have the comma [[65/64]] liable to be tempered out, thus equating [[8/5]] and [[13/8]]. Edos include [[13edo]], [[16edo]], [[19edo]], [[22edo]], [[29edo]], and others.


Harmonically, the arrangement forming a chord (degrees 0, 1, 4, 7, 10){{Clarify}} 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.  
Harmonically, the arrangement forming a chord (degrees 0, 1, 4, 7, 10){{Clarify}} 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.  
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There are MODMOS as well, but Kosmorsky has not explored them yet, as "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".
There are MODMOS as well, but Kosmorsky has not explored them yet, as "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 ==
Mode names are described by Kosmorsky, which use names from the [[wikipedia:Sefirot|Sefirot]] (or sephiroth). Kosmorsky describes the mode Keter to be akin to the lydian mode of 5L 2s, and the mode Malkuth like the locrian mode.
{{MOS modes|Mode Names=Malkuth;
Yesod;
Hod;
Netzach;
Tiferet;
Gevurah;
Chesed;
Binah;
Chokmah;
Keter}}
== Scale tree ==
== Scale tree ==
{{Scale tree|Comments=11/3: Muggles; 4/1: Magic/horcrux; 9/2: Magic/witchcraft; 5/1: Magic/telepathy; 6/1: Würschmidt↓; 5/2: Sephiroth; 13/5: Golden sephiroth; 6/5: Submajor; 13/8: Unnamed golden tuning}}
{{MOS tuning spectrum
== See also ==
| 6/5 = [[Submajor (temperament)|Submajor]]
| 13/8 = Unnamed golden tuning
| 5/2 = [[Sephiroth]]
| 13/5 = Golden sephiroth
| 11/3 = [[Muggles]]
| 4/1 = [[Magic]] / horcrux
| 9/2 = Magic / witchcraft / necromancy
| 5/1 = Magic / telepathy
| 6/1 = [[Würschmidt]] ↓
}}


== External links ==
* [https://ia800703.us.archive.org/12/items/TractatumDeModiSephiratorum/ModiSephiratorum.pdf Tractatum de Modi Sephiratorum] by Kosmorsky
* [https://ia800703.us.archive.org/12/items/TractatumDeModiSephiratorum/ModiSephiratorum.pdf Tractatum de Modi Sephiratorum] by Kosmorsky


[[Category:10-tone scales]]
[[Category:10-tone scales]]
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