3L 7s: Difference between revisions

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| Pattern = LssLssLsss

}}

==Name==

== Name ==

[[TAMNAMS]] suggests the temperament-agnostic name '''sephiroid''' for this scale, in reference to Kosmorsky's ''Tracatum de Modi Sephiratorum.''

==Intervals==

== Scale properties ==

~~:''This article assumes~~ [[~~TAMNAMS~~]] ~~for naming step ratios, mossteps~~, and ~~mosdegrees~~.''

==Theory==

=== Intervals ===

=== Generator chain ===

=== Modes ===

=== Proposed Names ===

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 $

}}

== Theory ==

=== The ''modi sephiratorum'' ===

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.

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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".

== ~~Modes~~ ==

== Scale tree ==

{{MOS ~~mode degrees}}~~

{{MOS tuning spectrum

=~~==Proposed Names===~~

| 6/5 = [[Submajor (temperament)|Submajor]]

~~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.~~

| 13/8 = Unnamed golden tuning

~~{{MOS modes~~|~~Mode Names~~=~~Malkuth;~~

| 5/2 = [[Sephiroth]]

~~Yesod;~~

| 13/5 = Golden sephiroth

~~Hod;~~

| 11/3 = [[Muggles]]

~~Netzach;~~

| 4/1 = [[Magic]] / horcrux

~~Tiferet;~~

| 9/2 = Magic / witchcraft / necromancy

~~Gevurah;~~

| 5/1 = Magic / telepathy

~~Chesed;~~

| 6/1 = [[Würschmidt]] ↓

~~Binah;~~

}}

~~Chokmah;~~

~~Keter~~}}

~~== 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}}

== External links ==

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

[[Category:10-tone scales]]

@@ Line 8: / Line 8: @@
 | Pattern = LssLssLsss
 }}
 {{MOS intro}}
-==Name==
+== Name ==
 [[TAMNAMS]] suggests the temperament-agnostic name '''sephiroid''' for this scale, in reference to Kosmorsky's ''Tracatum de Modi Sephiratorum.''
-==Intervals==
+== Scale properties ==
-:''This article assumes [[TAMNAMS]] for naming step ratios, mossteps, and mosdegrees.''
+{{TAMNAMS use}}
-{{MOS intervals|MOS Prefix=seph}}
-==Theory==
+=== Intervals ===
+{{MOS intervals}}
+=== Generator chain ===
+{{MOS genchain}}
+=== Modes ===
+{{MOS mode degrees}}
+=== Proposed Names ===
+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 $
+}}
+== Theory ==
 === The ''modi sephiratorum'' ===
 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.
@@ Line 28: / Line 52: @@
 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 ==
+== Scale tree ==
-{{MOS mode degrees}}
+{{MOS tuning spectrum
-===Proposed Names===
+| 6/5 = [[Submajor (temperament)|Submajor]]
-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.
+| 13/8 = Unnamed golden tuning
-{{MOS modes|Mode Names=Malkuth;
+| 5/2 = [[Sephiroth]]
-Yesod;
+| 13/5 = Golden sephiroth
-Hod;
+| 11/3 = [[Muggles]]
-Netzach;
+| 4/1 = [[Magic]] / horcrux
-Tiferet;
+| 9/2 = Magic / witchcraft / necromancy
-Gevurah;
+| 5/1 = Magic / telepathy
-Chesed;
+| 6/1 = [[Würschmidt]] ↓
-Binah;
+}}
-Chokmah;
-Keter}}
-== 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}}
 == External links ==
 * [https://ia800703.us.archive.org/12/items/TractatumDeModiSephiratorum/ModiSephiratorum.pdf Tractatum de Modi Sephiratorum] by Kosmorsky
 [[Category:10-tone scales]]