3L 7s: Difference between revisions

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== Scale properties ==

=== Intervals ===

=== Generator chain ===

=== Modes ===

=== Proposed Names ===

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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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== Scale tree ==

{{MOS tuning spectrum

| 11/3 = ~~Muggles~~

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

| ~~4/1 = Magic/horcrux~~

| 13/8 = Unnamed golden tuning

| ~~9/2 = Magic/witchcraft~~

| 5/2 = [[Sephiroth]]

~~| 5/1 = Magic/telepathy~~

~~| 6~~/1 = ~~Würschmidt ↓~~

| 5/2 = Sephiroth

| 13/5 = Golden sephiroth

| 6/5 = ~~Submajor~~

| 11/3 = [[Muggles]]

| 13/8 = ~~Unnamed golden tuning~~

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

| 9/2 = Magic / witchcraft / necromancy

| 5/1 = Magic / telepathy

| 6/1 = [[Würschmidt]] ↓

}}

@@ Line 14: / Line 14: @@
 == Scale properties ==
 {{TAMNAMS use}}
-{{MOS data}}
+=== Intervals ===
+{{MOS intervals}}
+=== Generator chain ===
+{{MOS genchain}}
+=== Modes ===
+{{MOS mode degrees}}
 === Proposed Names ===
@@ Line 36: / Line 44: @@
 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 46: / Line 54: @@
 == Scale tree ==
 {{MOS tuning spectrum
-| 11/3 = Muggles
+| 6/5 = [[Submajor (temperament)|Submajor]]
-| 4/1 = Magic/horcrux
+| 13/8 = Unnamed golden tuning
-| 9/2 = Magic/witchcraft
+| 5/2 = [[Sephiroth]]
-| 5/1 = Magic/telepathy
-| 6/1 = Würschmidt&nbsp;↓
-| 5/2 = Sephiroth
 | 13/5 = Golden sephiroth
-| 6/5 = Submajor
+| 11/3 = [[Muggles]]
-| 13/8 = Unnamed golden tuning
+| 4/1 = [[Magic]] / horcrux
+| 9/2 = Magic / witchcraft / necromancy
+| 5/1 = Magic / telepathy
+| 6/1 = [[Würschmidt]] ↓
 }}