3L 7s: Difference between revisions

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[[TAMNAMS]] calls this MOS pattern '''sephiroid''' (named after the abstract temperament [[sephiroth]]).

This MOS can represent tempered-flat chains of the 13th harmonic, which approximates phi (~833 cents). In the region of the spectrum around ~~23 edo~~ (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.

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.

If L = s, i.e. multiples of 10edo, the 13th harmonic becomes nearly perfect. ~~121 edo~~ seems to be the first to 'accurately' represent the comma (which might as well be represented accurately as it's 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 5/4 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]].

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 5/4 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]].

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 [~~http~~://ia600706.us.archive.org/23/items/TractatumDeModiSephiratorum/ModiSephiratorum.pdf ~~http://ia600706~~.~~us.archive.org/23/items/TractatumDeModiSephiratorum/ModiSephiratorum.pdf]~~

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.)

~~(I know it should be~~ "~~tractatus~~"~~, changing it is just a bother)~~

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".

There are MODMOS as well, but I haven't 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 ==

~~(ascending)~~

s s s L s s L s s L - Keter

s s s L s s L s s L - ~~Mode~~ Keter

s s L s s L s s L s - Chesed

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L s s s L s s L s s - Hod

--

== Scales tree ==

{| class="wikitable"

@@ Line 13: / Line 13: @@
 [[TAMNAMS]] calls this MOS pattern '''sephiroid''' (named after the abstract temperament [[sephiroth]]).
-This MOS can represent tempered-flat chains of the 13th harmonic, which approximates phi (~833 cents). In the region of the spectrum around 23 edo (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.
+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.
-If L = s, i.e. multiples of 10edo, the 13th harmonic becomes nearly perfect. 121 edo seems to be the first to 'accurately' represent the comma (which might as well be represented accurately as it's 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 5/4 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]].
+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 5/4 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]].
-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 [http://ia600706.us.archive.org/23/items/TractatumDeModiSephiratorum/ModiSephiratorum.pdf http://ia600706.us.archive.org/23/items/TractatumDeModiSephiratorum/ModiSephiratorum.pdf]
+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.)
-(I know it should be "tractatus", changing it is just a bother)
+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".
-There are MODMOS as well, but I haven't 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 ==
-(ascending)
+s s s L s s L s s L - Keter
-s s s L s s L s s L - Mode Keter
 s s L s s L s s L s - Chesed
@@ Line 45: / Line 43: @@
 L s s s L s s L s s - Hod
---
+== Scales tree ==
 {| class="wikitable"