Tetrahanson: Difference between revisions

(6 intermediate revisions by 4 users not shown)

Line 75:

=== {{nowrap|b39 & b15}} ===

This is restriction of [[catalan]] extension. This can maintain the structure of the 3rd-octave period in 3.4.5, 3.5.11, and 3.5.13. Well, 3.4.5 and 3.5.13, which do not include 7 nor 11 in their basis, should simply be called tetrahanson (and no-twos cata, respectively).

This is restriction of [[catalan]] extension. This can maintain the structure of the 3rd-octave period in 3.4.5, 3.5.11, and 3.5.13. Well, 3.4.5 and 3.5.13, which do not include 7 nor 11 in their basis, should simply be called tetrahanson (and no-twos cata, respectively). Another point that must be noted is the tetracatakleismic on 3.4.5.14.

{| class="wikitable"

Line 157:

<nowiki />* In 3.5.11.13-subgroup 13-throdd-limit minimax tuning

* [https://scaleworkshop.plainsound.org/scale/KXnc-_xfK] – 15-note scale ({{sl|9L 6s}}, sLsLLsLsLLsLsLL)

* [https://scaleworkshop.plainsound.org/scale/KXnc-_xfK] – 15-note scale ({{mos scalesig|9L 6s<3/1>|link=1}}, sLsLLsLsLLsLsLL)

* 2\3edt-equivalent [[Muddle]]s:

** sLsLLsLsLL parent with 2112121 target gives LsmLmLm minor? heptatonic

** sLLsLsLLsL parent with 2112121 target gives LmsLmLm major? heptatonic

{| class="wikitable"

Line 179:

Line 182:

|-

! ET<br />generator

! [[Eigenmonzo|Eigenmonzo<br />(unchanged-interval)]]

! [[Eigenmonzo|Eigenmonzo<br />(unchanged interval)]]

! Generator (¢)

! Comments

Line 279:

Line 282:

|}

[[Category:~~Temperaments~~]]

[[Category:Tetrahanson| ]]

[[Category:~~Nonoctave~~]]

[[Category:Rank-2 temperaments]]

[[Category:Non-octave temperaments]]

@@ Line 75: / Line 75: @@
 === {{nowrap|b39 &amp; b15}} ===
-This is restriction of [[catalan]] extension. This can maintain the structure of the 3rd-octave period in 3.4.5, 3.5.11, and 3.5.13. Well, 3.4.5 and 3.5.13, which do not include 7 nor 11 in their basis, should simply be called tetrahanson (and no-twos cata, respectively).
+This is restriction of [[catalan]] extension. This can maintain the structure of the 3rd-octave period in 3.4.5, 3.5.11, and 3.5.13. Well, 3.4.5 and 3.5.13, which do not include 7 nor 11 in their basis, should simply be called tetrahanson (and no-twos cata, respectively). Another point that must be noted is the tetracatakleismic on 3.4.5.14.
 {| class="wikitable"
@@ Line 157: / Line 157: @@
 <nowiki />* In 3.5.11.13-subgroup 13-throdd-limit minimax tuning
-* [https://scaleworkshop.plainsound.org/scale/KXnc-_xfK] – 15-note scale ({{sl|9L 6s}}, sLsLLsLsLLsLsLL)
+* [https://scaleworkshop.plainsound.org/scale/KXnc-_xfK] – 15-note scale ({{mos scalesig|9L 6s<3/1>|link=1}}, sLsLLsLsLLsLsLL)
+* 2\3edt-equivalent [[Muddle]]s:
+** sLsLLsLsLL parent with 2112121 target gives LsmLmLm minor? heptatonic
+** sLLsLsLLsL parent with 2112121 target gives LmsLmLm major? heptatonic
 {| class="wikitable"
@@ Line 179: / Line 182: @@
 |-
 ! ET<br />generator
-! [[Eigenmonzo|Eigenmonzo<br />(unchanged-interval)]]
+! [[Eigenmonzo|Eigenmonzo<br />(unchanged interval)]]
 ! Generator (¢)
 ! Comments
@@ Line 279: / Line 282: @@
 |}
-[[Category:Temperaments]]
+[[Category:Tetrahanson| ]] <!-- main article -->
-[[Category:Nonoctave]]
+[[Category:Rank-2 temperaments]]
+[[Category:Non-octave temperaments]]