Sensamagic: Difference between revisions

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~~The~~ '''~~sensamagic~~''' ~~temperament~~ is the [[rank-3 temperament]] [[tempering out]] [[245/243]], the sensamagic comma. It has a canonical 11-limit [[extension]] adding [[385/384]] and [[896/891]] to the comma list.

'''Sensamagic''' is the [[Rank-3 temperament|rank-3]] [[temperament]] [[tempering out]] [[245/243]], the sensamagic comma. It has a canonical 11-limit [[extension]] adding [[385/384]] and [[896/891]] to the comma list.

The temperament was named after the corresponding comma, which was named by [[Gene Ward Smith]] in 2010. See [[245/243 #Etymology]].

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== Interval lattice ==

[[File:Lattice_Sensamagic.png]]

File:Lattice_Sensamagic.png|11-limit sensamagic

</gallery>

== Notation ==

Sensamagic can be notated the same as 2.3.7 [[just intonation]] since they share the same lattice structure.

Sensamagic can be notated the same as 2.3.7 [[just intonation]] since they share the same lattice structure. One way to do this is to take the conventional [[circle-of-fifths notation]] with an additional module of accidentals for the [[64/63]] comma. In this system, 7/4 is a minor seventh, 5/4 an augmented second, and 11/8 a diminished fifth.

One way to do this is to take the conventional [[circle-of-fifths notation]] with an additional module of accidentals for the [[64/63]] comma. In this system, 7/4 is a minor seventh, 5/4 an augmented second, and 11/8 a diminished fifth.

{| class="wikitable center-1 center-3"

{| class="wikitable center-~~all~~"

|+Sensamagic nomenclature<br>for selected intervals

! Ratio

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|-

| 5/4

| Double up augmented 2nd

| Double-up augmented 2nd

| C-^^D#

|-

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|}

Alternatively, it can be notated the same as full prime-limit just intonation, with a distinct accidental module for each prime harmonic. That makes some intervals more intuitive, at the cost of hiding the structure of sensamagic tempering. For example, it is customary of the 5/4 to be a major third, and 7/4 to be a minor seventh. As a result, the fact that the 5/3 is a stack of two 9/7's is not revealed, and the related chords can be ~~confusing~~.

Alternatively, it can be notated the same as full prime-limit just intonation, with a distinct accidental module for each prime harmonic. That makes some intervals more intuitive, at the cost of hiding the structure of sensamagic tempering. For example, it is customary of the 5/4 to be a major third, and 7/4 to be a minor seventh. As a result, the fact that the 5/3 is a stack of two 9/7's is not revealed, and the related chords can be less convenient.

== Chords ==

Sensamagic enables [[essentially tempered chord]]s of [[Sensamagic chords|sensamagic]], [[Keenanismic chords|keenanismic]], [[Pentacircle chords|pentacircle]], and [[Undecimal sensamagic chords|undecimal sensamagic]].

The [[sensamagic dominant chord]] is a dominant seventh chord useful for tonal harmony in this temperament.

[[Category:Temperaments]]

@@ Line 1: / Line 1: @@
-The '''sensamagic''' temperament is the [[rank-3 temperament]] [[tempering out]] [[245/243]], the sensamagic comma. It has a canonical 11-limit [[extension]] adding [[385/384]] and [[896/891]] to the comma list.
+'''Sensamagic''' is the [[Rank-3 temperament|rank-3]] [[temperament]] [[tempering out]] [[245/243]], the sensamagic comma. It has a canonical 11-limit [[extension]] adding [[385/384]] and [[896/891]] to the comma list.
 The temperament was named after the corresponding comma, which was named by [[Gene Ward Smith]] in 2010. See [[245/243 #Etymology]].
@@ Line 6: / Line 6: @@
 == Interval lattice ==
-[[File:Lattice_Sensamagic.png]]
+<gallery>
+File:Lattice_Sensamagic.png|11-limit sensamagic
+</gallery>
 == Notation ==
-Sensamagic can be notated the same as 2.3.7 [[just intonation]] since they share the same lattice structure.
+Sensamagic can be notated the same as 2.3.7 [[just intonation]] since they share the same lattice structure. One way to do this is to take the conventional [[circle-of-fifths notation]] with an additional module of accidentals for the [[64/63]] comma. In this system, 7/4 is a minor seventh, 5/4 an augmented second, and 11/8 a diminished fifth.
-One way to do this is to take the conventional [[circle-of-fifths notation]] with an additional module of accidentals for the [[64/63]] comma. In this system, 7/4 is a minor seventh, 5/4 an augmented second, and 11/8 a diminished fifth.
+{| class="wikitable center-1 center-3"
-{| class="wikitable center-all"
 |+Sensamagic nomenclature<br>for selected intervals
 ! Ratio
@@ Line 24: / Line 24: @@
 |-
 | 5/4
-| Double up augmented 2nd
+| Double-up augmented 2nd
 | C-^^D#
 |-
@@ Line 36: / Line 36: @@
 |}
-Alternatively, it can be notated the same as full prime-limit just intonation, with a distinct accidental module for each prime harmonic. That makes some intervals more intuitive, at the cost of hiding the structure of sensamagic tempering. For example, it is customary of the 5/4 to be a major third, and 7/4 to be a minor seventh. As a result, the fact that the 5/3 is a stack of two 9/7's is not revealed, and the related chords can be confusing.
+Alternatively, it can be notated the same as full prime-limit just intonation, with a distinct accidental module for each prime harmonic. That makes some intervals more intuitive, at the cost of hiding the structure of sensamagic tempering. For example, it is customary of the 5/4 to be a major third, and 7/4 to be a minor seventh. As a result, the fact that the 5/3 is a stack of two 9/7's is not revealed, and the related chords can be less convenient.
 == Chords ==
 Sensamagic enables [[essentially tempered chord]]s of [[Sensamagic chords|sensamagic]], [[Keenanismic chords|keenanismic]], [[Pentacircle chords|pentacircle]], and [[Undecimal sensamagic chords|undecimal sensamagic]].
+The [[sensamagic dominant chord]] is a dominant seventh chord useful for tonal harmony in this temperament.
 [[Category:Temperaments]]