Lattice: Difference between revisions

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'''~~Harmonic Lattice Diagrams~~''' ~~are~~ an instrument to visualize relations of tones. It's a projection of a multi-dimensional structure onto a 2D screen.

A '''harmonic lattice diagram''' ('''lattice''') is an instrument to visualize relations of tones. It's a projection of a multi-dimensional structure onto a 2D screen.

<ul><li>Beginner's guide to lattices: See chapter 1.3 of [http://www.tallkite.com/AlternativeTunings.html Alternative Tunings: Theory, Notation and Practice] by [[~~KiteGiedraitis|~~Kite Giedraitis]]~~</li><li>~~[http://tonalsoft.com/~~monzo~~/~~lattices~~/~~lattices~~.~~htm Harmonic Lattice Diagrams~~] ~~by Joseph L. Monzo~~ [http://~~www~~.~~webcitation~~.~~org/5xeHLDlo9 Permalink~~]

~~</li><li>~~[http://www.huygens-fokker.org/docs/fokkerpb.html Unison Vectors and Periodicity Blocks in the Three-Dimensional (3-5-7-) Harmonic Lattice of Notes] by Adriaan Fokker [http://~~www~~.~~webcitation.org~~/~~5xeGyOWPA Permalink]<~~/~~li><li>[http:~~/~~/x31eq.com/lattice~~.htm~~#7limit Octave Equivalent Music Lattices~~] by ~~Graham Breed~~ [~~http://www~~.~~webcitation.org/5xeJ48wUh Permalink~~]~~</li></ul>~~

The '''Tonnetz''' is the lattice that represents [[12edo]]'s mapping of [[5-limit]] intervals.

[[Category:~~lattice~~]]

[[Category:~~theory~~]]

== Examples ==

File:Lattice Marvel.png|A square lattice representing [[marvel]] temperament.

File:41equal lattice 5-limit.png|A hexagonal lattice representing [[41edo]]'s mapping of [[5-limit]] intervals, using [[ups and downs notation]].

File:Lattice32.png|A hexagonal lattice representing a subset of [[7-limit]] intervals, using [[color notation]].

</gallery>

== External links ==

* Beginner's guide to lattices: See chapter 1.3 of [http://www.tallkite.com/AlternativeTunings.html ''Alternative Tunings: Theory, Notation and Practice''] by [[Kite Giedraitis]] (2016)

* [http://www.tonalsoft.com/enc/l/lattice.aspx "lattice/lattice diagram"] on [[Tonalsoft Encyclopedia]]

* [http://x31eq.com/lattice.htm#7limit "Octave Equivalent Music Lattices"] by [[Graham Breed]] (2008)

* [http://www.huygens-fokker.org/docs/fokkerpb.html "Unison Vectors and Periodicity Blocks in the Three-Dimensional (3-5-7-) Harmonic Lattice of Notes"] by [[Adriaan Fokker]] (1969)

* [http://tonalsoft.com/monzo/lattices/lattices.htm "Harmonic Lattice Diagrams"] by [[Joe Monzo|Joseph L. Monzo]] (1998)

[[Category:Lattice| ]]

[[Category:Theory]]

@@ Line 1: / Line 1: @@
-'''Harmonic Lattice Diagrams''' are an instrument to visualize relations of tones. It's a projection of a multi-dimensional structure onto a 2D screen.
+{{Wikipedia|Lattice (music)}}
+A '''harmonic lattice diagram''' ('''lattice''') is an instrument to visualize relations of tones. It's a projection of a multi-dimensional structure onto a 2D screen.
-<ul><li>Beginner's guide to lattices: See chapter 1.3 of [http://www.tallkite.com/AlternativeTunings.html Alternative Tunings: Theory, Notation and Practice] by [[KiteGiedraitis|Kite Giedraitis]]</li><li>[http://tonalsoft.com/monzo/lattices/lattices.htm Harmonic Lattice Diagrams] by Joseph L. Monzo [http://www.webcitation.org/5xeHLDlo9 Permalink]
+{{Wikipedia|Tonnetz}}
-</li><li>[http://www.huygens-fokker.org/docs/fokkerpb.html Unison Vectors and Periodicity Blocks in the Three-Dimensional (3-5-7-) Harmonic Lattice of Notes] by Adriaan Fokker [http://www.webcitation.org/5xeGyOWPA Permalink]</li><li>[http://x31eq.com/lattice.htm#7limit Octave Equivalent Music Lattices] by Graham Breed [http://www.webcitation.org/5xeJ48wUh Permalink]</li></ul>
+The '''Tonnetz''' is the lattice that represents [[12edo]]'s mapping of [[5-limit]] intervals.
-[[Category:lattice]]
-[[Category:theory]]
+== Examples ==
+<gallery>
+File:Lattice Marvel.png|A square lattice representing [[marvel]] temperament.
+File:41equal lattice 5-limit.png|A hexagonal lattice representing [[41edo]]'s mapping of [[5-limit]] intervals, using [[ups and downs notation]].
+File:Lattice32.png|A hexagonal lattice representing a subset of [[7-limit]] intervals, using [[color notation]].
+</gallery>
+== External links ==
+* Beginner's guide to lattices: See chapter 1.3 of [http://www.tallkite.com/AlternativeTunings.html ''Alternative Tunings: Theory, Notation and Practice''] by [[Kite Giedraitis]] (2016)
+* [http://www.tonalsoft.com/enc/l/lattice.aspx "lattice/lattice diagram"] on [[Tonalsoft Encyclopedia]]
+* [http://x31eq.com/lattice.htm#7limit "Octave Equivalent Music Lattices"] by [[Graham Breed]] (2008)
+* [http://www.huygens-fokker.org/docs/fokkerpb.html "Unison Vectors and Periodicity Blocks in the Three-Dimensional (3-5-7-) Harmonic Lattice of Notes"] by [[Adriaan Fokker]] (1969)
+* [http://tonalsoft.com/monzo/lattices/lattices.htm "Harmonic Lattice Diagrams"] by [[Joe Monzo|Joseph L. Monzo]] (1998)
+[[Category:Lattice| ]] <!-- main article -->
+[[Category:Theory]]