Tritriadic scale: Difference between revisions

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A '''tritriadic scale''' is a 7-note [[just intonation]] [[scale]] generated from a chain of three ''T'':''M'':''D'' [[triad]]s whose roots are separated by the ''D''/''T'' [[interval]] (where ''T'' stands for "tonic", ''M'' for "mediant" and ''D'' for "dominant")<ref>[http://www.tonalsoft.com/enc/t/tritriadic.aspx "tritriadic"]. ''www.tonalsoft.com''. Retrieved July 24, 2021.</ref>. These three chords can be interpreted as (pseudo)subdominant, root and (pseudo)dominant. Since a tritriadic scale is generally assumed to be octave-repeating, it is obtained by [[octave reduction|octave-reducing]] the notes from all three chords so that they fit within an octave.

A tritriadic scale is a special case of a [[cross-set scale]]. We can express a ''T'':''M'':''D'' tritriadic scale as CrossSet({1/1, ''M''/''T'', ''D''/''T''}, {''T''/''D'', 1/1, ''D''/''T''}).

The concept of tritriadic scales was first developed by John Chalmers in 1986<ref>[https://xh.xentonic.org/tables-of-contents.html "Xenharmonikôn Tables of Contents"]. ''xh.xentonic.org''. Retrieved 24 July, 2021.</ref>.

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 A '''tritriadic scale''' is a 7-note [[just intonation]] [[scale]] generated from a chain of three ''T'':''M'':''D'' [[triad]]s whose roots are separated by the ''D''/''T'' [[interval]] (where ''T'' stands for "tonic", ''M'' for "mediant" and ''D'' for "dominant")<ref>[http://www.tonalsoft.com/enc/t/tritriadic.aspx "tritriadic"]. ''www.tonalsoft.com''. Retrieved July 24, 2021.</ref>. These three chords can be interpreted as (pseudo)subdominant, root and (pseudo)dominant. Since a tritriadic scale is generally assumed to be octave-repeating, it is obtained by [[octave reduction|octave-reducing]] the notes from all three chords so that they fit within an octave.
+A tritriadic scale is a special case of a [[cross-set scale]]. We can express a ''T'':''M'':''D'' tritriadic scale as CrossSet({1/1, ''M''/''T'', ''D''/''T''}, {''T''/''D'', 1/1, ''D''/''T''}).
 The concept of tritriadic scales was first developed by John Chalmers in 1986<ref>[https://xh.xentonic.org/tables-of-contents.html "Xenharmonikôn Tables of Contents"]. ''xh.xentonic.org''. Retrieved 24 July, 2021.</ref>.