List of approaches to musical tuning: Difference between revisions

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* [[Equal-step tuning]]s: Tunings that use a single interval (and combinations thereof) to form a subtle monoculture of intervals. These include [[edo]]s (equal divisions of the octave), but also [[edonoi]] (equal divisions of [[nonoctave]] intervals).

* [[MOS scale|Moment of symmetry (MOS)]]: Tunings (or better, scales) that use iterations of a generating interval, modulo a period interval, to produce scales of two step-sizes.

* [[Tetrachord|Tetrachordal scales]]: the use of divided fourths as building blocks for composition.

* [[Tetrachord|Tetrachordal scales]]: the use of divided fourths or fifths as building blocks for composition.

=== Frequency ratio-based ===

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** etc.

* [[Timbral tuning]]: An approach similar to just intonation, but using an instrument's actual, non-harmonic overtone spectrum (e.g. the partials of a metal bar, drum head, or synthesized timbre) to relate frequencies instead of the harmonic series.

* [[Regular temperament]]s (including [[linear temperament]]s): a centuries-old practice that has recently undergone a mathematical facelift, in which just intonation is selectively and ~~regularly~~ detuned in various ways, to better meet a variety of compositional desires

* [[Regular temperament]]s (including [[linear temperament]]s): a centuries-old practice that has recently undergone a mathematical facelift, in which just intonation is selectively, regularly and consistently detuned in various ways to better meet a variety of compositional desires; most often making JI easier to navigate by [[tempering out]] [[Comma basis|commas]] to equate similarly sized pitches.

* [[Historical temperaments]]: The (somewhat forgotten) use of [[Pythagorean tuning]], [[meantone]] tunings and [[well temperament]]s in Western common practice music.

* [[Historical temperaments]]: The (somewhat forgotten) use of [[Pythagorean tuning]], [[meantone]] tunings and historic [[well temperament]]s in Western common practice music.

* [[Xenharmonic series]]: Just intonation but the entire matrix of just intervals is stretched, squished or otherwise warped or manipulated for interesting effect.

@@ Line 13: / Line 13: @@
 * [[Equal-step tuning]]s: Tunings that use a single interval (and combinations thereof) to form a subtle monoculture of intervals. These include [[edo]]s (equal divisions of the octave), but also [[edonoi]] (equal divisions of [[nonoctave]] intervals).
 * [[MOS scale|Moment of symmetry (MOS)]]: Tunings (or better, scales) that use iterations of a generating interval, modulo a period interval, to produce scales of two step-sizes.
-* [[Tetrachord|Tetrachordal scales]]: the use of divided fourths as building blocks for composition.
+* [[Tetrachord|Tetrachordal scales]]: the use of divided fourths or fifths as building blocks for composition.
 === Frequency ratio-based ===
@@ Line 33: / Line 33: @@
 ** etc.
 * [[Timbral tuning]]: An approach similar to just intonation, but using an instrument's actual, non-harmonic overtone spectrum (e.g. the partials of a metal bar, drum head, or synthesized timbre) to relate frequencies instead of the harmonic series.
-* [[Regular temperament]]s (including [[linear temperament]]s): a centuries-old practice that has recently undergone a mathematical facelift, in which just intonation is selectively and regularly detuned in various ways, to better meet a variety of compositional desires
+* [[Regular temperament]]s (including [[linear temperament]]s): a centuries-old practice that has recently undergone a mathematical facelift, in which just intonation is selectively, regularly and consistently detuned in various ways to better meet a variety of compositional desires; most often making JI easier to navigate by [[tempering out]] [[Comma basis|commas]] to equate similarly sized pitches.
-* [[Historical temperaments]]: The (somewhat forgotten) use of [[Pythagorean tuning]], [[meantone]] tunings and [[well temperament]]s in Western common practice music.
+* [[Historical temperaments]]: The (somewhat forgotten) use of [[Pythagorean tuning]], [[meantone]] tunings and historic [[well temperament]]s in Western common practice music.
 * [[Xenharmonic series]]: Just intonation but the entire matrix of just intervals is stretched, squished or otherwise warped or manipulated for interesting effect.