EDT: Difference between revisions

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It has been argued that pitches a tritave apart can never truly be heard as equivalent in all of the ways that octaves are, with some claiming that the [http://www.mmk.ei.tum.de/persons/ter/top/octequiv.html tonotopic representation of the mammalian auditory system]{{dead link}} is inherently biased towards octave-equivalence. With proper context, experience, and training, however, at least some people find that they can experience some degree of tritave equivalence, especially when using timbres whose overtones consist of primarily or only odd harmonics such as clarinets, square waves, or triangle waves. While is not known whether odd harmonics actually facilitate the ability to hear in tritave-equivalence, it is known that musically valuable organizations of pitch can arise through the equal division of non-octave intervals, regardless of whether the period is perceived as being truly chroma-equivalent, and as such the multitude of equal divisions of the tritave are rich and ripe for exploration.

The [[Bohlen–Pierce scale]], most commonly consisting of 13 equal divisions of the tritave (although a justly-intoned version exists as well), seems to have been the ~~second~~ such arrangement to be seriously studied and made into music~~, the first being the [[Obikhod]] pitch set of the Russian Orthodox Church which seems to have been by extension of the diatonic scale~~. The BP scale was independently discovered by Heinz Bohlen, John Pierce and Kees Van Prooijen. Bohlen found it while looking for triads with equal-difference tones, Prooijen uncovered it while searching for equally-tempered scales with accurate higher harmonics, and Pierce stumbled upon it trying to find consonant chords other than 4:5:6. Though they all started with different goals in mind, each of them amazingly ended up at the same destination.

The [[Bohlen–Pierce scale]], most commonly consisting of 13 equal divisions of the tritave (although a justly-intoned version exists as well), seems to have been the first such arrangement to be seriously studied and made into music. The BP scale was independently discovered by Heinz Bohlen, John Pierce and Kees Van Prooijen. Bohlen found it while looking for triads with equal-difference tones, Prooijen uncovered it while searching for equally-tempered scales with accurate higher harmonics, and Pierce stumbled upon it trying to find consonant chords other than 4:5:6. Though they all started with different goals in mind, each of them amazingly ended up at the same destination.

== Rank two temperaments ==

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 It has been argued that pitches a tritave apart can never truly be heard as equivalent in all of the ways that octaves are, with some claiming that the [http://www.mmk.ei.tum.de/persons/ter/top/octequiv.html tonotopic representation of the mammalian auditory system]{{dead link}} is inherently biased towards octave-equivalence. With proper context, experience, and training, however, at least some people find that they can experience some degree of tritave equivalence, especially when using timbres whose overtones consist of primarily or only odd harmonics such as clarinets, square waves, or triangle waves. While is not known whether odd harmonics actually facilitate the ability to hear in tritave-equivalence, it is known that musically valuable organizations of pitch can arise through the equal division of non-octave intervals, regardless of whether the period is perceived as being truly chroma-equivalent, and as such the multitude of equal divisions of the tritave are rich and ripe for exploration.
-The [[Bohlen–Pierce scale]], most commonly consisting of 13 equal divisions of the tritave (although a justly-intoned version exists as well), seems to have been the second such arrangement to be seriously studied and made into music, the first being the [[Obikhod]] pitch set of the Russian Orthodox Church which seems to have been by extension of the diatonic scale. The BP scale was independently discovered by Heinz Bohlen, John Pierce and Kees Van Prooijen. Bohlen found it while looking for triads with equal-difference tones, Prooijen uncovered it while searching for equally-tempered scales with accurate higher harmonics, and Pierce stumbled upon it trying to find consonant chords other than 4:5:6. Though they all started with different goals in mind, each of them amazingly ended up at the same destination.
+The [[Bohlen–Pierce scale]], most commonly consisting of 13 equal divisions of the tritave (although a justly-intoned version exists as well), seems to have been the first such arrangement to be seriously studied and made into music. The BP scale was independently discovered by Heinz Bohlen, John Pierce and Kees Van Prooijen. Bohlen found it while looking for triads with equal-difference tones, Prooijen uncovered it while searching for equally-tempered scales with accurate higher harmonics, and Pierce stumbled upon it trying to find consonant chords other than 4:5:6. Though they all started with different goals in mind, each of them amazingly ended up at the same destination.
 == Rank two temperaments ==

EDT: Difference between revisions

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