Meantone family: Difference between revisions
Wikispaces>guest **Imported revision 250459704 - Original comment: ** |
Wikispaces>hstraub **Imported revision 250783434 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
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Maqamic temperament is a linear mimicry of maqam music within the regular mapping paradigm, much as pelogic temperament is a linear mimicry of the gamelan pelog scale. It is the temperament that you get if you take, at face value, the simplest harmonic mapping consistent with the scalar structure of the maqamat. It deliberately ignores the issue of whether or not those dyads are resolved by the auditory system as such when played melodically (as maqam music is generally a melodic art form), intending instead to serve as a vehicle for the adventurous microtonalist who wants to explore a harmonic context for maqam music. | Maqamic temperament is a linear mimicry of maqam music within the regular mapping paradigm, much as pelogic temperament is a linear mimicry of the gamelan pelog scale. It is the temperament that you get if you take, at face value, the simplest harmonic mapping consistent with the scalar structure of the maqamat. It deliberately ignores the issue of whether or not those dyads are resolved by the auditory system as such when played melodically (as maqam music is generally a melodic art form), intending instead to serve as a vehicle for the adventurous microtonalist who wants to explore a harmonic context for maqam music. | ||
Melodically, it is a "linearized" version of the maqam modal system; it elevates the notion of "the diatonic scale with quartertones" out of the realm of 24-equal into a higher-dimensional rank 2 temperament. If the maqamat are taken to be rank 2, they all end up being MODMOS's of the proper 3L4s MOS. This MOS takes a neutral third as a generator, and the usual 5L2s diatonic scale is itself a MODMOS. The "quarter-tone" chroma in this setup is exactly half of the usual chromatic semitone from 5L2s (regardless of how it's intonated). | Melodically, it is a "linearized" version of the maqam modal system; it elevates the notion of "the diatonic scale with quartertones" out of the realm of 24-equal into a higher-dimensional rank 2 temperament. If the maqamat are taken to be rank 2, they all end up being [[MODMOS Scales|MODMOS]]'s of the proper 3L4s MOS. This MOS takes a neutral third as a generator, and the usual 5L2s diatonic scale is itself a MODMOS. The "quarter-tone" chroma in this setup is exactly half of the usual chromatic semitone from 5L2s (regardless of how it's intonated). | ||
Harmonically, intervals in this temperament are mapped to reflect some of the intonational choices that actual arabic maqam musicians make when playing maqam music on a fretless instrument such as an oud. Sometimes notes that share the same notational representation are intoned very differently under different circumstances; for example, while the fourths are generally intoned very close to 4/3, it's common to adaptively intone the minor 7th closer to 7/4. When this happens, the two notes are said to share a tempered equivalence class, and the comma between the two versions of the note is said to vanish, no matter how large it is. Real-life intonational differences existing within these equivalence classes can then be viewed as a form of adaptive intonation within this temperament, paralleling how western string quartets will often intone their major chords to be as close to 4:5:6 as possible, despite that 81/80 vanishes over the larger structure of the music. | Harmonically, intervals in this temperament are mapped to reflect some of the intonational choices that actual arabic maqam musicians make when playing maqam music on a fretless instrument such as an oud. Sometimes notes that share the same notational representation are intoned very differently under different circumstances; for example, while the fourths are generally intoned very close to 4/3, it's common to adaptively intone the minor 7th closer to 7/4. When this happens, the two notes are said to share a tempered equivalence class, and the comma between the two versions of the note is said to vanish, no matter how large it is. Real-life intonational differences existing within these equivalence classes can then be viewed as a form of adaptive intonation within this temperament, paralleling how western string quartets will often intone their major chords to be as close to 4:5:6 as possible, despite that 81/80 vanishes over the larger structure of the music. | ||
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Maqamic temperament is a linear mimicry of maqam music within the regular mapping paradigm, much as pelogic temperament is a linear mimicry of the gamelan pelog scale. It is the temperament that you get if you take, at face value, the simplest harmonic mapping consistent with the scalar structure of the maqamat. It deliberately ignores the issue of whether or not those dyads are resolved by the auditory system as such when played melodically (as maqam music is generally a melodic art form), intending instead to serve as a vehicle for the adventurous microtonalist who wants to explore a harmonic context for maqam music.<br /> | Maqamic temperament is a linear mimicry of maqam music within the regular mapping paradigm, much as pelogic temperament is a linear mimicry of the gamelan pelog scale. It is the temperament that you get if you take, at face value, the simplest harmonic mapping consistent with the scalar structure of the maqamat. It deliberately ignores the issue of whether or not those dyads are resolved by the auditory system as such when played melodically (as maqam music is generally a melodic art form), intending instead to serve as a vehicle for the adventurous microtonalist who wants to explore a harmonic context for maqam music.<br /> | ||
<br /> | <br /> | ||
Melodically, it is a &quot;linearized&quot; version of the maqam modal system; it elevates the notion of &quot;the diatonic scale with quartertones&quot; out of the realm of 24-equal into a higher-dimensional rank 2 temperament. If the maqamat are taken to be rank 2, they all end up being MODMOS's of the proper 3L4s MOS. This MOS takes a neutral third as a generator, and the usual 5L2s diatonic scale is itself a MODMOS. The &quot;quarter-tone&quot; chroma in this setup is exactly half of the usual chromatic semitone from 5L2s (regardless of how it's intonated).<br /> | Melodically, it is a &quot;linearized&quot; version of the maqam modal system; it elevates the notion of &quot;the diatonic scale with quartertones&quot; out of the realm of 24-equal into a higher-dimensional rank 2 temperament. If the maqamat are taken to be rank 2, they all end up being <a class="wiki_link" href="/MODMOS%20Scales">MODMOS</a>'s of the proper 3L4s MOS. This MOS takes a neutral third as a generator, and the usual 5L2s diatonic scale is itself a MODMOS. The &quot;quarter-tone&quot; chroma in this setup is exactly half of the usual chromatic semitone from 5L2s (regardless of how it's intonated).<br /> | ||
<br /> | <br /> | ||
Harmonically, intervals in this temperament are mapped to reflect some of the intonational choices that actual arabic maqam musicians make when playing maqam music on a fretless instrument such as an oud. Sometimes notes that share the same notational representation are intoned very differently under different circumstances; for example, while the fourths are generally intoned very close to 4/3, it's common to adaptively intone the minor 7th closer to 7/4. When this happens, the two notes are said to share a tempered equivalence class, and the comma between the two versions of the note is said to vanish, no matter how large it is. Real-life intonational differences existing within these equivalence classes can then be viewed as a form of adaptive intonation within this temperament, paralleling how western string quartets will often intone their major chords to be as close to 4:5:6 as possible, despite that 81/80 vanishes over the larger structure of the music.<br /> | Harmonically, intervals in this temperament are mapped to reflect some of the intonational choices that actual arabic maqam musicians make when playing maqam music on a fretless instrument such as an oud. Sometimes notes that share the same notational representation are intoned very differently under different circumstances; for example, while the fourths are generally intoned very close to 4/3, it's common to adaptively intone the minor 7th closer to 7/4. When this happens, the two notes are said to share a tempered equivalence class, and the comma between the two versions of the note is said to vanish, no matter how large it is. Real-life intonational differences existing within these equivalence classes can then be viewed as a form of adaptive intonation within this temperament, paralleling how western string quartets will often intone their major chords to be as close to 4:5:6 as possible, despite that 81/80 vanishes over the larger structure of the music.<br /> | ||