41edo: Difference between revisions

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== 41edo as a Universal Tuning ==

41's claim to fame as a "universal tuning" is the fact that it approximates scales present in many important world music traditions, and thus is good for both combining and exploring cultural playstyles.

41's claim to fame as a "universal tuning" is the fact that it approximates scales present in many important world music traditions, and thus is good for both combining and exploring cultural playstyles. It makes no claim to perfectly and faithfully represent the musical cultures listed, as doing so would require far more notes and small details than are present in 41. That being said, it has certain attributes that allow it to approximate common scales in these cultures with far more accuracy than most comparable EDOs.

=== Western ===

Due to 41edo's extremely accurate perfect fifth, it makes a good tuning for schismatic temperament, which in turn is a good approximation of the standard [[12edo]] scale, and when arranged as a Bbb-D gamut, approximates the 12 note [[Pythagorean tuning]] known as [[Kirnberger I]]. This extends the Ptolemy Diatonic Scale ('''7 6 4 7 6 7 4'''), which 41 approximates excellently, by completing the circle of fifths with pure 3/2s. By using this system and occasionally substituting in alternate major seconds and sixths when necessary, it becomes quite reminiscent of (and ~~improves~~ on) 12edo harmony. Additionally, the Pythagorean Pentatonic scale can be used for melodies overtop due to the strong quartal nature of the scale. The Pythagorean diatonic scale exists as an option as well, but use may be limited unless [[Gentle chords|Gentle triads]] are ideal.

Due to 41edo's extremely accurate perfect fifth, it makes a good tuning for [[schismatic]] temperament and the 12-note MOS, which in turn is a good approximation of the standard [[12edo]] scale, and when arranged as a Bbb-D gamut, approximates the 12-note roughly [[Pythagorean tuning]] known as [[Kirnberger I]]. This extends the Ptolemy Diatonic Scale ('''7 6 4 7 6 7 4'''), which 41 approximates excellently, by completing the circle of fifths with pure 3/2s. By using this system and occasionally substituting in alternate major seconds and sixths when necessary, it becomes quite reminiscent of (and can improve on) 12edo harmony. Additionally, the Pythagorean Pentatonic scale can be used for melodies overtop due to the strong quartal nature of the scale. The Pythagorean diatonic scale exists as an option as well, but use may be limited unless [[Gentle chords|Gentle triads]] are ideal. An alternate option is approximating a Just Intonation scale such as the [[Duodene|Asymmetric scale]], a common option for a 5-limit JI scale, or [[Centaur]], a 7-limit JI scale using "blue" or subminor intervals for the accidental notes. There exist other options for 5-limit JI scales, all of which have some reasonable approximation in 41 due to its relative excellence in the 5-limit.

=== Middle Eastern ===

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=== Blues ===

Due to its pure sounding major thirds and approximations of standard western harmony, 41 naturally is good for jazz and blues music, though a great strength of this system as opposed to many others is its excellent harmonic seventh, alongside MOS scales that supply them, [[Miracle]] in particular.

Due to its pure sounding major thirds and approximations of standard western harmony, 41 naturally is good for jazz and blues music, though a great strength of this system as opposed to many others is its excellent harmonic seventh, alongside MOS scales that supply them, [[Magic]] and [[Miracle]] in particular.

Coltrane changes can be represented with two Pythagorean major thirds and a pental one, or a temperament like Magic, whose MOSes are characterized by circles of major thirds, giving options for rotating major and minor triads within one scale.

Coltrane changes can be represented with two Pythagorean major thirds and a pental one, or a temperament like Magic, whose MOSes are characterized by circles of major thirds, giving options for rotating major and minor triads within one scale. Similarly, the Whole Tone scale is represented by [[Baldy6|Baldy[6]]], with two pental major thirds and four Pythagorean. This scale can be extended to an 11-note MOS, including a single 4:5:7:9:11 chord and numerous subsets.

[[Superkleismic]] presents another option for this purpose, featuring circles of minor thirds, and generating harmonic sevenths with very low complexity.

Blue notes, rather than being considered inflections, can be notated as accidentals instead, such as the "blue third" which is represented by a neutral third, or any number of septimal intervals that ~~sound great~~ in a blues context.

Blue notes, rather than being considered inflections, can be notated as accidentals instead, such as the "blue third" which is represented by a neutral third, or any number of septimal intervals that are useful in a blues context.

=== Other ===

@@ Line 1,852: / Line 1,852: @@
 == 41edo as a Universal Tuning ==
-'s claim to fame as a "universal tuning" is the fact that it approximates scales present in many important world music traditions, and thus is good for both combining and exploring cultural playstyles.
+'s claim to fame as a "universal tuning" is the fact that it approximates scales present in many important world music traditions, and thus is good for both combining and exploring cultural playstyles. It makes no claim to perfectly and faithfully represent the musical cultures listed, as doing so would require far more notes and small details than are present in 41. That being said, it has certain attributes that allow it to approximate common scales in these cultures with far more accuracy than most comparable EDOs.
 === Western ===
-Due to 41edo's extremely accurate perfect fifth, it makes a good tuning for schismatic temperament, which in turn is a good approximation of the standard [[12edo]] scale, and when arranged as a Bbb-D gamut, approximates the 12 note [[Pythagorean tuning]] known as [[Kirnberger I]]. This extends the Ptolemy Diatonic Scale ('''7 6 4 7 6 7 4'''), which 41 approximates excellently, by completing the circle of fifths with pure 3/2s. By using this system and occasionally substituting in alternate major seconds and sixths when necessary, it becomes quite reminiscent of (and improves on) 12edo harmony. Additionally, the Pythagorean Pentatonic scale can be used for melodies overtop due to the strong quartal nature of the scale. The Pythagorean diatonic scale exists as an option as well, but use may be limited unless [[Gentle chords|Gentle triads]] are ideal.
+Due to 41edo's extremely accurate perfect fifth, it makes a good tuning for [[schismatic]] temperament and the 12-note MOS, which in turn is a good approximation of the standard [[12edo]] scale, and when arranged as a Bbb-D gamut, approximates the 12-note roughly [[Pythagorean tuning]] known as [[Kirnberger I]]. This extends the Ptolemy Diatonic Scale ('''7 6 4 7 6 7 4'''), which 41 approximates excellently, by completing the circle of fifths with pure 3/2s. By using this system and occasionally substituting in alternate major seconds and sixths when necessary, it becomes quite reminiscent of (and can improve on) 12edo harmony. Additionally, the Pythagorean Pentatonic scale can be used for melodies overtop due to the strong quartal nature of the scale. The Pythagorean diatonic scale exists as an option as well, but use may be limited unless [[Gentle chords|Gentle triads]] are ideal. An alternate option is approximating a Just Intonation scale such as the [[Duodene|Asymmetric scale]], a common option for a 5-limit JI scale, or [[Centaur]], a 7-limit JI scale using "blue" or subminor intervals for the accidental notes. There exist other options for 5-limit JI scales, all of which have some reasonable approximation in 41 due to its relative excellence in the 5-limit.
 === Middle Eastern ===
@@ Line 1,876: / Line 1,876: @@
 === Blues ===
-Due to its pure sounding major thirds and approximations of standard western harmony, 41 naturally is good for jazz and blues music, though a great strength of this system as opposed to many others is its excellent harmonic seventh, alongside MOS scales that supply them, [[Miracle]] in particular.
+Due to its pure sounding major thirds and approximations of standard western harmony, 41 naturally is good for jazz and blues music, though a great strength of this system as opposed to many others is its excellent harmonic seventh, alongside MOS scales that supply them, [[Magic]] and [[Miracle]] in particular.
-Coltrane changes can be represented with two Pythagorean major thirds and a pental one, or a temperament like Magic, whose MOSes are characterized by circles of major thirds, giving options for rotating major and minor triads within one scale.
+Coltrane changes can be represented with two Pythagorean major thirds and a pental one, or a temperament like Magic, whose MOSes are characterized by circles of major thirds, giving options for rotating major and minor triads within one scale. Similarly, the Whole Tone scale is represented by [[Baldy6|Baldy[6]]], with two pental major thirds and four Pythagorean. This scale can be extended to an 11-note MOS, including a single 4:5:7:9:11 chord and numerous subsets.
 [[Superkleismic]] presents another option for this purpose, featuring circles of minor thirds, and generating harmonic sevenths with very low complexity.
-Blue notes, rather than being considered inflections, can be notated as accidentals instead, such as the "blue third" which is represented by a neutral third, or any number of septimal intervals that sound great in a blues context.
+Blue notes, rather than being considered inflections, can be notated as accidentals instead, such as the "blue third" which is represented by a neutral third, or any number of septimal intervals that are useful in a blues context.
 === Other ===