Bird's eye view of temperaments by accuracy: Difference between revisions

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=== No-2's focus ===
=== No-2's focus ===


==== [[Bohlen-Pierce-Stearns]] ====
==== [[BPS]] ====
[[Bird's eye view of temperaments by accuracy#Note counts|Note count]]:
[[Bird's eye view of temperaments by accuracy#Note counts|Note count]]:
* 7 for {5, 7, 25, 35, 49} ([[4L 5s (3/1-equivalent)|4L 5s<3/1>]])  
* 7 for {5, 7, 25, 35, 49} ([[4L 5s (3/1-equivalent)|4L 5s<3/1>]])  
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[[#Generator tunings|Generator tuning]]: 10\13edt
[[#Generator tunings|Generator tuning]]: 10\13edt


This is arguably the most important temperament of the nonoctave [[3.5.7 subgroup]]. This temperament has a tritave period, and a generator of [[~]][[9/7]]. The tritave-reduced 7th harmonic, [[7/3]], is found at -1 generators, and the tritave reduced 5th harmonic, [[5/3]], is found at +2 generators, tempering out [[245/243]]. It is as simple as a good temperament in its subgroup can be, covering the entire no-evens 7-throdd-limit tonality diamond in 7 notes, with no redundant or missing notes, and any simpler temperament would have to equate simple consonances and have very low accuracy. Its accuracy is quite good, with a no-evens 7-throdd-limit minimax error of 4.73 cents. An excellent scale to explore this temperament is the 9-note mos, or lambda scale, which can be considered the 3.5.7 analog of the diatonic scale.
BPS is arguably the most important temperament of the nonoctave [[3.5.7 subgroup]]. This temperament has a tritave period, and a generator of [[~]][[9/7]]. The tritave-reduced 7th harmonic, [[7/3]], is found at -1 generators, and the tritave reduced 5th harmonic, [[5/3]], is found at +2 generators, tempering out [[245/243]]. It is as simple as a good temperament in its subgroup can be, covering the entire no-evens 7-throdd-limit tonality diamond in 7 notes, with no redundant or missing notes, and any simpler temperament would have to equate simple consonances and have very low accuracy. Its accuracy is quite good, with a no-evens 7-throdd-limit minimax error of 4.73 cents. An excellent scale to explore this temperament is the 9-note mos, or lambda scale, which can be considered the 3.5.7 analog of the diatonic scale.


=== No-3's focus ===
=== No-3's focus ===