Kite's uniform solfege: Difference between revisions

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=== Rank-2 temperaments ===

The second row of the temperament's mapping directly yields a solfege string. This string, plus the pergen, can serve to name the temperament. For example, 11-limit [[Porcupine|Triyo/Porcupine]] has a mapping [⟨1 2 3 2 4], ⟨0 -3 -5 6 -4]]. The pergen is (P8, P4/3), and its solfege is given [[List of uniform solfeges for pergens#.237 .28P8.2C P4.2F3.29 third-4th|here]]. One simply uses syllables from columns 0, -3, -5, 6 and -4 to get DaSaMoThaFu. Since primes 2 and 3 are always DaSa by definition, they can be omitted. The temperament can be defined by the pergen plus the solfege string as "third-4th MoThaFu". The ~~temperament isn~~'t precisely ~~defined~~, since the first row of the mapping isn't used, and theoretically those numbers could change. But unless the period is a small fraction of an octave, such alternate mappings will be extremely inaccurate. So the pergen/string naming format ~~defines~~ all <u>reasonable</u> varieties of the temperament.

The second row of the temperament's mapping directly yields a solfege string. This string, plus the [[pergen]], can serve to concisely name the temperament.

For example, 11-limit [[Porcupine|Triyo/Porcupine]] has a mapping [⟨1 2 3 2 4], ⟨0 -3 -5 6 -4]]. The pergen is (P8, P4/3), and its solfege is given [[List of uniform solfeges for pergens#.237 .28P8.2C P4.2F3.29 third-4th|here]]. One simply uses syllables from columns 0, -3, -5, 6 and -4 to get DaSaMoThaFu. Since primes 2 and 3 are always DaSa by definition, they can be omitted. The temperament can be defined by the pergen plus the solfege string as "third-4th MoThaFu". Two 13-limit extensions are MoThaFuLo and MoThaFuSi. More examples: [[Pajara]] is "half-8ve MoTha" and [[Injera]] is "half-8ve MaThu". You can tell injera is in the meantone family because the first solfege is Ma. You can tell it's a weak extension of meantone because the pergen differs from meantone's.

The solfege string doesn't precisely define the temperament, since the first row of the mapping isn't used, and theoretically those numbers could change. But unless the period is a small fraction of an octave, such alternate mappings will be extremely inaccurate. So the pergen/string naming format covers all <u>reasonable</u> varieties of the temperament. For pergens that split the octave into 5 or more periods, [[Val#Shorthand notation|wart notation]] can possibly be used. (to do: elaborate)

== Application to Bosanquet keyboards ==

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 === Rank-2 temperaments ===
-The second row of the temperament's mapping directly yields a solfege string. This string, plus the pergen, can serve to name the temperament. For example, 11-limit [[Porcupine|Triyo/Porcupine]] has a mapping [⟨1 2 3 2 4], ⟨0 -3 -5 6 -4]]. The pergen is (P8, P4/3), and its solfege is given [[List of uniform solfeges for pergens#.237 .28P8.2C P4.2F3.29 third-4th|here]]. One simply uses syllables from columns 0, -3, -5, 6 and -4 to get DaSaMoThaFu. Since primes 2 and 3 are always DaSa by definition, they can be omitted. The temperament can be defined by the pergen plus the solfege string as "third-4th MoThaFu". The temperament isn't precisely defined, since the first row of the mapping isn't used, and theoretically those numbers could change. But unless the period is a small fraction of an octave, such alternate mappings will be extremely inaccurate. So the pergen/string naming format defines all <u>reasonable</u> varieties of the temperament.
+The second row of the temperament's mapping directly yields a solfege string. This string, plus the [[pergen]], can serve to concisely name the temperament.
+For example, 11-limit [[Porcupine|Triyo/Porcupine]] has a mapping [⟨1 2 3 2 4], ⟨0 -3 -5 6 -4]]. The pergen is (P8, P4/3), and its solfege is given [[List of uniform solfeges for pergens#.237 .28P8.2C P4.2F3.29 third-4th|here]]. One simply uses syllables from columns 0, -3, -5, 6 and -4 to get DaSaMoThaFu. Since primes 2 and 3 are always DaSa by definition, they can be omitted. The temperament can be defined by the pergen plus the solfege string as "third-4th MoThaFu". Two 13-limit extensions are MoThaFuLo and MoThaFuSi. More examples: [[Pajara]] is "half-8ve MoTha" and [[Injera]] is "half-8ve MaThu". You can tell injera is in the meantone family because the first solfege is Ma. You can tell it's a weak extension of meantone because the pergen differs from meantone's.
+The solfege string doesn't precisely define the temperament, since the first row of the mapping isn't used, and theoretically those numbers could change. But unless the period is a small fraction of an octave, such alternate mappings will be extremely inaccurate. So the pergen/string naming format covers all <u>reasonable</u> varieties of the temperament. For pergens that split the octave into 5 or more periods, [[Val#Shorthand notation|wart notation]] can possibly be used. (to do: elaborate)
 == Application to Bosanquet keyboards ==