Kite's thoughts on enharmonic unisons: Difference between revisions

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Just as a temperament can be defined by a list of primes (or more generally a JI subgroup) and a list of linearly independent commas, a notation can be defined by a list of accidentals and a list of linearly independent EUs. For example, conventional notation (the usual 7 letters plus sharps and flats) with a dd2 EU must be 19edo, because that EU reduces the infinite chain of 5ths to a closed loop of 19 notes. Conventional notation plus ups and downs with a vvA1 EU must be (P8, P5/2), because P5 = vM3 + ^m3 = vM3 + ^m3 + vvA1 = vM3 + vM3.

Just as a temperament can be defined by a list of primes (or more generally a JI subgroup) and a list of linearly independent commas, a notation can be defined by a list of accidentals and a list of linearly independent EUs. Furthermore, that notation implies a certain edo or pergen.For example, conventional notation (the usual 7 letters plus sharps and flats) with a dd2 EU must be 19edo, because that EU reduces the infinite chain of 5ths to a closed loop of 19 notes. Conventional notation plus ups and downs with a vvA1 EU must be (P8, P5/2), because P5 = vM3 + ^m3 = vM3 + ^m3 + vvA1 = vM3 + vM3.

Some notations have just one EU, others are multi-EU. A multi-comma temperament can be defined by various equivalent but different comma lists. Likewise, a multi-EU notation can be defined by various EUs. Some notations define a canonical list of EUs.

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-Just as a temperament can be defined by a list of primes (or more generally a JI subgroup) and a list of linearly independent commas, a notation can be defined by a list of accidentals and a list of linearly independent EUs. For example, conventional notation (the usual 7 letters plus sharps and flats) with a dd2 EU must be 19edo, because that EU reduces the infinite chain of 5ths to a closed loop of 19 notes. Conventional notation plus ups and downs with a vvA1 EU must be (P8, P5/2), because P5 = vM3 + ^m3 = vM3 + ^m3 + vvA1 = vM3 + vM3.
+Just as a temperament can be defined by a list of primes (or more generally a JI subgroup) and a list of linearly independent commas, a notation can be defined by a list of accidentals and a list of linearly independent EUs. Furthermore, that notation implies a certain edo or pergen.For example, conventional notation (the usual 7 letters plus sharps and flats) with a dd2 EU must be 19edo, because that EU reduces the infinite chain of 5ths to a closed loop of 19 notes. Conventional notation plus ups and downs with a vvA1 EU must be (P8, P5/2), because P5 = vM3 + ^m3 = vM3 + ^m3 + vvA1 = vM3 + vM3.
 Some notations have just one EU, others are multi-EU. A multi-comma temperament can be defined by various equivalent but different comma lists. Likewise, a multi-EU notation can be defined by various EUs. Some notations define a canonical list of EUs.