Interval arithmetic: Difference between revisions
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Adding together two intervals can make awkward names, e.g m3 + m2 = dim 4th. To make them less awkward, one can add or subtract an [[enharmonic unison]], EU for short, which changes the spelling but not the tuning. | Adding together two intervals can make awkward names, e.g m3 + m2 = dim 4th. To make them less awkward, one can add or subtract an [[enharmonic unison]], EU for short, which changes the spelling but not the tuning. | ||
EUs can be essential for microtonal interval arithmetic. For example, the Porcupine | EUs can be essential for microtonal interval arithmetic. For example, the Porcupine genchain can instead be named using [[Pergen|ups and downs]]. This preserves the three foundational properties of conventional notation: octave-equivalent, fifth-generated, and heptatonic. | ||
…M6 vM7 ^1 M2 vM3 ^4 P5 vM6 ^m7 '''P1''' vM2 ^m3 P4 v5 ^m6 m7 v8 ^m2 m3… | …M6 vM7 ^1 M2 vM3 ^4 P5 vM6 ^m7 '''P1''' vM2 ^m3 P4 v5 ^m6 m7 v8 ^m2 m3… | ||