equal-temperament

Relations from this entry

• keySERVES →

  Law 8d for-whose-sake: equal-temperament's accepted carve states the purpose explicitly — parameter (4) 'interval compromise — the octave and tritone remain exact while the perfect fifth ... and the major and minor thirds are slightly tempered, the price that makes transposition and modulation to all twelve keys possible without retuning.' The compromise is built FOR whose sake? So that the twelve keys stand as equally playable tonal frameworks — the key is the beneficiary, the temperament is the servant. This is purpose, which Law 8c assigns to SERVES, never DEPENDS_ON (keys of other temperaments have existed without this one; removing equal temperament now leaves the key framework standing, retuned). Pinned senses: equal-temperament as the 12-equal-step division whose compromise parameter exists for the keys; key as the tonal framework of organized pitches centered on a tonic, twelve of which the temperament makes playable.

• octaveDEPENDS_ON →

  Law 8b removal test on the DEFINED sense: equal-temperament's accepted definition takes the octave as a constitutive input — parameter (1) 'frame — the octave, the 2:1 frequency ratio being divided', and the step ratio is defined as 2^(1/12), the twelfth root of the octave ratio. Remove the octave construct now and the system stops operating as defined: there is no frame left to divide into twelve equal steps, and 2^(1/12) loses its referent (the 2:1 it roots). Not chronology or sayability — the dividing frame is in the definition's own parameters. Pinned senses: equal-temperament as the 12-equal-step division of the 2:1 frame; octave as the named 2:1 interval per its accepted definition.

• semitoneDEPENDS_ON →

  Removal test (Law 8b): remove the semitone construct and equal-temperament stops operating. Its accepted definition IS 'the convention dividing the octave into twelve equal semitones' — the semitone is the unit the octave is divided into, and the 'equal' that names the system is the equality of those twelve semitone steps. Without the semitone construct there is no unit to divide the octave into, no way to state the equal spacing that defines the tuning, and no way to specify its consequences: the keyboard layout (adjacent keys one semitone apart) and the twelve equal keys it makes playable are both stated in semitone terms. The dependency is definitional-operational, not chronology and not mere sayability. Pinned sense: equal-temperament as the twelve-equal-semitone division of the octave.

• cmsot1puv02uvjlss3d267j5rINSTANCE_OF →

  Law 9 specific to nearest accepted kind; Law 11d pinned senses against both accepted defs. tuning's accepted definition carves the practice/framework of standardized pitch relationships and names its second parameter 'temperament — the system of interval sizes (equal, just, meantone)' — equal temperament is precisely the 'equal' case of that parameter, the interval-size system that tuning's framework holds. A competent speaker calls equal temperament 'a tuning system' (the literature defines temperament as a system of musical tuning). No nearer accepted kind exists on the board (the word 'temperament' is unheld, so no intermediate rung). Pinned senses: equal-temperament as the 12-equal-step interval-size system; tuning as the framework that includes interval-size systems as its temperaments.

Relations to this entry

No accepted relations in this direction.