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'''88-cent equal temperament''' (also known as '''1ed88¢''' or '''APS88¢''') uses equal steps of 88 [[cent]]s each. It is equivalent to 13.6364edo, and is a subset of [[150edo]] (every eleventh step). | '''88-cent equal temperament''' ('''88cET''', also known as '''1ed88¢''' or '''APS88¢''') uses equal steps of 88 [[cent]]s each. It is equivalent to 13.6364edo, and is a subset of [[150edo]] (every eleventh step). | ||
== Theory == | == Theory == | ||
88-cent [[Equal-step tuning|equal temperament]] uses 88 cents, or 11\150 of an octave, to generate a [[nonoctave]] rank-1 scale. Since the 88-cent step is an excellent generator for the [[octacot]] temperament, it can be viewed as the generator chain of octacot, stripped of octaves. However viewed, octacot and 88-cent equal temperament are very closely related, and the chords of 88-cent equal temperament are listed on the page [[Chords of octacot]]. From this it may be seen that octacot, and hence 88 cent equal temperament , share an abundance of [[essentially tempered | 88-cent [[Equal-step tuning|equal temperament]] uses 88 cents, or 11\150 of an octave, to generate a [[nonoctave]] rank-1 scale. Since the 88-cent step is an excellent generator for the [[octacot]] temperament, it can be viewed as the generator chain of octacot, stripped of octaves. However viewed, octacot and 88-cent equal temperament are very closely related, and the chords of 88-cent equal temperament are listed on the page [[Chords of octacot]]. From this it may be seen that octacot, and hence 88 cent equal temperament , share an abundance of [[essentially tempered chord]]s. | ||
Eight steps of 88 cents gives 704 cents, two cents sharp of 3/2, and eighteen gives 1584 cents, two cents flat of 5/2. Taken together this tells us that (5/2)<sup>4</sup>/(3/2)<sup>9</sup> = [[20000/19683]], the minimal diesis or tetracot comma, must be being tempered out. Eleven steps of 88 cents gives 968 cents, less than a cent flat of 7/4, and this tells us that (7/4)<sup>8</sup>/(3/2)<sup>11</sup> = 5764801/5668704 must be tempered out also. Taking this, multiplying it by the tetracot comma and taking the fourth root yields [[245/243]], which therefore must be tempered out also. The tetracot comma and 245/243 taken together define 7-limit octacot. | Eight steps of 88 cents gives 704 cents, two cents sharp of 3/2, and eighteen gives 1584 cents, two cents flat of 5/2. Taken together this tells us that (5/2)<sup>4</sup>/(3/2)<sup>9</sup> = [[20000/19683]], the minimal diesis or tetracot comma, must be being tempered out. Eleven steps of 88 cents gives 968 cents, less than a cent flat of 7/4, and this tells us that (7/4)<sup>8</sup>/(3/2)<sup>11</sup> = 5764801/5668704 must be tempered out also. Taking this, multiplying it by the tetracot comma and taking the fourth root yields [[245/243]], which therefore must be tempered out also. The tetracot comma and 245/243 taken together define 7-limit octacot. | ||
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== Scales == | == Scales == | ||
* [[ | * [[Symmetrical scales of 88cET]] | ||
== Music == | == Music == | ||
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[[Category:Equal-step tuning]] | [[Category:Equal-step tuning]] | ||