Equal-step tuning: Difference between revisions
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Other edonoi contain no approximation of an octave or a compound octave (at least, not for a while), and continue generating new tones as they continue upward or downward. Such scales lack a very familiar compositional redundancy, that of [[octave equivalence]] – this might necessitate special attention. | Other edonoi contain no approximation of an octave or a compound octave (at least, not for a while), and continue generating new tones as they continue upward or downward. Such scales lack a very familiar compositional redundancy, that of [[octave equivalence]] – this might necessitate special attention. | ||
== Alpha-beta-gamma family == | == Alpha-beta-gamma family of equal divisions == | ||
Wendy Carlos invented in the 1980's the Alpha, Beta, and Gamma scales. These are scales that divides 3/2 with steps very near to the successive superparticular complementary pair folding in 3/2, namely 6/5 and 5/4. The happy equal divisions are 9ed3/2, 11ed3/2, and 20ed3/2. However, these scales belong to a much vaster family, where also applies the same principle of divisions of a ratio with steps very near to the successive superparticular complementary pair folding into it. Below is a table showing the first members of this family: | Wendy Carlos invented in the 1980's the Alpha, Beta, and Gamma scales. These are scales that divides 3/2 with steps very near to the successive superparticular complementary pair folding in 3/2, namely 6/5 and 5/4. The happy equal divisions are 9ed3/2, 11ed3/2, and 20ed3/2. However, these scales belong to a much vaster family, where also applies the same principle of divisions of a ratio with steps very near to the successive superparticular complementary pair folding into it. Below is a table showing the first members of this family: | ||
{| class="wikitable" | {| class="wikitable" | ||