Decimal: Difference between revisions

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Decimal serves as a structural archetype for a 10-tone system that views the [[4:5:6]] and [[10:12:15|1/(4:5:6)]] chords as a major–minor pair (which is equated in decimal temperament as 25/24 is tempered out), and the [[6:7:8]] and [[21:24:28|1/(6:7:8)]] chords as another major–minor pair, neutralized in decimal via vanishing of 49/48.

A more accurate system based on 10 interval classes that does not neutralize these chords is [[pajara]], where 50/49 remains tempered and 49/48 is equated to 25/24. An even more accurate one is [[miracle]], which equates 50/49 with 49/48, though its structure is more complex than that of pajara~~, but easily extends to the [[11-limit]]~~. Both of these temperaments also temper out the marvel comma, [[225/224]].

A more accurate system based on 10 interval classes that does not neutralize these chords is [[pajara]], where 50/49 remains tempered and 49/48 is equated to 25/24. An even more accurate one is [[miracle]], which equates 50/49 with 49/48, though its structure is more complex than that of pajara. Both of these temperaments also temper out the marvel comma, [[225/224]].

For technical data, see [[Dicot family #Decimal]].

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 Decimal serves as a structural archetype for a 10-tone system that views the [[4:5:6]] and [[10:12:15|1/(4:5:6)]] chords as a major–minor pair (which is equated in decimal temperament as 25/24 is tempered out), and the [[6:7:8]] and [[21:24:28|1/(6:7:8)]] chords as another major–minor pair, neutralized in decimal via vanishing of 49/48.
-A more accurate system based on 10 interval classes that does not neutralize these chords is [[pajara]], where 50/49 remains tempered and 49/48 is equated to 25/24. An even more accurate one is [[miracle]], which equates 50/49 with 49/48, though its structure is more complex than that of pajara, but easily extends to the [[11-limit]]. Both of these temperaments also temper out the marvel comma, [[225/224]].
+A more accurate system based on 10 interval classes that does not neutralize these chords is [[pajara]], where 50/49 remains tempered and 49/48 is equated to 25/24. An even more accurate one is [[miracle]], which equates 50/49 with 49/48, though its structure is more complex than that of pajara. Both of these temperaments also temper out the marvel comma, [[225/224]].
 For technical data, see [[Dicot family #Decimal]].