30edt: Difference between revisions

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'''[[Edt|Division of the third harmonic]] into 30 equal parts''' (30edt) is related to [[19edo|19 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 4.5715 cents stretched and the step size is about 63.3985 cents. It is consistent to the [[~~9-odd-limit|~~10-integer-limit]].

'''[[Edt|Division of the third harmonic]] into 30 equal parts''' (30edt) is related to [[19edo|19 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 4.5715 cents stretched and the step size is about 63.3985 cents. It is consistent to the [[10-[[integer-limit]]. It is a [[phoenix]] tuning and exhibits all the benefits of such tunings.

Because 19edo has the 3rd, 5th, 7th, and 13th harmonics all flat (the latter two very flat), it benefits greatly from octave stretching. 30edt is one possible alternative; at the cost of sharpening the octave, it achieves much better matches to the odd harmonics; the 3 (tritave) is by definition just, the 5 slightly sharp, and the 7 and 13 slightly flat.

Because [[19edo]] has the 3rd, 5th, 7th, and 13th harmonics all flat (the latter two very flat), it benefits greatly from octave stretching. 30edt is one possible alternative; at the cost of sharpening the octave, it achieves much better matches to the odd harmonics; the 3 (tritave) is by definition just, the 5 slightly sharp, and the 7 and 13 slightly flat.

While the fifth is just, the fourth is noticeably sharper and less accurate than in 19edo, being close to that of [[26edo]].

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 {{Infobox ET}}
-'''[[Edt|Division of the third harmonic]] into 30 equal parts''' (30edt) is related to [[19edo|19 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 4.5715 cents stretched and the step size is about 63.3985 cents. It is consistent to the [[9-odd-limit|10-integer-limit]].
+'''[[Edt|Division of the third harmonic]] into 30 equal parts''' (30edt) is related to [[19edo|19 edo]], but with the 3/1 rather than the 2/1 being just. The octave is about 4.5715 cents stretched and the step size is about 63.3985 cents. It is consistent to the [[10-[[integer-limit]]. It is a [[phoenix]] tuning and exhibits all the benefits of such tunings.
-Because 19edo has the 3rd, 5th, 7th, and 13th harmonics all flat (the latter two very flat), it benefits greatly from octave stretching. 30edt is one possible alternative; at the cost of sharpening the octave, it achieves much better matches to the odd harmonics; the 3 (tritave) is by definition just, the 5 slightly sharp, and the 7 and 13 slightly flat.
+Because [[19edo]] has the 3rd, 5th, 7th, and 13th harmonics all flat (the latter two very flat), it benefits greatly from octave stretching. 30edt is one possible alternative; at the cost of sharpening the octave, it achieves much better matches to the odd harmonics; the 3 (tritave) is by definition just, the 5 slightly sharp, and the 7 and 13 slightly flat.
 While the fifth is just, the fourth is noticeably sharper and less accurate than in 19edo, being close to that of [[26edo]].