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 10-[[integer-limit]]~~. It is a [[phoenix]] tuning and exhibits all the benefits of such tunings~~.

'''[[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 [[octave stretch|stretched]] by about 4.5715 [[cents]] and the step size is about 63.3985 cents. It is consistent to the 10-[[integer-limit]].

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 [[harmonic]]s 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]].

30edt is a [[phoenix]] tuning and exhibits all the benefits of such tunings.

==Harmonics==

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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 10-[[integer-limit]]. It is a [[phoenix]] tuning and exhibits all the benefits of such tunings.
+'''[[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 [[octave stretch|stretched]] by about 4.5715 [[cents]] and the step size is about 63.3985 cents. It is consistent to the 10-[[integer-limit]].
-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 [[harmonic]]s 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]].
+edt is a [[phoenix]] tuning and exhibits all the benefits of such tunings.
 ==Harmonics==