30edt: Difference between revisions

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== Theory ==

30edt is related to [[19edo]], but with the [[3/1]] rather than the [[2/1]] being [[just]], which results in octaves being is [[stretched and compressed tuning|stretched]] by about 4.5715{{cent}}. It is [[consistent]] to the 10-[[integer-limit]].

30edt is related to [[19edo]], but with the [[3/1]] rather than the [[2/1]] being [[just]], which results in octaves being is [[stretched and compressed tuning|stretched]] by about 4.5715{{cent}}. Like 19edo, 30edt is [[consistent]] to the [[integer-limit|10-integer-limit]].

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.

Because [[19edo]] has the [[3/1|3rd]], [[5/1|5th]], [[7/1|7th]], and [[13/1|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]].

While the fifth is closer to just than in 19edo, 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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=== Subsets and supersets ===

Since 30 factors into primes as 2 × 3 × 5, 30edt has subset edts {{EDs|equave=t| 2, 3, 5, 6, 10, and 15 }}.

== Intervals ==

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; [[Ray Perlner]]

* [https://www.youtube.com/watch?v=fEQ13hzs3fY ''Fugue for Piano in 30EDT Bohlen-Pierce-Stearns{{lbrack}}9{{rbrack}} sLsLssLsL "Dur I"''] (2024)

== See also ==

* [[11edf]] – relative edf

* [[19edo]] – relative edo

* [[49ed6]] – relative ed6

* [[53ed7]] – relative ed7

* [[68ed12]] – relative ed12

* [[93ed30]] – relative ed30

[[Category:Listen]]

@@ Line 3: / Line 3: @@
 == Theory ==
-edt is related to [[19edo]], but with the [[3/1]] rather than the [[2/1]] being [[just]], which results in octaves being is [[stretched and compressed tuning|stretched]] by about 4.5715{{cent}}. It is [[consistent]] to the 10-[[integer-limit]].
+edt is related to [[19edo]], but with the [[3/1]] rather than the [[2/1]] being [[just]], which results in octaves being is [[stretched and compressed tuning|stretched]] by about 4.5715{{cent}}. Like 19edo, 30edt is [[consistent]] to the [[integer-limit|10-integer-limit]].
-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.
+Because [[19edo]] has the [[3/1|3rd]], [[5/1|5th]], [[7/1|7th]], and [[13/1|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]].
+While the fifth is closer to just than in 19edo, 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 ===
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 === Subsets and supersets ===
 Since 30 factors into primes as 2 × 3 × 5, 30edt has subset edts {{EDs|equave=t| 2, 3, 5, 6, 10, and 15 }}.
 == Intervals ==
@@ Line 255: / Line 253: @@
 ; [[Ray Perlner]]
 * [https://www.youtube.com/watch?v=fEQ13hzs3fY ''Fugue for Piano in 30EDT Bohlen-Pierce-Stearns{{lbrack}}9{{rbrack}} sLsLssLsL "Dur I"''] (2024)
+== See also ==
+* [[11edf]] – relative edf
+* [[19edo]] – relative edo
+* [[49ed6]] – relative ed6
+* [[53ed7]] – relative ed7
+* [[68ed12]] – relative ed12
+* [[93ed30]] – relative ed30
 [[Category:Listen]]