29-limit: Difference between revisions

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* Mode 15 of the harmonic or subharmonic series.

The 29-limit intervals of the 2.3.29 subgroup are [[submajor and supraminor]], with [[29/27]] being a supraminor second, [[32/29]] a submajor second, [[29/24]] a supraminor third, and [[36/29]] a submajor third. While lower-limit supraminor and submajor intervals exist, such as [[14/13]], [[11/10]], and [[17/14]], these combine multiple primes higher than 3, unlike the 29-limit ones. The [[29/1|29th harmonic]] is thus quite simple to classify by [[5L 2s|diatonic]] classification, and has a characteristic [[interval quality]] like harmonics [[5/1|5]], [[7/1]], etc. ~~Note that primes~~ [[17/1|17]] and [[23/1|23]] are not so friendly in terms of interval categorization, and many wish to exclude them, leading to the 2.3.5.7.11.13.19.29 subgroup.

The 29-limit intervals of the 2.3.29 subgroup are [[submajor and supraminor]], with [[29/27]] being a supraminor second, [[32/29]] a submajor second, [[29/24]] a supraminor third, and [[36/29]] a submajor third. While lower-limit supraminor and submajor intervals exist, such as [[14/13]], [[11/10]], and [[17/14]], these combine multiple primes higher than 3, unlike the 29-limit ones. The [[29/1|29th harmonic]] is thus quite simple to classify by [[5L 2s|diatonic]] classification, and has a characteristic [[interval quality]] like harmonics [[5/1|5]], [[7/1]], etc. Primes [[17/1|17]] and [[23/1|23]] are not so friendly in terms of interval categorization, and may be considered discordant to the fundamental, being a semitone and a tritone when [[octave reduced]] respectively. Thus many people wish to exclude them, leading to the 2.3.5.7.11.13.19.29 subgroup.

However, the 29-limit approaches the point where [[consonance]] stops being registered, and intervals become very close to each other, such as [[29/28]] only being wider than [[30/29]] by [[841/840]], a comma of 2.06{{c}}. This difference is [[JND|unnoticeable]] melodically, and very difficult to hear harmonically.

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 * Mode 15 of the harmonic or subharmonic series.
-The 29-limit intervals of the 2.3.29 subgroup are [[submajor and supraminor]], with [[29/27]] being a supraminor second, [[32/29]] a submajor second, [[29/24]] a supraminor third, and [[36/29]] a submajor third. While lower-limit supraminor and submajor intervals exist, such as [[14/13]], [[11/10]], and [[17/14]], these combine multiple primes higher than 3, unlike the 29-limit ones. The [[29/1|29th harmonic]] is thus quite simple to classify by [[5L 2s|diatonic]] classification, and has a characteristic [[interval quality]] like harmonics [[5/1|5]], [[7/1]], etc. Note that primes [[17/1|17]] and [[23/1|23]] are not so friendly in terms of interval categorization, and many wish to exclude them, leading to the 2.3.5.7.11.13.19.29 subgroup.
+The 29-limit intervals of the 2.3.29 subgroup are [[submajor and supraminor]], with [[29/27]] being a supraminor second, [[32/29]] a submajor second, [[29/24]] a supraminor third, and [[36/29]] a submajor third. While lower-limit supraminor and submajor intervals exist, such as [[14/13]], [[11/10]], and [[17/14]], these combine multiple primes higher than 3, unlike the 29-limit ones. The [[29/1|29th harmonic]] is thus quite simple to classify by [[5L 2s|diatonic]] classification, and has a characteristic [[interval quality]] like harmonics [[5/1|5]], [[7/1]], etc. Primes [[17/1|17]] and [[23/1|23]] are not so friendly in terms of interval categorization, and may be considered discordant to the fundamental, being a semitone and a tritone when [[octave reduced]] respectively. Thus many people wish to exclude them, leading to the 2.3.5.7.11.13.19.29 subgroup.
 However, the 29-limit approaches the point where [[consonance]] stops being registered, and intervals become very close to each other, such as [[29/28]] only being wider than [[30/29]] by [[841/840]], a comma of 2.06{{c}}. This difference is [[JND|unnoticeable]] melodically, and very difficult to hear harmonically.