5-limit: Difference between revisions
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The '''5-limit''' consists of all ratios in [[just intonation]] whose ratios contain no prime factors greater than 5; for example [[5/4]], [[16/15]], and [[81/80]]. The 5-limit is considered the basis of western harmony, with the ratios of the [[5-odd-limit]] being considered consonances. The main consonant chords of the 5-limit are the [[4:5:6]] major triad and the [[10:12:15]] minor triad. The smallest [[EDO]]s that approximate this these triads within 20 cents are [[12edo|12]], [[15edo|15]], [[19edo|19]], [[22edo|22]], etc. | The '''5-limit''' (aka '''pental''') consists of all ratios in [[just intonation]] whose ratios contain no prime factors greater than 5; for example [[5/4]], [[16/15]], and [[81/80]]. The 5-limit is considered the basis of western harmony, with the ratios of the [[5-odd-limit]] being considered consonances. The main consonant chords of the 5-limit are the [[4:5:6]] major triad and the [[10:12:15]] minor triad. The smallest [[EDO]]s that approximate this these triads within 20 cents are [[12edo|12]], [[15edo|15]], [[19edo|19]], [[22edo|22]], etc. | ||
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Revision as of 03:39, 3 March 2026
The 5-limit (aka pental) consists of all ratios in just intonation whose ratios contain no prime factors greater than 5; for example 5/4, 16/15, and 81/80. The 5-limit is considered the basis of western harmony, with the ratios of the 5-odd-limit being considered consonances. The main consonant chords of the 5-limit are the 4:5:6 major triad and the 10:12:15 minor triad. The smallest EDOs that approximate this these triads within 20 cents are 12, 15, 19, 22, etc.
