1789edo: Difference between revisions
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Using the maximal evenness method of finding rank two temperaments, we get a 37 & 1789 temperament. | Using the maximal evenness method of finding rank two temperaments, we get a 37 & 1789 temperament. | ||
=== | === French decimal temperament === | ||
Since 1789edo contains the 2.5 subgroup, it can be used for the finite "decimal" temperament - that is, where all the interval targets in just intonation are expressed as terminating decimals. For example, [[5/4]], [[25/16]], [[128/125]], [[32/25]], 625/512, etc. This rings particularly true for the French attempts to decimalize a lot more things than we are used to today. This property of 1789edo is amplified by poor approximation of 3 and 7, allowing for cognitive separation of the intervals (or whatever is left of it at such small step size). | Since 1789edo contains the 2.5 subgroup, it can be used for the finite "decimal" temperament - that is, where all the interval targets in just intonation are expressed as terminating decimals. For example, [[5/4]], [[25/16]], [[128/125]], [[32/25]], 625/512, etc. This rings particularly true for the French attempts to decimalize a lot more things than we are used to today. This property of 1789edo is amplified by poor approximation of 3 and 7, allowing for cognitive separation of the intervals (or whatever is left of it at such small step size). | ||
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* Jacobin[111] | * Jacobin[111] | ||
* Jacobin[222] | * Jacobin[222] | ||
* | * FrenchDecimal[265] | ||
* | * FrenchDecimal[1524] | ||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||