User:Nick Vuci/TonalityDiamond: Difference between revisions
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# '''Using one row as the numerator and the other as the denominator, fill in the cells with the ratios they form.''' | # '''Using one row as the numerator and the other as the denominator, fill in the cells with the ratios they form.''' | ||
# '''Make sure the decimal form of the ratio is between 1 and 2. If it is not, double one of the numbers until it is.''' | # '''Make sure the decimal form of the ratio is between 1 and 2. If it is not, double one of the numbers until it is.''' | ||
Some finer points: | |||
- the numbers of the odd-limit are generally arranged in one of two ways: a) ascending numerically (ie, 2 3 5 7 etc) or, b) ascending by tonal order (ie 2 5 3 7) | |||
- in order to make the rows | |||
== History == | == History == | ||
The tonality diamond | The tonality diamond was first formally explained by [https://archive.org/details/max-f-meyer-the-musicians-arithmetic Max F Meyer in his 1929 publication ''The Musician's Arithmetic''] using the 7-odd-limit. Even though Harry Partch gives a different story for how he discovered the concept, it is likely this source that gave him the idea, which he then extended to the 11-odd-limit and made the basis of his tonal system. | ||
The first novel xenharmonic temperament — George Secor's later-named "Miracle" temperament — was made to approximate Partch's 11-limit diamond. | |||