User:Moremajorthanmajor/5L 2s (8/3-equivalent): Difference between revisions
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{{Infobox MOS | {{Infobox MOS | ||
| | |Tuning=5L 2s<8/3>}} | ||
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{{MOS intro|Scale Signature=5L 2s<8/3>}}Among the most well-known variants of this '''17/12 diatonic''' MOS proper are [[17ed8/3]]<nowiki/>s diatonic scale along with both the Pythagorean diatonic scale and the various meantone systems. Other similar scales referred to by the term "diatonic" can be arrived at different ways – for example, through just intonation procedures, or with tetrachords. However, it should be noted that at least the majority of the other scales that fall under this category – such as the just intonation scales that use more than one size of whole tone – are actually JI detemperings or tempered approximations of them that both closely resemble and are derived from this MOS. | |||
==On the term ''diatonic''== | ==On the term ''diatonic''== | ||
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If 4\7 (four degrees of 7ED8/3) is at one extreme and 3\5 (three degrees of 5ED8/3) is at the other, all other possible 5L 2s scales exist in a continuum between them. You can chop this continuum up by taking "freshman sums" of the two edges - adding together the numerators, then adding together the denominators (i.e. adding them together as if you would be adding the complex numbers analogous real and imaginary parts). Thus, between 4\7 and 3\5 you have (4+3)\(7+5) = 7\12, seven degrees of 12ED8/3. | If 4\7 (four degrees of 7ED8/3) is at one extreme and 3\5 (three degrees of 5ED8/3) is at the other, all other possible 5L 2s scales exist in a continuum between them. You can chop this continuum up by taking "freshman sums" of the two edges - adding together the numerators, then adding together the denominators (i.e. adding them together as if you would be adding the complex numbers analogous real and imaginary parts). Thus, between 4\7 and 3\5 you have (4+3)\(7+5) = 7\12, seven degrees of 12ED8/3. | ||
If we carry this freshman-summing out a little further, new, larger [[ | If we carry this freshman-summing out a little further, new, larger [[Ed8/3|ED8/3]]<nowiki/>s pop up in our continuum. | ||
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*Chroma-negative generator: 679.218 cents (2\5) to 727.734 cents (3\7) | *Chroma-negative generator: 679.218 cents (2\5) to 727.734 cents (3\7) | ||
{{Scale | {{MOS tuning spectrum|Scale Signature=5L 2s<8/3>}} | ||
Tunings above 7\12 on this chart are called "negative tunings" (as they lessen the size of the fifth) and include 17/12 meantone systems such as 1/3-comma (close to 11\19) and 1/4-comma (close to 18\31). As these tunings approach 4\7, the majors become flatter and the minors become sharper. | Tunings above 7\12 on this chart are called "negative tunings" (as they lessen the size of the fifth) and include 17/12 meantone systems such as 1/3-comma (close to 11\19) and 1/4-comma (close to 18\31). As these tunings approach 4\7, the majors become flatter and the minors become sharper. | ||
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==Approaches to Functional Harmony== | ==Approaches to Functional Harmony== | ||
{{see also| Diatonic functional harmony}} | {{see also| Diatonic functional harmony}} | ||