Meantone: Difference between revisions
→Target tunings: adopt a more compact format |
Linked commas, made target scale size based on harmonics rather than all intervals in an odd limit |
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| Title = Meantone | | Title = Meantone | ||
| Subgroups = 2.3.5, 2.3.5.7 | | Subgroups = 2.3.5, 2.3.5.7 | ||
| Comma basis = 81/80 (2.3.5); <br>81/80, 126/125 (2.3.5.7) | | Comma basis = [[81/80]] (2.3.5); <br>[[81/80]], [[126/125]] (2.3.5.7) | ||
| Generator = 3/2 | | Generator = 3/2 | ||
| Mapping = 1; 1 4 10 | | Mapping = 1; 1 4 10 | ||
| Pergen = (P8, | | Pergen = (P8, M2) | ||
| Color name = Guti | | Color name = Guti | ||
| Edo join 1 = 12 | Edo join 2 = 19 | | Edo join 1 = 12 | Edo join 2 = 19 | ||
| Line 15: | Line 15: | ||
| Generator tuning = 696.7 | | Generator tuning = 696.7 | ||
| MOS scales = [[2L 3s]], [[5L 2s]], [[7L 5s]], [[12L 7s]] | | MOS scales = [[2L 3s]], [[5L 2s]], [[7L 5s]], [[12L 7s]] | ||
| Odd limit 1 = 5 | Mistuning 1 = 5.4 | Complexity 1 = | | Odd limit 1 = 5 | Mistuning 1 = 5.4 | Complexity 1 = 7 | ||
| Odd limit 2 = 9 | Mistuning 2 = 10.8 | Complexity 2 = | | Odd limit 2 = 9 | Mistuning 2 = 10.8 | Complexity 2 = 12 | ||
}} | }} | ||
'''Meantone''' is a familiar historical [[temperament]] based on a [[chain of fifths]] (or fourths), possessing two [[generator|generating intervals]]: the [[octave]] and the [[3/2|fifth]], from which all pitches are composed. This qualifies it as a [[rank-2 temperament]]. The octave is typically pure or close to pure, and the fifth is a few [[cents]] narrower than pure. The rationale for narrowing the fifth is to temper out the [[syntonic comma]], 81/80, which means that stacking four fifths (such as {{dash|C, G, D, A, E|hair|med}}) results in a major third (C–E) that is close to the just interval [[5/4]] rather than the more complex Pythagorean interval [[81/64]]; good tunings of meantone also lead to soft [[diatonic]] and [[Chromatic scale|chromatic]] scales, which are desirable for interval categorization. | '''Meantone''' is a familiar historical [[temperament]] based on a [[chain of fifths]] (or fourths), possessing two [[generator|generating intervals]]: the [[octave]] and the [[3/2|fifth]], from which all pitches are composed. This qualifies it as a [[rank-2 temperament]]. The octave is typically pure or close to pure, and the fifth is a few [[cents]] narrower than pure. The rationale for narrowing the fifth is to temper out the [[syntonic comma]], 81/80, which means that stacking four fifths (such as {{dash|C, G, D, A, E|hair|med}}) results in a major third (C–E) that is close to the just interval [[5/4]] rather than the more complex Pythagorean interval [[81/64]]; good tunings of meantone also lead to soft [[diatonic]] and [[Chromatic scale|chromatic]] scales, which are desirable for interval categorization. | ||