Major second (diatonic interval category): Difference between revisions
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Being an abstract mos degree, and not a specific interval, the diatonic major third does not have a fixed tuning, but instead has a range of ways it can be tuned, based on the tuning of the generator used in making the scale. | Being an abstract mos degree, and not a specific interval, the diatonic major third does not have a fixed tuning, but instead has a range of ways it can be tuned, based on the tuning of the generator used in making the scale. | ||
The tuning range of the diatonic major second ranges from 342.8 to 480{{c}}. The generator for a given tuning in cents, ''n'', for the diatonic major second can be found by {{ | The tuning range of the diatonic major second ranges from 342.8 to 480{{c}}. The generator for a given tuning in cents, ''n'', for the diatonic major second can be found by {{nowrap| (''n'' + 1200)/2. For example, the third 192{{c}} gives us {{nowrap| (192 + 1200)/2 {{=}} 1392/2 {{=}} 696{{c}} }}, corresponding to 50edo. | ||
Several example tunings are provided below: | Several example tunings are provided below: | ||
{| class="wikitable" | {| class="wikitable center-all left-1" | ||
|- | |- | ||
! Tuning | ! Tuning | ||
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If the diatonic perfect fifth is treated as [[3/2]], approximating various intervals with the diatonic major second leads to the following temperaments: | If the diatonic perfect fifth is treated as [[3/2]], approximating various intervals with the diatonic major second leads to the following temperaments: | ||
{| class="wikitable" | {| class="wikitable center-2 center-5" | ||
|+ | |+ | ||
! Just interval | ! Just<br>interval | ||
! Cents | ! Cents | ||
! Temperament | ! Temperament | ||
! | ! Vanishing<br>comma | ||
! Generator (eigenmonzo tuning) | ! Generator<br>(eigenmonzo tuning) | ||
|- | |- | ||
| 21/19 | | 21/19 | ||