Irvian mode: Difference between revisions
m set lemma bold |
|||
| Line 23: | Line 23: | ||
Even-length Irvian modes with odd number of years per cycle (that is notes) have a feature where they aren't 100% symmetrical - two middle years follow a pattern of non-leap - leap. If the ''K'' is chosen as (''C''-1)/2 instead of ''C''/2, the sequence will be leap, nonleap. Thus it is called ''almost symmetrical'' in the calendar lore. That being said, they fulfill their function just like odd cycles do, and therefore belong in Irvian modes. | Even-length Irvian modes with odd number of years per cycle (that is notes) have a feature where they aren't 100% symmetrical - two middle years follow a pattern of non-leap - leap. If the ''K'' is chosen as (''C''-1)/2 instead of ''C''/2, the sequence will be leap, nonleap. Thus it is called ''almost symmetrical'' in the calendar lore. That being said, they fulfill their function just like odd cycles do, and therefore belong in Irvian modes. | ||
== | ==Example on a standard 12edo piano== | ||
The 12edo piano key layout, which is predominantly use in the world today, is an example of an Irvian mode that is subject to even-length leap rule modification.<blockquote>'''Year is leap if the remainder of (7 x Year + 6) / 12 is less than 7.'''</blockquote>Such a pattern generates keys number '''1-3-5-6-8-10-12-1''' to be the keys on the scale, which is a '''5L 2s''' scale in a pattern of '''LLsLLLs'''. White keys are leap years, and black keys are common years. | The 12edo piano key layout, which is predominantly use in the world today, is an example of an Irvian mode that is subject to even-length leap rule modification.<blockquote>'''Year is leap if the remainder of (7 x Year + 6) / 12 is less than 7.'''</blockquote>Such a pattern generates keys number '''1-3-5-6-8-10-12-1''' to be the keys on the scale, which is a '''5L 2s''' scale in a pattern of '''LLsLLLs'''. White keys are leap years, and black keys are common years. | ||
Years 1,3,6,8,10, that is notes C, D, F, G, A have a long interval - a tone - after them, while E and B, with remainder of 6, have a semitone. When started on C turns out to be plain C major. In this case, the accumulator K is taken to be C/2 instead of (C-1)/2 as with odd cycles, therefore middle of the cycle is nonleap-leap, that is F and F#. Choosing 5 instead of 6 for the K would produce a Lydian scale on C, or a F major scale - patterns of keys are reversed. | Years 1,3,6,8,10, that is notes C, D, F, G, A have a long interval - a tone - after them, while E and B, with remainder of 6, have a semitone. When started on C turns out to be plain C major. In this case, the accumulator K is taken to be C/2 instead of (C-1)/2 as with odd cycles, therefore middle of the cycle is nonleap-leap, that is F and F#. Choosing 5 instead of 6 for the K would produce a Lydian scale on C, or a F major scale - patterns of keys are reversed. | ||
== Other examples == | |||
=== 17edo === | === 17edo === | ||
| Line 41: | Line 41: | ||
L L s L L L s L L s | L L s L L L s L L s | ||
=== 22edo === | === 22edo === | ||
| Line 60: | Line 46: | ||
0-2-4-5-7-9-10-12-14-16-17-19-21-0, proper Irvian mapping as directly taken from the formula. | 0-2-4-5-7-9-10-12-14-16-17-19-21-0, proper Irvian mapping as directly taken from the formula. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ | |+ | ||