Pinetone: Difference between revisions
→How it works: added interval table and some other little things |
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We see 11/8 as the 4th in Lydian dark major. In Meantone[7] this is an augmented fourth. The meantone extension representing 11/8 with an augmented fourth is called Meanenneadecal, referencing the fact that it is most at home in [[19edo]]. Tuning the scale to 19edo (or 12edo or 31edo) will collapse it into a Meanenneadecal[7] diatonic scale. Similarly, tuning the scale to 15edo, 22edo, or 29edo will collapse it to Porcupine[7] scale. 27edo, 34edo, and 41edo are good tunings for the porcutone diatonic if tuning to an edo is desired. | We see 11/8 as the 4th in Lydian dark major. In Meantone[7] this is an augmented fourth. The meantone extension representing 11/8 with an augmented fourth is called Meanenneadecal, referencing the fact that it is most at home in [[19edo]]. Tuning the scale to 19edo (or 12edo or 31edo) will collapse it into a Meanenneadecal[7] diatonic scale. Similarly, tuning the scale to 15edo, 22edo, or 29edo will collapse it to Porcupine[7] scale. 27edo, 34edo, and 41edo are good tunings for the porcutone diatonic if tuning to an edo is desired. | ||
27edo: 1L | 27edo: 1L 4m 2s = (5, 4, 3) = (222.2222c, 177.7778c, 133.3333c) | ||
34edo: 1L | 34edo: 1L 4m 2s = (6, 5, 4) = (211.7647c, 176.4706c, 141.1765c) | ||
41edo: 1L | 41edo: 1L 4m 2s = (7, 6, 5) = (204.8780c, 175.6098c, 146.3415c) | ||
{| class="wikitable" | {| class="wikitable" | ||
|+Intervals of the porcutone diatonic | |+Intervals of the porcutone diatonic | ||
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!1-step | !1-step | ||
|s | |s | ||
m | |||
L | L | ||
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|- | |- | ||
!2-step | !2-step | ||
| | |m + s | ||
m + m | |||
L + | L + m | ||
|minor 3rd | |minor 3rd | ||
major 3rd | major 3rd | ||
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large 3rd | large 3rd | ||
|6/5 | |6/5, 40/33 | ||
11/9 | 100/81, 11/9 | ||
5/4 | 5/4, 33/20 | ||
|320.690 | |320.690 | ||
348.110 | 348.110 | ||
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|- | |- | ||
!3-step | !3-step | ||
| | |2m + s | ||
L + | L + m + s | ||
L + | L + 2m | ||
|perfect 4th | |perfect 4th | ||
perfect 4th | perfect 4th | ||
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large 4th | large 4th | ||
|4/3 | |4/3, 33/25 | ||
15/11 | 27/20, 15/11 | ||
11/8 | 25/18, 11/8 | ||
|494.745 | |494.745 | ||
530.469 | 530.469 | ||
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|- | |- | ||
!4-step | !4-step | ||
| | |2m + 2s | ||
3m + s | |||
L + | L + 2m + s | ||
|diminished 5th | |diminished 5th | ||
perfect 5th | perfect 5th | ||
| Line 263: | Line 263: | ||
large 5th | large 5th | ||
|16/11 | |36/25, 16/11 | ||
22/15 | 40/27, 22/15 | ||
3/2 | 3/2, 50/33 | ||
|641.380 | |641.380 | ||
668.800 | 668.800 | ||
| Line 277: | Line 277: | ||
|- | |- | ||
!5-step | !5-step | ||
| | |3m + 2s | ||
L + | L + 2m + 2s | ||
L + | L + 3m + s | ||
|minor 6th | |minor 6th | ||
minor 6th | minor 6th | ||
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large 6th | large 6th | ||
|8/5 | |8/5, 40/33 | ||
18/11 | 81/50, 18/11 | ||
5/3 | 5/3, 33/20 | ||
|815.435 | |815.435 | ||
851.159 | 851.159 | ||
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|- | |- | ||
!6-step | !6-step | ||
| | |4m + 2s | ||
L + | L + 3m + 2s | ||
L + | L + 4m + s | ||
|minor 7th | |minor 7th | ||
minor 7th | minor 7th | ||