Pinetone: Difference between revisions

Line 142:

|146.635 320.690 494.745 641.380 815.435 1025.214 1199.269

|}

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) 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 4m 2s = (5, 4, 3) = (222.2222c, 177.7778c, 133.3333c)

Line 423:

dim min 4

|10:12:15

~~110~~:~~144~~:~~165~~

16:21:24

|320.690, 704.524

Line 452:

|aug maj 2

major

|48:55:72

|14:16:21

4:5:6

|237.198, 704.524

Line 482:

|aug maj 2

major

|48:55:72

|14:16:21

4:5:6

|237.198, 704.524

Line 527:

|minor (sub) dim min 6

dim min 4 (sub) dim min 6

|~~275~~:~~330~~:~~432~~

|40:48:63

~~275~~:~~360~~:~~432~~

80:105:126

|320.690, 788.015

Line 557:

|aug min 2 diminished

major diminished

|~~243~~:~~275~~:~~360~~

|135:150:198

~~243~~:~~297~~:~~360~~

105:128:154

|~~176~~.055, 668.800

|174.055, 668.800

348.110, 668.800

Line 573:

dim min 4

|10:12:15

~~110~~:~~144~~:~~165~~

16:21:24

|320.690, 704.524

467.325, 704.524

|}

As with the porcutone diatonic, tuning the porcutone chromatic to 19edo ~~or 31edo~~ collapses it to the Meantone[12] (~~Meanenneadecal~~[12]) chromatic scale. Tuning it to 15edo, 22edo, or 29edo collapses it to Porcupine[8]. Step ~~patterns~~, mappings and sizes for tunings to 27edo, 34edo, and 41edo are as follows:

As with the porcutone diatonic, tuning the porcutone chromatic to 19edo collapses it to the Meantone[12] (Flattone[12]) chromatic scale. Tuning it to 15edo, 22edo, or 29edo collapses it to Porcupine[8]. Step signatures, mappings and sizes for tunings to 27edo, 34edo, and 41edo are as follows:

27edo: 7L 1m 4s = (3, 2, 1) = (133.3333c, 88.8889c, 44.4444c)

27edo: 7L 1m 4s = (3, 2, 1) = (133.3333c, 88.8889c, 44.4444c) (Aug maj 2 is 7/6)

34edo: 7L 1m 4s = (4, 2, 1) = (141.1765c, 70.5882c, 35.2941c)

34edo: 7L 1m 4s = (4, 2, 1) = (141.1765c, 70.5882c, 35.2941c) (Aug maj 2 is 7/6 and 8/7)

41edo: 7L 1m 4s = (5, 2, 1) = (146.3415c, 58.5366c, 29.2683c)

41edo: 7L 1m 4s = (5, 2, 1) = (146.3415c, 58.5366c, 29.2683c) (Aug maj 2 is 8/7)

104edo: 7L 1m 4s = (13, 5, 2) = (150c, 57.6923c, 23.0769c) (Aug maj 2 is 8/7)

And allowing octave stretch, the tuning may be optimized via TE tuning to:

Line 593:

Line 595:

41edo with 1200.2039c octave: 7L 1m 4s = (5, 2, 1) = (146.3663c, 58.5465c, 29.2733c)

For comparison, the TE step signature and sizes for the ptolemismic porcupine chromatic is

7L 1m 4s = (146.6352c, 63.1434c, 27.4197c).

and the TE step signature and sizes for the supermagic porcupine chromatic is

7L 1m 4s = (149.5159c, 58.8799c, 23.6254c)

I like to keep the small step large enough to sound like a melodic interval, so I either tune to TE ptolemismic, or to 41edo if an equal tuning is desired.

== The porcutone octatonic ==

@@ Line 142: / Line 142: @@
 |146.635 320.690 494.745 641.380 815.435 1025.214 1199.269
 |}
-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) 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.
 edo: 1L 4m 2s = (5, 4, 3) = (222.2222c, 177.7778c, 133.3333c)
@@ Line 423: / Line 423: @@
 dim min 4
 |10:12:15
-:144:165
+:21:24
 |320.690, 704.524
@@ Line 452: / Line 452: @@
 |aug maj 2
 major
-|48:55:72
+|14:16:21
 :5:6
 |237.198, 704.524
@@ Line 482: / Line 482: @@
 |aug maj 2
 major
-|48:55:72
+|14:16:21
 :5:6
 |237.198, 704.524
@@ Line 527: / Line 527: @@
 |minor (sub) dim min 6
 dim min 4 (sub) dim min 6
-|275:330:432
+|40:48:63
-:360:432
+:105:126
 |320.690, 788.015
@@ Line 557: / Line 557: @@
 |aug min 2 diminished
 major diminished
-|243:275:360
+|135:150:198
-:297:360
+:128:154
-|176.055, 668.800
+|174.055, 668.800
 .110, 668.800
@@ Line 573: / Line 573: @@
 dim min 4
 |10:12:15
-:144:165
+:21:24
 |320.690, 704.524
 .325, 704.524
 |}
-As with the porcutone diatonic, tuning the porcutone chromatic to 19edo or 31edo collapses it to the Meantone[12] (Meanenneadecal[12]) chromatic scale. Tuning it to 15edo, 22edo, or 29edo collapses it to Porcupine[8]. Step patterns, mappings and sizes for tunings to 27edo, 34edo, and 41edo are as follows:
+As with the porcutone diatonic, tuning the porcutone chromatic to 19edo collapses it to the Meantone[12] (Flattone[12]) chromatic scale. Tuning it to 15edo, 22edo, or 29edo collapses it to Porcupine[8]. Step signatures, mappings and sizes for tunings to 27edo, 34edo, and 41edo are as follows:
-edo: 7L 1m 4s = (3, 2, 1) = (133.3333c, 88.8889c, 44.4444c)
+edo: 7L 1m 4s = (3, 2, 1) = (133.3333c, 88.8889c, 44.4444c) (Aug maj 2 is 7/6)
-edo: 7L 1m 4s = (4, 2, 1) = (141.1765c, 70.5882c, 35.2941c)
+edo: 7L 1m 4s = (4, 2, 1) = (141.1765c, 70.5882c, 35.2941c) (Aug maj 2 is 7/6 and 8/7)
-edo: 7L 1m 4s = (5, 2, 1) = (146.3415c, 58.5366c, 29.2683c)
+edo: 7L 1m 4s = (5, 2, 1) = (146.3415c, 58.5366c, 29.2683c) (Aug maj 2 is 8/7)
+edo: 7L 1m 4s = (13, 5, 2) = (150c, 57.6923c, 23.0769c) (Aug maj 2 is 8/7)
 And allowing octave stretch, the tuning may be optimized via TE tuning to:
@@ Line 593: / Line 595: @@
 edo with 1200.2039c octave: 7L 1m 4s = (5, 2, 1) = (146.3663c, 58.5465c, 29.2733c)
+For comparison, the TE step signature and sizes for the ptolemismic porcupine chromatic is
+L 1m 4s = (146.6352c, 63.1434c, 27.4197c).
+and the TE step signature and sizes for the supermagic porcupine chromatic is
+L 1m 4s = (149.5159c, 58.8799c, 23.6254c)
+I like to keep the small step large enough to sound like a melodic interval, so I either tune to TE ptolemismic, or to 41edo if an equal tuning is desired.
 == The porcutone octatonic ==