Pinetone: Difference between revisions

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|146.635 320.690 494.745 641.380 815.435 1025.214 1199.269

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=== Tuning options ===

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.

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[http://x31eq.com/cgi-bin/rt.cgi?ets=1ce_4p_2ce&limit=2_3_5_11 TE ptolemismic: 1L 4m 2s] = (209.77855c, 174.05488c, 146.63528c)

=== Intervals and chords ===

The table below show the sizes, interval names, ratios approximated, tuning, and occurence of all intervals of the ptolemismic porcutone diatonic scale within an octave, tuned to TE tuning.

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Porcupine tetrads in the table below are named after the third above the tonic and the third above the fifth, apart from tetrads with a diminished fifth.

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The ptolemismic porcutone chromatic scale is distinctly xenharmonic, and yet is related to the familiar chromatic scale.

=== Intervals and triads ===

Mode -3 has 3/2 perfect fifths available above D, D♯, E, F, F♯, G, G♯, and C♯.

Mode 3 has 3/2 perfect fifths available above D, E♭, E, F, G♭, G, A♭, and D♭.

Mode -3 has 4:5:6 major triads available above E, F, F♯, G, and G♯

Mode -3 has 4:5:6 major triads available above E, F, F♯, G, and G♯.

Mode 3 has 4:5:6 major triads available above E♭, E, F, G♭, and G

Mode 3 has 4:5:6 major triads available above E♭, E, F, G♭, and G.

The following tables show the (3, 4) and (4, 3) triads available of mode 3 and mode -3 of the porcutone chromatic scale:

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We can see that the large step of Tetracot[7] is the medium step of the porcutone diatonic, and the small step of Tetracot[7] is the small step of the porcutone diatonic. The large step of the porcutone diatonic is the augmented second of tetracot[7].

==== Tuning options ====

=== Tuning options ===

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:

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|142.775 209.542 385.433 528.209 704.101 879.992 1022.768 1198.660

|}

=== Intervals and Triads ===

{| class="wikitable"

|+3-step stacked triads of the left handed porcutone octatonic (G♯-G gamut)

@@ Line 142: / Line 142: @@
 |146.635 320.690 494.745 641.380 815.435 1025.214 1199.269
 |}
+=== Tuning options ===
 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.
@@ Line 162: / Line 164: @@
 [http://x31eq.com/cgi-bin/rt.cgi?ets=1ce_4p_2ce&limit=2_3_5_11 TE ptolemismic: 1L 4m 2s] = (209.77855c, 174.05488c, 146.63528c)
+=== Intervals and chords ===
 The table below show the sizes, interval names, ratios approximated, tuning, and occurence of all intervals of the ptolemismic porcutone diatonic scale within an octave, tuned to TE tuning.
@@ Line 413: / Line 416: @@
 |27:33:40
 |}
 Porcupine tetrads in the table below are named after the third above the tonic and the third above the fifth, apart from tetrads with a diminished fifth.
@@ Line 573: / Line 575: @@
 The ptolemismic porcutone chromatic scale is distinctly xenharmonic, and yet is related to the familiar chromatic scale.
+=== Intervals and triads ===
 Mode -3 has 3/2 perfect fifths available above D, D♯, E, F, F♯, G, G♯, and C♯.
 Mode 3 has 3/2 perfect fifths available above D, E♭, E, F, G♭, G, A♭, and D♭.
-Mode -3 has 4:5:6 major triads available above E, F, F♯, G, and G♯
+Mode -3 has 4:5:6 major triads available above E, F, F♯, G, and G♯.
-Mode 3 has 4:5:6 major triads available above E♭, E, F, G♭, and G
+Mode 3 has 4:5:6 major triads available above E♭, E, F, G♭, and G.
 The following tables show the (3, 4) and (4, 3) triads available of mode 3 and mode -3 of the porcutone chromatic scale:
@@ Line 785: / Line 788: @@
 We can see that the large step of Tetracot[7] is the medium step of the porcutone diatonic, and the small step of Tetracot[7] is the small step of the porcutone diatonic. The large step of the porcutone diatonic is the augmented second of tetracot[7].
-==== Tuning options ====
+=== Tuning options ===
 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:
@@ Line 1,240: / Line 1,243: @@
 |142.775 209.542 385.433 528.209 704.101 879.992 1022.768 1198.660
 |}
+=== Intervals and Triads ===
 {| class="wikitable"
 |+3-step stacked triads of the left handed porcutone octatonic (G♯-G gamut)