Pinetone: Difference between revisions
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* Locrian dark diminished: ~ 12/11 6/5 4/3 16/11 8/5 9/5 2/1 | * Locrian dark diminished: ~ 12/11 6/5 4/3 16/11 8/5 9/5 2/1 | ||
Tuned to TE (math over, here's tuning of the modes in cents, and their names, which combine the diatonic mode names with the functional Porcupine[7] mode names) | [http://x31eq.com/cgi-bin/rt.cgi?ets=1ce_3p_4p&limit=2_3_5_11 Tuned to TE] (math over, here's tuning of the modes in cents, and their names, which combine the diatonic mode names with the functional Porcupine[7] mode names) | ||
* Lydian dark major: 174.055 383.834 557.888 704.524 878.579 1052.633 1199.269 | * Lydian dark major: 174.055 383.834 557.888 704.524 878.579 1052.633 1199.269 | ||
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The just Porcutone chromatic has 7 large steps of 27/25, 1 medium step of 25/24, and 4 small steps of the porcupine comma, 250/243, hence it also tempers to Porcupine[8]. | The just Porcutone chromatic has 7 large steps of 27/25, 1 medium step of 25/24, and 4 small steps of the porcupine comma, 250/243, hence it also tempers to Porcupine[8]. | ||
Tempering out 100/99, the Ptolemismic Porcutone chromatic has 7 large steps of 12/11~27/25, 1 medium step of 25/24~33/32, and 7 small steps of 250/243~55/54. | Tempering out 100/99, the [[Ptolemismic chromatic|Ptolemismic Porcutone chromatic]] has 7 large steps of 12/11~27/25, 1 medium step of 25/24~33/32, and 7 small steps of 250/243~55/54 ([http://x31eq.com/cgi-bin/rt.cgi?ets=7%261ce%264p&limit=2.3.5.11 Here for TE steps]) | ||
Porcupine[7] has generator chain G-F-E-D-C-B-A. Porcupine[8] adds one note to the generator chain. Using Porcupine[7] note names, that’s either Ab or G#. | Porcupine[7] has generator chain G-F-E-D-C-B-A. Porcupine[8] adds one note to the generator chain. Using Porcupine[7] note names, that’s either Ab or G#. | ||
If we use a Bosanquet mapping on a keyboard using, we can map the porcutone diatonic to 7 white keys and the porcutone chromatic to 7 white keys and 5 chromatic keys. We colour the chromatic keys blue, apart from G#, which we colour pink, so that the white and pink keys make a porcutone octatonic scale, a detempered Porcupine[8]. This gives us a Meantone gamut of F-A#, and we also get a porcutone pentatonic on the blue and pink keys – F#-G#-A#-C#-D#. | If we use a Bosanquet mapping on a keyboard using, we can map the porcutone diatonic to 7 white keys and the porcutone chromatic to 7 white keys and 5 chromatic keys. We colour the chromatic keys blue, apart from G#, which we colour pink, so that the white and pink keys make a porcutone octatonic scale, a detempered Porcupine[8]. This gives us a Meantone gamut of F-A#, and we also get a porcutone pentatonic on the blue and pink keys – F#-G#-A#-C#-D#. | ||
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We could tune the scale in many different ways. The TE tuning given above consists of 7 large steps of 146.6352c, 1 medium step of 63.1434c, and 4 small steps of 27.4197c. | We could tune the scale in many different ways. The TE tuning given above consists of 7 large steps of 146.6352c, 1 medium step of 63.1434c, and 4 small steps of 27.4197c. | ||
We could instead tune to [[POTE tuning|POTE]] no-7 ptolemismic, resulting in a very similar 7L 1m 4s = (146.7247c, 63.1818c, 27.4363c). | We could instead tune to [[POTE tuning|POTE]] no-7 ptolemismic, resulting in a very similar 7L 1m 4s = [http://x31eq.com/cgi-bin/rt.cgi?limit=2_3_5_11&ets=7_1ce_4p&tuning=po (146.7247c, 63.1818c, 27.4363c)]. | ||
For reference, the 5-limit JI tuning of (27/25, 25/24, 250/243) is equal to (133.2376c, 70.6724c, 49.1661c). There are also least squares and minimax. I hope to figure those out. | For reference, the 5-limit JI tuning of (27/25, 25/24, 250/243) is equal to (133.2376c, 70.6724c, 49.1661c). There are also least squares and minimax. I hope to figure those out. | ||