User:Flirora/JI Scales - Revision history

Flirora at 20:22, 21 March 2021

2021-03-21T20:22:03Z

← Older revision		Revision as of 20:22, 21 March 2021
Line 22:		Line 22:

	It might be possible to construct larger scales using this method.		It might be possible to construct larger scales using this method.

			<pre>
			! fliJI1.scl
			! Created using Scale Workshop 1.2
			!
			! https://sevish.com/scaleworkshop/index.htm?name=fliJI1&data=21%2F20%0A9%2F8%0A7%2F6%0A5%2F4%0A4%2F3%0A7%2F5%0A3%2F2%0A14%2F9%0A5%2F3%0A7%2F4%0A15%2F8%0A2%2F1&freq=440&midi=69&vert=1&horiz=3&colors=white%20black%20white%20white%20black%20white%20black%20white%20white%20black%20white%20black&waveform=triangle&ampenv=organ
			!
			fliJI1
			12
			!
			21/20
			9/8
			7/6
			5/4
			4/3
			7/5
			3/2
			14/9
			5/3
			7/4
			15/8
			2/1
			</pre>

Flirora at 06:11, 8 January 2021

2021-01-08T06:11:58Z

← Older revision		Revision as of 06:11, 8 January 2021
Line 19:		Line 19:
	C Db<sup>7</sup><sub>5</sub> D Eb<sup>7</sup> E<sup>5</sup> F Gb<sup>7</sup><sub>5</sub> G Ab<sub>5</sub> A<sup>5</sup> Bb<sup>7</sup> B<sup>5</sup> C		C Db<sup>7</sup><sub>5</sub> D Eb<sup>7</sup> E<sup>5</sup> F Gb<sup>7</sup><sub>5</sub> G Ab<sub>5</sub> A<sup>5</sup> Bb<sup>7</sup> B<sup>5</sup> C

	Ab<sub>5</sub> is the oddball here; you could plausibly replace it with A<sup>7</sup> (14/9) for an extra 3/2 to make the flat keys more usable.		Ab<sub>5</sub> is the oddball here; you could plausibly replace it with Ab<sup>7</sup> (14/9) for an extra 3/2 to make the flat keys more usable.

	It might be possible to construct larger scales using this method.		It might be possible to construct larger scales using this method.

Flirora: Created page with "== Interval dividing method == # Start with 1/1 and 2/1 # Find the largest interval between two adjacent notes # Use a method to create an interval between those notes # Inse..."

2021-01-08T06:11:44Z

Created page with "== Interval dividing method == # Start with 1/1 and 2/1 # Find the largest interval between two adjacent notes # Use a method to create an interval between those notes # Inse..."

New page

== Interval dividing method ==

# Start with 1/1 and 2/1
# Find the largest interval between two adjacent notes
# Use a method to create an interval between those notes
# Insert the new interval into your list
# Repeat steps 2 – 4 until you're satisfied

Naïvely taking the mediant results in too many similar superparticular intervals (since the mediant of 1 and a superparticular interval is another superparticular interval). I found better results from taking either the mediant or the mean, whichever one had a lower prime limit (arbitrarily selecting the mean if the prime limits are equal). 12 notes gives

1/1 11/10 10/9 9/8 7/6 5/4 4/3 7/5 3/2 5/3 7/4 15/8 2/1

but since there's only one 11-limit interval, I decided to take 11/10 out and replace it with the next note to be added, 8/5. I additionally decided to take out 10/9 to replace it with 21/20, giving

1/1 21/20 9/8 7/6 5/4 4/3 7/5 3/2 8/5 5/3 7/4 15/8 2/1

or in [[Functional Just System]],

C Db75 D Eb7 E5 F Gb75 G Ab5 A5 Bb7 B5 C

Ab5 is the oddball here; you could plausibly replace it with A7 (14/9) for an extra 3/2 to make the flat keys more usable.

It might be possible to construct larger scales using this method.