Whitewood

Subgroups	2.3.5, 2.3.5.7
Comma basis	2187/2048 (2.3.5); 36/35, 2187/2048 (2.3.5.7)
Reduced mapping	⟨7; 0 1 -1]
ET join	7 & 14
Generators (CWE)	~5/4 = 392.7 ¢
MOS scales	7L 7s, 7L 14s, ...
Ploidacot	heptaploid acot
Pergen	(P8/7, ^1)
Color name	Lawati
Minimax error	5-odd-limit: 16.2 ¢; 9-odd-limit: 40.6 ¢
Target scale size	5-odd-limit: 14 notes; 9-odd-limit: 21 notes

Whitewood is the rank-2 temperament tempering out 2187/2048, the Pythagorean chromatic semitone. As a result, the circle of fifths closes after seven steps, and every interval on the chain of fifths is neutral in quality. The whitewood temperament adds prime 5 as an independent generator, adding major and minor intervals on either side of the neutral ones.

The canonical extenison to prime 7 adds 36/35 to the commas, thus equating 5-limit major and minor intervals with 7-limit subminor and supermajor ones. It finds 7/4 at the minor seventh, 7/6 at the minor third, and 9/7 at the major third.

For technical data, see Whitewood family #Whitewood.

Intervals

In the following table, odd harmonics and subharmonics 1–9 are in bold.

Period	Generator -1		Generator 0		Generator 1
	Cents*	Approx. ratios	Cents*	Approx. ratios	Cents*	Approx. ratios
0			0.0	1/1	49.9	64/63, 135/128
1	121.5	16/15, 28/27	171.4	9/8, 35/32	221.3	8/7, 10/9
2	293.0	6/5, 7/6	342.9	32/27, 81/64, 128/105	392.7	5/4
3	464.4	21/16	514.3	4/3	564.2	45/32
4	635.8	64/45	685.7	3/2	735.6	32/21
5	807.3	8/5, 14/9	857.1	27/16, 128/81	907.0	5/3, 12/7
6	978.7	7/4, 9/5	1028.6	16/9, 64/35	1078.5	15/8, 27/14
7	1150.1	63/32, 256/135	1200.0	2/1

*in 7-limit CWE tuning

Tunings

Todo: complete section