Flattone

Flattone is an alternative extension to 5-limit meantone, the temperament that tempers out the syntonic comma (81/80). It is generated by a fifth that is typically flatter than that of meantone, and nine of those reach the pitch class of 8/7, so that 7/4 is a diminished seventh (C-B𝄫), 7/6 is a diminished third (C-E𝄫), and 7/5 is a doubly diminshed fifth (C-G𝄫).

11- and 13-limit extensions are fairly obvious, using the heavily tempered chromatic semitone for the undecimal quartertone of 33/32 and the tridecimal third tone of 27/26. 11/8 is an augmented fourth, and 13/8 is a minor sixth, conflated with 8/5.

Reasonable tunings lie between 19edo and 26edo. 19edo is the point where 7/4 and 12/7 are conflated. Any tuning whose fifth is sharper than 19edo's has the sizes of 7/4 and 12/7 inverted, so they can be more properly analysed as septimal meantone. Similarly, 26edo is the point where 7/5 and 10/7 are conflated. Any tuning whose fifth is flatter than 26edo's has the sizes of 7/5 and 10/7 inverted, so they can be more properly analysed as a flatter-of-flattone temperament.

See Meantone family #Flattone for technical data.

Interval chain

In the following table, odd harmonics 1–13 are in bold.

#	Cents*	Approximate Ratios
0	0.0	1/1
1	693.0	3/2
2	186.1	9/8, 10/9, 11/10
3	879.1	5/3
4	372.1	5/4, 16/13, 26/21
5	1065.1	11/6, 13/7, 15/8, 24/13
6	558.2	11/8, 18/13
7	51.2	25/24, 27/26, 33/32, 36/35, 55/54, 64/63
8	744.2	20/13, 32/21
9	237.3	8/7, 15/13
10	930.3	12/7
11	423.3	9/7
12	1116.4	27/14, 40/21
13	609.4	10/7

* in 13-limit CTE tuning

Scales

• Flattone12 – 12-tone chromatic scale in 13-limit POTE tuning