# Septimal diesis

Septimal diesis on C  .

In music, septimal diesis (or slendro diesis) is an interval with the ratio of 49:48[citation needed]  , which is the difference between the septimal whole tone and the septimal minor third. It is about 35.7 cents wide, which is narrower than a quarter-tone but wider than the septimal comma. It may also be the ratio 36:35,[1][2][3] or 48.77 cents.

## In equal temperament

In 12 equal temperament this interval is not tempered out; the septimal whole tone and septimal minor third are replaced by the normal whole tone and minor third. This makes the diesis a semitone, about twice its "correct" size. The septimal diesis is tempered out by a number of equally tempered tuning systems, including 19-ET, 24-ET and 29-ET ; these tunings do not distinguish between the septimal whole tone and septimal minor third. It is not tempered out however by 22-ET or 31-ET (or indeed any equal temperament with at least 30 steps).

## References

1. ^ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxv. ISBN 978-80-88683-28-5.
2. ^ "Stichting Huygens-Fokker: List of intervals". Huygens-fokker.org. Retrieved 2013-10-18.
3. ^ "Wendy Carlos Beta scale". Microtonal-synthesis.com. Retrieved 2013-10-18.