Septimal third tone

In today's article we are going to talk about Septimal third tone, a topic that you have probably heard about, but that you may not know all the details about. Septimal third tone is a topic that has aroused great interest in recent times, since its relevance and impact covers different areas. This is a topic that has been present throughout history, but is currently taking on special importance due to various factors. Throughout this article, we are going to delve into Septimal third tone to better understand its meaning, its impact and its relevance in today's society. Read on to find out everything you need to know about Septimal third tone!

Septimal third tone on C Playⓘ.

A septimal 1/3-tone (in music) is an interval with the ratio of 28:27,[1] which is the difference between the perfect fourth and the supermajor third. It is about 62.96 cents wide. The septimal 1/3-tone can be viewed either as a musical interval in its own right, or as a comma; if it is tempered out in a given tuning system, the distinction between these two intervals is lost. The septimal 1/3-tone may be derived from the harmonic series as the interval between the twenty-seventh and twenty-eighth harmonics. It may be considered a diesis.[2]

The septimal 1/3-tone, along with the septimal diesis is tempered out by five-tone equal temperament, and equal temperaments which divide the octave into a small multiple of 5 steps, such as 15-TET and 25-TET. This family of scales is known as Blackwood temperament in honor of Easley Blackwood, Jr., who first analyzed 10-note subsets of 15-TET that take advantage of the temperament.

When added to the 15:14 semitone, the 21:20 semitone and 28:27 semitone produce the 9:8 tone (major tone) and 10:9 tone (minor tone), respectively.

It is the difference between 7/6 and 9/8 (tritē and paramesē).[3][4]

Septimal sixth tone

The septimal sixth tone, also called the jubilisma, is a 7-limit musical interval approximately the size of 1/6 of a whole tone (203.91/6=33.99 cents). An interval with the ratio of 50:49 (playⓘ), about 34.98 cents, which in just intonation is the difference between the lesser septimal (7:5) tritone, and its inversion, the greater septimal tritone (10:7). This interval is tempered out by 12-TET and 22-TET, but not by 19-TET, 31-TET or any other odd division of the octave.

References

  1. ^ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxiv. ISBN 0-8247-4714-3. 1/3-tone, Archytas inferior 1/4-tone.
  2. ^ Thomas Christensen, ed. (2002). The Cambridge History of Western Music Theory, p.186. ISBN 9780521623711.
  3. ^ Huffman, Carl (2005). Archytas of Tarentum: Pythagorean, Philosopher and Mathematician King, p.420. ISBN 9781139444071.
  4. ^ Andrew Barker, ed. (2004). Greek Musical Writings: Volume 2, Harmonic and Acoustic Theory, p.51. ISBN 9780521616973.