World Library  
Flag as Inappropriate
Email this Article

Septimal major third

Article Id: WHEBN0005489015
Reproduction Date:

Title: Septimal major third  
Author: World Heritage Encyclopedia
Language: English
Subject: Quarter tone, Septimal kleisma, Supermajor interval, Diminished fourth, Septimal comma
Collection: 7-Limit Tuning and Intervals, Major Intervals, Thirds (Music)
Publisher: World Heritage Encyclopedia
Publication
Date:
 

Septimal major third

Septimal major third
Inverse septimal minor sixth
Name
Other names Supermajor third
Abbreviation S3, SM3
Size
Semitones ~4½
Interval class ~4½
Just interval 9:7[1]
Cents
Equal temperament 400
Just intonation 435
9/7 major third from C to E7 upside-down [2] About this sound Play  . This, "extremely large third", is also found between C- and E7 upside-down- and may resemble a neutral third or blue note.[3]

In music, the septimal major third About this sound play  , also called the supermajor third (by Hermann Helmholtz among others[4][5][6]) and sometimes Bohlen–Pierce third is the musical interval exactly or approximately equal to a just 9:7 ratio[4][7] of frequencies, or alternately 14:11.[7] It is equal to 435 cents,[4] sharper than a just major third (5:4) by the septimal quarter tone (36:35) (About this sound play  ). In 24-TET the septimal major third is approximated by 9 quarter tones, or 450 cents (About this sound play  ).

The septimal major third has a characteristic brassy sound which is much less sweet than a pure major third, but is classed as a 9-limit consonance. Together with the root 1:1 and the perfect fifth of 3:2, it makes up the septimal major triad, or supermajor triad About this sound play  . However, in terms of the overtone series, this is a utonal rather than otonal chord, being an inverted 6:7:9, i.e. a 99:97:96 chord. The septimal major triad can also be represented by the ratio 14:18:21.[8] The septimal major triad contains an interval of a septimal minor third between its third and fifth ( 3:2 / 9:7 = 7:6 ). Similarly, the septimal major third is the interval between the third and the fifth of the septimal minor triad.

In the early meantone era the interval made its appearance as the alternative major third in remote keys, under the name diminished fourth. Tunings of the meantone fifth in the neighborhood of Zarlino's 27-comma meantone will give four septimal thirds among the twelve major thirds of the tuning; this entails that three septimal major triads appear along with one chord containing a septimal major third with an ordinary minor third above it, making up a wolf fifth.

Sources

  1. ^ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxiii. ISBN 0-8247-4714-3. Septimal major third.
  2. ^ Fonville, John. "Ben Johnston's Extended Just Intonation- A Guide for Interpreters", p.112, Perspectives of New Music, Vol. 29, No. 2 (Summer, 1991), pp. 106-137.
  3. ^ Fonville (1991), p.128.
  4. ^ a b c Hermann L. F Von Helmholtz (2007). On the Sensations of Tone, p.187. ISBN 1-60206-639-6.
  5. ^ Royal Society (Great Britain) (1880, digitized Feb 26, 2008). Proceedings of the Royal Society of London, Volume 30, p.531. Harvard University.
  6. ^ Society of Arts (Great Britain) (1877, digitized Nov 19, 2009). Journal of the Society of Arts, Volume 25, p.670. The Society.
  7. ^ a b Andrew Horner, Lydia Ayres (2002). Cooking with Csound: Woodwind and Brass Recipes, p.131. ISBN 0-89579-507-8. "Super-Major Second".
  8. ^ "Just Chord Tunings"
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
 
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
 
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.
 



Copyright © World Library Foundation. All rights reserved. eBooks from Hawaii eBook Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.