Editing Fundamental frequency (section)

{{Short description|Lowest frequency of a periodic waveform, such as sound}}
{{Use American English|date=January 2019}}
[[File:Harmonic partials on strings.svg|thumb|250px|[[Vibration]] and [[standing wave]]s in a string, The fundamental and the first six [[overtone]]s]]

The '''fundamental frequency''', often referred to simply as the '''''fundamental''''' (abbreviated as '''{{var|f}}<sub>0</sub>''' or '''{{var|f}}<sub>1</sub>''' ), is defined as the lowest [[frequency]] of a [[Periodic signal|periodic]] [[waveform]].<ref>{{Cite web |last=Nishida |first=Silvia Mitiko |title=Som, intensidade, frequência |url=https://www2.ibb.unesp.br/nadi/Museu2_qualidade/Museu2_corpo_humano/Museu2_como_funciona/Museu_homem_nervoso/Museu2_homem_nervoso_audicao/Museu2_qualidade_homem_nervoso_audicao_som.htm |access-date=2024-09-05 |website=Instituto de Biociências da [[Unesp]]}}</ref> In music, the fundamental is the musical [[pitch (music)|pitch]] of a note that is perceived as the lowest [[Harmonic series (music)#Partial|partial]] present. In terms of a superposition of [[Sine wave|sinusoid]]s, the fundamental frequency is the lowest frequency sinusoidal in the sum of harmonically related frequencies, or the frequency of the difference between adjacent frequencies.  In some contexts, the fundamental is usually abbreviated as '''{{var|f}}<sub>0</sub>''', indicating the lowest frequency [[Zero-based numbering|counting from zero]].<ref>{{cite web |url=http://www.phon.ucl.ac.uk/home/johnm/sid/sidf.htm |title=sidfn |publisher=Phon.UCL.ac.uk |access-date=2012-11-27 |archive-url=https://web.archive.org/web/20130106050848/http://www.phon.ucl.ac.uk/home/johnm/sid/sidf.htm |archive-date=2013-01-06 |url-status=dead }}</ref><ref>{{cite web|url= http://www.acoustics.hut.fi/publications/files/theses/lemmetty_mst/chap3.html |last=Lemmetty |first=Sami |title=Phonetics and Theory of Speech Production |publisher=Acoustics.hut.fi |date=1999 |access-date=2012-11-27}}</ref><ref>{{cite web |url=http://fourier.eng.hmc.edu/e101/lectures/Fundamental_Frequency.pdf |archive-url=https://web.archive.org/web/20140514122624/http://fourier.eng.hmc.edu/e101/lectures/Fundamental_Frequency.pdf |archive-date=2014-05-14 |url-status=dead |title=Fundamental Frequency of Continuous Signals |date=2011 |publisher=Fourier.eng.hmc.edu |access-date=2012-11-27 }}</ref> In other contexts, it is more common to abbreviate it as '''{{var|f}}<sub>1</sub>''', the first [[harmonic]].<ref>{{cite web |url=https://nchsdduncanapphysics.wikispaces.com/file/view/Standing+Waves+in+a+Tube+II.pdf |title=Standing Wave in a Tube II – Finding the Fundamental Frequency |publisher=Nchsdduncanapphysics.wikispaces.com |access-date=2012-11-27 |archive-date=2014-03-13 |archive-url=https://web.archive.org/web/20140313133719/https://nchsdduncanapphysics.wikispaces.com/file/view/Standing+Waves+in+a+Tube+II.pdf |url-status=dead }}</ref><ref>{{cite web |url=http://physics.kennesaw.edu/P11_standwaves3.pdf |title=Physics: Standing Waves |publisher=Physics.Kennesaw.edu |access-date=2012-11-27 |archive-date=2019-12-15 |archive-url=https://web.archive.org/web/20191215062640/https://csm.kennesaw.edu/physics/ |url-status=dead }}</ref><ref>{{cite web |url= http://www.colorado.edu/physics/phys1240/phys1240_fa05/notes/lect24_Tu11_22_4up.pdf |title=Phys 1240: Sound and Music |last=Pollock |first=Steven |publisher=Colorado.edu |date=2005 |access-date=2012-11-27 |archive-url=https://web.archive.org/web/20140515180200/http://www.colorado.edu/physics/phys1240/phys1240_fa05/notes/lect24_Tu11_22_4up.pdf |archive-date=2014-05-15 |url-status=dead}}</ref><ref>{{cite web |url= http://hyperphysics.phy-astr.gsu.edu/hbase/waves/string.html |title=Standing Waves on a String |publisher=Hyperphysics.phy-astr.gsu.edu |access-date=2012-11-27}}</ref><ref>{{cite web |url=http://openlearn.open.ac.uk/mod/oucontent/view.php?id=397877&section=5.13.2 |title=Creating musical sounds |work=OpenLearn |publisher=Open University |access-date=2014-06-04 |archive-date=2020-04-09 |archive-url=https://web.archive.org/web/20200409044223/https://www.open.edu/openlearn/science-maths-technology/engineering-and-technology/technology/creating-musical-sounds/content-section-0 |url-status=dead }}</ref> (The second harmonic is then {{var|f}}<sub>2</sub> = 2⋅{{var|f}}<sub>1</sub>, etc.)

According to Benward and Saker's ''Music: In Theory and Practice'':<ref>Benward, Bruce and Saker, Marilyn (1997/2003). ''Music: In Theory and Practice'', Vol. I, 7th ed.; p. xiii. McGraw-Hill. {{ISBN|978-0-07-294262-0}}.</ref>
{{Blockquote|1=Since the fundamental is the lowest frequency and is also perceived as the loudest, the ear identifies it as the specific pitch of the musical tone &#91;[[harmonic spectrum]]&#93;.... The individual partials are not heard separately but are blended together by the ear into a single tone.}}