Editing Tetrachord (section)

===Romantic era===
[[File:Locrian tetrachord.png|thumb|upright=1.3|[[Descending tetrachord]] in the modern [[locrian mode|B Locrian]] (also known as the upper minor tetrachord): <sub>{{music|scale|8}}</sub>–{{music|b}}<sub>{{music|scale|7}}</sub>–{{music|b}}<sub>{{music|scale|6}}</sub>–{{music|b}}<sub>{{music|scale|5}}</sub> (b–a–g–f). This tetrachord spans a tritone instead of a perfect fourth.[[File:Locrian tetrachord.mid]]]]

[[File:Phrygian half cadence in C.png|thumb|upright=1.3|The [[Phrygian mode|Phrygian]] [[chord progression|progression]] creates a descending tetrachord<ref>[http://classicalmusicblog.com/2007/08/phrygian-progression.html "Phrygian Progression"], ''Classical Music Blog''. {{Webarchive|url=https://web.archive.org/web/20111006081406/http://classicalmusicblog.com/2007/08/phrygian-progression.html |date=2011-10-06 }}</ref>{{Unreliable source?|reason=just a blog, describes itself as a "work in progress" (i.e., it is unstable), makes several dubious claims, such as that there were musicologists in ancient Greece|date=November 2015}} [[bassline]]: <sub>{{music|scale|8}}</sub>–{{music|b}}<sub>{{music|scale|7}}</sub>–{{music|b}}<sub>{{music|scale|6}}</sub>–<sub>{{music|scale|5}}</sub>. [[Phrygian half cadence]]: i–v6–iv6–V in C minor (bassline: c–b{{music|b}}–a{{music|b}}–g)[[File:Phrygian half cadence in C.mid]]]]

Tetrachords based upon [[equal temperament]] tuning were used to explain common [[heptatonic scale]]s. Given the following vocabulary of tetrachords (the digits give the number of semitones in consecutive intervals of the tetrachord, adding to five):
{| class="wikitable" style="margin-left: 4em;"
|-
! Tetrachord !! Halfstep String
|-
| Major || 2 2 1
|-
| Minor || 2 1 2
|-
| Harmonic || 1 3 1
|-
| Upper Minor || 1 2 2
|}
the following scales could be derived by joining two tetrachords with a [[whole step]] (2) between:{{sfn|Dupré|1962|loc=2:35}}<ref>[[Joseph Schillinger]], ''The Schillinger System of Musical Composition'', 2 vols. (New York: Carl Fischer, 1941), 1:112–114. {{ISBN|978-0306775215}}.</ref>
{| class="wikitable" style="margin-left: 4em;"
|-
! Component tetrachords !! Halfstep string !! Resulting scale
|-
| Major + major || 2 2 1 : 2 : 2 2 1 || Diatonic major
|-
| Minor + upper minor || 2 1 2 : 2 : 1 2 2 || Natural minor
|-
| Major + harmonic || 2 2 1 : 2 : 1 3 1 || Harmonic major
|-
| Minor + harmonic || 2 1 2 : 2 : 1 3 1 || Harmonic minor
|-
| Harmonic + harmonic || 1 3 1 : 2 : 1 3 1 ||[[Double harmonic scale]]<ref>Joshua Craig Podolsky, ''Advanced Lead Guitar Concepts'' (Pacific, Missouri: Mel Bay, 2010): 111. {{ISBN|978-0-7866-8236-2}}.</ref><ref>{{cite web|url=http://www.docs.solfege.org/3.21/C/scales/dha.html|title=Double harmonic scale and its modes|website=docs.solfege.org|access-date=2015-04-12|url-status=dead|archive-url=https://web.archive.org/web/20150618200916/http://www.docs.solfege.org/3.21/C/scales/dha.html|archive-date=2015-06-18}}</ref> or Gypsy major<ref>[[Jonathan Bellman]], ''The "Style hongrois" in the Music of Western Europe'' (Boston: Northeastern University Press, 1993): 120. {{ISBN|1-55553-169-5}}.</ref>
|-
| Major + upper minor || 2 2 1 : 2 : 1 2 2 || Melodic major
|-
| Minor + major || 2 1 2 : 2 : 2 2 1 || Melodic minor
|-
| Upper minor + harmonic || 1 2 2 : 2 : 1 3 1 || Neapolitan minor
|}
All these scales are formed by two complete disjunct tetrachords: contrarily to Greek and Medieval theory, the tetrachords change here from scale to scale (i.e., the C major tetrachord would be C–D–E–F, the D major one D–E–F{{music|sharp}}–G, the C minor one C–D–E{{music|flat}}–F, etc.). The 19th-century theorists of ancient Greek music believed that this had also been the case in Antiquity, and imagined that there had existed Dorian, Phrygian or Lydian tetrachords. This misconception was denounced in Otto Gombosi's thesis (1939).<ref>Otto Johannes Gombosi, ''Tonarten und Stimmungen der Antiken Musik'', Kopenhagen, Ejnar Munksgaard, 1939.</ref>