Editing Mode (music) (section)

==Greek modes==
{{Main|Musical system of ancient Greece}}

Early Greek treatises describe three interrelated concepts that are related to the later, medieval idea of "mode": (1) [[musical scale|scales]] (or "systems"), (2) ''tonos'' – pl. ''tonoi'' – (the more usual term used in medieval theory for what later came to be called "mode"), and (3) ''harmonia'' (harmony) – pl. ''harmoniai'' – this third term subsuming the corresponding ''tonoi'' but not necessarily the converse.<ref name=Mathiesen-2001a-6iiie>{{harvp|Mathiesen|2001a|loc=6(iii)(e)}}</ref>

===Greek scales===
{{Image frame|content=<score sound="1">
{
\override Score.TimeSignature #'stencil = ##f
\relative c' { 
  \clef treble \time 4/4
  e4^\markup { Enharmonic genus } feh geses a b ceh deses e

} }
</score>

<score sound="1">
{
\override Score.TimeSignature #'stencil = ##f
\relative c' { 
  \clef treble \time 4/4
  e4^\markup { Chromatic genus } f ges a b c des e

} }
</score>

<score sound="1">
{
\override Score.TimeSignature #'stencil = ##f
\relative c' { 
  \clef treble \time 4/4
  e4^\markup { Diatonic genus } f g a b c d e
} }
</score>|width=300|caption=The three genera of the Dorian [[octave species]] on E}}

The Greek scales in the [[Aristoxenus|Aristoxenian]] tradition were:<ref>{{harvp|Barbera|1984|p=240}}</ref><ref name=Mathiesen-2001a-6iiid>{{harvp|Mathiesen|2001a|loc=6(iii)(d)}}</ref>

:{|
|- style="vertical-align:bottom;font-size:80%;"
| '''[[Aristoxenus|Aristoxenian]]<br/>scale''' || '''rough<br/>modern<br/>pitch''' || '''[[Aristoxenus]]' description'''
|- style="vertical-align:top;"
| [[Mixolydian mode#Greek Mixolydian|Mixolydian]] || b–{{prime|b}} || ''hypate hypaton–paramese''
|- style="vertical-align:top;"
| [[Lydian mode|Lydian]] || {{prime|c}}–c{{pprime}} || ''parhypate hypaton–trite diezeugmenon''
|- style="vertical-align:top;"
| [[Phrygian mode#Ancient Greek Phrygian mode|Phrygian]] || {{prime|d}}–d{{pprime}} || ''lichanos hypaton–paranete diezeugmenon''
|- style="vertical-align:top;"
| [[Dorian mode|Dorian]] || {{prime|e}}–e{{pprime}} || ''hypate meson–nete diezeugmenon''
|- style="vertical-align:top;"
| [[Hypolydian mode|Hypolydian]] || {{prime|f}}–f{{pprime}} || ''parhypate meson–trite hyperbolaion''
|- style="vertical-align:top;"
| [[Hypophrygian mode|Hypophrygian]]  || {{prime|g}}–g{{pprime}} || ''lichanos meson–paranete hyperbolaion''
|- style="vertical-align:top;"
| Common,<br/> [[Locrian mode|Locrian]], or<br/> [[Hypodorian mode|Hypodorian]] || {{nobr|{{prime|a}}–a{{pprime}} or  }}<br/> a–{{prime|a}} || ''mese–nete hyperbolaion'' or<br/> ''proslambnomenos–mese''
|}

These names are derived from ancient Greeks' cultural subgroups ([[Dorians]]), small regions in central Greece ([[Locris]]), and certain [[Anatolia]]n peoples ([[Lydia]], [[Phrygia]])  (not ethnically Greek, but in close contact with them). The association of these ethnic names with the [[octave species]] appears to precede [[Aristoxenus]], who criticized their application to the ''tonoi'' by the earlier theorists whom he called the "Harmonicists". According to {{harvp|Bélis|2001}}, he felt that their diagrams, which exhibit 28&nbsp;consecutive dieses, were
: "...&nbsp;devoid of any musical reality since more than two quarter-tones are never heard in succession."<ref>{{harvp|Bélis|2001}}</ref>

Depending on the positioning (spacing) of the interposed tones in the [[tetrachord]]s, three ''genera'' of the seven octave species can be recognized. The diatonic genus (composed of tones and semitones), the chromatic genus (semitones and a minor third), and the [[enharmonic genus]] (with a major third and two [[quarter tone]]s or [[diesis|dieses]]).<ref>{{harvp|Cleonides|1965|pp=35–36}}</ref> The framing interval of the perfect fourth is fixed, while the two internal pitches are movable. Within the basic forms, the intervals of the chromatic and diatonic genera were varied further by three and two "shades" (''chroai''), respectively.<ref>{{harvp|Cleonides|1965|pp=39–40}}</ref><ref>{{harvp|Mathiesen|2001a|loc=6(iii)(c)}}</ref>

In contrast to the medieval modal system, these scales and their related ''tonoi'' and ''harmoniai'' appear to have had no hierarchical relationships amongst the notes that could establish contrasting points of tension and rest, although the ''mese'' ("middle note") might have functioned as some sort of central, returning tone for the melody.<ref>{{harvp|Palisca|2006|p=77}}</ref>

===''Tonoi''===
The term ''tonos'' (pl. ''tonoi'') was used in four senses:
: "as note, interval, region of the voice, and pitch. We use it of the region of the voice whenever we speak of Dorian, or Phrygian, or Lydian, or any of the other tones".<ref name=Cleonides-1965-p44>{{harvp|Cleonides|1965|p=44}}</ref>
[[Cleonides]] attributes thirteen ''tonoi'' to Aristoxenus, which represent a progressive [[Transposition (music)|transposition]] of the entire system (or scale) by semitone over the range of an octave between the Hypodorian and the Hypermixolydian.<ref name=Mathiesen-2001a-6iiie /> According to Cleonides, Aristoxenus's transpositional ''tonoi'' were named analogously to the octave species, supplemented with new terms to raise the number of degrees from seven to thirteen.<ref name=Cleonides-1965-p44 /> However, according to the interpretation of at least three modern authorities, in these transpositional ''tonoi'' the Hypodorian is the lowest, and the Mixolydian next-to-highest – the reverse of the case of the octave species,<ref name=Mathiesen-2001a-6iiie /><ref>{{harvp|Solomon|1984|pp=244–245}}</ref><ref>{{harvp|West|1992|loc={{Page needed|date=March 2018}}}}</ref> with nominal base pitches as follows (descending order):
:{|
|- style="font-size:80%;vertical-align:bottom;"
|align=center| '''nominal<br/>modern<br/>base'''
| '''[[Aristoxenus|Aristoxenian school]] name'''
|-
! F
| [[mixolydian mode|Hypermixolydian]] (or [[Phrygian mode#Ancient_Greek_anchor|Hyperphrygian]])
|-
! E
| High [[Mixolydian]] or Hyperiastian 
|-
!  E{{sup|{{music|flat}}}}
| Low [[Mixolydian]] or Hyperdorian 
|-
! D
| [[Lydian mode#Ancient_Greek_anchor|Lydian]]
|-
!  C{{sup|{{music|sharp}}}}
| Low [[Lydian mode#Ancient_Greek_anchor|Lydian]] or [[Aeolian mode#Ancient_Greek_anchor|Aeolian]]
|-
! C
| [[Phrygian mode#Ancient_Greek_anchor|Phrygian]]
|-
! B
| Low [[Phrygian mode#Ancient_Greek_anchor|Phrygian]] or Iastian 
|-
!  B{{sup|{{music|flat}}}}
| [[Dorian mode#Greek_Dorian_anchor|Dorian]]
|-
! A
| [[Hypolydian]]
|-
!  G{{sup|{{music|sharp}}}}
| Low [[Hypolydian]] or Hypoaeolian 
|-
! G
| [[Hypophrygian]]
|-
!  F{{sup|{{music|sharp}}}}
| Low [[Hypophrygian]] or Hypoiastian 
|-
! F
| [[Hypodorian]]
|}

[[Ptolemy]], in his ''Harmonics'', ii.3–11, construed the ''tonoi'' differently, presenting all seven octave species within a fixed octave, through chromatic inflection of the scale degrees (comparable to the modern conception of building all seven modal scales on a single tonic). In Ptolemy's system, therefore there are only seven ''tonoi''.<ref name=Mathiesen-2001a-6iiie /><ref>{{harvp|Mathiesen|2001c}}</ref> [[Pythagoras]] also construed the intervals arithmetically (if somewhat more rigorously, initially allowing for 1:1 = Unison, 2:1 = Octave, 3:2 = Fifth, 4:3 = Fourth and 5:4 = Major Third within the octave). In their diatonic genus, these ''tonoi'' and corresponding ''harmoniai'' correspond with the intervals of the familiar modern major and minor scales. See [[Pythagorean tuning]] and [[Pythagorean interval]].

===''Harmoniai''===
{| class="wikitable" align="right" style="text-align:center;"
|+''Harmoniai'' of the School of Eratocles ([[enharmonic genus]])
! Mixolydian
| {{1/4}} || {{1/4}} || 2 || {{1/4}} || {{1/4}} || 2 || 1
|-
! Lydian
| {{1/4}} || 2 || {{1/4}} || {{1/4}} || 2 || 1 || {{1/4}}
|-
! Phrygian
| 2 || {{1/4}} || {{1/4}} || 2 || 1 || {{1/4}} || {{1/4}}
|-
! Dorian
| {{1/4}} || {{1/4}} || 2 || 1 || {{1/4}} || {{1/4}} || 2
|-
! Hypolydian
| {{1/4}} || 2 || 1 || {{1/4}} || {{1/4}} || 2 || {{1/4}}
|-
! Hypophrygian
| 2 || 1 || {{1/4}} || {{1/4}} || 2 || {{1/4}} || {{1/4}}
|-
! Hypodorian
| 1 || {{1/4}} || {{1/4}} || 2 || {{1/4}} || {{1/4}} || 2
|}
In music theory the Greek word ''harmonia'' can signify the enharmonic genus of [[tetrachord]], the seven octave species, or a style of music associated with one of the ethnic types or the ''tonoi'' named by them.<ref>{{harvp|Mathiesen|2001b}}</ref>

Particularly in the earliest surviving writings, ''harmonia'' is regarded not as a scale, but as the epitome of the stylised singing of a particular district or people or occupation.<ref name="Winnington-Ingram-1936-2–3" /> When the late-6th-century poet [[Lasus of Hermione]] referred to the Aeolian ''harmonia'', for example, he was more likely thinking of a [[Melody type|melodic style]] characteristic of Greeks speaking the [[Aeolic Greek|Aeolic dialect]] than of a scale pattern.<ref name=Anderson-Mathiesen-2001>{{harvp|Anderson and Mathiesen|2001}}</ref> By the late 5th century BC, these regional types are being described in terms of differences in what is called ''harmonia'' – a word with several senses, but here referring to the pattern of intervals between the notes sounded by the strings of a [[Lyre|lyra]] or a [[Cithara|kithara]].

However, there is no reason to suppose that, at this time, these tuning patterns stood in any straightforward and organised relations to one another. It was only around the year 400 that attempts were made by a group of theorists known as the harmonicists to bring these ''harmoniai'' into a single system and to express them as orderly transformations of a single structure. Eratocles was the most prominent of the harmonicists, though his ideas are known only at second hand, through Aristoxenus, from whom we learn they represented the ''harmoniai'' as cyclic reorderings of a given series of intervals within the octave, producing seven [[octave species]]. We also learn that Eratocles confined his descriptions to the enharmonic genus.<ref>{{harvp|Barker|1984–89|loc=2:14–15}}</ref>

=== Philosophical ''harmoniai'' in Plato and Aristotle===
In the ''[[The Republic (Plato)|Republic]]'', [[Plato]] uses the term inclusively to encompass a particular type of scale, range and register, characteristic rhythmic pattern, textual subject, etc.<ref name=Mathiesen-2001a-6iiie /> Plato held that playing music in a particular ''harmonia'' would incline one towards specific behaviors associated with it, and suggested that soldiers should listen to music in Dorian or Phrygian ''harmoniai'' to help harden them but avoid music in Lydian, Mixolydian, or Ionian ''harmoniai'', for fear of being softened. Plato believed that a change in the musical modes of the state would cause a wide-scale social revolution.<ref>{{harvp|Plato|1902|loc=III.10–III.12 = 398C–403C}}</ref>

The philosophical writings of Plato and [[Aristotle]] ({{circa|350 BC}}) include sections that describe the effect of different ''harmoniai'' on mood and character formation. For example, Aristotle stated in his ''[[Politics (Aristotle)|Politics]]'':<ref>{{harvp|Aristotle|1895|loc=viii:1340a:40–1340b:5}}</ref>

{{Blockquote|But melodies themselves do contain imitations of character. This is perfectly clear, for the ''harmoniai'' have quite distinct natures from one another, so that those who hear them are differently affected and do not respond in the same way to each. To some, such as the one called Mixolydian, they respond with more grief and anxiety, to others, such as the relaxed ''harmoniai'', with more mellowness of mind, and to one another with a special degree of moderation and firmness, Dorian being apparently the only one of the ''harmoniai'' to have this effect, while Phrygian creates ecstatic excitement. These points have been well expressed by those who have thought deeply about this kind of education; for they cull the evidence for what they say from the facts themselves.<ref name=Barker-1984-89-1:175-176>{{harvp|Barker|1984–89|loc=1:175–176}}</ref>}}

Aristotle continues by describing the effects of rhythm, and concludes about the combined effect of rhythm and ''harmonia'' (viii:1340b:10–13): {{blockquote|From all this it is clear that music is capable of creating a particular quality of character [{{math|ἦθος}}] in the soul, and if it can do that, it is plain that it should be made use of, and that the young should be educated in it.<ref name=Barker-1984-89-1:175-176 />}}

The word ''[[ethos]]'' ({{math|ἦθος}}) in this context means "moral character", and Greek ethos theory concerns the ways that music can convey, foster, and even generate ethical states.<ref name=Anderson-Mathiesen-2001 />

===''Melos''===
Some treatises also describe "melic" composition ({{math|μελοποιΐα}}), "the employment of the materials subject to harmonic practice with due regard to the requirements of each of the subjects under consideration"<ref>{{harvp|Cleonides|1965|p=35}}</ref> – which, together with the scales, ''tonoi'', and ''harmoniai'' resemble elements found in medieval modal theory.<ref>{{harvp|Mathiesen|2001a|loc=6(iii)}}</ref> According to [[Aristides Quintilianus]], melic composition is subdivided into three classes: dithyrambic, nomic, and tragic.<ref>{{harvp|Mathiesen|1983|loc=i.12}}</ref> These parallel his three classes of rhythmic composition: systaltic, diastaltic and hesychastic. Each of these broad classes of melic composition may contain various subclasses, such as erotic, comic and panegyric, and any composition might be elevating (diastaltic), depressing (systaltic), or soothing (hesychastic).<ref>{{harvp|Mathiesen|2001a|p=4}}</ref>

According to [[Thomas J. Mathiesen]], music as a performing art was called ''melos'', which in its perfect form ({{math|μέλος τέλειον}}) comprised not only the melody and the text (including its elements of rhythm and diction) but also stylized dance movement. Melic and rhythmic composition (respectively, {{math|μελοποιΐα}} and {{math|ῥυθμοποιΐα}}) were the processes of selecting and applying the various components of melos and rhythm to create a complete work. According to Aristides Quintilianus:
{{Blockquote|And we might fairly speak of perfect melos, for it is necessary that melody, rhythm and diction be considered so that the perfection of the song may be produced: in the case of melody, simply a certain sound; in the case of rhythm, a motion of sound; and in the case of diction, the meter. The things contingent to perfect melos are motion-both of sound and body-and also chronoi and the rhythms based on these.<ref>{{harvp|Mathiesen|1983|p=75}}</ref>}}