Editing Mode (music) (section)

===''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]].