View source for Halftone

[[File:halftone6.wav|thumb|Halftone[6] example in 16edf and 4<nowiki>|</nowiki>1 mode]]

'''Halftone''' is a [[nonoctave]] (fifth-repeating) [[regular temperament]] in the 3/2.5/2.7/2 fractional subgroup that tempers out 9604/9375 and has a generator of a flat [[7/5]] of around 570-580 cents. It could be used as a harmonic basis for "1/2 prime" (3/2.5/2.7/2.11/2.13/2 etc.) systems with the equivalence as [[3/2]], similar to [[meantone]] for full prime-limit systems with the equivalence as [[2/1]] and [[BPS]] for no-twos systems with the equivalence as [[3/1]]. Halftone temperament can be extended to the 11-limit (3/2.5/2.7/2.11/2) by additionally tempering out 1232/1215, the difference between [[15/14]] and [[88/81]] (the fifth-reduction of 11/2). Small [[EDF]]s that [[support]] halftone include [[5edf]], [[6edf]], [[11edf]], [[16edf]], [[21edf]], and [[27edf]].

If tone clusters with intervals of supraminor seconds or less are ignored, the most fundamental 3/2.5/2.7/2 chord that is narrower than a perfect fifth is 45:50:63 (1-[[10/9]]-[[7/5]]), essentially a diminished triad with a major second instead of a minor third. There is also a more "major-sounding" counterpart of it 50:63:70 (1-[[63/50]]-[[7/5]]), a diminished triad with a major third instead of a minor third. These chords generally sound more consonant than a standard diminished triad but far less than a standard major or minor triad. Both of these are well approximated in halftone because it equates 4 [[7/5]] generators with [[10/9]].

For technical data, see [[Subgroup temperaments#Halftone]].

== Interval chain ==
{|class="wikitable"
|-
| 53.040
| 182.823
| 312.606
| 442.389
| 572.172
| 0
| 129.783
| 259.566
| 389.349
| 519.132
| 648.915
|-
| [[28/27]]
| [[10/9]]
| [[25/21]]
| 125/98~98/75
| [[7/5]]
| [[1/1]]
| [[15/14]]
| 225/196~147/125
| [[63/50]]
| [[27/20]]
| 81/56
|}

== MOS scales ==
Halftone possesses MOS scales with 4 ([[1L 3s (3/2-equivalent)|1L 3s⟨3/2⟩]] or "neptunian"), 5 ([[1L 4s (3/2-equivalent)|1L 4s⟨3/2⟩]]), 6 ([[5L 1s (3/2-equivalent)|5L 1s⟨3/2⟩]]) and 11 ([[5L 6s (3/2-equivalent)|5L 6s⟨3/2⟩]]/[[6L 5s (3/2-equivalent)|6L 5s⟨3/2⟩]]) notes. The tetratonic scale is usable, but the tempered 10/9 is not present in it, so the pentatonic and hexatonic scales are the smallest options for halftone.


[[Category:Halftone| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Non-octave temperaments]]