View source for Gentle tuning

[[File:Gentle12.png|thumb|The chromatic MOS of a gentle-fifth temperament. Note the two step sizes.]]
'''Gentle tuning''' (aka the '''gentle region''' of fifths) is the regular tuning of the perfect fifth somewhere between the tunings given by 29edo and 17edo (~703.4 to 705.9 cents), producing MOS [[diatonic]] scales with step size ratios between 5:2 and 3:1 (and consequently [[chromatic]] scales between 3:2 and 2:1, including the [[Golden generator|golden tuning]] of p-chromatic). As a result, the [[major third]] generated is between 413.8 and 423.5 cents, and approximates 14/11. It is so named because melodically it functions as a "gentle" version of [[Superpyth]]; conversely, it can instead be seen as exaggerating the characteristics of Pythagorean tuning as it compares with 12-tone equal temperament and is usable as a replacement for Pythagorean tuning. One notable characteristic of gentle tuning is that it narrows the diatonic semitone towards a size of 70 cents, described by some theorists as an ideal leading tone; Aura, however, considers it to be between a leading tone and a diesis or quarter tone in function, being able to either lead to the tonic or "skip over" it.

== Regular temperament theory ==
Gentle tuning is associated with the 2.3.(11/7).(13/7) temperament, 29 & 46, that finds 14/11 at the major third and 13/11 at the minor third, which has a number of names depending on the subgroup (see [[#Names]]). Therefore, the chromatic semitone is equated to 14/13 and the diatonic semitone is equated to 22/21; the whole tone is equated to 44/39.

This implies the use of these thirds as elements of 13-limit harmony over the 11th and 13th harmonics themselves, similar to, but more intense and approach-specific than, the prioritization of 9/7 and 7/6 in Archy (and in septal harmony as a whole) as opposed to 7/4; both approaches are patterned off of [[Meantone]], which is often described outside of a regular temperament context as tempering the fifth to bring the major and minor third more in-tune with 5/4 and 6/5, where 5/4 is simply treated as "the major third" rather than a generator of just intonation in its own right.

To extend to the 2.3.7.11.13 subgroup, 7/6 is equated to two chromatic semitones (so that 7/4 is C-G##). As a result, 11/8 is placed at the augmented third and 13/8 at the augmented fifth (this is the same interval that becomes 8/5 in [[Schismic]]). 

For flatter tunings (flat of 46edo), 5/4 is equated to three chromatic semitones (so that a major triad is C-C###-G). There is no stable mapping of 5 for sharper tunings due to 17edo's inaccuracy in approximating prime 5. This is similar to [[Archy]] tunings approaching 5edo.

==== Chords ====
While it is not particularly simple in just intonation, the primary chords implied by the temperament's structure are the major 22:28:33 and minor 22:26:33 which are complements of one another and also the diatonic major and minor chords (so that their union, P1-m3-M3-P5, is essentially tempered). Standard 5- and 7-limit chords are somewhat unviable when using standard diatonic logic, as a 4:5:6:7 chord is C-C###-G-G##, with all four notes overlapping on two nominals, and the supermajor and subminor triads are C-C##-G and C-Gbb-G, again overlapping.

==== Names ====
The most common name for this temperament, applying in the strict sense to the full 2.3.5.7.11.13 temperament, is ''Leapday.'' As a 2.3.(11/7).(13/7) temperament, however, the technical name is ''Pepperoni'' and as a 2.3.7.11.13 temperament the technical name is ''Leapfrog.'' Other names that may be used for this temperament or for gentle tuning as a whole are ''neogothic'' (in reference to the quality of the generated thirds), ''[[Parapyth]]'' (technically referring to a rank-3 temperament whose 3/2 generates Pepperoni), and simply ''gentle.''

== Interval chain ==
{| class="wikitable"
|+
! colspan="3" |Generators up
! colspan="3" |Generators down
|-
!#
!Cents
!Regular interpretation (2.3.7.11.13)
!#
!Cents
!Regular interpretation (2.3.7.11.13)
|-
|0
|0.00
|1/1
|0
|1,200.00
|2/1
|-
|1
|704.35
|3/2
|1
|495.65
|4/3
|-
|2
|208.70
|9/8
|2
|991.30
|16/9
|-
|3
|913.04
|22/13
|3
|286.96
|13/11
|-
|4
|417.39
|14/11
|4
|782.61
|11/7
|-
|5
|1,121.74
|21/11
|5
|78.26
|22/21
|-
|6
|626.09
|13/9
|6
|573.91
|18/13
|-
|7
|130.43
|14/13
|7
|1,069.57
|13/7
|-
|8
|834.78
|13/8
|8
|365.22
|16/13
|-
|9
|339.13
|11/9
|9
|860.87
|18/11
|-
|10
|1,043.48
|11/6, 20/11
|10
|156.52
|11/10, 12/11
|-
|11
|547.83
|11/8, 15/11
|11
|652.17
|16/11, 22/15
|-
|12
|52.17
|33/32, 40/39
|12
|1,147.83
|64/33, 39/20
|-
|13
|756.52
|14/9, 20/13
|13
|443.48
|9/7, 13/10
|-
|14
|260.87
|7/6
|14
|939.13
|12/7
|-
|15
|965.22
|7/4
|15
|234.78
|8/7
|}
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