//
// Copyright 2019-2020 Hans W. Uhlig, Richard I. Christopher. All Rights Reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//      http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//

use super::Degree;
use crate::types::{Cents, Note, Steps};
use std::fmt;

/// [PerfectQuality](musictheory::types::PerfectQuality) is the
/// [Interval](musictheory::types::Interval) Quality of the First, Fourth, and Fifth.
#[derive(Copy, Clone, PartialOrd, PartialEq, Debug)]
pub enum PerfectQuality {
    TripleDiminished,
    DoubleDiminished,
    Diminished,
    Perfect,
    Augmented,
    DoubleAugmented,
    TripleAugmented,
}

/// [MajorQuality](musictheory::types::MajorQuality) is the [Interval](musictheory::types::Interval)
/// Quality of the Second, Third, Sixth, and Seventh.
#[derive(Copy, Clone, PartialOrd, PartialEq, Debug)]
pub enum MajorQuality {
    TripleDiminished,
    DoubleDiminished,
    Diminished,
    Major,
    Minor,
    Augmented,
    DoubleAugmented,
    TripleAugmented,
}

impl fmt::Display for PerfectQuality {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        match *self {
            PerfectQuality::TripleDiminished => write!(f, "ddd"),
            PerfectQuality::DoubleDiminished => write!(f, "dd"),
            PerfectQuality::Diminished => write!(f, "d"),
            PerfectQuality::Perfect => write!(f, "P"),
            PerfectQuality::Augmented => write!(f, "A"),
            PerfectQuality::DoubleAugmented => write!(f, "AA"),
            PerfectQuality::TripleAugmented => write!(f, "AAA"),
        }
    }
}

impl fmt::Display for MajorQuality {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        match *self {
            MajorQuality::TripleDiminished => write!(f, "ddd"),
            MajorQuality::DoubleDiminished => write!(f, "dd"),
            MajorQuality::Diminished => write!(f, "d"),
            MajorQuality::Major => write!(f, "M"),
            MajorQuality::Minor => write!(f, "m"),
            MajorQuality::Augmented => write!(f, "A"),
            MajorQuality::DoubleAugmented => write!(f, "AA"),
            MajorQuality::TripleAugmented => write!(f, "AA"),
        }
    }
}

/// [Interval](musictheory::types::Interval) is the distance between two
/// [PitchClasses](musictheory::types::PitchClass).
#[derive(Copy, Clone, PartialOrd, PartialEq, Debug)]
pub enum Interval {
    First(PerfectQuality),
    Second(MajorQuality),
    Third(MajorQuality),
    Fourth(PerfectQuality),
    Fifth(PerfectQuality),
    Sixth(MajorQuality),
    Seventh(MajorQuality),
    Octave(PerfectQuality),
    Ninth(MajorQuality),
    Tenth(MajorQuality),
    Eleventh(PerfectQuality),
    Twelfth(PerfectQuality),
    Thirteenth(MajorQuality),
    Fourteenth(MajorQuality),
}

impl Interval {
    /// [Degrees](musictheory::types::Degree) are matched to
    /// [Interval](musictheory::types::Interval).
    pub fn degree(&self) -> Degree {
        match *self {
            Interval::First(_) => Degree::Tonic,
            Interval::Second(_) => Degree::Supertonic,
            Interval::Third(_) => Degree::Mediant,
            Interval::Fourth(_) => Degree::Subdominant,
            Interval::Fifth(_) => Degree::Dominant,
            Interval::Sixth(_) => Degree::Submediant,
            Interval::Seventh(_) => Degree::Subtonic,
            Interval::Octave(_) => Degree::Tonic,
            Interval::Ninth(_) => Degree::Supertonic,
            Interval::Tenth(_) => Degree::Mediant,
            Interval::Eleventh(_) => Degree::Subdominant,
            Interval::Twelfth(_) => Degree::Dominant,
            Interval::Thirteenth(_) => Degree::Submediant,
            Interval::Fourteenth(_) => Degree::Subtonic,
        }
    }
    /// Get [Steps](musictheory::types::Steps) measurement for this
    /// [Interval](musictheory::types::Interval).
    pub fn steps(&self) -> Steps {
        fn ptou(base: u16, q: PerfectQuality) -> Steps {
            let steps = match q {
                PerfectQuality::TripleDiminished => 9,
                PerfectQuality::DoubleDiminished => 10,
                PerfectQuality::Diminished => 11,
                PerfectQuality::Perfect => 12,
                PerfectQuality::Augmented => 13,
                PerfectQuality::DoubleAugmented => 14,
                PerfectQuality::TripleAugmented => 15,
            } + base as i16;
            Steps::from((steps % 12) as u16)
        }
        fn mtou(base: u16, q: MajorQuality) -> Steps {
            let steps = match q {
                MajorQuality::TripleDiminished => 8,
                MajorQuality::DoubleDiminished => 9,
                MajorQuality::Diminished => 10,
                MajorQuality::Minor => 11,
                MajorQuality::Major => 12,
                MajorQuality::Augmented => 13,
                MajorQuality::DoubleAugmented => 14,
                MajorQuality::TripleAugmented => 15,
            } + base as i16;
            Steps::from((steps % 12) as u16)
        }
        match *self {
            Interval::First(q) => ptou(0, q),
            Interval::Second(q) => mtou(2, q),
            Interval::Third(q) => mtou(4, q),
            Interval::Fourth(q) => ptou(5, q),
            Interval::Fifth(q) => ptou(7, q),
            Interval::Sixth(q) => mtou(9, q),
            Interval::Seventh(q) => mtou(11, q),
            Interval::Octave(q) => ptou(12, q),
            Interval::Ninth(q) => mtou(14, q),
            Interval::Tenth(q) => mtou(16, q),
            Interval::Eleventh(q) => ptou(17, q),
            Interval::Twelfth(q) => ptou(19, q),
            Interval::Thirteenth(q) => mtou(21, q),
            Interval::Fourteenth(q) => mtou(23, q),
        }
    }
    /// Interval Mappings for Notes
    #[rustfmt::skip]
    pub fn distance(l: Note, r: Note) -> Option<Interval> {
        use super::{Accidental::*, Interval::*, Note::*};
        match (l, r) {

            // Note C(_)
            (C(DoubleFlat), C(DoubleFlat)) => Some(First(PerfectQuality::Perfect)),
            (C(DoubleFlat), C(Flat)) => Some(First(PerfectQuality::Augmented)),
            (C(DoubleFlat), C(Natural)) => Some(First(PerfectQuality::DoubleAugmented)),
            (C(DoubleFlat), D(DoubleFlat)) => Some(Second(MajorQuality::Major)),
            (C(DoubleFlat), D(Flat)) => Some(Second(MajorQuality::Augmented)),
            (C(DoubleFlat), D(Natural)) => Some(Second(MajorQuality::DoubleAugmented)),
            (C(DoubleFlat), E(DoubleFlat)) => Some(Third(MajorQuality::Major)),
            (C(DoubleFlat), E(Flat)) => Some(Third(MajorQuality::Augmented)),
            (C(DoubleFlat), E(Natural)) => Some(Third(MajorQuality::DoubleAugmented)),
            (C(DoubleFlat), F(DoubleFlat)) => Some(Fourth(PerfectQuality::Perfect)),
            (C(DoubleFlat), F(Flat)) => Some(Fourth(PerfectQuality::Augmented)),
            (C(DoubleFlat), F(Natural)) => Some(Fourth(PerfectQuality::DoubleAugmented)),
            (C(DoubleFlat), G(DoubleFlat)) => Some(Fifth(PerfectQuality::Perfect)),
            (C(DoubleFlat), G(Flat)) => Some(Fifth(PerfectQuality::Augmented)),
            (C(DoubleFlat), G(Natural)) => Some(Fifth(PerfectQuality::DoubleAugmented)),
            (C(DoubleFlat), A(DoubleFlat)) => Some(Sixth(MajorQuality::Major)),
            (C(DoubleFlat), A(Flat)) => Some(Sixth(MajorQuality::Augmented)),
            (C(DoubleFlat), A(Natural)) => Some(Sixth(MajorQuality::DoubleAugmented)),
            (C(DoubleFlat), B(DoubleFlat)) => Some(Seventh(MajorQuality::Major)),
            (C(DoubleFlat), B(Flat)) => Some(Sixth(MajorQuality::Augmented)),
            (C(DoubleFlat), B(Natural)) => Some(Seventh(MajorQuality::DoubleAugmented)),

            (C(Flat), C(DoubleFlat)) => Some(First(PerfectQuality::Diminished)),
            (C(Flat), C(Flat)) => Some(First(PerfectQuality::Perfect)),
            (C(Flat), C(Natural)) => Some(First(PerfectQuality::Augmented)),
            (C(Flat), D(DoubleFlat)) => Some(Second(MajorQuality::Minor)),
            (C(Flat), D(Flat)) => Some(Second(MajorQuality::Major)),
            (C(Flat), D(Natural)) => Some(Second(MajorQuality::Augmented)),
            (C(Flat), E(DoubleFlat)) => Some(Third(MajorQuality::Minor)),
            (C(Flat), E(Flat)) => Some(Third(MajorQuality::Major)),
            (C(Flat), E(Natural)) => Some(Third(MajorQuality::Augmented)),
            (C(Flat), F(DoubleFlat)) => Some(Fourth(PerfectQuality::Diminished)),
            (C(Flat), F(Flat)) => Some(Fourth(PerfectQuality::Perfect)),
            (C(Flat), F(Natural)) => Some(Fourth(PerfectQuality::Augmented)),
            (C(Flat), G(DoubleFlat)) => Some(Fifth(PerfectQuality::Diminished)),
            (C(Flat), G(Flat)) => Some(Fifth(PerfectQuality::Perfect)),
            (C(Flat), G(Natural)) => Some(Fifth(PerfectQuality::Augmented)),
            (C(Flat), A(DoubleFlat)) => Some(Sixth(MajorQuality::Minor)),
            (C(Flat), A(Flat)) => Some(Sixth(MajorQuality::Major)),
            (C(Flat), A(Natural)) => Some(Sixth(MajorQuality::Augmented)),
            (C(Flat), B(DoubleFlat)) => Some(Seventh(MajorQuality::Minor)),
            (C(Flat), B(Flat)) => Some(Seventh(MajorQuality::Major)),
            (C(Flat), B(Natural)) => Some(Seventh(MajorQuality::Augmented)),

            (C(Natural), C(DoubleFlat)) => Some(First(PerfectQuality::DoubleDiminished)),
            (C(Natural), C(Flat)) => Some(First(PerfectQuality::Diminished)),
            (C(Natural), C(Natural)) => Some(First(PerfectQuality::Perfect)),
            (C(Natural), C(Sharp)) => Some(First(PerfectQuality::Augmented)),
            (C(Natural), C(DoubleSharp)) => Some(First(PerfectQuality::DoubleAugmented)),
            (C(Natural), D(DoubleFlat)) => Some(Second(MajorQuality::Diminished)),
            (C(Natural), D(Flat)) => Some(Second(MajorQuality::Minor)),
            (C(Natural), D(Natural)) => Some(Second(MajorQuality::Major)),
            (C(Natural), D(Sharp)) => Some(Second(MajorQuality::Augmented)),
            (C(Natural), D(DoubleSharp)) => Some(Second(MajorQuality::DoubleAugmented)),
            (C(Natural), E(DoubleFlat)) => Some(Third(MajorQuality::Diminished)),
            (C(Natural), E(Flat)) => Some(Third(MajorQuality::Minor)),
            (C(Natural), E(Natural)) => Some(Third(MajorQuality::Major)),
            (C(Natural), E(Sharp)) => Some(Third(MajorQuality::Augmented)),
            (C(Natural), E(DoubleSharp)) => Some(Third(MajorQuality::DoubleAugmented)),
            (C(Natural), F(DoubleFlat)) => Some(Fourth(PerfectQuality::DoubleDiminished)),
            (C(Natural), F(Flat)) => Some(Fourth(PerfectQuality::Diminished)),
            (C(Natural), F(Natural)) => Some(Fourth(PerfectQuality::Perfect)),
            (C(Natural), F(Sharp)) => Some(Fourth(PerfectQuality::Augmented)),
            (C(Natural), F(DoubleSharp)) => Some(Fourth(PerfectQuality::DoubleAugmented)),
            (C(Natural), G(DoubleFlat)) => Some(Fifth(PerfectQuality::DoubleDiminished)),
            (C(Natural), G(Flat)) => Some(Fifth(PerfectQuality::Diminished)),
            (C(Natural), G(Natural)) => Some(Fifth(PerfectQuality::Perfect)),
            (C(Natural), G(Sharp)) => Some(Fifth(PerfectQuality::Augmented)),
            (C(Natural), G(DoubleSharp)) => Some(Fifth(PerfectQuality::DoubleAugmented)),
            (C(Natural), A(DoubleFlat)) => Some(Sixth(MajorQuality::Diminished)),
            (C(Natural), A(Flat)) => Some(Sixth(MajorQuality::Minor)),
            (C(Natural), A(Natural)) => Some(Sixth(MajorQuality::Major)),
            (C(Natural), A(Sharp)) => Some(Sixth(MajorQuality::Augmented)),
            (C(Natural), A(DoubleSharp)) => Some(Sixth(MajorQuality::DoubleAugmented)),
            (C(Natural), B(DoubleFlat)) => Some(Seventh(MajorQuality::Diminished)),
            (C(Natural), B(Flat)) => Some(Seventh(MajorQuality::Minor)),
            (C(Natural), B(Natural)) => Some(Seventh(MajorQuality::Major)),
            (C(Natural), B(Sharp)) => Some(Seventh(MajorQuality::Augmented)),

            (C(Sharp), C(Natural)) => Some(First(PerfectQuality::Diminished)),
            (C(Sharp), C(Sharp)) => Some(First(PerfectQuality::Perfect)),
            (C(Sharp), C(DoubleSharp)) => Some(First(PerfectQuality::Augmented)),
            (C(Sharp), D(Natural)) => Some(Second(MajorQuality::Minor)),
            (C(Sharp), D(Sharp)) => Some(Second(MajorQuality::Major)),
            (C(Sharp), D(DoubleSharp)) => Some(Second(MajorQuality::Augmented)),
            (C(Sharp), E(Natural)) => Some(Third(MajorQuality::Minor)),
            (C(Sharp), E(Sharp)) => Some(Third(MajorQuality::Major)),
            (C(Sharp), F(Natural)) => Some(Fourth(PerfectQuality::Diminished)),
            (C(Sharp), E(DoubleSharp)) => Some(Third(MajorQuality::Augmented)),
            (C(Sharp), F(Sharp)) => Some(Fourth(PerfectQuality::Perfect)),
            (C(Sharp), F(DoubleSharp)) => Some(Fourth(PerfectQuality::Augmented)),
            (C(Sharp), G(Natural)) => Some(Fifth(PerfectQuality::Diminished)),
            (C(Sharp), G(Sharp)) => Some(Fifth(PerfectQuality::Perfect)),
            (C(Sharp), G(DoubleSharp)) => Some(Fifth(PerfectQuality::Augmented)),
            (C(Sharp), A(Natural)) => Some(Sixth(MajorQuality::Minor)),
            (C(Sharp), A(Sharp)) => Some(Sixth(MajorQuality::Major)),
            (C(Sharp), A(DoubleSharp)) => Some(Sixth(MajorQuality::Augmented)),
            (C(Sharp), B(Natural)) => Some(Seventh(MajorQuality::Minor)),
            (C(Sharp), B(Sharp)) => Some(Seventh(MajorQuality::Major)),
            (C(Sharp), B(DoubleSharp)) => Some(Seventh(MajorQuality::Augmented)),

            (C(DoubleSharp), C(Natural)) => Some(First(PerfectQuality::DoubleDiminished)),
            (C(DoubleSharp), C(Sharp)) => Some(First(PerfectQuality::Diminished)),
            (C(DoubleSharp), C(DoubleSharp)) => Some(First(PerfectQuality::Perfect)),
            (C(DoubleSharp), D(Natural)) => Some(Second(MajorQuality::Diminished)),
            (C(DoubleSharp), D(Sharp)) => Some(Second(MajorQuality::Minor)),
            (C(DoubleSharp), D(DoubleSharp)) => Some(Second(MajorQuality::Major)),
            (C(DoubleSharp), E(Natural)) => Some(Third(MajorQuality::Diminished)),
            (C(DoubleSharp), E(Sharp)) => Some(Third(MajorQuality::Minor)),
            (C(DoubleSharp), E(DoubleSharp)) => Some(Third(MajorQuality::Major)),
            (C(DoubleSharp), F(Natural)) => Some(Fourth(PerfectQuality::DoubleDiminished)),
            (C(DoubleSharp), F(Sharp)) => Some(Fourth(PerfectQuality::Diminished)),
            (C(DoubleSharp), F(DoubleSharp)) => Some(Fourth(PerfectQuality::Perfect)),
            (C(DoubleSharp), G(Natural)) => Some(Fifth(PerfectQuality::DoubleDiminished)),
            (C(DoubleSharp), G(Sharp)) => Some(Fifth(PerfectQuality::Diminished)),
            (C(DoubleSharp), G(DoubleSharp)) => Some(Fifth(PerfectQuality::Perfect)),
            (C(DoubleSharp), A(Natural)) => Some(Sixth(MajorQuality::Diminished)),
            (C(DoubleSharp), A(Sharp)) => Some(Sixth(MajorQuality::Minor)),
            (C(DoubleSharp), A(DoubleSharp)) => Some(Sixth(MajorQuality::Major)),
            (C(DoubleSharp), B(Natural)) => Some(Seventh(MajorQuality::Diminished)),
            (C(DoubleSharp), B(Sharp)) => Some(Seventh(MajorQuality::Minor)),
            (C(DoubleSharp), B(DoubleSharp)) => Some(Seventh(MajorQuality::Major)),

            // NOTE D(_)
            (D(DoubleFlat), D(DoubleFlat)) => Some(First(PerfectQuality::Perfect)),
            (D(DoubleFlat), D(Flat)) => Some(First(PerfectQuality::Augmented)),
            (D(DoubleFlat), D(Natural)) => Some(First(PerfectQuality::DoubleAugmented)),
            (D(DoubleFlat), E(DoubleFlat)) => Some(Second(MajorQuality::Major)),
            (D(DoubleFlat), E(Flat)) => Some(Second(MajorQuality::Augmented)),
            (D(DoubleFlat), E(Natural)) => Some(Second(MajorQuality::DoubleAugmented)),
            (D(DoubleFlat), F(DoubleFlat)) => Some(Third(MajorQuality::Minor)),
            (D(DoubleFlat), F(Flat)) => Some(Third(MajorQuality::Major)),
            (D(DoubleFlat), F(Natural)) => Some(Third(MajorQuality::Augmented)),
            (D(DoubleFlat), G(DoubleFlat)) => Some(Fourth(PerfectQuality::Perfect)),
            (D(DoubleFlat), G(Flat)) => Some(Fourth(PerfectQuality::Augmented)),
            (D(DoubleFlat), G(Natural)) => Some(Fourth(PerfectQuality::DoubleAugmented)),
            (D(DoubleFlat), A(DoubleFlat)) => Some(Fifth(PerfectQuality::Perfect)),
            (D(DoubleFlat), A(Flat)) => Some(Fifth(PerfectQuality::Augmented)),
            (D(DoubleFlat), A(Natural)) => Some(Fifth(PerfectQuality::DoubleAugmented)),
            (D(DoubleFlat), B(DoubleFlat)) => Some(Sixth(MajorQuality::Major)),
            (D(DoubleFlat), B(Flat)) => Some(Sixth(MajorQuality::Augmented)),
            (D(DoubleFlat), B(Natural)) => Some(Sixth(MajorQuality::DoubleAugmented)),
            (D(DoubleFlat), C(DoubleFlat)) => Some(Seventh(MajorQuality::Minor)),
            (D(DoubleFlat), C(Flat)) => Some(Seventh(MajorQuality::Major)),
            (D(DoubleFlat), C(Natural)) => Some(Seventh(MajorQuality::Augmented)),

            (D(Flat), D(DoubleFlat)) => Some(First(PerfectQuality::Diminished)),
            (D(Flat), D(Flat)) => Some(First(PerfectQuality::Perfect)),
            (D(Flat), D(Natural)) => Some(First(PerfectQuality::Augmented)),
            (D(Flat), E(DoubleFlat)) => Some(Second(MajorQuality::Minor)),
            (D(Flat), E(Flat)) => Some(Second(MajorQuality::Major)),
            (D(Flat), E(Natural)) => Some(Second(MajorQuality::Augmented)),
            (D(Flat), F(DoubleFlat)) => Some(Third(MajorQuality::Diminished)),
            (D(Flat), F(Flat)) => Some(Third(MajorQuality::Minor)),
            (D(Flat), F(Natural)) => Some(Third(MajorQuality::Major)),
            (D(Flat), G(DoubleFlat)) => Some(Fourth(PerfectQuality::Diminished)),
            (D(Flat), G(Flat)) => Some(Fourth(PerfectQuality::Perfect)),
            (D(Flat), G(Natural)) => Some(Fourth(PerfectQuality::Augmented)),
            (D(Flat), A(DoubleFlat)) => Some(Fifth(PerfectQuality::Diminished)),
            (D(Flat), A(Flat)) => Some(Fifth(PerfectQuality::Perfect)),
            (D(Flat), A(Natural)) => Some(Fifth(PerfectQuality::Augmented)),
            (D(Flat), B(DoubleFlat)) => Some(Sixth(MajorQuality::Minor)),
            (D(Flat), B(Flat)) => Some(Sixth(MajorQuality::Major)),
            (D(Flat), B(Natural)) => Some(Sixth(MajorQuality::Augmented)),
            (D(Flat), C(DoubleFlat)) => Some(Seventh(MajorQuality::Diminished)),
            (D(Flat), C(Flat)) => Some(Seventh(MajorQuality::Minor)),
            (D(Flat), C(Natural)) => Some(Seventh(MajorQuality::Major)),

            (D(Natural), D(DoubleFlat)) => Some(First(PerfectQuality::DoubleDiminished)),
            (D(Natural), D(Flat)) => Some(First(PerfectQuality::Diminished)),
            (D(Natural), D(Natural)) => Some(First(PerfectQuality::Perfect)),
            (D(Natural), D(Sharp)) => Some(First(PerfectQuality::Augmented)),
            (D(Natural), D(DoubleSharp)) => Some(First(PerfectQuality::DoubleAugmented)),
            (D(Natural), E(DoubleFlat)) => Some(Second(MajorQuality::Diminished)),
            (D(Natural), E(Flat)) => Some(Second(MajorQuality::Minor)),
            (D(Natural), E(Natural)) => Some(Second(MajorQuality::Major)),
            (D(Natural), E(Sharp)) => Some(Second(MajorQuality::Augmented)),
            (D(Natural), E(DoubleSharp)) => Some(Second(MajorQuality::DoubleAugmented)),
            (D(Natural), F(DoubleFlat)) => Some(Third(MajorQuality::DoubleDiminished)),
            (D(Natural), F(Flat)) => Some(Third(MajorQuality::Diminished)),
            (D(Natural), F(Natural)) => Some(Third(MajorQuality::Minor)),
            (D(Natural), F(Sharp)) => Some(Third(MajorQuality::Major)),
            (D(Natural), F(DoubleSharp)) => Some(Third(MajorQuality::Augmented)),
            (D(Natural), G(DoubleFlat)) => Some(Fourth(PerfectQuality::DoubleDiminished)),
            (D(Natural), G(Flat)) => Some(Fourth(PerfectQuality::Diminished)),
            (D(Natural), G(Natural)) => Some(Fourth(PerfectQuality::Perfect)),
            (D(Natural), G(Sharp)) => Some(Fourth(PerfectQuality::Augmented)),
            (D(Natural), G(DoubleSharp)) => Some(Fourth(PerfectQuality::DoubleAugmented)),
            (D(Natural), A(DoubleFlat)) => Some(Fifth(PerfectQuality::DoubleDiminished)),
            (D(Natural), A(Flat)) => Some(Fifth(PerfectQuality::Diminished)),
            (D(Natural), A(Natural)) => Some(Fifth(PerfectQuality::Perfect)),
            (D(Natural), A(Sharp)) => Some(Fifth(PerfectQuality::Augmented)),
            (D(Natural), A(DoubleSharp)) => Some(Fifth(PerfectQuality::DoubleAugmented)),
            (D(Natural), B(DoubleFlat)) => Some(Sixth(MajorQuality::Diminished)),
            (D(Natural), B(Flat)) => Some(Sixth(MajorQuality::Minor)),
            (D(Natural), B(Natural)) => Some(Sixth(MajorQuality::Major)),
            (D(Natural), B(Sharp)) => Some(Sixth(MajorQuality::Augmented)),
            (D(Natural), B(DoubleSharp)) => Some(Sixth(MajorQuality::DoubleAugmented)),
            (D(Natural), C(Flat)) => Some(Seventh(MajorQuality::Diminished)),
            (D(Natural), C(DoubleFlat)) => Some(Seventh(MajorQuality::DoubleDiminished)),
            (D(Natural), C(Natural)) => Some(Seventh(MajorQuality::Minor)),
            (D(Natural), C(Sharp)) => Some(Seventh(MajorQuality::Major)),
            (D(Natural), C(DoubleSharp)) => Some(Seventh(MajorQuality::Augmented)),

            (D(Sharp), D(Natural)) => Some(First(PerfectQuality::Diminished)),
            (D(Sharp), D(Sharp)) => Some(First(PerfectQuality::Perfect)),
            (D(Sharp), D(DoubleSharp)) => Some(First(PerfectQuality::Augmented)),
            (D(Sharp), E(Natural)) => Some(Second(MajorQuality::Minor)),
            (D(Sharp), E(Sharp)) => Some(Second(MajorQuality::Major)),
            (D(Sharp), E(DoubleSharp)) => Some(Second(MajorQuality::Augmented)),
            (D(Sharp), F(Natural)) => Some(Third(MajorQuality::Diminished)),
            (D(Sharp), F(Sharp)) => Some(Third(MajorQuality::Minor)),
            (D(Sharp), F(DoubleSharp)) => Some(Third(MajorQuality::Major)),
            (D(Sharp), G(Natural)) => Some(Fourth(PerfectQuality::Diminished)),
            (D(Sharp), G(Sharp)) => Some(Fourth(PerfectQuality::Perfect)),
            (D(Sharp), G(DoubleSharp)) => Some(Fourth(PerfectQuality::Augmented)),
            (D(Sharp), A(Natural)) => Some(Fifth(PerfectQuality::Diminished)),
            (D(Sharp), A(Sharp)) => Some(Fifth(PerfectQuality::Perfect)),
            (D(Sharp), A(DoubleSharp)) => Some(Fifth(PerfectQuality::Augmented)),
            (D(Sharp), B(Natural)) => Some(Sixth(MajorQuality::Minor)),
            (D(Sharp), B(Sharp)) => Some(Sixth(MajorQuality::Major)),
            (D(Sharp), B(DoubleSharp)) => Some(Sixth(MajorQuality::Augmented)),
            (D(Sharp), C(Natural)) => Some(Seventh(MajorQuality::Diminished)),
            (D(Sharp), C(Sharp)) => Some(Seventh(MajorQuality::Minor)),
            (D(Sharp), C(DoubleSharp)) => Some(Seventh(MajorQuality::Major)),

            (D(DoubleSharp), D(Natural)) => Some(First(PerfectQuality::DoubleDiminished)),
            (D(DoubleSharp), D(Sharp)) => Some(First(PerfectQuality::Diminished)),
            (D(DoubleSharp), D(DoubleSharp)) => Some(First(PerfectQuality::Perfect)),
            (D(DoubleSharp), E(Natural)) => Some(Second(MajorQuality::Diminished)),
            (D(DoubleSharp), E(Sharp)) => Some(Second(MajorQuality::Minor)),
            (D(DoubleSharp), E(DoubleSharp)) => Some(Second(MajorQuality::Major)),
            (D(DoubleSharp), F(Natural)) => Some(Third(MajorQuality::DoubleDiminished)),
            (D(DoubleSharp), F(Sharp)) => Some(Third(MajorQuality::Diminished)),
            (D(DoubleSharp), F(DoubleSharp)) => Some(Third(MajorQuality::Minor)),
            (D(DoubleSharp), G(Natural)) => Some(Fourth(PerfectQuality::DoubleDiminished)),
            (D(DoubleSharp), G(Sharp)) => Some(Fourth(PerfectQuality::Diminished)),
            (D(DoubleSharp), G(DoubleSharp)) => Some(Fourth(PerfectQuality::Perfect)),
            (D(DoubleSharp), A(Natural)) => Some(Fifth(PerfectQuality::DoubleDiminished)),
            (D(DoubleSharp), A(Sharp)) => Some(Fifth(PerfectQuality::Diminished)),
            (D(DoubleSharp), A(DoubleSharp)) => Some(Fifth(PerfectQuality::Perfect)),
            (D(DoubleSharp), B(Natural)) => Some(Sixth(MajorQuality::Diminished)),
            (D(DoubleSharp), B(Sharp)) => Some(Sixth(MajorQuality::Minor)),
            (D(DoubleSharp), B(DoubleSharp)) => Some(Sixth(MajorQuality::Major)),
            (D(DoubleSharp), C(Natural)) => Some(Seventh(MajorQuality::DoubleDiminished)),
            (D(DoubleSharp), C(Sharp)) => Some(Seventh(MajorQuality::Diminished)),
            (D(DoubleSharp), C(DoubleSharp)) => Some(Seventh(MajorQuality::Minor)),

            // Note E(_)
            (E(DoubleFlat), E(DoubleFlat)) => Some(First(PerfectQuality::Perfect)),
            (E(DoubleFlat), E(Flat)) => Some(First(PerfectQuality::Augmented)),
            (E(DoubleFlat), E(Natural)) => Some(First(PerfectQuality::DoubleAugmented)),
            (E(DoubleFlat), F(DoubleFlat)) => Some(Second(MajorQuality::Minor)),
            (E(DoubleFlat), F(Flat)) => Some(Second(MajorQuality::Major)),
            (E(DoubleFlat), F(Natural)) => Some(Second(MajorQuality::Augmented)),
            (E(DoubleFlat), G(DoubleFlat)) => Some(Third(MajorQuality::Minor)),
            (E(DoubleFlat), G(Flat)) => Some(Third(MajorQuality::Major)),
            (E(DoubleFlat), G(Natural)) => Some(Third(MajorQuality::Augmented)),
            (E(DoubleFlat), A(DoubleFlat)) => Some(Fourth(PerfectQuality::Perfect)),
            (E(DoubleFlat), A(Flat)) => Some(Fourth(PerfectQuality::Augmented)),
            (E(DoubleFlat), A(Natural)) => Some(Fourth(PerfectQuality::DoubleAugmented)),
            (E(DoubleFlat), B(DoubleFlat)) => Some(Fifth(PerfectQuality::Perfect)),
            (E(DoubleFlat), B(Flat)) => Some(Fifth(PerfectQuality::Augmented)),
            (E(DoubleFlat), B(Natural)) => Some(Fifth(PerfectQuality::DoubleAugmented)),
            (E(DoubleFlat), C(DoubleFlat)) => Some(Sixth(MajorQuality::Minor)),
            (E(DoubleFlat), C(Flat)) => Some(Sixth(MajorQuality::Major)),
            (E(DoubleFlat), C(Natural)) => Some(Sixth(MajorQuality::Augmented)),
            (E(DoubleFlat), D(DoubleFlat)) => Some(Seventh(MajorQuality::Minor)),
            (E(DoubleFlat), D(Flat)) => Some(Seventh(MajorQuality::Major)),
            (E(DoubleFlat), D(Natural)) => Some(Seventh(MajorQuality::Augmented)),

            (E(Flat), E(DoubleFlat)) => Some(First(PerfectQuality::Diminished)),
            (E(Flat), E(Flat)) => Some(First(PerfectQuality::Perfect)),
            (E(Flat), E(Natural)) => Some(First(PerfectQuality::Augmented)),
            (E(Flat), F(DoubleFlat)) => Some(Second(MajorQuality::Diminished)),
            (E(Flat), F(Flat)) => Some(Second(MajorQuality::Minor)),
            (E(Flat), F(Natural)) => Some(Second(MajorQuality::Major)),
            (E(Flat), G(DoubleFlat)) => Some(Third(MajorQuality::Diminished)),
            (E(Flat), G(Flat)) => Some(Third(MajorQuality::Minor)),
            (E(Flat), G(Natural)) => Some(Third(MajorQuality::Major)),
            (E(Flat), A(DoubleFlat)) => Some(Fourth(PerfectQuality::Diminished)),
            (E(Flat), A(Flat)) => Some(Fourth(PerfectQuality::Perfect)),
            (E(Flat), A(Natural)) => Some(Fourth(PerfectQuality::Augmented)),
            (E(Flat), B(DoubleFlat)) => Some(Fifth(PerfectQuality::Diminished)),
            (E(Flat), B(Flat)) => Some(Fifth(PerfectQuality::Perfect)),
            (E(Flat), B(Natural)) => Some(Fifth(PerfectQuality::Augmented)),
            (E(Flat), C(DoubleFlat)) => Some(Sixth(MajorQuality::Diminished)),
            (E(Flat), C(Flat)) => Some(Sixth(MajorQuality::Minor)),
            (E(Flat), C(Natural)) => Some(Sixth(MajorQuality::Major)),
            (E(Flat), D(DoubleFlat)) => Some(Seventh(MajorQuality::Diminished)),
            (E(Flat), D(Flat)) => Some(Seventh(MajorQuality::Minor)),
            (E(Flat), D(Natural)) => Some(Seventh(MajorQuality::Major)),

            (E(Natural), E(DoubleFlat)) => Some(First(PerfectQuality::DoubleDiminished)),
            (E(Natural), E(Flat)) => Some(First(PerfectQuality::Diminished)),
            (E(Natural), E(Natural)) => Some(First(PerfectQuality::Perfect)),
            (E(Natural), E(Sharp)) => Some(First(PerfectQuality::Augmented)),
            (E(Natural), E(DoubleSharp)) => Some(First(PerfectQuality::DoubleAugmented)),
            (E(Natural), F(DoubleFlat)) => Some(Second(MajorQuality::DoubleDiminished)),
            (E(Natural), F(Flat)) => Some(Second(MajorQuality::Diminished)),
            (E(Natural), F(Natural)) => Some(Second(MajorQuality::Minor)),
            (E(Natural), F(Sharp)) => Some(Second(MajorQuality::Major)),
            (E(Natural), F(DoubleSharp)) => Some(Second(MajorQuality::Augmented)),
            (E(Natural), G(DoubleFlat)) => Some(Third(MajorQuality::DoubleDiminished)),
            (E(Natural), G(Flat)) => Some(Third(MajorQuality::Diminished)),
            (E(Natural), G(Natural)) => Some(Third(MajorQuality::Minor)),
            (E(Natural), G(Sharp)) => Some(Third(MajorQuality::Major)),
            (E(Natural), G(DoubleSharp)) => Some(Third(MajorQuality::Augmented)),
            (E(Natural), A(DoubleFlat)) => Some(Fourth(PerfectQuality::DoubleDiminished)),
            (E(Natural), A(Flat)) => Some(Fourth(PerfectQuality::Diminished)),
            (E(Natural), A(Natural)) => Some(Fourth(PerfectQuality::Perfect)),
            (E(Natural), A(Sharp)) => Some(Fourth(PerfectQuality::Augmented)),
            (E(Natural), A(DoubleSharp)) => Some(Fourth(PerfectQuality::DoubleAugmented)),
            (E(Natural), B(DoubleFlat)) => Some(Fifth(PerfectQuality::DoubleDiminished)),
            (E(Natural), B(Flat)) => Some(Fifth(PerfectQuality::Diminished)),
            (E(Natural), B(Natural)) => Some(Fifth(PerfectQuality::Perfect)),
            (E(Natural), B(Sharp)) => Some(Fifth(PerfectQuality::Augmented)),
            (E(Natural), B(DoubleSharp)) => Some(Fifth(PerfectQuality::DoubleAugmented)),
            (E(Natural), C(DoubleFlat)) => Some(Sixth(MajorQuality::DoubleDiminished)),
            (E(Natural), C(Flat)) => Some(Sixth(MajorQuality::Diminished)),
            (E(Natural), C(Natural)) => Some(Sixth(MajorQuality::Minor)),
            (E(Natural), C(Sharp)) => Some(Sixth(MajorQuality::Major)),
            (E(Natural), C(DoubleSharp)) => Some(Sixth(MajorQuality::Augmented)),
            (E(Natural), D(DoubleFlat)) => Some(Seventh(MajorQuality::DoubleDiminished)),
            (E(Natural), D(Flat)) => Some(Seventh(MajorQuality::Diminished)),
            (E(Natural), D(Natural)) => Some(Seventh(MajorQuality::Minor)),
            (E(Natural), D(Sharp)) => Some(Seventh(MajorQuality::Major)),
            (E(Natural), D(DoubleSharp)) => Some(Seventh(MajorQuality::Augmented)),

            (E(Sharp), E(Natural)) => Some(First(PerfectQuality::Diminished)),
            (E(Sharp), E(Sharp)) => Some(First(PerfectQuality::Perfect)),
            (E(Sharp), E(DoubleSharp)) => Some(First(PerfectQuality::Augmented)),
            (E(Sharp), F(Natural)) => Some(Second(MajorQuality::Diminished)),
            (E(Sharp), F(Sharp)) => Some(Second(MajorQuality::Minor)),
            (E(Sharp), F(DoubleSharp)) => Some(Second(MajorQuality::Major)),
            (E(Sharp), G(Natural)) => Some(Third(MajorQuality::Diminished)),
            (E(Sharp), G(Sharp)) => Some(Third(MajorQuality::Minor)),
            (E(Sharp), G(DoubleSharp)) => Some(Third(MajorQuality::Major)),
            (E(Sharp), A(Natural)) => Some(Fourth(PerfectQuality::Diminished)),
            (E(Sharp), A(Sharp)) => Some(Fourth(PerfectQuality::Perfect)),
            (E(Sharp), A(DoubleSharp)) => Some(Fourth(PerfectQuality::Augmented)),
            (E(Sharp), B(Natural)) => Some(Fifth(PerfectQuality::Diminished)),
            (E(Sharp), B(Sharp)) => Some(Fifth(PerfectQuality::Perfect)),
            (E(Sharp), B(DoubleSharp)) => Some(Fifth(PerfectQuality::Augmented)),
            (E(Sharp), C(Natural)) => Some(Sixth(MajorQuality::Diminished)),
            (E(Sharp), C(Sharp)) => Some(Sixth(MajorQuality::Minor)),
            (E(Sharp), C(DoubleSharp)) => Some(Sixth(MajorQuality::Major)),
            (E(Sharp), D(Natural)) => Some(Seventh(MajorQuality::Diminished)),
            (E(Sharp), D(Sharp)) => Some(Seventh(MajorQuality::Minor)),
            (E(Sharp), D(DoubleSharp)) => Some(Seventh(MajorQuality::Major)),

            (E(DoubleSharp), E(Natural)) => Some(First(PerfectQuality::DoubleDiminished)),
            (E(DoubleSharp), E(Sharp)) => Some(First(PerfectQuality::Diminished)),
            (E(DoubleSharp), E(DoubleSharp)) => Some(First(PerfectQuality::Perfect)),
            (E(DoubleSharp), F(Natural)) => Some(Second(MajorQuality::DoubleDiminished)),
            (E(DoubleSharp), F(Sharp)) => Some(Second(MajorQuality::Diminished)),
            (E(DoubleSharp), F(DoubleSharp)) => Some(Second(MajorQuality::Minor)),
            (E(DoubleSharp), G(Natural)) => Some(Third(MajorQuality::DoubleDiminished)),
            (E(DoubleSharp), G(Sharp)) => Some(Third(MajorQuality::Diminished)),
            (E(DoubleSharp), G(DoubleSharp)) => Some(Third(MajorQuality::Minor)),
            (E(DoubleSharp), A(Natural)) => Some(Fourth(PerfectQuality::DoubleDiminished)),
            (E(DoubleSharp), A(Sharp)) => Some(Fourth(PerfectQuality::Diminished)),
            (E(DoubleSharp), A(DoubleSharp)) => Some(Fourth(PerfectQuality::Perfect)),
            (E(DoubleSharp), B(Natural)) => Some(Fifth(PerfectQuality::DoubleDiminished)),
            (E(DoubleSharp), B(Sharp)) => Some(Fifth(PerfectQuality::Diminished)),
            (E(DoubleSharp), B(DoubleSharp)) => Some(Fifth(PerfectQuality::Perfect)),
            (E(DoubleSharp), C(Natural)) => Some(Sixth(MajorQuality::DoubleDiminished)),
            (E(DoubleSharp), C(Sharp)) => Some(Sixth(MajorQuality::Diminished)),
            (E(DoubleSharp), C(DoubleSharp)) => Some(Sixth(MajorQuality::Minor)),
            (E(DoubleSharp), D(Natural)) => Some(Seventh(MajorQuality::DoubleDiminished)),
            (E(DoubleSharp), D(Sharp)) => Some(Seventh(MajorQuality::Diminished)),
            (E(DoubleSharp), D(DoubleSharp)) => Some(Seventh(MajorQuality::Minor)),

            // Note F(_)
            (F(DoubleFlat), F(DoubleFlat)) => Some(First(PerfectQuality::Perfect)),
            (F(DoubleFlat), F(Flat)) => Some(First(PerfectQuality::Augmented)),
            (F(DoubleFlat), F(Natural)) => Some(First(PerfectQuality::DoubleAugmented)),
            (F(DoubleFlat), G(DoubleFlat)) => Some(Second(MajorQuality::Major)),
            (F(DoubleFlat), G(Flat)) => Some(Second(MajorQuality::Augmented)),
            (F(DoubleFlat), G(Natural)) => Some(Second(MajorQuality::DoubleAugmented)),
            (F(DoubleFlat), A(DoubleFlat)) => Some(Third(MajorQuality::Major)),
            (F(DoubleFlat), A(Flat)) => Some(Third(MajorQuality::Augmented)),
            (F(DoubleFlat), A(Natural)) => Some(Third(MajorQuality::DoubleAugmented)),
            (F(DoubleFlat), B(DoubleFlat)) => Some(Fourth(PerfectQuality::Augmented)),
            (F(DoubleFlat), B(Flat)) => Some(Fourth(PerfectQuality::DoubleAugmented)),
            (F(DoubleFlat), B(Natural)) => Some(Fourth(PerfectQuality::TripleAugmented)),
            (F(DoubleFlat), C(DoubleFlat)) => Some(Fifth(PerfectQuality::Perfect)),
            (F(DoubleFlat), C(Flat)) => Some(Fifth(PerfectQuality::Augmented)),
            (F(DoubleFlat), C(Natural)) => Some(Fifth(PerfectQuality::DoubleAugmented)),
            (F(DoubleFlat), D(DoubleFlat)) => Some(Sixth(MajorQuality::Major)),
            (F(DoubleFlat), D(Flat)) => Some(Sixth(MajorQuality::Augmented)),
            (F(DoubleFlat), D(Natural)) => Some(Sixth(MajorQuality::DoubleAugmented)),
            (F(DoubleFlat), E(DoubleFlat)) => Some(Seventh(MajorQuality::Major)),
            (F(DoubleFlat), E(Flat)) => Some(Seventh(MajorQuality::Augmented)),
            (F(DoubleFlat), E(Natural)) => Some(Seventh(MajorQuality::DoubleAugmented)),

            (F(Flat), F(DoubleFlat)) => Some(First(PerfectQuality::Diminished)),
            (F(Flat), F(Flat)) => Some(First(PerfectQuality::Perfect)),
            (F(Flat), F(Natural)) => Some(First(PerfectQuality::Augmented)),
            (F(Flat), G(DoubleFlat)) => Some(Second(MajorQuality::Minor)),
            (F(Flat), G(Flat)) => Some(Second(MajorQuality::Major)),
            (F(Flat), G(Natural)) => Some(Second(MajorQuality::Augmented)),
            (F(Flat), A(DoubleFlat)) => Some(Third(MajorQuality::Minor)),
            (F(Flat), A(Flat)) => Some(Third(MajorQuality::Major)),
            (F(Flat), A(Natural)) => Some(Third(MajorQuality::Augmented)),
            (F(Flat), B(DoubleFlat)) => Some(Fourth(PerfectQuality::Perfect)),
            (F(Flat), B(Flat)) => Some(Fourth(PerfectQuality::Augmented)),
            (F(Flat), B(Natural)) => Some(Fourth(PerfectQuality::DoubleAugmented)),
            (F(Flat), C(DoubleFlat)) => Some(Fifth(PerfectQuality::Diminished)),
            (F(Flat), C(Flat)) => Some(Fifth(PerfectQuality::Perfect)),
            (F(Flat), C(Natural)) => Some(Fifth(PerfectQuality::Augmented)),
            (F(Flat), D(DoubleFlat)) => Some(Sixth(MajorQuality::Minor)),
            (F(Flat), D(Flat)) => Some(Sixth(MajorQuality::Major)),
            (F(Flat), D(Natural)) => Some(Sixth(MajorQuality::Augmented)),
            (F(Flat), E(DoubleFlat)) => Some(Seventh(MajorQuality::Minor)),
            (F(Flat), E(Flat)) => Some(Seventh(MajorQuality::Major)),
            (F(Flat), E(Natural)) => Some(Seventh(MajorQuality::Augmented)),

            (F(Natural), F(DoubleFlat)) => Some(First(PerfectQuality::DoubleDiminished)),
            (F(Natural), F(Flat)) => Some(First(PerfectQuality::Diminished)),
            (F(Natural), F(Natural)) => Some(First(PerfectQuality::Perfect)),
            (F(Natural), F(Sharp)) => Some(First(PerfectQuality::Augmented)),
            (F(Natural), F(DoubleSharp)) => Some(First(PerfectQuality::DoubleAugmented)),
            (F(Natural), G(DoubleFlat)) => Some(Second(MajorQuality::Diminished)),
            (F(Natural), G(Flat)) => Some(Second(MajorQuality::Minor)),
            (F(Natural), G(Natural)) => Some(Second(MajorQuality::Major)),
            (F(Natural), G(Sharp)) => Some(Second(MajorQuality::Augmented)),
            (F(Natural), G(DoubleSharp)) => Some(Second(MajorQuality::DoubleAugmented)),
            (F(Natural), A(DoubleFlat)) => Some(Third(MajorQuality::Diminished)),
            (F(Natural), A(Flat)) => Some(Third(MajorQuality::Minor)),
            (F(Natural), A(Natural)) => Some(Third(MajorQuality::Major)),
            (F(Natural), A(Sharp)) => Some(Third(MajorQuality::Augmented)),
            (F(Natural), A(DoubleSharp)) => Some(Third(MajorQuality::DoubleAugmented)),
            (F(Natural), B(DoubleFlat)) => Some(Fourth(PerfectQuality::Diminished)),
            (F(Natural), B(Flat)) => Some(Fourth(PerfectQuality::Perfect)),
            (F(Natural), B(Natural)) => Some(Fourth(PerfectQuality::Augmented)),
            (F(Natural), B(Sharp)) => Some(Fourth(PerfectQuality::DoubleAugmented)),
            (F(Natural), B(DoubleSharp)) => Some(Fourth(PerfectQuality::TripleAugmented)),
            (F(Natural), C(DoubleFlat)) => Some(Fifth(PerfectQuality::DoubleDiminished)),
            (F(Natural), C(Flat)) => Some(Fifth(PerfectQuality::Diminished)),
            (F(Natural), C(Natural)) => Some(Fifth(PerfectQuality::Perfect)),
            (F(Natural), C(Sharp)) => Some(Fifth(PerfectQuality::Augmented)),
            (F(Natural), C(DoubleSharp)) => Some(Fifth(PerfectQuality::DoubleAugmented)),
            (F(Natural), D(DoubleFlat)) => Some(Sixth(MajorQuality::Diminished)),
            (F(Natural), D(Flat)) => Some(Sixth(MajorQuality::Minor)),
            (F(Natural), D(Natural)) => Some(Sixth(MajorQuality::Major)),
            (F(Natural), D(Sharp)) => Some(Sixth(MajorQuality::Augmented)),
            (F(Natural), D(DoubleSharp)) => Some(Sixth(MajorQuality::DoubleAugmented)),
            (F(Natural), E(DoubleFlat)) => Some(Seventh(MajorQuality::Diminished)),
            (F(Natural), E(Flat)) => Some(Seventh(MajorQuality::Minor)),
            (F(Natural), E(Natural)) => Some(Seventh(MajorQuality::Major)),
            (F(Natural), E(Sharp)) => Some(Seventh(MajorQuality::Augmented)),
            (F(Natural), E(DoubleSharp)) => Some(Seventh(MajorQuality::DoubleAugmented)),

            (F(Sharp), F(Natural)) => Some(First(PerfectQuality::Diminished)),
            (F(Sharp), F(Sharp)) => Some(First(PerfectQuality::Perfect)),
            (F(Sharp), F(DoubleSharp)) => Some(First(PerfectQuality::Augmented)),
            (F(Sharp), G(Natural)) => Some(Second(MajorQuality::Minor)),
            (F(Sharp), G(Sharp)) => Some(Second(MajorQuality::Major)),
            (F(Sharp), G(DoubleSharp)) => Some(Second(MajorQuality::Augmented)),
            (F(Sharp), A(Natural)) => Some(Third(MajorQuality::Minor)),
            (F(Sharp), A(Sharp)) => Some(Third(MajorQuality::Major)),
            (F(Sharp), A(DoubleSharp)) => Some(Third(MajorQuality::Augmented)),
            (F(Sharp), B(Natural)) => Some(Fourth(PerfectQuality::Perfect)),
            (F(Sharp), B(Sharp)) => Some(Fourth(PerfectQuality::Augmented)),
            (F(Sharp), B(DoubleSharp)) => Some(Fourth(PerfectQuality::DoubleAugmented)),
            (F(Sharp), C(Natural)) => Some(Fifth(PerfectQuality::Diminished)),
            (F(Sharp), C(Sharp)) => Some(Fifth(PerfectQuality::Perfect)),
            (F(Sharp), C(DoubleSharp)) => Some(Fifth(PerfectQuality::Augmented)),
            (F(Sharp), D(Natural)) => Some(Sixth(MajorQuality::Minor)),
            (F(Sharp), D(Sharp)) => Some(Sixth(MajorQuality::Major)),
            (F(Sharp), D(DoubleSharp)) => Some(Sixth(MajorQuality::Augmented)),
            (F(Sharp), E(Natural)) => Some(Seventh(MajorQuality::Minor)),
            (F(Sharp), E(Sharp)) => Some(Seventh(MajorQuality::Major)),
            (F(Sharp), E(DoubleSharp)) => Some(Seventh(MajorQuality::Augmented)),

            (F(DoubleSharp), F(Natural)) => Some(First(PerfectQuality::DoubleDiminished)),
            (F(DoubleSharp), F(Sharp)) => Some(First(PerfectQuality::Diminished)),
            (F(DoubleSharp), F(DoubleSharp)) => Some(First(PerfectQuality::Perfect)),
            (F(DoubleSharp), G(Natural)) => Some(Second(MajorQuality::Diminished)),
            (F(DoubleSharp), G(Sharp)) => Some(Second(MajorQuality::Minor)),
            (F(DoubleSharp), G(DoubleSharp)) => Some(Second(MajorQuality::Major)),
            (F(DoubleSharp), A(Natural)) => Some(Third(MajorQuality::Diminished)),
            (F(DoubleSharp), A(Sharp)) => Some(Third(MajorQuality::Minor)),
            (F(DoubleSharp), A(DoubleSharp)) => Some(Third(MajorQuality::Major)),
            (F(DoubleSharp), B(Natural)) => Some(Fourth(PerfectQuality::Diminished)),
            (F(DoubleSharp), B(Sharp)) => Some(Fourth(PerfectQuality::Perfect)),
            (F(DoubleSharp), B(DoubleSharp)) => Some(Fourth(PerfectQuality::Augmented)),
            (F(DoubleSharp), C(Natural)) => Some(Fifth(PerfectQuality::DoubleDiminished)),
            (F(DoubleSharp), C(Sharp)) => Some(Fifth(PerfectQuality::Diminished)),
            (F(DoubleSharp), C(DoubleSharp)) => Some(Fifth(PerfectQuality::Perfect)),
            (F(DoubleSharp), D(Natural)) => Some(Sixth(MajorQuality::Diminished)),
            (F(DoubleSharp), D(Sharp)) => Some(Sixth(MajorQuality::Minor)),
            (F(DoubleSharp), D(DoubleSharp)) => Some(Sixth(MajorQuality::Major)),
            (F(DoubleSharp), E(Natural)) => Some(Seventh(MajorQuality::Diminished)),
            (F(DoubleSharp), E(Sharp)) => Some(Seventh(MajorQuality::Minor)),
            (F(DoubleSharp), E(DoubleSharp)) => Some(Seventh(MajorQuality::Major)),

            // Note G(_)
            (G(DoubleFlat), G(DoubleFlat)) => Some(First(PerfectQuality::Perfect)),
            (G(DoubleFlat), G(Flat)) => Some(First(PerfectQuality::Augmented)),
            (G(DoubleFlat), G(Natural)) => Some(First(PerfectQuality::DoubleAugmented)),
            (G(DoubleFlat), A(DoubleFlat)) => Some(Second(MajorQuality::Major)),
            (G(DoubleFlat), A(Flat)) => Some(Second(MajorQuality::Augmented)),
            (G(DoubleFlat), A(Natural)) => Some(Second(MajorQuality::DoubleAugmented)),
            (G(DoubleFlat), B(DoubleFlat)) => Some(Third(MajorQuality::Major)),
            (G(DoubleFlat), B(Flat)) => Some(Third(MajorQuality::Augmented)),
            (G(DoubleFlat), B(Natural)) => Some(Third(MajorQuality::DoubleAugmented)),
            (G(DoubleFlat), C(DoubleFlat)) => Some(Fourth(PerfectQuality::Perfect)),
            (G(DoubleFlat), C(Flat)) => Some(Fourth(PerfectQuality::Augmented)),
            (G(DoubleFlat), C(Natural)) => Some(Fourth(PerfectQuality::DoubleAugmented)),
            (G(DoubleFlat), D(DoubleFlat)) => Some(Fifth(PerfectQuality::Perfect)),
            (G(DoubleFlat), D(Flat)) => Some(Fifth(PerfectQuality::Augmented)),
            (G(DoubleFlat), D(Natural)) => Some(Fifth(PerfectQuality::DoubleAugmented)),
            (G(DoubleFlat), E(DoubleFlat)) => Some(Sixth(MajorQuality::Major)),
            (G(DoubleFlat), E(Flat)) => Some(Sixth(MajorQuality::Augmented)),
            (G(DoubleFlat), E(Natural)) => Some(Sixth(MajorQuality::DoubleAugmented)),
            (G(DoubleFlat), F(DoubleFlat)) => Some(Seventh(MajorQuality::Minor)),
            (G(DoubleFlat), F(Flat)) => Some(Seventh(MajorQuality::Major)),
            (G(DoubleFlat), F(Natural)) => Some(Seventh(MajorQuality::Augmented)),

            (G(Flat), G(DoubleFlat)) => Some(First(PerfectQuality::Diminished)),
            (G(Flat), G(Flat)) => Some(First(PerfectQuality::Perfect)),
            (G(Flat), G(Natural)) => Some(First(PerfectQuality::Augmented)),
            (G(Flat), A(DoubleFlat)) => Some(Second(MajorQuality::Minor)),
            (G(Flat), A(Flat)) => Some(Second(MajorQuality::Major)),
            (G(Flat), A(Natural)) => Some(Second(MajorQuality::Augmented)),
            (G(Flat), B(DoubleFlat)) => Some(Third(MajorQuality::Minor)),
            (G(Flat), B(Flat)) => Some(Third(MajorQuality::Major)),
            (G(Flat), B(Natural)) => Some(Third(MajorQuality::Augmented)),
            (G(Flat), C(DoubleFlat)) => Some(Fourth(PerfectQuality::Diminished)),
            (G(Flat), C(Flat)) => Some(Fourth(PerfectQuality::Perfect)),
            (G(Flat), C(Natural)) => Some(Fourth(PerfectQuality::Augmented)),
            (G(Flat), D(DoubleFlat)) => Some(Fifth(PerfectQuality::Diminished)),
            (G(Flat), D(Flat)) => Some(Fifth(PerfectQuality::Perfect)),
            (G(Flat), D(Natural)) => Some(Fifth(PerfectQuality::Augmented)),
            (G(Flat), E(DoubleFlat)) => Some(Sixth(MajorQuality::Minor)),
            (G(Flat), E(Flat)) => Some(Sixth(MajorQuality::Major)),
            (G(Flat), E(Natural)) => Some(Sixth(MajorQuality::Augmented)),
            (G(Flat), F(DoubleFlat)) => Some(Seventh(MajorQuality::Diminished)),
            (G(Flat), F(Flat)) => Some(Seventh(MajorQuality::Minor)),
            (G(Flat), F(Natural)) => Some(Seventh(MajorQuality::Major)),

            (G(Natural), G(DoubleFlat)) => Some(First(PerfectQuality::DoubleDiminished)),
            (G(Natural), G(Flat)) => Some(First(PerfectQuality::Diminished)),
            (G(Natural), G(Natural)) => Some(First(PerfectQuality::Perfect)),
            (G(Natural), G(Sharp)) => Some(First(PerfectQuality::Augmented)),
            (G(Natural), G(DoubleSharp)) => Some(First(PerfectQuality::DoubleAugmented)),
            (G(Natural), A(DoubleFlat)) => Some(Second(MajorQuality::Diminished)),
            (G(Natural), A(Flat)) => Some(Second(MajorQuality::Minor)),
            (G(Natural), A(Natural)) => Some(Second(MajorQuality::Major)),
            (G(Natural), A(Sharp)) => Some(Second(MajorQuality::Augmented)),
            (G(Natural), A(DoubleSharp)) => Some(Second(MajorQuality::DoubleAugmented)),
            (G(Natural), B(DoubleFlat)) => Some(Third(MajorQuality::Diminished)),
            (G(Natural), B(Flat)) => Some(Third(MajorQuality::Minor)),
            (G(Natural), B(Natural)) => Some(Third(MajorQuality::Major)),
            (G(Natural), B(Sharp)) => Some(Third(MajorQuality::Augmented)),
            (G(Natural), B(DoubleSharp)) => Some(Third(MajorQuality::DoubleAugmented)),
            (G(Natural), C(DoubleFlat)) => Some(Fourth(PerfectQuality::DoubleDiminished)),
            (G(Natural), C(Flat)) => Some(Fourth(PerfectQuality::Diminished)),
            (G(Natural), C(Natural)) => Some(Fourth(PerfectQuality::Perfect)),
            (G(Natural), C(Sharp)) => Some(Fourth(PerfectQuality::Augmented)),
            (G(Natural), C(DoubleSharp)) => Some(Fourth(PerfectQuality::DoubleAugmented)),
            (G(Natural), D(DoubleFlat)) => Some(Fifth(PerfectQuality::DoubleDiminished)),
            (G(Natural), D(Flat)) => Some(Fifth(PerfectQuality::Diminished)),
            (G(Natural), D(Natural)) => Some(Fifth(PerfectQuality::Perfect)),
            (G(Natural), D(Sharp)) => Some(Fifth(PerfectQuality::Augmented)),
            (G(Natural), D(DoubleSharp)) => Some(Fifth(PerfectQuality::DoubleAugmented)),
            (G(Natural), E(DoubleFlat)) => Some(Sixth(MajorQuality::Diminished)),
            (G(Natural), E(Flat)) => Some(Sixth(MajorQuality::Minor)),
            (G(Natural), E(Natural)) => Some(Sixth(MajorQuality::Major)),
            (G(Natural), E(Sharp)) => Some(Sixth(MajorQuality::Augmented)),
            (G(Natural), E(DoubleSharp)) => Some(Sixth(MajorQuality::DoubleAugmented)),
            (G(Natural), F(DoubleFlat)) => Some(Seventh(MajorQuality::DoubleDiminished)),
            (G(Natural), F(Flat)) => Some(Seventh(MajorQuality::Diminished)),
            (G(Natural), F(Natural)) => Some(Seventh(MajorQuality::Minor)),
            (G(Natural), F(Sharp)) => Some(Seventh(MajorQuality::Major)),
            (G(Natural), F(DoubleSharp)) => Some(Seventh(MajorQuality::Augmented)),

            (G(Sharp), G(Natural)) => Some(First(PerfectQuality::Diminished)),
            (G(Sharp), G(Sharp)) => Some(First(PerfectQuality::Perfect)),
            (G(Sharp), G(DoubleSharp)) => Some(First(PerfectQuality::Augmented)),
            (G(Sharp), A(Natural)) => Some(Second(MajorQuality::Minor)),
            (G(Sharp), A(Sharp)) => Some(Second(MajorQuality::Major)),
            (G(Sharp), A(DoubleSharp)) => Some(Second(MajorQuality::Augmented)),
            (G(Sharp), B(Natural)) => Some(Third(MajorQuality::Minor)),
            (G(Sharp), B(Sharp)) => Some(Third(MajorQuality::Major)),
            (G(Sharp), B(DoubleSharp)) => Some(Third(MajorQuality::Augmented)),
            (G(Sharp), C(Natural)) => Some(Fourth(PerfectQuality::Diminished)),
            (G(Sharp), C(Sharp)) => Some(Fourth(PerfectQuality::Perfect)),
            (G(Sharp), C(DoubleSharp)) => Some(Fourth(PerfectQuality::Augmented)),
            (G(Sharp), D(Natural)) => Some(Fifth(PerfectQuality::Diminished)),
            (G(Sharp), D(Sharp)) => Some(Fifth(PerfectQuality::Perfect)),
            (G(Sharp), D(DoubleSharp)) => Some(Fifth(PerfectQuality::Augmented)),
            (G(Sharp), E(Natural)) => Some(Sixth(MajorQuality::Minor)),
            (G(Sharp), E(Sharp)) => Some(Sixth(MajorQuality::Major)),
            (G(Sharp), E(DoubleSharp)) => Some(Sixth(MajorQuality::Augmented)),
            (G(Sharp), F(Natural)) => Some(Seventh(MajorQuality::Diminished)),
            (G(Sharp), F(Sharp)) => Some(Seventh(MajorQuality::Minor)),
            (G(Sharp), F(DoubleSharp)) => Some(Seventh(MajorQuality::Major)),

            (G(DoubleSharp), G(Natural)) => Some(First(PerfectQuality::DoubleDiminished)),
            (G(DoubleSharp), G(Sharp)) => Some(First(PerfectQuality::Diminished)),
            (G(DoubleSharp), G(DoubleSharp)) => Some(First(PerfectQuality::Perfect)),
            (G(DoubleSharp), A(Natural)) => Some(Second(MajorQuality::Diminished)),
            (G(DoubleSharp), A(Sharp)) => Some(Second(MajorQuality::Minor)),
            (G(DoubleSharp), A(DoubleSharp)) => Some(Second(MajorQuality::Major)),
            (G(DoubleSharp), B(Natural)) => Some(Third(MajorQuality::Diminished)),
            (G(DoubleSharp), B(Sharp)) => Some(Third(MajorQuality::Minor)),
            (G(DoubleSharp), B(DoubleSharp)) => Some(Third(MajorQuality::Major)),
            (G(DoubleSharp), C(Natural)) => Some(Fourth(PerfectQuality::DoubleDiminished)),
            (G(DoubleSharp), C(Sharp)) => Some(Fourth(PerfectQuality::Diminished)),
            (G(DoubleSharp), C(DoubleSharp)) => Some(Fourth(PerfectQuality::Perfect)),
            (G(DoubleSharp), D(Natural)) => Some(Fifth(PerfectQuality::DoubleDiminished)),
            (G(DoubleSharp), D(Sharp)) => Some(Fifth(PerfectQuality::Diminished)),
            (G(DoubleSharp), D(DoubleSharp)) => Some(Fifth(PerfectQuality::Perfect)),
            (G(DoubleSharp), E(Natural)) => Some(Sixth(MajorQuality::Diminished)),
            (G(DoubleSharp), E(Sharp)) => Some(Sixth(MajorQuality::Minor)),
            (G(DoubleSharp), E(DoubleSharp)) => Some(Sixth(MajorQuality::Major)),
            (G(DoubleSharp), F(Natural)) => Some(Seventh(MajorQuality::DoubleDiminished)),
            (G(DoubleSharp), F(Sharp)) => Some(Seventh(MajorQuality::Diminished)),
            (G(DoubleSharp), F(DoubleSharp)) => Some(Seventh(MajorQuality::Minor)),

            // Note A(_)
            (A(DoubleFlat), A(DoubleFlat)) => Some(First(PerfectQuality::Perfect)),
            (A(DoubleFlat), A(Flat)) => Some(First(PerfectQuality::Augmented)),
            (A(DoubleFlat), A(Natural)) => Some(First(PerfectQuality::DoubleAugmented)),
            (A(DoubleFlat), B(DoubleFlat)) => Some(Second(MajorQuality::Major)),
            (A(DoubleFlat), B(Flat)) => Some(Second(MajorQuality::Augmented)),
            (A(DoubleFlat), B(Natural)) => Some(Second(MajorQuality::DoubleAugmented)),
            (A(DoubleFlat), C(DoubleFlat)) => Some(Third(MajorQuality::Minor)),
            (A(DoubleFlat), C(Flat)) => Some(Third(MajorQuality::Major)),
            (A(DoubleFlat), C(Natural)) => Some(Third(MajorQuality::Augmented)),
            (A(DoubleFlat), D(DoubleFlat)) => Some(Fourth(PerfectQuality::Perfect)),
            (A(DoubleFlat), D(Flat)) => Some(Fourth(PerfectQuality::Augmented)),
            (A(DoubleFlat), D(Natural)) => Some(Fourth(PerfectQuality::DoubleAugmented)),
            (A(DoubleFlat), E(DoubleFlat)) => Some(Fifth(PerfectQuality::Perfect)),
            (A(DoubleFlat), E(Flat)) => Some(Fifth(PerfectQuality::Augmented)),
            (A(DoubleFlat), E(Natural)) => Some(Fifth(PerfectQuality::DoubleAugmented)),
            (A(DoubleFlat), F(DoubleFlat)) => Some(Sixth(MajorQuality::Minor)),
            (A(DoubleFlat), F(Flat)) => Some(Sixth(MajorQuality::Major)),
            (A(DoubleFlat), F(Natural)) => Some(Sixth(MajorQuality::Augmented)),
            (A(DoubleFlat), G(DoubleFlat)) => Some(Seventh(MajorQuality::Minor)),
            (A(DoubleFlat), G(Flat)) => Some(Seventh(MajorQuality::Major)),
            (A(DoubleFlat), G(Natural)) => Some(Seventh(MajorQuality::Augmented)),

            (A(Flat), A(DoubleFlat)) => Some(First(PerfectQuality::Diminished)),
            (A(Flat), A(Flat)) => Some(First(PerfectQuality::Perfect)),
            (A(Flat), A(Natural)) => Some(First(PerfectQuality::Augmented)),
            (A(Flat), B(DoubleFlat)) => Some(Second(MajorQuality::Minor)),
            (A(Flat), B(Flat)) => Some(Second(MajorQuality::Major)),
            (A(Flat), B(Natural)) => Some(Second(MajorQuality::Augmented)),
            (A(Flat), C(DoubleFlat)) => Some(Third(MajorQuality::Diminished)),
            (A(Flat), C(Flat)) => Some(Third(MajorQuality::Minor)),
            (A(Flat), C(Natural)) => Some(Third(MajorQuality::Major)),
            (A(Flat), D(DoubleFlat)) => Some(Fourth(PerfectQuality::Diminished)),
            (A(Flat), D(Flat)) => Some(Fourth(PerfectQuality::Perfect)),
            (A(Flat), D(Natural)) => Some(Fourth(PerfectQuality::Augmented)),
            (A(Flat), E(DoubleFlat)) => Some(Fifth(PerfectQuality::Diminished)),
            (A(Flat), E(Flat)) => Some(Fifth(PerfectQuality::Perfect)),
            (A(Flat), E(Natural)) => Some(Fifth(PerfectQuality::Augmented)),
            (A(Flat), F(DoubleFlat)) => Some(Sixth(MajorQuality::Diminished)),
            (A(Flat), F(Flat)) => Some(Sixth(MajorQuality::Minor)),
            (A(Flat), F(Natural)) => Some(Sixth(MajorQuality::Major)),
            (A(Flat), G(DoubleFlat)) => Some(Seventh(MajorQuality::Diminished)),
            (A(Flat), G(Flat)) => Some(Seventh(MajorQuality::Minor)),
            (A(Flat), G(Natural)) => Some(Seventh(MajorQuality::Major)),

            (A(Natural), A(DoubleFlat)) => Some(First(PerfectQuality::DoubleDiminished)),
            (A(Natural), A(Flat)) => Some(First(PerfectQuality::Diminished)),
            (A(Natural), A(Natural)) => Some(First(PerfectQuality::Perfect)),
            (A(Natural), A(Sharp)) => Some(First(PerfectQuality::Augmented)),
            (A(Natural), A(DoubleSharp)) => Some(First(PerfectQuality::DoubleAugmented)),
            (A(Natural), B(DoubleFlat)) => Some(Second(MajorQuality::Diminished)),
            (A(Natural), B(Flat)) => Some(Second(MajorQuality::Minor)),
            (A(Natural), B(Natural)) => Some(Second(MajorQuality::Major)),
            (A(Natural), B(Sharp)) => Some(Second(MajorQuality::Augmented)),
            (A(Natural), B(DoubleSharp)) => Some(Second(MajorQuality::DoubleAugmented)),
            (A(Natural), C(DoubleFlat)) => Some(Third(MajorQuality::DoubleDiminished)),
            (A(Natural), C(Flat)) => Some(Third(MajorQuality::Diminished)),
            (A(Natural), C(Natural)) => Some(Third(MajorQuality::Minor)),
            (A(Natural), C(Sharp)) => Some(Third(MajorQuality::Major)),
            (A(Natural), C(DoubleSharp)) => Some(Third(MajorQuality::Augmented)),
            (A(Natural), D(DoubleFlat)) => Some(Fourth(PerfectQuality::DoubleDiminished)),
            (A(Natural), D(Flat)) => Some(Fourth(PerfectQuality::Diminished)),
            (A(Natural), D(Natural)) => Some(Fourth(PerfectQuality::Perfect)),
            (A(Natural), D(Sharp)) => Some(Fourth(PerfectQuality::Augmented)),
            (A(Natural), D(DoubleSharp)) => Some(Fourth(PerfectQuality::DoubleAugmented)),
            (A(Natural), E(DoubleFlat)) => Some(Fifth(PerfectQuality::DoubleDiminished)),
            (A(Natural), E(Flat)) => Some(Fifth(PerfectQuality::Diminished)),
            (A(Natural), E(Natural)) => Some(Fifth(PerfectQuality::Perfect)),
            (A(Natural), E(Sharp)) => Some(Fifth(PerfectQuality::Augmented)),
            (A(Natural), E(DoubleSharp)) => Some(Fifth(PerfectQuality::DoubleAugmented)),
            (A(Natural), F(DoubleFlat)) => Some(Sixth(MajorQuality::DoubleDiminished)),
            (A(Natural), F(Flat)) => Some(Sixth(MajorQuality::Diminished)),
            (A(Natural), F(Natural)) => Some(Sixth(MajorQuality::Minor)),
            (A(Natural), F(Sharp)) => Some(Sixth(MajorQuality::Major)),
            (A(Natural), F(DoubleSharp)) => Some(Sixth(MajorQuality::Augmented)),
            (A(Natural), G(DoubleFlat)) => Some(Seventh(MajorQuality::DoubleDiminished)),
            (A(Natural), G(Flat)) => Some(Seventh(MajorQuality::Diminished)),
            (A(Natural), G(Natural)) => Some(Seventh(MajorQuality::Minor)),
            (A(Natural), G(Sharp)) => Some(Seventh(MajorQuality::Major)),
            (A(Natural), G(DoubleSharp)) => Some(Seventh(MajorQuality::Augmented)),

            (A(Sharp), A(Natural)) => Some(First(PerfectQuality::Diminished)),
            (A(Sharp), A(Sharp)) => Some(First(PerfectQuality::Perfect)),
            (A(Sharp), A(DoubleSharp)) => Some(First(PerfectQuality::Augmented)),
            (A(Sharp), B(Natural)) => Some(Second(MajorQuality::Minor)),
            (A(Sharp), B(Sharp)) => Some(Second(MajorQuality::Major)),
            (A(Sharp), B(DoubleSharp)) => Some(Second(MajorQuality::Augmented)),
            (A(Sharp), C(Natural)) => Some(Third(MajorQuality::Diminished)),
            (A(Sharp), C(Sharp)) => Some(Third(MajorQuality::Minor)),
            (A(Sharp), C(DoubleSharp)) => Some(Third(MajorQuality::Major)),
            (A(Sharp), D(Natural)) => Some(Fourth(PerfectQuality::Diminished)),
            (A(Sharp), D(Sharp)) => Some(Fourth(PerfectQuality::Perfect)),
            (A(Sharp), D(DoubleSharp)) => Some(Fourth(PerfectQuality::Augmented)),
            (A(Sharp), E(Natural)) => Some(Fifth(PerfectQuality::Diminished)),
            (A(Sharp), E(Sharp)) => Some(Fifth(PerfectQuality::Perfect)),
            (A(Sharp), E(DoubleSharp)) => Some(Fifth(PerfectQuality::Augmented)),
            (A(Sharp), F(Natural)) => Some(Sixth(MajorQuality::Diminished)),
            (A(Sharp), F(Sharp)) => Some(Sixth(MajorQuality::Minor)),
            (A(Sharp), F(DoubleSharp)) => Some(Sixth(MajorQuality::Major)),
            (A(Sharp), G(Natural)) => Some(Seventh(MajorQuality::Diminished)),
            (A(Sharp), G(Sharp)) => Some(Seventh(MajorQuality::Minor)),
            (A(Sharp), G(DoubleSharp)) => Some(Seventh(MajorQuality::Major)),

            (A(DoubleSharp), A(Natural)) => Some(First(PerfectQuality::DoubleDiminished)),
            (A(DoubleSharp), A(Sharp)) => Some(First(PerfectQuality::Diminished)),
            (A(DoubleSharp), A(DoubleSharp)) => Some(First(PerfectQuality::Perfect)),
            (A(DoubleSharp), B(Natural)) => Some(Second(MajorQuality::Diminished)),
            (A(DoubleSharp), B(Sharp)) => Some(Second(MajorQuality::Minor)),
            (A(DoubleSharp), B(DoubleSharp)) => Some(Second(MajorQuality::Major)),
            (A(DoubleSharp), C(Natural)) => Some(Third(MajorQuality::DoubleDiminished)),
            (A(DoubleSharp), C(Sharp)) => Some(Third(MajorQuality::Diminished)),
            (A(DoubleSharp), C(DoubleSharp)) => Some(Third(MajorQuality::Minor)),
            (A(DoubleSharp), D(Natural)) => Some(Fourth(PerfectQuality::DoubleDiminished)),
            (A(DoubleSharp), D(Sharp)) => Some(Fourth(PerfectQuality::Diminished)),
            (A(DoubleSharp), D(DoubleSharp)) => Some(Fourth(PerfectQuality::Perfect)),
            (A(DoubleSharp), E(Natural)) => Some(Fifth(PerfectQuality::DoubleDiminished)),
            (A(DoubleSharp), E(Sharp)) => Some(Fifth(PerfectQuality::Diminished)),
            (A(DoubleSharp), E(DoubleSharp)) => Some(Fifth(PerfectQuality::Perfect)),
            (A(DoubleSharp), F(Natural)) => Some(Sixth(MajorQuality::DoubleDiminished)),
            (A(DoubleSharp), F(Sharp)) => Some(Sixth(MajorQuality::Diminished)),
            (A(DoubleSharp), F(DoubleSharp)) => Some(Sixth(MajorQuality::Minor)),
            (A(DoubleSharp), G(Natural)) => Some(Seventh(MajorQuality::DoubleDiminished)),
            (A(DoubleSharp), G(Sharp)) => Some(Seventh(MajorQuality::Diminished)),
            (A(DoubleSharp), G(DoubleSharp)) => Some(Seventh(MajorQuality::Minor)),

            // Note B(_)
            (B(DoubleFlat), B(DoubleFlat)) => Some(First(PerfectQuality::Perfect)),
            (B(DoubleFlat), B(Flat)) => Some(First(PerfectQuality::Augmented)),
            (B(DoubleFlat), B(Natural)) => Some(First(PerfectQuality::DoubleAugmented)),
            (B(DoubleFlat), C(DoubleFlat)) => Some(Second(MajorQuality::Minor)),
            (B(DoubleFlat), C(Flat)) => Some(Second(MajorQuality::Major)),
            (B(DoubleFlat), C(Natural)) => Some(Second(MajorQuality::Augmented)),
            (B(DoubleFlat), D(DoubleFlat)) => Some(Third(MajorQuality::Minor)),
            (B(DoubleFlat), D(Flat)) => Some(Third(MajorQuality::Major)),
            (B(DoubleFlat), D(Natural)) => Some(Third(MajorQuality::Augmented)),
            (B(DoubleFlat), E(DoubleFlat)) => Some(Fourth(PerfectQuality::Perfect)),
            (B(DoubleFlat), E(Flat)) => Some(Fourth(PerfectQuality::Augmented)),
            (B(DoubleFlat), E(Natural)) => Some(Fourth(PerfectQuality::DoubleAugmented)),
            (B(DoubleFlat), F(DoubleFlat)) => Some(Fifth(PerfectQuality::Diminished)),
            (B(DoubleFlat), F(Flat)) => Some(Fifth(PerfectQuality::Perfect)),
            (B(DoubleFlat), F(Natural)) => Some(Fifth(PerfectQuality::Augmented)),
            (B(DoubleFlat), G(DoubleFlat)) => Some(Sixth(MajorQuality::Minor)),
            (B(DoubleFlat), G(Flat)) => Some(Sixth(MajorQuality::Major)),
            (B(DoubleFlat), G(Natural)) => Some(Sixth(MajorQuality::Augmented)),
            (B(DoubleFlat), A(DoubleFlat)) => Some(Seventh(MajorQuality::Minor)),
            (B(DoubleFlat), A(Flat)) => Some(Seventh(MajorQuality::Major)),
            (B(DoubleFlat), A(Natural)) => Some(Seventh(MajorQuality::Augmented)),

            (B(Flat), B(DoubleFlat)) => Some(First(PerfectQuality::Diminished)),
            (B(Flat), B(Flat)) => Some(First(PerfectQuality::Perfect)),
            (B(Flat), B(Natural)) => Some(First(PerfectQuality::Augmented)),
            (B(Flat), C(DoubleFlat)) => Some(Second(MajorQuality::Diminished)),
            (B(Flat), C(Flat)) => Some(Second(MajorQuality::Minor)),
            (B(Flat), C(Natural)) => Some(Second(MajorQuality::Major)),
            (B(Flat), D(DoubleFlat)) => Some(Third(MajorQuality::Diminished)),
            (B(Flat), D(Flat)) => Some(Third(MajorQuality::Minor)),
            (B(Flat), D(Natural)) => Some(Third(MajorQuality::Major)),
            (B(Flat), E(DoubleFlat)) => Some(Fourth(PerfectQuality::Diminished)),
            (B(Flat), E(Flat)) => Some(Fourth(PerfectQuality::Perfect)),
            (B(Flat), E(Natural)) => Some(Fourth(PerfectQuality::Augmented)),
            (B(Flat), F(DoubleFlat)) => Some(Fifth(PerfectQuality::DoubleDiminished)),
            (B(Flat), F(Flat)) => Some(Fifth(PerfectQuality::Diminished)),
            (B(Flat), F(Natural)) => Some(Fifth(PerfectQuality::Perfect)),
            (B(Flat), G(DoubleFlat)) => Some(Sixth(MajorQuality::Diminished)),
            (B(Flat), G(Flat)) => Some(Sixth(MajorQuality::Minor)),
            (B(Flat), G(Natural)) => Some(Sixth(MajorQuality::Major)),
            (B(Flat), A(DoubleFlat)) => Some(Seventh(MajorQuality::Diminished)),
            (B(Flat), A(Flat)) => Some(Seventh(MajorQuality::Minor)),
            (B(Flat), A(Natural)) => Some(Seventh(MajorQuality::Major)),

            (B(Natural), B(DoubleFlat)) => Some(First(PerfectQuality::DoubleDiminished)),
            (B(Natural), B(Flat)) => Some(First(PerfectQuality::Diminished)),
            (B(Natural), B(Natural)) => Some(First(PerfectQuality::Perfect)),
            (B(Natural), B(Sharp)) => Some(First(PerfectQuality::Augmented)),
            (B(Natural), B(DoubleSharp)) => Some(First(PerfectQuality::DoubleAugmented)),
            (B(Natural), C(DoubleFlat)) => Some(Second(MajorQuality::DoubleDiminished)),
            (B(Natural), C(Flat)) => Some(Second(MajorQuality::Diminished)),
            (B(Natural), C(Natural)) => Some(Second(MajorQuality::Minor)),
            (B(Natural), C(Sharp)) => Some(Second(MajorQuality::Major)),
            (B(Natural), C(DoubleSharp)) => Some(Second(MajorQuality::Augmented)),
            (B(Natural), D(DoubleFlat)) => Some(Third(MajorQuality::DoubleDiminished)),
            (B(Natural), D(Flat)) => Some(Third(MajorQuality::Diminished)),
            (B(Natural), D(Natural)) => Some(Third(MajorQuality::Minor)),
            (B(Natural), D(Sharp)) => Some(Third(MajorQuality::Major)),
            (B(Natural), D(DoubleSharp)) => Some(Third(MajorQuality::Augmented)),
            (B(Natural), E(DoubleFlat)) => Some(Fourth(PerfectQuality::DoubleDiminished)),
            (B(Natural), E(Flat)) => Some(Fourth(PerfectQuality::Diminished)),
            (B(Natural), E(Natural)) => Some(Fourth(PerfectQuality::Perfect)),
            (B(Natural), E(Sharp)) => Some(Fourth(PerfectQuality::Augmented)),
            (B(Natural), E(DoubleSharp)) => Some(Fourth(PerfectQuality::DoubleAugmented)),
            (B(Natural), F(DoubleFlat)) => Some(Fifth(PerfectQuality::TripleDiminished)),
            (B(Natural), F(Flat)) => Some(Fifth(PerfectQuality::DoubleDiminished)),
            (B(Natural), F(Natural)) => Some(Fifth(PerfectQuality::Diminished)),
            (B(Natural), F(Sharp)) => Some(Fifth(PerfectQuality::Perfect)),
            (B(Natural), F(DoubleSharp)) => Some(Fifth(PerfectQuality::Augmented)),
            (B(Natural), G(DoubleFlat)) => Some(Sixth(MajorQuality::DoubleDiminished)),
            (B(Natural), G(Flat)) => Some(Sixth(MajorQuality::Diminished)),
            (B(Natural), G(Natural)) => Some(Sixth(MajorQuality::Minor)),
            (B(Natural), G(Sharp)) => Some(Sixth(MajorQuality::Major)),
            (B(Natural), G(DoubleSharp)) => Some(Sixth(MajorQuality::Augmented)),
            (B(Natural), A(DoubleFlat)) => Some(Seventh(MajorQuality::DoubleDiminished)),
            (B(Natural), A(Flat)) => Some(Seventh(MajorQuality::Diminished)),
            (B(Natural), A(Natural)) => Some(Seventh(MajorQuality::Minor)),
            (B(Natural), A(Sharp)) => Some(Seventh(MajorQuality::Major)),
            (B(Natural), A(DoubleSharp)) => Some(Seventh(MajorQuality::Augmented)),

            (B(Sharp), B(Natural)) => Some(First(PerfectQuality::Diminished)),
            (B(Sharp), B(Sharp)) => Some(First(PerfectQuality::Perfect)),
            (B(Sharp), B(DoubleSharp)) => Some(First(PerfectQuality::Augmented)),
            (B(Sharp), C(Natural)) => Some(Second(MajorQuality::Diminished)),
            (B(Sharp), C(Sharp)) => Some(Second(MajorQuality::Minor)),
            (B(Sharp), C(DoubleSharp)) => Some(Second(MajorQuality::Major)),
            (B(Sharp), D(Natural)) => Some(Third(MajorQuality::Diminished)),
            (B(Sharp), D(Sharp)) => Some(Third(MajorQuality::Minor)),
            (B(Sharp), D(DoubleSharp)) => Some(Third(MajorQuality::Major)),
            (B(Sharp), E(Natural)) => Some(Fourth(PerfectQuality::Diminished)),
            (B(Sharp), E(Sharp)) => Some(Fourth(PerfectQuality::Perfect)),
            (B(Sharp), E(DoubleSharp)) => Some(Fourth(PerfectQuality::Augmented)),
            (B(Sharp), F(Natural)) => Some(Fifth(PerfectQuality::DoubleDiminished)),
            (B(Sharp), F(Sharp)) => Some(Fifth(PerfectQuality::Diminished)),
            (B(Sharp), F(DoubleSharp)) => Some(Fifth(PerfectQuality::Perfect)),
            (B(Sharp), G(Natural)) => Some(Sixth(MajorQuality::Diminished)),
            (B(Sharp), G(Sharp)) => Some(Sixth(MajorQuality::Minor)),
            (B(Sharp), G(DoubleSharp)) => Some(Sixth(MajorQuality::Major)),
            (B(Sharp), A(Natural)) => Some(Seventh(MajorQuality::Diminished)),
            (B(Sharp), A(Sharp)) => Some(Seventh(MajorQuality::Minor)),
            (B(Sharp), A(DoubleSharp)) => Some(Seventh(MajorQuality::Major)),

            (B(DoubleSharp), B(Natural)) => Some(First(PerfectQuality::DoubleDiminished)),
            (B(DoubleSharp), B(Sharp)) => Some(First(PerfectQuality::Diminished)),
            (B(DoubleSharp), B(DoubleSharp)) => Some(First(PerfectQuality::Perfect)),
            (B(DoubleSharp), C(Natural)) => Some(Second(MajorQuality::DoubleDiminished)),
            (B(DoubleSharp), C(Sharp)) => Some(Second(MajorQuality::Diminished)),
            (B(DoubleSharp), C(DoubleSharp)) => Some(Second(MajorQuality::Minor)),
            (B(DoubleSharp), D(Natural)) => Some(Third(MajorQuality::DoubleDiminished)),
            (B(DoubleSharp), D(Sharp)) => Some(Third(MajorQuality::Diminished)),
            (B(DoubleSharp), D(DoubleSharp)) => Some(Third(MajorQuality::Minor)),
            (B(DoubleSharp), E(Natural)) => Some(Fourth(PerfectQuality::DoubleDiminished)),
            (B(DoubleSharp), E(Sharp)) => Some(Fourth(PerfectQuality::Diminished)),
            (B(DoubleSharp), E(DoubleSharp)) => Some(Fourth(PerfectQuality::Perfect)),
            (B(DoubleSharp), F(Natural)) => Some(Fifth(PerfectQuality::TripleDiminished)),
            (B(DoubleSharp), F(Sharp)) => Some(Fifth(PerfectQuality::DoubleDiminished)),
            (B(DoubleSharp), F(DoubleSharp)) => Some(Fifth(PerfectQuality::Diminished)),
            (B(DoubleSharp), G(Natural)) => Some(Sixth(MajorQuality::DoubleDiminished)),
            (B(DoubleSharp), G(Sharp)) => Some(Sixth(MajorQuality::Diminished)),
            (B(DoubleSharp), G(DoubleSharp)) => Some(Sixth(MajorQuality::Minor)),
            (B(DoubleSharp), A(Natural)) => Some(Seventh(MajorQuality::DoubleDiminished)),
            (B(DoubleSharp), A(Sharp)) => Some(Seventh(MajorQuality::Diminished)),
            (B(DoubleSharp), A(DoubleSharp)) => Some(Seventh(MajorQuality::Minor)),

            // Fallback
            (_, _) => None
        }
    }

    /// Get [Cents](musictheory::types::Cents) measurement for this
    /// [Interval](musictheory::types::Interval).
    pub fn cents(&self) -> Cents {
        self.steps().cents()
    }
}

impl fmt::Display for Interval {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        match *self {
            Interval::First(q) => write!(f, "{}1", q),
            Interval::Second(q) => write!(f, "{}2", q),
            Interval::Third(q) => write!(f, "{}3", q),
            Interval::Fourth(q) => write!(f, "{}4", q),
            Interval::Fifth(q) => write!(f, "{}5", q),
            Interval::Sixth(q) => write!(f, "{}6", q),
            Interval::Seventh(q) => write!(f, "{}7", q),
            Interval::Octave(q) => write!(f, "{}8", q),
            Interval::Ninth(q) => write!(f, "{}9", q),
            Interval::Tenth(q) => write!(f, "{}10", q),
            Interval::Eleventh(q) => write!(f, "{}11", q),
            Interval::Twelfth(q) => write!(f, "{}12", q),
            Interval::Thirteenth(q) => write!(f, "{}13", q),
            Interval::Fourteenth(q) => write!(f, "{}14", q),
        }
    }
}

#[cfg(test)]
mod tests {
    use crate::types::interval::{MajorQuality::*, PerfectQuality::*};
    use crate::types::{
        Accidental, Accidental::*, Interval, Interval::*, MajorQuality, Note,
        Note::*, PerfectQuality, PitchClass, Steps,
    };

    #[test]
    #[rustfmt::skip]
    fn test_all_distances() {
        let flats = [
            A(Natural), B(DoubleFlat), B(Flat), B(Natural), C(Flat), C(Natural), D(DoubleFlat),
            D(Flat), D(Natural), E(Flat), E(Natural), F(Flat), F(Natural), G(Flat), G(Natural),
            A(DoubleFlat), A(Flat)
        ];
        let sharps = [
            A(Natural), A(Sharp), B(Natural), B(Sharp), C(Natural), C(Sharp), C(DoubleSharp),
            D(Natural), D(Sharp), D(DoubleSharp), E(Natural), E(Sharp), F(Sharp), F(DoubleSharp),
            G(Natural), G(Sharp), G(DoubleSharp),
        ];
        fn test(notes: [Note;17]) {
            for l in notes.iter() {
                for r in notes.iter() {
                    if let Some(interval) = Interval::distance(*l, *r) {
                        let steps = Steps::distance(&l.pitch_class(), &r.pitch_class());
                        assert_eq!(interval.steps(), steps,
                                   "Interval::distance({}, {}) = {} {} Expected: {}",
                                   l, r, interval, interval.steps(), steps,
                        );
                        println!("Interval::distance({}, {}) = {} {}", l, r, interval, steps);
                    } else {
                        println!("Interval::distance({}, {}) = None", l, r);
                    }
                }
            }
        }
        test(sharps);
        test(flats);
    }

    #[test]
    fn test_interval_distance() {
        fn test(l: Note, r: Note, expect: Option<Interval>) {
            let result = Interval::distance(l, r);
            assert_eq!(
                result, expect,
                "Interval::distance({}, {}) = {:?} Expected: {:?}",
                l, r, result, expect
            );
        }
        test(
            C(Natural),
            F(Natural),
            Some(Fourth(PerfectQuality::Perfect)),
        );
        test(F(Natural), C(Natural), Some(Fifth(PerfectQuality::Perfect)));
        test(
            D(Natural),
            B(DoubleFlat),
            Some(Sixth(MajorQuality::Diminished)),
        );
        test(
            A(Flat),
            F(DoubleFlat),
            Some(Sixth(MajorQuality::Diminished)),
        );
        test(
            G(Sharp),
            F(Natural),
            Some(Seventh(MajorQuality::Diminished)),
        );
    }
}