Paid apps -

EarMaster - Music Theory
EarMaster is a great tool for ear training, sight-singing and rhythm at all skill levels, from beginner to very advanced. The app includes all you need to build up your music theory skills and become a better musician. EarMaster is deep! The free initial download of app comes with 20+ lessons of Beginner’s course. It has Bundles and Workshops as one-time purchase items in its IAP store. The Beginner Bundle with 219 lessons plus Beginner Workshops with 22 courses cost $5.99 normally and cost $3.99 during sale which is dirt cheap.
https://apps.apple.com/us/app/earmas...y/id1105030163

Complete Ear Trainer
Develop your relative pitch to the full by improving your aural skills and your music theory knowledge. This will better many aspects of your life as a musician, be it regarding improvisation, composition, arrangement, interpretation, singing, or playing in a band.
https://apps.apple.com/us/app/comple...r/id1012455471

Ear Training University
The goal of Relative Pitch ear training is to learn to follow the flow of music, *effortlessly* by ear. The Ear Training University (ETU) app was carefully designed to take all the guess work out of how to learn this skill. Whether you’re a complete beginner in ear training or have done ear training before, ETU’s approach is sure to find any weaknesses your ears may have and systematically build your sense of Relative Pitch from the ground up.
https://apps.apple.com/us/app/ear-tr...y/id1354638884

Rhythm Sight Reading Trainer
Improve your sight reading quickly with immediate feedback of timing accuracy. Carefully graduated levels from simple to professional allow you to start at your best level and improve at your own pace, more rapidly than on your own instrument. Practice anytime and anywhere. Many advanced features.
https://apps.apple.com/us/app/rhythm...er/id396302174

Music Rhythm Trainer
Rhythm Trainer is a series of fun field-tested exercises for mastering your essential rhythmic skills no matter what instrument you play.
https://apps.apple.com/us/app/music-...r/id1319997438

Tonality: Music Theory
Tonality is the ultimate chord, scale, and general music theory reference tool for musicians of all skill levels. It allows you to explore a large database of chords and scales and includes tons of MIDI functionality, including 4 bundled Audio Unit (AUv3) plugins.
https://apps.apple.com/us/app/tonali...y/id1467552236

TONALY: Write & practice music
Write songs, find chords, and learn scales based on the circle of fifths! For every skill-level This app is for musicians of all kinds, songwriters, and producers. Beginners and advanced. No matter if it's your intention to get better on your instrument or playfully find chords and inspiration for your songs or productions.
https://apps.apple.com/us/app/tonaly...c/id1242467844

Tenuto
Tenuto is a collection of 24 highly-customizable exercises designed to enhance your musicality. From recognizing chords on a keyboard to identifying intervals by ear, it has an exercise for you. Tenuto also includes six musical calculators for accidentals, intervals, scales, chords, analysis symbols, and twelve-tone matrices.

Theory Lessons
Theory Lessons features 39 music theory lessons from musictheory.net, presented in their original animated versions.
https://apps.apple.com/us/app/theory...ns/id493157418
Perfect Pitch & Relative Pitch
Ear Training Courses by David Lucas Burge.

Chord!
Guitar Songbook, Chords & Scales

Vocalist Pro
Vocalist develops your singing skills and vocal range by giving you various singing exercises, ranging from very simple to advanced.
FREE apps -
Tenuto & Theory Lessons
Free on their website (see Paid apps above)
Tenuto
Theory Lessons
The Rhythm Trainer

Aural Wiz
Learn to recognize intervals, scales, modes chords and cadences with Aural Wiz. Whether you are a music student preparing for aural tests as part of your formal musical training or a musician just working towards improving your aural skills, Aural Wiz would be an indispensable companion for you.

Functional Ear Trainer
Functional Ear Trainer teaches you to distinguish between tones in the context of a particular musical key. You begin to recognize the role (or function) of each tone in this key, which is incredibly similar to its role in other keys of the same scale.
https://apps.apple.com/us/app/functi...r/id1088761926

SolFi Ear Trainer 3
SolFi Ear Trainer 3 is an ear training application for students of music to improve their listening skills. It contains some basic exercises used by many schools to teach their students. It assumes the user has some knowledge of music theory.

Ella: Sight Singing & Reading
(with gamified leaderboard)
Ella is a sight-singing ear-training app that helps you improve your musical ear with fun and engaging exercises.
https://apps.apple.com/us/app/ella-s...g/id1301456113
Ella - The Best Sight Singing App
(the app can actually play ALL the notes before we sing - not just the first note)

Chet - Ear Training Games
(with gamified leaderboard)
Chet is an ear training game for musicians of all levels. Compete with other musicians to achieve high scores in a wide variety of challenges that test your ear. Intervals, Scales, Arpeggios, Chords, Tonal Sequences and Atonal Sequences.
https://apps.apple.com/us/app/chet-e...g/id1405525467

Music Theory with Audio
Dramatically improve and develop your LISTENING SKILLS and tone control, identify complex written CHORDS, increase your knowledge base of MUSIC THEORY, and even learn all about your favorite classical COMPOSERS. With the latest in Brainscape’s proven cognitive science techniques, you’ll learn faster and more efficiently than with any other music app on the market!

Sing-O-Meter - Perfect Pitch!
Learn to sing, improve, become a pop star or even an opera singer ... Sing-O-Meter guides you through many different levels with a clear visual feedback. No matter if you just want to give singing a try or if you sing professionally for many years. Sing-O-Meter helps you to get better at singing, control your voice and it trains your perception of pitch.
https://apps.apple.com/us/app/sing-o...h/id1448696483

Vocalizer for iOS
Vocalizer is an app that plays vocal exercise for you so you can sing along to warm up your voice.

Vocalist Lite
Vocalist develops your singing skills and vocal range by giving you various singing exercises, ranging from very simple to advanced.

VoCo Vocal Coach
VoCo is a vocal coaching App. It is designed for Voice Students, Performers, Vocal Coaches, Choir Directors & Music Teachers.
Videos
Master rhythms in less than 5 minutes. Music reading training
Play any RHYTHM easily - perfect your timing and sight reading!
Decoding Rhythm: how to play rhythms that seem hard (but really aren't)
Learn how to SIGHT SING. Interactive singing lesson!
Interactive Rhythm Practice: from simple to syncopated!
Cheers!

EarMaster - Music Theory
EarMaster is a great tool for ear training, sight-singing and rhythm at all skill levels, from beginner to very advanced. The app includes all you need to build up your music theory skills and become a better musician. EarMaster is deep! The free initial download of app comes with 20+ lessons of Beginner’s course. It has Bundles and Workshops as one-time purchase items in its IAP store. The Beginner Bundle with 219 lessons plus Beginner Workshops with 22 courses cost $5.99 normally and cost $3.99 during sale which is dirt cheap.
https://apps.apple.com/us/app/earmas...y/id1105030163

Complete Ear Trainer
Develop your relative pitch to the full by improving your aural skills and your music theory knowledge. This will better many aspects of your life as a musician, be it regarding improvisation, composition, arrangement, interpretation, singing, or playing in a band.
https://apps.apple.com/us/app/comple...r/id1012455471

Ear Training University
The goal of Relative Pitch ear training is to learn to follow the flow of music, *effortlessly* by ear. The Ear Training University (ETU) app was carefully designed to take all the guess work out of how to learn this skill. Whether you’re a complete beginner in ear training or have done ear training before, ETU’s approach is sure to find any weaknesses your ears may have and systematically build your sense of Relative Pitch from the ground up.
https://apps.apple.com/us/app/ear-tr...y/id1354638884

Rhythm Sight Reading Trainer
Improve your sight reading quickly with immediate feedback of timing accuracy. Carefully graduated levels from simple to professional allow you to start at your best level and improve at your own pace, more rapidly than on your own instrument. Practice anytime and anywhere. Many advanced features.
https://apps.apple.com/us/app/rhythm...er/id396302174

Music Rhythm Trainer
Rhythm Trainer is a series of fun field-tested exercises for mastering your essential rhythmic skills no matter what instrument you play.
https://apps.apple.com/us/app/music-...r/id1319997438

Tonality: Music Theory
Tonality is the ultimate chord, scale, and general music theory reference tool for musicians of all skill levels. It allows you to explore a large database of chords and scales and includes tons of MIDI functionality, including 4 bundled Audio Unit (AUv3) plugins.
https://apps.apple.com/us/app/tonali...y/id1467552236

TONALY: Write & practice music
Write songs, find chords, and learn scales based on the circle of fifths! For every skill-level This app is for musicians of all kinds, songwriters, and producers. Beginners and advanced. No matter if it's your intention to get better on your instrument or playfully find chords and inspiration for your songs or productions.
https://apps.apple.com/us/app/tonaly...c/id1242467844

Tenuto
Tenuto is a collection of 24 highly-customizable exercises designed to enhance your musicality. From recognizing chords on a keyboard to identifying intervals by ear, it has an exercise for you. Tenuto also includes six musical calculators for accidentals, intervals, scales, chords, analysis symbols, and twelve-tone matrices.

Theory Lessons
Theory Lessons features 39 music theory lessons from musictheory.net, presented in their original animated versions.
https://apps.apple.com/us/app/theory...ns/id493157418
Perfect Pitch & Relative Pitch
Ear Training Courses by David Lucas Burge.

Chord!
Guitar Songbook, Chords & Scales

Vocalist Pro
Vocalist develops your singing skills and vocal range by giving you various singing exercises, ranging from very simple to advanced.
FREE apps -
Tenuto & Theory Lessons
Free on their website (see Paid apps above)
Tenuto
Theory Lessons
The Rhythm Trainer

Aural Wiz
Learn to recognize intervals, scales, modes chords and cadences with Aural Wiz. Whether you are a music student preparing for aural tests as part of your formal musical training or a musician just working towards improving your aural skills, Aural Wiz would be an indispensable companion for you.

Functional Ear Trainer
Functional Ear Trainer teaches you to distinguish between tones in the context of a particular musical key. You begin to recognize the role (or function) of each tone in this key, which is incredibly similar to its role in other keys of the same scale.
https://apps.apple.com/us/app/functi...r/id1088761926

SolFi Ear Trainer 3
SolFi Ear Trainer 3 is an ear training application for students of music to improve their listening skills. It contains some basic exercises used by many schools to teach their students. It assumes the user has some knowledge of music theory.

Ella: Sight Singing & Reading
(with gamified leaderboard)
Ella is a sight-singing ear-training app that helps you improve your musical ear with fun and engaging exercises.
https://apps.apple.com/us/app/ella-s...g/id1301456113
Ella - The Best Sight Singing App
(the app can actually play ALL the notes before we sing - not just the first note)

Chet - Ear Training Games
(with gamified leaderboard)
Chet is an ear training game for musicians of all levels. Compete with other musicians to achieve high scores in a wide variety of challenges that test your ear. Intervals, Scales, Arpeggios, Chords, Tonal Sequences and Atonal Sequences.
https://apps.apple.com/us/app/chet-e...g/id1405525467

Music Theory with Audio
Dramatically improve and develop your LISTENING SKILLS and tone control, identify complex written CHORDS, increase your knowledge base of MUSIC THEORY, and even learn all about your favorite classical COMPOSERS. With the latest in Brainscape’s proven cognitive science techniques, you’ll learn faster and more efficiently than with any other music app on the market!

Sing-O-Meter - Perfect Pitch!
Learn to sing, improve, become a pop star or even an opera singer ... Sing-O-Meter guides you through many different levels with a clear visual feedback. No matter if you just want to give singing a try or if you sing professionally for many years. Sing-O-Meter helps you to get better at singing, control your voice and it trains your perception of pitch.
https://apps.apple.com/us/app/sing-o...h/id1448696483

Vocalizer for iOS
Vocalizer is an app that plays vocal exercise for you so you can sing along to warm up your voice.

Vocalist Lite
Vocalist develops your singing skills and vocal range by giving you various singing exercises, ranging from very simple to advanced.

VoCo Vocal Coach
VoCo is a vocal coaching App. It is designed for Voice Students, Performers, Vocal Coaches, Choir Directors & Music Teachers.
Videos
Master rhythms in less than 5 minutes. Music reading training
Play any RHYTHM easily - perfect your timing and sight reading!
Decoding Rhythm: how to play rhythms that seem hard (but really aren't)
Learn how to SIGHT SING. Interactive singing lesson!
Interactive Rhythm Practice: from simple to syncopated!
Cheers!