The reason there’s a problem with instruments and non-scriptural songs in worship is because there is a great, yawning gap in the scriptural mandate where you would look to find a warrant for dispensing with the inspired psalter and introducing musical instruments.
That principle applies to all of worship, whether in the congregation, the family, or private devotions. Offering something as worship which is not divinely required as worship isn’t really worship at all (does anyone out there still know the term ‘will-worship’?).
But that does not require a ban on non-inspired praise songs or musical instruments outside of worship, because not all of life is worship. Not all of life is worship, says Matthew Vogan in a two-part series (here and here), and so says Glen Scrivener much more dramatically here.
So if people are musically inclined and talented, by all means they should take up harp and psaltery and make a loud noise skillfully (although a quieter noise might be better from the less skillful). There is a requirement to do whatever you do to the best of your ability and to the glory of God, whether work or household chores or daily routines. These things may include more or less of what is overtly conscious of God, and more or less of what directly draws attention to his glory, but if there is such a thing as eating and drinking to his glory, there must be such a thing as writing or singing a hymn about his greatness to his glory.
Prayer is an interesting one though. Private and public prayer should be scriptural in wording and tone, but extempore prayer is in general preferred to reading or reciting set forms of prayer – not least because there is no Book of Prayers provided in the scriptures.
[In reference to this.]