The Natural Mantra

Chanting a mantra repeatedly has been a well-known practice to calm (clam) the mind and to feel relaxed and focused.  This practice is especially common in Indic religions.

There are many mantras which have stood the test of time.  The effectiveness of a mantra depends on its perceived sacredness, its association with deities, or its mention in important scriptures.

Some of the popular mantras are:

The Gayatri mantra

ॐ भूर्भुवस्व: | तत्सवितुर्वरेण्यम् | भर्गो देवस्य धीमहि | धियो यो न: प्रचोदयात्

The Pavamana mantra

असतोमा सद्गमय । तमसोमा ज्योतिर् गमय । मृत्योर्मामृतं गमय ॥

The Shanti mantras

ॐ पूर्णमदः पूर्णमिदम् पूर्णात् पूर्णमुदच्यते |
पूर्णस्य पूर्णमादाय पूर्णमेवावशिष्यते ||
ॐ शान्तिः शान्तिः शान्तिः || 

ॐ सह नाववतु |
सह नौ भुनक्तु |
सह वीर्यं करवावहै |
तेजस्विनावधीतमस्तु मा विद्विषावहै॥
ॐ शान्तिः शान्तिः शान्तिः॥

The Soka Gakkai mantra

Namu Myōhō Renge Kyō (南無妙法蓮華經)

Mahamrityunjaya Mantra (one of my favorites)

The mool mantra In Sikhism

ੴ ਸਤਿ ਨਾਮੁ ਕਰਤਾ ਪੁਰਖੁ ਨਿਰਭਉ ਨਿਰਵੈਰੁ ਅਕਾਲ ਮੂਰਤਿ ਅਜੂਨੀ ਸੈਭੰ ਗੁਰ ਪ੍ਰਸਾਦਿ॥

...

Do you notice anything common between them?

There is a preponderance of the nasal consonants in all of these. The "mmm" and "nnnn" sounds predominate.

Many of these chants begin with "Om".

The "mmm" sound is the most effortless sound while exhaling. These mantras often involve rhythmic breathing and a constant speed of chanting.

I consider the mantra "Aum" or "Om" to be the most natural mantra. It is essentially "mmm" but includes an initial segment when the lips are open. It is linguistically neutral and its various meanings are obvious constructions.

You can try: Inhale through the nostrils, and while exhaling, if you keep your lips open and then closed, and make your exhalation audible (by involving your vocal chord), the sound is: aa ... aa ... mmmm .... mmmm.

I find, for example, the following chant, to be quite effective.

The longer mantras engage the mind a little more by having to remember the sequence of consonants and therefore can be more effective in quickly getting to a state of mental silence. The "mmm" sound reverberates through the skull, and the mild effort involved in repeating a long mantra focuses the mind.  Also the alliteration and repetition of the nasal consonants can be somewhat resonant.

It is similar to the background musicality of a tanpura in Indian classical music.

The mantra is obviously more effective if you give it a religious significance or meaning, which puts the mind in a certain soft emotional state of devoutness or surrender. Silent meditation is harder (to calm the mind), but chanting achieves the same effect much quicker.