The Pythagorean tone interval 9/8 is 204 cents, slightly larger than the equal-tempered tone interval of 200, and the leimma is about 90 cents, lower than the semitone of 100 cents. 21 of the 42 notes between the tonic and the octave are higher in pitch than their counterparts in the equal-tempered scale and 21 are lower in pitch. The number value 21 of the Godname EHYEH is the number of notes in the seven scales either of higher or lower pitch than their modern-day counterparts. The Hypolydian mode is closest in pitch to the equal-tempered scale, or rather it ought to be said that this artificial scale is nearest the perfect Pythagorean scale compared with the other modes. With variations of pitch between 2 and 10 cents, the two are virtually indistinguishable to most ears, at least for single notes — chords can be another matter. Over the frequency range most common in music (500 Hz to 4,000 Hz), the ear can just detect an interval of less than one-thirtieth of a semitone, i.e., about three cents. But it is harder to detect differences of pitch in real life than in the laboratory, and sensitivity falls below 500 Hz, dropping to about 30 cents at a frequency of 62 Hz. On the other hand, differences of pitch are easier to detect in musical sounds than in pure tones. All the notes of the Hypolydian mode except the perfect fourth are slightly higher in pitch than the modern scale. But all 16 non-Pythagorean notes differ sufficiently to be differentiated. 15 of them are lower in pitch than their equal-tempered counterparts. This is the number value of the Godname YAH, which is a curious coincidence because the equal-tempered scale cannot be said to be of God’s making, although He might be well-pleased that Western music invented it! The Lydian mode is the only one whose notes are all lower in the equal-tempered scale, the fourth being more than a semitone lower (112 compared with 100). The Hypophrygian is the only mode whose notes in the modern scale are all higher than their classical counterparts, five of the seven notes being more than a semitone higher. Melodies played according to modes other than the Hypolydian on instruments tuned to the modern scale will sound differently to their playing according to their pure pitches.

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