调 is the simplified form of traditional 調. It is a pictophonetic compound: the speech radical 讠 (yán, the simplified form of 言) carries the meaning, while 周 (zhōu) supplies the sound. The speech radical marks 调 as a word that began in the realm of the voice, of tones, words, and the harmonizing of speech and sound.

The phonetic 周 zhōu means "all around, complete, well-rounded." That sense of bringing things into a rounded whole sits quietly under both readings of 调: to tune is to bring sounds into accord, to blend is to bring flavors into balance, to mediate is to bring two sides into agreement. The radical and phonetic together point to harmony achieved through the voice and, by extension, through careful arrangement.

调 is a polyphone, and the reading splits the senses cleanly:

1. diào (falling tone). To transfer or move from one place to another: 调动 diàodòng (to transfer, to mobilize), 调查 diàochá (to investigate). Also a melody, key, or pitch: 曲调 qǔdiào (a tune), 音调 yīndiào (pitch), 声调 shēngdiào (a tone). By extension, an accent or manner of speech: 腔调 qiāngdiào (an accent), 论调 lùndiào (a line of argument).
2. tiáo (rising tone). To adjust, to bring into balance: 调整 tiáozhěng (to adjust), 调节 tiáojié (to regulate). To blend or mix: 调味 tiáowèi (to season), 调料 tiáoliào (seasoning), 调和 tiáohé (to harmonize). To mediate: 调解 tiáojiě (to mediate), 调停 tiáotíng (to mediate a dispute).

The thread through both readings is arrangement. In the falling tone diào the arrangement is of position and of pitch: where a person is posted, how high a note sits, what an accent sounds like. In the rising tone tiáo the arrangement is of balance: tuning a dial, blending a sauce, reconciling a quarrel. Hear the tone and you know whether 调 is moving and pitching things or harmonizing them.

In the falling tone diào, one branch of 调 is about moving things into place. 调动 diàodòng is to transfer a person to a new post, or to mobilize resources and energy. 调度 diàodù is to dispatch and schedule, the work of a controller directing trains, flights, or crews. From "moving people to find things out" comes 调查 diàochá, to investigate or conduct a survey: an inquiry sent out to gather facts. The common image is of resources and questions being directed to where they are needed.

The other branch of the falling tone diào lives in sound. 调子 diàozi is a tune or melody, and by extension the pitch of a voice or even the mood of a piece of writing. 音调 yīndiào is pitch, how high or low a sound sits. 声调 shēngdiào is a tone in the linguistic sense: the four tones of Mandarin are its 声调. Widen further and 调 names the manner of speech itself: 腔调 qiāngdiào is an accent or a way of talking, 论调 lùndiào is the slant or line of an argument. From a single note to a whole accent, this branch of 调 is the pitch and color of the voice.

Let the tone rise from falling diào to rising tiáo and 调 turns from moving and pitching things to harmonizing them. 调整 tiáozhěng is to adjust, to set something right by fine degrees. 调节 tiáojié is to regulate, to keep a level steady, as a thermostat regulates heat. In the kitchen, 调味 tiáowèi is to season and 调料 tiáoliào is the seasoning itself, while 调和 tiáohé is to blend flavors or, more broadly, to harmonize. Among people, 调解 tiáojiě is to mediate a dispute and 调停 tiáotíng is to step in and settle a quarrel. Across all of these the rising tone tiáo names the act of bringing things into balance.

Hold one idea at the center of 调: arrangement, with the speech radical 讠 reminding you it began in the realm of sound. The phonetic 周 means "well-rounded, complete," and that is what 调 does in every sense, it brings things into a rounded whole. The tone tells you which kind of arrangement you mean.

Hear the falling tone diào and think of moving and pitching. A person is 调动 to a new post; an inquiry is sent out as a 调查; a dispatcher does the 调度. Or the arrangement is of sound: the four 声调 of Mandarin, the 调子 of a song, the 腔调 of an accent. Then let the tone rise to tiáo and the arrangement turns to balance. You 调整 a plan, 调节 a temperature, 调味 a dish, 调解 a quarrel. Falling diào moves and pitches; rising tiáo blends and harmonizes. The cleanest pair to lock it in is 调查 diàochá, to investigate, against 调整 tiáozhěng, to adjust: one tone sends out, the other brings into balance.