in the course of their research , the inventors have analyzed the relationships between inductive reactance and capacitive reactance and the harmonic balance of magnetic properties of the entire component parts of inductive devices and specifically a transformer . the following steps are necessary to provide such relationships in accordance with the tru - scale reactance transformation system . dimensions . ( geometry ) all dimensions have an harmonic ratio to each other and to the frequency of the system according to the tru - scale matrix . the thickness of the laminations are an harmonic of the frequency of the system . the number of laminations in the core is an harmonic of the frequency of the system . core material has an alloy ratio according to the tru - scale matrix . example — percent of silica to iron , percent of nickel to iron , and / or percent of cobalt to iron . ( a ) tru - scale method : the peak to peak power of the transformer is calculated , the peak flux density is calculated for the transformer at the calculated power level , and the core is selected with a flux density at ½ the maximum residual flux density at the calculated power level . ( b ) in contrast , in the standard method : the total average power of the transformer is estimated , and the estimated total flux density is calculated for that power and compared to core properties at saturation flux density for the material selected at a 50 degree celsius temperature rise in the core . ( a ) tru - scale method : each winding has its own sector on the bobbin and is isolated from the other . an extra winding and sector are added for the tuning of the magnetic circuit . ( b ) in contrast , in the standard method : one sector is used for all windings . two or more sectors will sometimes be used for a split winding and / or a multiple output transformer such as : split winding transformer — put one half of one of the windings on each side of another winding . multiple output transformer — a multiple output transformer typically is for several different voltages available from the same transformer instead of tapping several locations on one winding . ( a ) tru - scale method : the primary winding with a number of turns according to the tru - scale matrix is used and the gage is selected to approximately 161 amperes per square centimeter . the number of turns selected is ideally an harmonic of the system frequency and the flux density is at ½ the maximum residual flux density at maximum load . the next windings ( secondary , tertiary , etc .) are designed to the desired output voltage for each with the number of turns selected from the tru - scale matrix . the gage is selected to match the primary winding &# 39 ; s current density at maximum load . tuning is accomplished by selecting the additional winding &# 39 ; s number of turns from the tru - scale matrix and selecting the gage to have the winding &# 39 ; s current density match the primary winding . ( b ) in contrast , in the standard method : use the number of turns and gage of wire for each winding as estimated from the operating current density at maximum load and / or the desired estimated winding inductance and core operating at the saturation flux density at full load with the winding window is filled to as close to 100 percent as possible . in summary , the present invention using an harmonic tru - scale reactance transformation system in a tru - scale transformer has all the parts of the transformer designed , evaluated and treated as directly related to each other . each component has an harmonic relationship with the other components , including the electrical system parameters such as the frequency of the system . in contrast , a standard transformer has each individual part of the transformer designed , evaluated and treated as a separate entity , thereby yielding only indirect relationships with the other parts . for example , the magnetic components are designed separately from the electrical components and the parts are put together and evaluated . sometimes a more efficient design is discovered , but it is only through trial and error , with no consistent method of repeating efficient designs , and lacking any harmonic relationships . however , the benefits of the tru - scale reactance transformation system can be realized by adding an additional winding and establishing a resonant state with the magnetic and / or electrical and / or inductive properties of the transformer , using a capacitor or other reactive component of appropriate size according to the tru - scale matrix . in this manner , the impedance because of transfer of energy from one state to the other ( i . e ., electrical to magnetic ), as well as other causes , can be minimized . by keeping the additional winding electrically isolated but magnetically coupled to the circuit , the negative effects of an additional winding in a circuit ( as in a filter ) will not be realized , but the benefits of reduced impedance will be realized . to illustrate the benefits of the invention , fig1 ( a ) shows an output according to the above - referenced standard method . fig1 ( b ) shows an output according to the tru - scale reactance transformation system . the sparseness of the fig1 ( a ) output contrasts with the denseness of the fig1 ( b ) output , thereby illustrating the benefit of introducing resonance to reduce emf collisions . the inventors have conducted tests , including the following two types . in a first test type , a tru - scale improved transformer model ( itm ), 1500 watt design was compared with a square d transformer , 1500 watt standard design , in relation to heat rise . as clearly shown in the results , certified by an independent ph . d . electrical consultant , there was a substantial reduction in the heat factor because of employment of the harmonic relationships resulting from the use of the tru - scale matrix . there was a 53 . 4 degree temperature differential when itm was compared with the baseline at the 150 minute mark . after an additional 4 . 5 hours the itm was still below 102 degrees . a second test was performed comparing the radio shack baseline and the harmonic tru - scale consumer electric transformer ( cet ) and the results of the percent reduction of 92 . 30 % and 26 . 10 % clearly showed highly significant results from the present invention . the inventors also conducted tests on the heat rise of the radio shack baseline and a tru - scale cet . the tru - scale effects are self evident to anyone familiar with the art . it should also be noted that the power source is not critical to the invention . the source can be a standard power grid , nuclear - based , wind - based or any other type of power source . what the invention does is to harmonically relate the component parts ( electrical - mechanical - magnetic fields ) as a single whole to eliminate loss through any type of distortion ( heat - flux - impedance ). this invention includes any type of inductive devices , movable or stationary , micro or macro , which requires a series of harmonic relationships using the tru - scale reactance transformation series as a means of reducing non - harmonic effects . while the invention has been described in detail above with reference to embodiments , various modifications within the scope and spirit of the invention will be apparent to ordinarily skilled artisans . as a result , the invention should be construed as limited only by the scope of the following claims .