In order to study the temporal variations of correlations between two time series,a running correlation coefficient(RCC)could be used.An RCC is calculated for a given time window,and the window is then moved sequentia...In order to study the temporal variations of correlations between two time series,a running correlation coefficient(RCC)could be used.An RCC is calculated for a given time window,and the window is then moved sequentially through time.The current calculation method for RCCs is based on the general definition of the Pearson product-moment correlation coefficient,calculated with the data within the time window,which we call the local running correlation coefficient(LRCC).The LRCC is calculated via the two anomalies corresponding to the two local means,meanwhile,the local means also vary.It is cleared up that the LRCC reflects only the correlation between the two anomalies within the time window but fails to exhibit the contributions of the two varying means.To address this problem,two unchanged means obtained from all available data are adopted to calculate an RCC,which is called the synthetic running correlation coefficient(SRCC).When the anomaly variations are dominant,the two RCCs are similar.However,when the variations of the means are dominant,the difference between the two RCCs becomes obvious.The SRCC reflects the correlations of both the anomaly variations and the variations of the means.Therefore,the SRCCs from different time points are intercomparable.A criterion for the superiority of the RCC algorithm is that the average value of the RCC should be close to the global correlation coefficient calculated using all data.The SRCC always meets this criterion,while the LRCC sometimes fails.Therefore,the SRCC is better than the LRCC for running correlations.We suggest using the SRCC to calculate the RCCs.展开更多
Basing upon the tonality analytic method, the present paper aims at： （1） Drawing attention to the subordination of the minor key vs. the major key in the chord classification, using the same methodology; and （2） ...Basing upon the tonality analytic method, the present paper aims at： （1） Drawing attention to the subordination of the minor key vs. the major key in the chord classification, using the same methodology; and （2） Showing the differences for the major key and the minor （harmonic） key in the classification of chords, as an aspect of importance for interpreting a piece＇s tonal structure diagram. The relations between chords appearing in the major and minor （harmonic） key will be shown by applying the comparisons of： （1） third-based chords; and （2） degrees in the C major and A minor keys, on which the same diatonic chords appear.展开更多
基金supported by the Key Program of the National Natural Science Foundation of China (No. 41330960)the Global Change Research Program of China (No. 2015CB953900)
文摘In order to study the temporal variations of correlations between two time series,a running correlation coefficient(RCC)could be used.An RCC is calculated for a given time window,and the window is then moved sequentially through time.The current calculation method for RCCs is based on the general definition of the Pearson product-moment correlation coefficient,calculated with the data within the time window,which we call the local running correlation coefficient(LRCC).The LRCC is calculated via the two anomalies corresponding to the two local means,meanwhile,the local means also vary.It is cleared up that the LRCC reflects only the correlation between the two anomalies within the time window but fails to exhibit the contributions of the two varying means.To address this problem,two unchanged means obtained from all available data are adopted to calculate an RCC,which is called the synthetic running correlation coefficient(SRCC).When the anomaly variations are dominant,the two RCCs are similar.However,when the variations of the means are dominant,the difference between the two RCCs becomes obvious.The SRCC reflects the correlations of both the anomaly variations and the variations of the means.Therefore,the SRCCs from different time points are intercomparable.A criterion for the superiority of the RCC algorithm is that the average value of the RCC should be close to the global correlation coefficient calculated using all data.The SRCC always meets this criterion,while the LRCC sometimes fails.Therefore,the SRCC is better than the LRCC for running correlations.We suggest using the SRCC to calculate the RCCs.
文摘Basing upon the tonality analytic method, the present paper aims at： （1） Drawing attention to the subordination of the minor key vs. the major key in the chord classification, using the same methodology; and （2） Showing the differences for the major key and the minor （harmonic） key in the classification of chords, as an aspect of importance for interpreting a piece＇s tonal structure diagram. The relations between chords appearing in the major and minor （harmonic） key will be shown by applying the comparisons of： （1） third-based chords; and （2） degrees in the C major and A minor keys, on which the same diatonic chords appear.
